Optomechatronic Actuators, Manipulation, and Systems Control

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Volume 6374

Optomechatronic Actuators, Manipulation, and Systems Control Yukitoshi Otani, Farrokh Janabi-Sharifi, Editors , October 2006 Conference Location: Boston, MA, USA Conference Date: 1 October 2006 Publisher: SPIE-International Society for Optical Engine ISBN-10: 0819464724 ISBN-13: 978-0819464729

TABLE OF CONTENTS

OPTICAL ACTUATOR Laser motor Hideki Okamura Proc. SPIE Vol. 6374, 637401 (Oct. 19, 2006)

Light-driven polymer actuators for propulsion and light control LaQuieta Huey, Sergey S. Sarkisov, Michael J. Curley, Grigory Adamovsky, and Jai-Ching Wang Proc. SPIE Vol. 6374, 637402 (Oct. 19, 2006)

Positioning control of Nafion-Au ionic polymer metal composite: the effect of counter ion on the deformation patterns of IPMC Akitoshi Itoh, Tetsuichi Amari, and Toshihiro Tanaka Proc. SPIE Vol. 6374, 637403 (Oct. 19, 2006)

Optical driving of actuator using poly-vinylidine difluoride cantilever Y. Mizutani, S. Nishimura, Y. Otani, and N. Umeda Proc. SPIE Vol. 6374, 637404 (Oct. 19, 2006)

Two-dimensional magnetic force actuator using temperature sensitive ferrite driven by light beam Y. Mizutani, Y. Otani, and N. Umeda

Proc. SPIE Vol. 6374, 637405 (Oct. 19, 2006)

OPTOMECHATRONIC MEASUREMENT Analysis of mechanical characteristics by birefringence microscope Mizue Ebisawa, Yukitoshi Otani, and Norihiro Umeda Proc. SPIE Vol. 6374, 637407 (Oct. 19, 2006)

Simultaneous measurement of nanometric longitudinal displacement and micrometric lateral displacement by using one line CCD camera Masaaki Adachi and Yasuto Nishide Proc. SPIE Vol. 6374, 637408 (Oct. 19, 2006)

MEMS acoustic sensor using PMN-PT single-crystal diaphragm Sung Q. Lee, Hae Jin Kim, Kang Ho Park, Yong K. Hong, and Kee S. Moon Proc. SPIE Vol. 6374, 637409 (Oct. 19, 2006)

OPTOMECHATRONIC ACTUATION DEVICES PMN-PT piezoelectric near field optical probe for data storage Yong K. Hong, Sung Q. Lee, Eun Kyoung Kim, Kang Ho Park, and Kee S. Moon Proc. SPIE Vol. 6374, 63740A (Oct. 19, 2006)

Real-time high-displacement amplified bimorph scanning mirror Paul E. Patterson and Jason M. Zara Proc. SPIE Vol. 6374, 63740B (Oct. 19, 2006)

Optimization of electrostatic side-drive micromotor torque using a new rotor-poleshaping technique Mohamed A. Basha and S. Safavi-Naeini Proc. SPIE Vol. 6374, 63740C (Oct. 19, 2006)

Liquid crystal optics for laser beam modulation M. Kurihara and N. Hashimoto Proc. SPIE Vol. 6374, 63740D (Oct. 19, 2006)

Reconfigurable microfluidic chip based on a light-sensitive hydrogel Khaled Al-Aribe, George K. Knopf, and Amarjeet S. Bassi Proc. SPIE Vol. 6374, 63740E (Oct. 19, 2006)

Low-cost deformable mirror for laser focussing

W. Greger, T. Hösel, T. Fellner, A. Schoth, C. Mueller, J. Wilde, and H. Reinecke Proc. SPIE Vol. 6374, 63740F (Oct. 19, 2006)

The simple and practical variable optical attenuator using a piezoelectric sheet containing an optical fiber Seungtaek Kim, Heuiseok Kang, Sungbok Kang, Won Kim, Hoon Jeong, and Youngjune Cho Proc. SPIE Vol. 6374, 63740G (Oct. 19, 2006)

A novel capacitive type miniature microphone with a flexure hinge diaphragm Hye Jin Kim, Sung Q. Lee, and Kang Ho Park Proc. SPIE Vol. 6374, 63740H (Oct. 19, 2006)

Liquid pressure varifocus lens using a fibrous actuator Ryoichi Kuwano, Yasuhiro Mizutani, Tsuyoshi Tokunaga, and Yukitoshi Otani Proc. SPIE Vol. 6374, 63740I (Oct. 19, 2006)

Sol-Gel-based 1x2 power splitter for a plastic optical fiber H. Jeong, Y. J. Cho, and S. T. Kim Proc. SPIE Vol. 6374, 63740J (Oct. 19, 2006)

OPTICAL ACTUATOR AND MICRO/NANO MANIPULATION Liquid crystal laser manipulation system for controlling microscopic particles Marenori Kawamura, Mao Ye, and Susumu Sato Proc. SPIE Vol. 6374, 63740K (Oct. 19, 2006)

Imaging technology of three-dimensional distribution for sugar chain on single living cell membrane Kazuya Yamamoto, Ichirou Ishimaru, Yoshiki Fujii, Toshiki Yasokawa, Katsumi Ishizaki, Makoto Yoshida, Kaoru Takegawa, Naotaka Tanaka, Shigeki Kuriyama, Tsutomu Masaki, and Seiji Nakai Proc. SPIE Vol. 6374, 63740L (Oct. 19, 2006)

Laser irradiation induced vibrations in solids Bodo Richert and Hideki Okamura Proc. SPIE Vol. 6374, 63740M (Oct. 19, 2006)

Light-driven micromanipulator and its application for 3D fabrications Yukitoshi Otani, Yuji Hirai, Yasuhiro Mizutani, Norihiro Umeda, and Toru Yoshizawa Proc. SPIE Vol. 6374, 63740N (Oct. 19, 2006)

Optimal actuation of microcantilevers by a laser beam Sagnik Pal and Anjan K. Ghosh Proc. SPIE Vol. 6374, 63740O (Oct. 19, 2006)

Development of PC controlled laser manipulation system with image processing functions Yoshio Tanaka, Akitsugu Murakami, Ken Hirano, Hideya Nagata, and Mitsuru Ishikawa Proc. SPIE Vol. 6374, 63740P (Oct. 19, 2006)

VISION-BASED TRACKING AND CONTROL A robust vision-based technique for human arm kinematics identification Omid Talakoub and Farrokh Janabi Sharifi Proc. SPIE Vol. 6374, 63740Q (Oct. 12, 2006)

A fuzzy adaptive PD-controller-based micro-assembly system Junping Wang, Xiaodong Tao, Deokhwa Hong, and Hyungsuck Cho Proc. SPIE Vol. 6374, 63740R (Oct. 12, 2006)

An algorithm of calculating the scanning start angle and the scanning angle of linear array CCD panoramic aerial camera Gang Zhou and Lin-Pei Zhai Proc. SPIE Vol. 6374, 63740S (Oct. 12, 2006)

Mark position measurement by visual feedback with laser S. Nara and S. Takahashi Proc. SPIE Vol. 6374, 63740T (Oct. 12, 2006)

SYSTEM IDENTIFICATION AND MODELING I Catheter kinematics and control to enhance cardiac ablation Yusof Ganji and Farrokh Janabi-Sharifi Proc. SPIE Vol. 6374, 63740U (Oct. 12, 2006)

An investigation of phenomenal parasitics and robust control of parallel-plate electrostatic micro-actuators Guchuan Zhu, Jean-François Chianetta, Mehran Hosseini, and Yves-Alain Peter Proc. SPIE Vol. 6374, 63740V (Oct. 12, 2006)

Hybrid neural networks and genetic algorithms for identification of complex Bragg gratings Ali Rostami, Arash Yazdanpanah-Goharrizi, Amin Yazdanpanah-Goharrizi, and F. Janabi-Sharifi Proc. SPIE Vol. 6374, 63740W (Oct. 12, 2006)

Identification of complex Bragg gratings based on optical transfer function estimation using genetic algorithm A. Rostami, A. Yazdanpanah-Goharrizi, A. Yazdanpanah-Goharrizi, and F. Janabi-Sharifi Proc. SPIE Vol. 6374, 63740X (Oct. 12, 2006)

Physical parameters identification of nonuniform fiber Bragg gratings using interpolation method A. Rostami, A. Yazdanpanah, and F. Janabi-Sharifi Proc. SPIE Vol. 6374, 63740Y (Oct. 12, 2006)

SYSTEM IDENTIFICATION AND MODELING II Circuit modeling of multiple quantum well lasers optimized by carrier tunneling A. Rostami, H. Rasooli, and F. Janabi-Sharifi Proc. SPIE Vol. 6374, 63740Z (Oct. 12, 2006)

A micro-optical electromechanical system (MOEMS) for high-precision displacement sensor design using ring resonator array A. Rostami, A. Ghanbari, and F. Janabi-Sharifi Proc. SPIE Vol. 6374, 637410 (Oct. 12, 2006)

Tunable dispersion management using thermo-optical effect in ring resonator G. Rostami, A. Rostami, and F. Janabi-Sharifi Proc. SPIE Vol. 6374, 637411 (Oct. 12, 2006)

Invited Paper

Laser motor Hideki Okamura* Dept. of Physics, International Christian University, 3-10-2 Osawa, Mitaka, Tokyo, JAPAN 181-8585; ABSTRACT Light driven actuators that have already been proposed are intended for applications on a rather small scale, however, commercially available laser oscillators have sufficient energy to drive much larger objects. Is it possible to realize light-driven actuators that can replace electrical motors? In this paper, a discussion regarding this goal is presented on basis of the conversion efficiencies from light energy into mechanical energy. Several methods of actuation, including the one that is based on radiation pressure, were compared from this perspective. The energy conversion efficiencies for converting the motion of the actuator element into a useful form of motion are separately considered. It was concluded that light-absorption type actuators with a continuous operation scheme are the most promising for achieving a high efficiency. Based on these findings, a new scheme, called the laser motor, is proposed. In the proposed scheme, a pulsed laser shines on an elastic material and induces a specific form of vibrations in it. By using two lasers, a traveling wave is formed. Another object is pressed against the vibrating surface and a relative movement between the two objects is then created. Keywords: Optomechanical actuator, laser, energy conversion, radiation pressure, elastic wave, traveling wave, stationary wave, space elevator, micro robot

1. INTRODUCTION There have been many reports and proposals about manipulating objects by light. It is well known that light has not only energy, but also momentum and these actuators can use either of these two properties. The optical tweezer was the earliest example to utilize the momentum of light. One can manipulate small dielectric materials using a focused laser beam 1, 2. Manipulation of atoms is also realized which can be used for laser cooling 3. A similar manipulation is also possible for molecules 4. Other types of actuators utilize the energy of light. The most common type is based on the photothermal effect 5, 6. The light energy is converted into heat, and then through thermal expansion, the material bends by itself and asserts a force on the neighboring object. The temperature dependent phase transition, photostrictive effect 7, and photochemical reaction 8 can also induce changes in the dimensions of a material. In this type of actuator element, the material bends, shrinks, or stretches, which can be reclaimed as a mechanical motion. Also, applications using the photovoltaic effect or solar cell could also be included in the discussion since it also performs the conversion of light energy into different kinds of energy which can eventually be converted into mechanical energy 9. Light-driven actuators share the property that energy is delivered in a non-contact mode and an object can be remotely driven, and that these devices can be controlled by light so other methods for control are unnecessary. There is no need to carry batteries or other energy sources, therefore they can be very small and light. Another advantage is their high tolerance toward electro-magnetic noise. Based on these properties, they will be able to be used in various environments in which conventional actuators cannot be used. These properties make them applicable to new applications such as micro-robots and light-driven climber. The light-driven actuators reported so far can produce only small forces. Optical tweezers can produce a force in the range of pN or nN. A polymer film can produce a force of 10-5 N when bending upon irradiation 6. Due to these small forces, it cannot actuate large objects, thus applications are limited to small objects. Optical tweezers, for instance, can handle a size only up to 100 µm. *[email protected]; http://subsite.icu.ac.jp/people/okamura/

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 637401, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.689380

Proc. of SPIE Vol. 6374 637401-1

However, the energy of light is actually high enough to manipulate much larger objects. Commercial laser oscillators of more than 10W of output power are easily obtainable. This is a power capable of accelerating a 1kg object to 5m/s in one second, or moving a 1kg object upward at a constant speed of 1m/s. As will be explained later, the currently proposed light-driven actuators have conversion efficiencies much less than unity, and application of these techniques for larger objects seems impossible. If in some way the efficient conversion of light energy into mechanical energy is realized, all these things will be able to be performed using light. It will be possible to replace applications which could only be performed by a motor or some other means. Various new applications will then become feasible. In this paper, various types of light-driven actuators are reviewed from the viewpoint of energy conversion. This discussion will give us some insights into how one can achieve an efficient conversion of light energy into mechanical energy. Conversion efficiency is not a concern for small objects, because even if most of the energy is wasted, these techniques are still useful. For a larger object, the situation is different. One definitely needs a high efficiency in order to obtain a large magnitude of force. Finally, I will propose a scheme that can potentially offer a high efficiency and continuous linear or rotational motion.

2. ENERGY CONVERSION EFFICIENCIES Energy conversion efficiency is defined as the ratio between the work that is done by the actuator and the light energy that fell upon the actuator. Light driven actuators have various shapes and mechanisms, however, they all share the same property that they convert light energy into mechanical energy. Therefore, in the following discussions, the efficiencies are compared for several types of actuator elements. This will give us some insight into realizing an energy efficient energy conversion. We divide the light-driven actuators into two groups, that is, one that uses radiation pressure and one that uses light energy, and each type will be considered below. Note that these are the efficiencies for the actuator elements. The efficiency as a system includes the mechanism to convert the motion of the actuator element into a useful form of motion. This will be separately discussed. 2.1 Radiation pressure type actuators Light can assert a force on objects through radiation pressure, or the momentum of light. Optical tweezers, laser cooling, and the solar sail all fall in this category. It is also possible to oscillate a microscopic oscillator with light 10, 11. The force induced by this effect is usually very small. One example to show this is that a very large sail is required for solar sailing. For optical tweezers the force is on the order of pN. This is too small a force to manipulate macroscopic objects, and therefore, optical tweezers are useful only for microscopic objects. Why is this force so small? This is a natural consequence from the property of light. The energy, E of light and its momentum, p are given by E = hν and p = h/λ = E/c, respectively, where ν is frequency, λ is wavelength, c is the speed of light, and h is Planck’s constant. Also, the force F is given by F = dp dt . Since c is a very large number, p becomes much smaller than E. Thus there is a limitation on the force for this type of actuator. Let us estimate the efficiency of the optical tweezers. The typical laser power for an optical tweezer is 10mW and the force produced at this laser power is on the order of pN. If we displace the object by 1 mm in 1 sec, therefore, the work done is 1 pN × 1 mm = 1 × 10-15 J, and the light energy during this period is 10 mW × 1 s = 10 mJ. The conversion efficiency is then roughly 1 × 10-15 J/ 10 mJ = 10-12 = 10-10 %. For the actuation of an object by radiation pressure, most of the light energy is not used. Light retains most of its energy after an interaction with matter. Only a small red-shift in the wavelength of the scattered or refracted light due to the Doppler effect accounts for the mechanical energy that is produced. 2.2 Light absorption type actuators In this type of actuator, light is absorbed and its energy is used to change the state of the material. Some of the effects used for actuators are summarized in Table 1. All these types of effects convert light into different forms of energy. The first 4 types of actuators in Table 1 are accompanied by a volume change. Ablation utilizes the reaction force from the particle leaving the object upon irradiation of an intense laser pulse. The ferroelectric transition can also be used for actuators. The last one may seem different from the rest of the listings, but it is also the conversion of light energy into another form of energy (in this case, electricity) so it can be included here.

Proc. of SPIE Vol. 6374 637401-2

Table 1. Various types of light-absorption type light-driven actuators Type of effect

Principle

Materials

Photothermal effect

Heat expansion, etc

Optical fiber, PVDF Polymer film, etc

Photochemical effect

Isomerization

Liquid-crystal network with azobenzene chromophore

Photostrictive effect

Piezoelectric

PLZT ceramics

Vaporization,

Vaporization of water,

Structural change, etc

Shape Memory alloy, etc

Ablation

Reaction of particles

Metal, etc

Ferroic transition

Temperature increase

Temperature sensitive magnet, etc

Solar cell, photovoltaic effect

Electronic excitation

Phase transition (Volume change)

Si semiconductor, etc

Next, we will compare these processes in terms of efficiency. Firstly, let us take up the actuator using the PVDF polymer film 6. This actuator is mainly based on the photothermal effect. It bends upon irradiation and assert force. The force was measured to be 6.6 × 10-5 N and the efficiency was obtained to be 8.3 × 10-5 %. There are not many reports about the evaluation of efficiency other than this report, so we will make estimations for the rest. Temperature sensitive transition type actuators are expected to have a rather high efficiency because the energy of the laser beam can be easily converted into heat with only a small loss. In our lab, we are testing an actuator based on a temperature sensitive alloy. A rough estimate of the conversion efficiency was on the order of 1%. Photochemical type and ferroic tansion type actuators are supposed to give similar efficiency since the cause of the energy loss is similar. Ablation is unlikely to score better than these types of actuators because some energy is wasted in unwanted heating of the body. Also, there is a loss due to the velocity distribution of the leaving particles. Only the perpendicular component of them to the surface is effective for propulsion, and the rest of the energy is averaged out and does not contribute. The efficiency of the solar cell can reach 50% if one chooses the right wavelength. The one for a motor is 80% under favorable conditions. The overall efficiency is the product of these two, so for a carefully designed system, the overall efficiency from light energy into mechanical energy will be close to 40%. NASA demonstrated the practicality of this combination by a model airplane that is propelled by a laser beam. The light energy is converted to electrical energy by a solar panel that is attached to the bottom of the airplane. It does not need to carry any fuel and can fly for an unlimited time as long as the laser beam is tracking the airplane 9. 2.3 What is the method of choice? The results of these discussions are summarized in Table 2. The phase-transition type actuator seems to be the most promising among these, except for the solar cell. The photothermal effect is not a very efficient process, but still provides a higher efficiency than the optical tweezer. The efficiency of the optical tweezer is by far the lowest. Considering that there is a theoretical limitation for the force due to radiation pressure, it can be naturally concluded that an efficient conversion will have to resort to absorption type actuators. Table 2. Energy conversion efficiencies for various types of light-driven actuator elements.

Category Radiation Pressure Absorption (photo-thermal) Absorption (Phase transition, heat induced) Absorption (photo-current)

Type

Typical Force

Efficiency

Optical tweezer

~ 1 pN

~10-10 %

6.6 × 10-5 N

8.3 × 10-5 %

Polymer film (PVDF) Temperature sensitive alloy Solar cell + motor

Proc. of SPIE Vol. 6374 637401-3

~3 N

~1 % (estimate) ~40% (Theoretical)

2.4 Conversion to a linear/rotary motion In the previous section, we focused on the actuator elements and discussed the principle of actuation. In this section, we examine the manner in which actuators produce force. The strokes of light driven actuators are typically on the order of micrometers. An oscillating object at such a small amplitude is of little use, therefore, for this type of motions a conversion into a linear/rotary motion is usually desirable. Some examples are shown in Fig. 1. For a volume-change type actuator, the typical motion is bending. Actuators that use ablation or vaporization make use of the reaction force from the substance that leaves an object. Another example shown here is an actuator based on the temperature sensitive magnet. By making use of the property that magnets lose their magnetic properties above the Curie temperature, the force between the magnets can be turned on and off by irradiation. Upon irradiation, the magnet loses its magnetic property, and the two magnets will move apart from each other by a spring. Bending Light

Reaction of ablation/vaporization Light

Temperature sensitive magnet

Light

Fig. 1. Some examples of actuator motions.

The conversion to a linear or rotary motion usually requires that a cycle be formed. For instance, a bending motion is repeated for a microactuator to walk 12. Another example of a cycle is depicted in Fig. 2. In this case, two actuator elements are combined so that they form a 90° angle. Each one moves at a time, forming a 4-stroke cycle, and by repeating this cycle, they could rotate a disk 6. This is a demonstration of conversion from a bending motion to a rotary motion.

sssssssa

U

a

—%4su-#44'

sssa sssssa Fig. 2. An example of a conversion from a bending motion to a translational motion.

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One will notice that the translational motion is produced during only one of the four steps. The force in the return path does not do any work. Even so it requires a similar amount of energy to bend. Therefore, roughly speaking, only one fourth of the energy produced by the actuator is converted into a translational motion. Force is used for propulsion only in a fraction of the steps in the whole cycle, so some waste of energy cannot be avoided if a cycle is to be formed. There is another kind of problem for this kind of walking motion. For one thing, there is no retaining force for the object while the actuator is not in contact with the object. This will lead to a backlash and will further degrade the efficiency. Another problem is the translation of an object based on bending or expansion that becomes a walking type motion. It tends to be slow and inefficient, i.e., the speed will suffer. As can be seen from the above discussion, through the process of conversion from a oscillating motion into a linear or rotary motion, only a fraction of the energy can be converted into a translational energy. The overall efficiency is reduced by this process.

3. NEW PROPOSAL – LASER MOTOR In this report, we would like to propose a new scheme involving a potentially efficient light-driven actuator, which can convert light energy into mechanical energy in a more direct way. As is evident from the above discussions, if one wants to manipulate macroscopic objects by light, it has to use the energy of light, not its momentum. This suggests that the actuator cannot generate a momentum by itself and the relative motion has to be generated between two objects. Naturally it will consist of two parts, and to avoid exploiting a walking cycle, which will ruin the efficiency and speed, the two objects will be in physical contact with each other and directly induces a relative motion. Based on the above argument, one can draw the sketch that is shown in Fig. 3. This is one possible scheme for realizing the efficient conversion from light energy into mechanical energy. We called this a laser motor due to its resemblance to a conventional motor.

Fig. 3. Schematic drawing for rotary and linear laser motors.

How will it be possible to induce a relative motion between the two objects? This will be realized by generating traveling elastic waves in the object with light pulses. Fig. 4 shows the case where a Rayliegh wave is employed (the bulk wave will also work). The Rayligh wave is a surface wave, and has the characteristic that each portion along the surface takes a circular motion. The direction of rotation is the opposite to the direction that the wave is propagating. Therefore, if one presses another object against the surface, this object is driven in the opposite direction of the wave propagation. As will be explained later, the direction of wave propagation can be reversed by changing the laser irradiation timing.

Proc. of SPIE Vol. 6374 637401-5

j—L

V

Direction of wave propagation Fig. 4. Schematic of actuation. The surface Rayliegh wave pushes the object into the efficient as

The principle of laser motor is summarized in Fig. 4. It is known that a laser can induce elastic waves in solids 14. It is one of the advantages of using lasers. Lasers can produce intense light pulses whose energy is concentrated in a fraction of time. Also, the timing and position of the irradiation can be precisely controlled. The irradiation timing of the laser pulses are tailored and induce the desired wavelength of the elastic wave. Positions of the irradiation are controlled by a mask or filter on the surface of the object. Light is selectively absorbed in either or both of the two objects. Various kinds of schemes, including heat deposition, ablation, phase transition, and photostrictive effects, can be used for exciting a vibration. For the best performance, the most efficient method will have to be found. By changing the schedule of light irradiations, one can control the speed and direction of the motion. The diagram for the laser motor is summarized in Fig. 5.

Laser irradiation Vibration

Heat deposition (photothermal effect) Radiation pressure Light-induced phase transition Ablation Photon-phonon coupling Photovoltaic effect Photostrictive effect

Linear/rotary motion Fig. 5. Diagram for the laser motor. A pulsed laser shines on some elastic material and induces vibration on the surface. By using two lasers of different wavelengths, a traveling wave is formed. A linear or rotary motion is induced between the vibrating object and the other object that is in contact with the vibrating object.

3.1 How to induce a traveling wave laser pulse irradiation can induce a vibration in an object. In this case, a clearly defined wave of a fixed wavelength needs to be excited. This could be realized by irradiating an object at its resonant frequency. By tuning the interval of the irradiation, one can induce a stationary wave with a single frequency, A1 (z, t) = sin(ω t)cos(kz) . A second laser oscillator induces another stationary wave on the object with a different phase, A2 (z,t) = sin(ω t + π / 2)cos(kz + π / 2) . When the two stationary waves are superposed, one obtains, A1 (z,t) + A2 (z,t) = sin(ω t)cos(kz) + sin(ω t + π / 2)cos(kz + π / 2) = sin(ω t − kz)

(1)

This is the traveling wave that we are looking for. If one wishes to reverse the direction of the motor, one simply changes the irradiation timing. There is no need to change the location of the excitation. Now, the second wave A2(z, t) becomes, A2′ (z,t) = sin(ω t − π / 2)cos(kz + π / 2) . Therefore,

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A1 (z,t) + A2′ (z,t) = sin(ω t)cos(kz) + sin(ω t − π / 2)cos(kz + π / 2) = sin(ω t + kz)

(2)

Eq. (2) represents a traveling wave going in the opposite direction to eq. (1) The scheme for the irradiation timing is depicted in Fig. 6. Time Å® éû ä‘ B1 B2

Time Å® éû ä‘

B1 B2

Fig. 6. Irradiation timing. B1 and B2 refer to the timing scheme of laser irradiation. The top and the bottom irradiation schemes induce a traveling wave propagating in the opposite directions.

3.2 Experimental

—

——

r

r

r :-= -

t I

.—

J

c-'

T—

____ L2______

—1

To demonstrate that clearly defined elastic waves of single frequency can be induced by laser, we conducted an experiment using a Q-sw Nd:YAG laser (wavelength 1064 nm) and a copper ring as a target. In Fig. 7, the experimental result is shown. The repetition rate was tuned to the resonant frequency of the ring. The bottom trace indicates laser irradiations. The upper trace is the voltage from the transducer attached to the surface of the target. A vibration that is in phase with the exciting laser is induced. The amplitude of the vibration can be estimated from the voltage of the transducer that is on the order of 10 nm 13. In this experiment the vibration was induced by the photothermal effect. By using more efficient mechanism, and by using a material with higher Q-factor, the amplitude can become much larger.

Fig. 7. Experimental result for the induction of a stationary wave in a copper ring.

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3.3 Advantages of Laser Motor This method has the advantage that the light doubles as a method to convey energy and as a method to control the operation. In the case of NASA’s light plane, light is used to transmit just the energy, so the control of a motor has to be done by a separate transmission channel such as a radio wave. In the case of the laser motor, one can even reverse the direction by simply changing the irradiation timing. To summarize the advantages of the laser motor, No wire, no battery Fully controllable by light Light weight, small size. Much faster than walk-type motion Not affected by electric or magnetic disturbances High holding force, zero backlash - (very useful when used for elevators) Long range operation. (Laser can reach a great distance) 3.4 Possible Applications In this section, some possible applications are illustrated. For the application as a space elevator (Fig. 8b), the laser motor has to cling to a ribbon. For this special purpose, a variant of the laser motor that can move along a ribbon is shown in Fig. 10. The rippon is sandwiched between 2 motors which hold it. Due to the high holding force of the laser motor, this will be a particularly suitable example of such an application.

(a)

Iazer2

(b)

—Ribbon 20 Laser —motor 23

— 34 Laser — 31 Motor 1

35 Laser Motor 2

Fig. 8. Possible applications. (a) Micro car that can be controlled and driven by laser pulses of three different wavelengths. (b) A space elevator. The laser station fixed on the ground irradiates the elevator to supply energy.

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(a)

111111

11111111111I 11111111111I I

Laser motor

Laser

I

I

11111111111111I 11111111111 I

I

Laser

(b)

Fig. 9. Possible applications. (a) Remote control slider/adjuster for hard to reach locations. Each knob on the board is equipped with a laser motor and can be remotely operated. (b) Remote adjustment of the angle of mirror/screen/tile on the building from the outside. The adjuster screw can be operated by the laser motor.

Laser V un bbon

Laser Fig. 10. A variant of the laser motor. The laser motor itself will slide on the rail/ribbon.

4. CONCLUSION We investigated the possibility of realizing a light-driven actuator that can manipulate macroscopic objects. The energy conversion efficiency is the key factor, therefore, we compared energy conversion efficiencies of various types of actuators, both on the element itself and on the process to convert the motion into a usable form of motion. We showed that an efficient actuator has to be an energy absorbing type, and therefore, it will require at least two objects to induce a relative motion between them. Also, it was found that a continuous operation is desirable. Based on these finings, we proposed a new scheme, called the laser motor, which continuously operates and is potentially fast. It uses pulsed lasers to induce a traveling elastic wave, and then the induced elastic wave is converted into a linear or rotary motion. A mathematical treatment showed that two independent waves should be excited, which is easily attainable using two lasers and appropriate filters. A traveling wave can be formed by a superposition of the two independent waves. Reversing the direction can easily be done by changing the irradiation timing. Some results from preliminary experiments of inducing vibrations in solids were also shown.

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REFERENCES 1. A. Ashkin, Phys. Rev. Lett. 24, 156-159 (1970). 2. A. Ashkin, "History of Optical Trapping and Manipulation of Small-Neutral Particle, Atoms, and Molecules." IEEE Journal of Selected Topics in Quantum Electronics 6(6), 841-856 (2000). 3. H. Okamura, P. Corkum, and D. Villeneuve, “Trapping H2 molecules with intense laser pulse,” The 49th Spring Meeting of Japan Society of Applied Physics and Related Societies, Kawasaki, 2002, 30aD5/III, p.902. 4. H. Okamura, "Molecular Optics - control of molecular motion by strong laser field," Bunko-kenkyu, Journal of the spectroscopical Society of Japan, 50, 101-109 (2001) (in Japanese). 5. S. Inaba, H. Kumazaki, and K. Hane, "Photothermal vibration of fiber core for vibration-type sensor", Jpn. J. Appl. Phys., 34, 2018-2021 (1995). 6. S. S. Sarkisov, M. J. Curley, L. Huey, A. Fields, S. S. Sarkisov II, G. Adamovsky, “Light-driven actuators based on polymer films,” Opt. Eng., 45, 034302 (2006). 7. P. Poosanaas, K. Tonooka, K. Uchino, “Photostrictive actuators,” Machanics 10, 467-487 (2000). 8. Y. Yu, M. Nakano, T. Ikeda, “Directed bending of a polymer film by light,” Nature, 425, 145 (2003). 9. NASA: NASA research team successfully flies first laser-powered aircraft, http://www.nasa.gov/lb/vision/earth/improvingflight/laser_plane.html 10. O. Hahtela and I. Tittonen, “Optical actuation of a macroscopic mechanical oscillator”, Appl. Phys. B, 81, 589-596 (2005). 11. T. Carmon, H. Rokhsara, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal Behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett., 94, 223902 (2005). 12. Y. Otani, “Light driven running machine,” Hikari-aliance, 10, 40−42 (1999)． 13. B. V. Richert, R. Hamamura, R. Ono, and H. Okamura, ”Observation of resonant standing waves in a copper ring induced by laser irradiation”, The 53rd Spring Meeting of Japan Society of Applied Physics and Related Societies, Tokyo, 2006, 25a-ZD-9/III, p.1062. 14. Z. Shen, S. Zhang, and J. Cheng, “Theoretical study on surface acoustic wave generated by a laser pulse in solids,” Anal. Sci., 17 , S204-s207 (2001).

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Light-driven polymer actuators for propulsion and light control LaQuieta Huey,*a Sergey S. Sarkisov,b Michael J. Curley,a Grigory Adamovskyc Jai-Ching Wanga a

Alabama Agricultural and Mechanical University, Department of Physics, Normal, Alabama 35762, USA b SSS Optical Technologies, LLC, Huntsville, Alabama 35816, USA c NASA Glenn Research Center, Cleveland, Ohio 44135, USA ABSTRACT

New light-driven actuators based on films of polymer polyvinylidene fluoride are described. The actuators employ the photomechanical bending of the polymer film caused by low power (10 mW and less) laser radiation. The photomechanical effect combines various physical mechanisms, such as anisotropic thermal expansion, converse piezoelectric mechanism along with photovoltaic and pyroelectric ones, while the mechanism of thermal expansion is dominant for slow motion. Mechanical vibrations of the strips of the photomechanical polymer were observed with periodic pulsed laser excitation. The resonance frequency is inversely proportional to the square of the length of the strip, in full agreement with the theory. Resonance frequency measurements were used to determine the modulus of elasticity of the films, which was close to 3.0x109 Pa. Two possible applications were discussed: optical fiber switch and adaptive mirror propelled by the proposed actuators. The actuators have a potential of being used as the components of future light-driven micro/nano systems. Keywords: photomechanical effect, optical actuator, photomechanical polymer

1. INTRODUCTION Modern optical smart structures,1 which adapt themselves to external and internal changes measured by various optical sensors, lack simple and compact actuators that can be driven by the same low power light radiation used to operate sensors. Current solutions utilize electrically driven actuators, which require electric current to be delivered by wires from an electric power source. Rapidly growing industry of optical switching experiences similar problem. Currently available optical switches typically use electrically driven piezoelectric actuator elements requiring an external high voltage for actuation.2 Consequently, there is a great need for a simple, efficient and compact photomechanical actuator, which can be driven by low power light radiation in visible or mid-infrared range delivered through conventional optic fibers. The photomechanical (or optomechanical) effect could be defined as a bulk dimensional change in a photosensitive body induced by the influence of an applied optical field.3 Several physical mechanisms have been reported in the literature to generate a significant photomechanical effect: photothermal mechanism,3-6 photostriction,7 and molecular re-orientation caused by polarized light.8, 9 The focus of this study was on the applications of the light-driven actuators using photomechanical effect in thin films of polymer polyvinylidene fluoride known as PVDF.

2. EXPERIMENT It has been shown in the past that the illumination of a strip of PVDF film with continuous laser radiation produces a static bending of the strip.10 The direction of bending is always the same, no matter which side of the strip is illuminated. The bending strip exerts a static force to an external object. The force is proportional to the power of the incident laser beam. It can be as high as 10-4 N per 10 mW of the laser beam power. The force, as well as the deflection, does not depend on the shape of the beam and its position in the strip as long as the beam *

E-mail: [email protected] Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 637402, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.684337

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stays away from the edges. In this study our focus was on the vibrations of PVDF strip produced by pulsed laser radiation, which is important for propulsion-related applications. Thin film samples of PVDF (β-phase, solid solution of polycrystalline phase in amorphous phase) with a thickness of 28, 52, and 110 µm were studied. The films were uniaxially stretched and polarized with a positive corona during the extrusion process and then rolled up and stored in rolls. Fig. 1 shows microscopic images of a typical film. Optical image reveals some phase inhomogeneities in the volume probably due to the crystalline phase of PVDF dissolved in polymer phase. AFM image reveals surface imperfections such as scratches and pits created by the corona discharge during the electrostatic poling process. The density of the defects is such that they do not affect the performance of the films as photomechanical actuators. Rectangular strips of various length and width were cut from the films with long dimension along or across the direction of stretching. In order to increase the absorption of an incident laser beam, the strips were coated with 80-nm chromium layers on one side using DC magnetron sputtering. The experimental setup is presented in Fig. 2. The illumination of a strip of a PVDF film with a pulsed beam from an infrared laser generates periodic vibration of the strip. In order to visualize the vibration, a weak continuous probe laser beam from a semiconductor laser was pointed on the free end of the strip, close to the edge. The reflected beam made a spot on a distant screen. Vibration of the strip produced displacement of the probe ∆y, as is shown in Fig. 2. Pulses of laser light were produced by a mechanical chopper placed after the laser. The frequency of the light pulses was varied by varying the frequency of the chopper wheel. The frequency reading was taken form the digital display of the chopper. The amplitude of vibrations (in arbitrary units) was evaluated as ∆y/2.

3. EXPERIMENTAL RESULTS AND DISCUSSION It was possible to observe the mechanical resonance of the vibrations of the strips periodically illuminated with laser pulses. Typical resonance curve of a vibrating strip is presented in Fig. 3. In this particular case (5-mm wide strip) two resonances at 12 and 33 Hz were observed. The vibration at the higher resonance frequency had greater amplitude. The theoretical model of a vibrating beam with one fixed end was applied to this case.11 The resonance frequency of the 1-st vibrating mode of the beam can be expressed as

f =

3.516 t 4πl 2

E , 3ρ

(1)

where f is the frequency, E is the Young’s modulus of elasticity, t is the thickness of the film, l is the length, ρ is the mass density of the film (1.917 X103 kg/m3). Eq. (1) was used to determine the Young’s modulus of PVDF strips of different sizes, thicknesses, and cuts. Experimental data is presented in Figs. 4 through 6. The resonance frequency was plotted versus the inverse square of the length of a strip. According to Eq. (1) the linear fit of the data must give a slope factor that can be used to find the modulus of elasticity, with all the other parameters known. The modulus of elasticity was determined as close to 3.0x109 Pa for the films of 52 and 110 µm, and twice as high for the 28-µm film, regardless of the cut. The difference in moduli needs to be further investigated. The elasticity of 28-µm or thinner film of PVDF could be higher due to some unaccounted fabrication peculiarities. On the other side, it could be an indication that the simple model of an elastic vibrating beam fails to describe thinner films. Experimental investigation of the effects of thermo-mechanical fatigue was conducted with the films used for the actuators. In the first experiment, a strip of chromium-coated 52-µm polymer film clamped between two glass plates with dimensions 2 by 22 mm was periodically activated by a 15-mW laser beam from a He-Ne laser at a resonance frequency of 43.5 Hz. The amplitude of the vibrations of its free end and its position was monitored with a weak probe beam from a semiconductor laser (laser pointer, 635-nm wavelength). The total time of the continuous operation of the actuator was 77 hours (equivalent to 1.2x107 cycles of switching of an optical switch based on the actuator) until the probe laser broke down. During this time no noticeable decrease of the amplitude of the vibration or shift of the position of the free end due to some inelastic bending was observed. The actuator turned out to be more reliable then the laser source. In the second experiment, a strip of the same film was illuminated with a beam from an Nd:YAG laser (1064-nm wavelength) at significantly higher power. The beam

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with a power of 150 mW produced almost immediately inelastic deformation of the film, in other words melted it down, and no light-driven actuation was observed afterwards. However, periodic illumination of a 3 by 25-mm strip with a 63-mW beam at a resonance frequency of 24 Hz performed over 10 hours did not show any degradation of the amplitude of the vibrations or inelastic bending of the film. The amplitude and the shift were also monitored with a weak probe beam from a probe semiconductor laser. That was equivalent to approximately 9.0x105 cycles of vibration. These experimental results point to sufficiently good performance of the polymer actuator in terms of its lifetime.

4. APPLICATIONS 4.1. Photonic switch A prototype photonic switch was built using thin films of PVDF.12 All the components of the switch are mounted on platform 1 (Fig. 7). The core element of the switch is a flexible reflector (2, 3) made of metal-coated PVDF film. The reflector is fixed on holder 4. In its inactive state the reflector takes position 2. In its active, deformed, state the reflector takes position 3. Activation of the reflector into active state is achieved by illumination with light beam 5, which is focused by optical element 6 into beam 7 converging on the back side of the reflector coated with absorbing coating 8. A low-power semiconductor laser 9 sends probe beam 10 to the reflector. When the reflector is in inactive position 2, probe beam 10 is reflected and turns into beam 11 that goes to optical element 12 that focuses it in optical fiber 13. Fiber 13 transmits light to photodetector 14 connected to Channel 1 of a two-channel oscilloscope 15. When the reflector is in active position 3, probe beam 10 is reflected and turns into beam 16. Beam 16 goes through optical element 17 to fiber 18 that transmits light to photodetector 19 connected to Channel 2 of oscilloscope 15. Light beam 5 is chopped by mechanical chopper 20. The chopper synchronizes oscilloscope 15. When light beam 5 is cut off by chopper 20, the reflector is in inactive position 2, and the light from laser 9 goes to photodetector 14 that produces high-level signal in Channel 1 of the oscilloscope. There is no light going to photodetector 19, and the signal in Channel 2 is at zero level. When light beam 5 illuminates the reflector, the signal in Channel 1 is at zero level, and the signal in Channel 2 is at high level. Thus, illumination of the reflector with control light beam 5 produces a switching effect between Channels 1 and 2. The reflector was made as a strip of gold-coated 52-µm-thick PVDF film with dimensions 7x1 mm. It was illuminated with a 15-mW beam from a He-Ne laser. Fig. 8 depicts a typical oscillogram of the signals in the channels of the switch. The minimum switching time observed was 3 ms (for a 1x7-mm strip made of 52-µm film). The speed of switching can be increased by the reduction of the size of the PVDF reflector, in accordance with the findings discussed in Section 3. 4.2. Adaptive mirror The photomechanical polymer films were also tested as a basis for adaptive mirrors.12 Fig. 9 shows the configuration of the experiment with a defocusing convex reflector activated by the primary incident beam (selfdefocusing). Experimental mirror for self-defocusing was made of a 52-µm film coated with chromium. The power of the incident self-defocusing beam was controlled with a set of neutral density filters. The crosssectional view of the beam was obtained with a Spiricon beam profiler (Fig. 10). As one can see, the beam widens up significantly after reflection form the film when its power increases. This is an indication of defocusing caused by the formation of a convex mirror in the illuminated region of the film. A power of 12 mW from a He-Ne laser was sufficient to make a well defined reversible defocusing convex reflector out of initially flat film. In other configurations, the shape of the reflector could be controlled by a secondary control beam dedicated to shape up a relatively weak primary beam (Fig. 11). In this experiment, films of PVDF were coated with high reflectance gold coating on one side and with an absorbing coating on another side. Fig. 12 shows how the control beam defocuses the probe reflected from a convex photomechanical mirror (52-µm-thick in this case). The temporal response of the mirror has two components: fast and slow. The fast response lasts for few hundred milliseconds. The slow response, resulting in final wide spread of the probe, takes up to three seconds. After that the spread of the probe reaches saturation. Fig. 13 shows focusing of the probe by the same control beam using a 110-µm-thick concave mirror. The plot of the focal distance of the mirror versus the power of the control beam is presented in Fig. 14. The focal distance goes down with the power and approaches a saturation level of 4.5 mm. Further decrease of the focal distance (increase of the focusing power) of the mirror can be achieved by the reduction of the size of the control beam.

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5. CONCLUSIONS Photomechanical actuators based on PVDF films powered by pulsed mW laser beams can be used to propel optical fiber switches and adaptive reflectors. The theoretical model of a uniform elastic beam with one end clamped turned out to be accurate enough to describe resonance vibrations of the PVDF strips activated by pulsating laser beam, if the thickness of the strips exceeds 28 µm. Using the model and the experimental data on the resonance frequency versus the length of a strip, the modulus of elasticity of PVDF films was determined as close to 3.0x109 Pa. The fatigue effects did not show up for hundreds of hours of continuous operation of the PVDF actuators. Preliminary demonstrations showed the feasibility of a photonic switch and adaptive mirror based on the photo-mechanical actuators.

ACKNOWLEDGMENTS LaQuieta Huey and Michael Curley acknowledge support from the Department of Education HBGI Title III Program at AAMU.

REFERENCES 1.

J. Dakin and B. Culshaw, “Optical Fiber Sensors. Volume 4: Applications, Analysis, and Future Trends”, pp. 409- 435, Artech House, Inc., Boston, MA (1997). 2. P. De Dobbelaere, K. Falta, and S. Gloeckner, “Advances in integrated 2-D MEMS-based solutions for optical network applications,” IEEE Communications Magazine 41, S16-S23 (2003). 3. S. Inaba, H. Kumazaki, and K. Hane, “Photothermal vibration of fiber core for vibration-type sensor,” Jpn. J. Appl. Phys. 34, 2018-2021 (1995). 4. M.G. Kuzyk, D.W. Garvey, S.R. Vigil, and D.J. Welker, “All-optical devices in polymer optical fiber,” Chemical Physics 245, 533-544 (1999). 5. Yu. Otani, Ya. Matsuba, and T. Yoshizawa, “Photothermal actuator composed of optical fibers,” in Optomechatronic Systems II, Hyung Suck Cho, Editor, Proceedings of SPIE Vol. 4564, 216-219 (2001). 6. H. Finkelman, E. Nishikawa, G.G. Pereira, and M. Warner, “A new opto-mechanical effect in solids,” Phys. Rev. Lett. 87, 015501-1- 4 (2001). 7. P. Poosanaas, K. Tonooka, and K. Uchino, “Photostrictive actuators,” Mechatronics 10, 467-487 (2000). 8. P. Krecmer, A.M. Moulin, R.J. Stephenson, T. Rayment, M.E. Welland, and S.R. Elliott, “Reversible nanocontraction and dilation in a solid induced by polarized light,” Science 277, 1799-1802 (1997). 9. Ya. Yu, M. Nakano, and T. Ikeda, “Photomechanics: Directed bending of a polymer film by light,” Nature 425, 145 (2003). 10. Sergey S. Sarkisov, Michael J. Curley, Aisha Fields, Sergey S. Sarkisov II, Grigory Adamovsky, Photomechanical effect in films of polyvinylidene fluoride, Appl. Phys. Lett. 85, No. 14 (2004) 27472749. 11. S. Timoshenko, “Vibration problems in engineering,” Wiley, New York, NY (1974). 12. Sergey S. Sarkisov, Michael J. Curley, Grigory Adamovsky, Sergey S. Sarkisov, Jr., Aisha Fields, U.S. Patent No. 6999221, February 14, 2006, Bimorphic Polymeric Photomechanical Actuator.

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(a)

nM nM

300

30000 N

30000 N

20000

10000 NN

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10000

Figure 1. Optical (a) and atomic force (b) microscopic images of the PVDF film (52-µm-thick) used in the experiments. Total magnification of the optical microscope used was x400.

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10 9

∆y 8

7 1

5

6

4

3

2

Figure 2. Schematic of the experimental set-up for the study of mechanical vibrations of a PVDF strip initiated by a pulsed laser beam. A strip of metal coated PVDF film 1 is clamped between two glass slides 2. After being illuminated with laser beam 3 (that can be moved laterally in the vertical and horizontal direction with respect to the strip, as shown by arrows 4), the strip bends and takes new position 5. The free end of the strip is illuminated with a low power continuous laser probe beam 6. When the strip is in the initial, inactive position, the probe beam is reflected in direction 7 and makes a light spot 8 on a screen. When the strip driven by beam 3 is deflected, the probe beam is reflected in direction 9 and light spot 10. The light spot made by the probe beam has displacement ∆y. amplitude/2 35 30

amplitude

25 20 15 10 5 0 10

20

30

40

frequency

Figure 3. Amplitude of the vibrations (in arbitrary units) of a rectangular strip of PVDF versus the frequency (in Hz) of the laser pulses illuminating the strip. The data corresponds to a 52-µm thick strip with dimensions 20 by 5 mm. The strip was illuminated with a 70-mW IR laser beam at 1064 nm from a CW Nd:YAG laser. The resonance frequencies observed are 12 and 33 Hz.

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80 70 60

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(b) Figure 4. Plot of the resonance frequency (in Hz) versus inversed square of the length (in meters) for the strips made of 28 µm thick PVDF film. Figure (a) is the data plotted for the strips with longer dimensions along the direction of stretching, and figure (b) is for the strips cut across the stretching direction. The Young’s modulus was found to be (6.51 ±0.693) x 109 Pa and (8.15 ±0.97) x 109 Pa for (a) and (b) respectively. The 28 µm strips were suspended in air.

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(b) Figure 5. Plot of the resonance frequency (in Hz) versus inversed square of the length (in meters) for the strips made of 52µm-thick PVDF film. Figure (a) is the data plotted for the strips with longer dimension along the direction of stretching, and figure (b) is for the strips cut across the stretching direction. The Young’s modulus was found to be (2.44 ± 0.48) x 109 Pa and (3.50 ± 0.49) x 109 Pa for (a) and (b) respectively.

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Figure 6. This graph depicts the 110-µm strip (cut along the stretching direction). Young’s modulus here was found to be (3.59 ± 1.29) X 109 Pa. The amplitude of vibrations of the strip cut across the stretching direction was small and hard to measure.

14

19 18

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Figure 7. The configuration of a photonic switch based on the light-driven PVDF actuator.

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Figure 8. Oscillogram of the intensity of light in Channels 1 and 2 (pulses with small dip on the top) of the photonic switch.

Self-focusing

Self-defocusing Photomechanical mirror

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Focusing lens

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Figure 9. Self-focusing (a) and self-defocusing (b) of a laser beam illuminating the photomechanical deformable mirror.

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(a)

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Figure 10. Image of the spot of the beam reflected from a defocusing adaptive mirror made of a 52-µm film when the power of the incident beam increases from (a) 1 (in relative units) to (b) 500, and (c) 800. A power level of 800 rel. units corresponds to 12 mW of radiation from a He-Ne laser. Defocusing of the probe beam with control laser beam

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Figure 11. Defocusing (a) and focusing (b) of a probe laser beam with a control beam coming from the opposite side of the photomechanical mirror.

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(a)

(b)

Figure 12. Image of the spot created by a probe beam (from laser pointer) reflected from a 52-µm-thick photomechanical mirror controlled by a control beam from a 12-mW He-Ne laser when (a) the control beam is OFF and (b) control beam is ON. The control beam causes defocusing of the probe.

(a)

(b)

Figure 13. Image of the spot created by a probe beam (from laser pointer) reflected from a 110-µm-thick photomechanical mirror controlled by a control beam from a 12-mW He-Ne laser when (a) the control beam is OFF and (b) control beam is ON. The control beam causes focusing of the probe.

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8.0 7.5 7.0 6.5 6.0 5.5 5.0 4.5 4.0 0

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Figure 14. Focal distance of the concave photomechanical mirror (110-µm-thick film of PVDF) versus the power of the control laser beam.

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Positioning control of Nafion-Au ionic polymer metal composite (The Effect of Counter Ion on The Deformation Patterns of IPMC) Akitoshi Itoh*a, Tetsuichi Amarib, Toshihiro Tanakab Dept. of Mechanical Engineering, Tokyo Denki Univ. /2-2, Kanda Nishiki-cho, Chiyoda-ku, Tokyo, 101-8457, Japan; b Graduate School Student, Tokyo Denki Univ.

a

ABSTRACT This paper describes the positioning control method of Au-Nafion IPMC. Au-Nafion IPMC can be classified into two types whether the residual strain is generated to the cathode side(SDT) or the anode side(ODT). SDT can be controlled its position by normal integral control. ODT can also be controlled by restricting the maximum changing speed in the integral control. Experimental result showed the close relationship between the direction of the residual strain and the density or the amount of the counter ion. Keywords: Ionic Polymer Metal Composite, Counter ion, Positioning control, Displacement control, Nafion

1. INTRODUCTION Ionic Polymer Metal Composite (IPMC) is a polymer-metal composite that is made by plating metal on the ionic conductive polymer-gel film. IPMC was invented by Oguro, et.al.[1] in 1991. This soft actuator attracts so many researchers' attention by its high speed response, large deformation quantity and softness. So many researches of theoretical, experimental and application have been done up to the present[2]. The positioning control of IPMC, however, has been considered very difficult since the initial large deformation of IPMC decreased rapidly. There was a report that could succeed the positioning control during one second[3]. This was achieved by the tuning of the shape of the application voltage. On the other hand, however, there are some reports that the initial deformation of the Au-plated IPMC was not so attenuated[4]. In this study, the deformation characteristics of the Nafion based Au plated IPMC was investigated. The results showed that the deformation patterns were classified into two types. They were classified by whether the direction of the residual deformation is the same anode side of initial deformation or the reversal cathode side. Both types of IPMC can be controlled its position by the individually fitted control methods. The following frequency limits of both types were clarified. It is considered from many experimental results that the decision of the type classification was closely related to the concentration or the amount of the driving Na+ ion in the Nafion film.

2. MANUFACTURING METHOD OF AU-NAFION IPMC To make IPMC actuator, both sides of the Nafion film surface has to plate metal for the electrodes. Gold (Au) and platinum (Pt) have been used for the material of the plate metal in the most of the previous researches. In the first stage of this research, the authors used Pt for the electrodes. The manufacturing method of Pt-Nafion IPMC, however, was so unstable that it was difficult to acquire the reproducibility of the property. The deformation quantity was also small. In the case of Au-Nafion IPMC, however, it is easier to produce equal quality test peace and the deformation quantity is larger than that of Pt-Nafion IPMC. This is caused by the softness (small Young's modulus) and the high conductivity of Au. Therefore, in this study, Au-Nafion IPMC was mainly used. *[email protected]; phone 81 3 5280 3600; fax 81 3 5280 3569; www.mec.m.dendai.ac.jp

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 637403, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.685574

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The manufacturing methods of Au-Nafion IPMC in this study were as follows. 1) 30 mm square Nafion film was roughened by a sand paper. 2) The surface of the Nafion film was cleaned by a supersonic cleaner with alkaline detergent. 3) The film was cleaned again by boiled purified water. 4) The film was soaked in the 2.60x10-2 mol/l dichrolo phenanthroline gold complex (AuCl2(Cl2H8N2)Cl) solution and gold ion was adsorbed into Nafion. 5) The film was soaked in the 4.81x10-3 mol/l sodium sulfite (Na2SO4) solution and deoxidization was done in the temperature range between 333K and 353K. 6) Process 3) to 5) was repeated several times to increase the thickness of the gold layer. 7) The film was boiled by the purified water. 8) The film was soaked in the 1.13mol/l sodium hydroxide (NaOH) to introduce Na+ as counter ion. The test peaces made by the above method showed the motion reproducibility constantly and this method was mainly used in this study. The ion conductive polymer-gel film used in this study is above mentioned Nafion made by Dupont. The thickness of the IPMC was the summary of the thickness of Nafion layer and that of the plated metal layers. The thicknesses of the plated metal layers were controlled by the number of reputation of process 3) to 5). The thickness of the Nafion layers does not equal to the original Nafion film by the roughened process. However, it was closely related to the thickness of the original film. In this study, three kinds of Nafion film were used. The thicknesses of each Nafion are, 51µm (NF-112), 127 µm (NF-115) and 183 µm (N-117). Table 1 shows the quantities of the initial deformation of each Au-Nafion IPMC by using same rectangular (2x15mm) shaped IPMC and same application voltage (2V). The thinner the thickness of the Nafion film is, the larger the generated deformation quantity is. Table 1. Differences of the generating displacement of Au-Nafion IPMC by the thickness of the Nafion materials. DEFORMATION QUANTITIES Kind of Nafion N117 NF115 NF112

Thickness of Nafion 183 µm 127 µm 51 µm

Displacement 2.90 mm 8.35 mm 22.68 mm

3. EXPERIMENTAL APPARATUS AND PROCEDURE Fig.1 depicts the schematic diagram of the experimental system. IPMC was cut to the 2x20 mm rectangular shape and an end of the IPMC was fixed between electrodes in the 5mm length in the vertical line. The generated deformation quantities are measured by a laser displacement meter (KEYENCE Co. Ltd, LB-60).

Control PC

IPMC Test Peace

H8 PWM Pulse Driver

Laser Displacement Meter

Fig.1 Schematic diagram of the experimental system

Electric voltage is applied by the form of 100Hz polarity reversal type Pulse Width Modulation (PWM) generated by one-chip computer (Hitachi H8-3048) through amplifier. The duty ratio of the PWM pulse can be controlled with the 14 bit resolution between the duty ratio of 0.1 - 0.9. Personal computer is measured the output voltage of the laser

Proc. of SPIE Vol. 6374 637403-2

displacement meter through D/A converter, recorded the data, and decide the application PWM duty ratio by the control equation. The reason why the high frequency PWM pulse was applied instead of the normal DC voltage is as follows. In the first stage of this study, the possibility of PWM pulse to prevent the attenuation of the initial deformation of IPMC was investigated. The results showed that the tendencies of the deformation (especially in the step response) are almost the same between the application of PWM pulse and DC voltage. More precisely, the deformation quantities of the PWM pulse application were larger than the DC voltage in the range of small voltage area (in the case of PWM pulse, average voltage was used). In this system, the resolution of the PWM pulse is higher than the DC voltage and the composition of the experimental system is simpler. Those are the reasons to adopt PWM pulse.

4. DEFORMATION BEHAVIORS OF IPMC ON THE STEP RESPONSE Fig.2 shows an example of the deformation behaviors of Pt-N117 IPMC to 1.5V DC step voltage application. Pt-N117 was the most popular IPMC. In the beginning, initial deformation is generated to the cathode side. Then, the initial deformation was attenuated rapidly. Finally, the residual deformation was appeared to the anode side. It was thought in many researches that this rapid attenuation of the large initial deformation makes the positioning control very difficult. Therefore, the authors started this study from the investigation of the step response of the gold plating three kinds of Nafion IPMC (Au-N117, Au-NF115, Au-NF112). 1.2

Displacement[mm]

1.0 Step Response

0.8 0.6 0.4 0.2 0.0 0.0

1.0

2.0

3.0

4.0 5.0 Time[s]

6.0

7.0

8.0

Fig.2 An example of the step response experiment of Pt-N117 IPMC. Change of the displacement of the tip is shown under the application of DC 1.5V

Fig.3 (Au-N117) and Fig.4 (Au-NF112) are examples of the step response during 60s when a ± 2V polarity reversal type 100Hz PWM pulse was applied in the various duty ratio. The average voltage of each duty ratio is, 1/10=1.6V, 2/10=1.2V, 3/10=0.8V, 4/10=0.4V, 5/10=0V, 6/10=-0.4V, 7/10=-0.8V, 8/10=-1.2V and 9/10=-1.6V.

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Displacement[mm]

1.0 Duty Ratio 1/10 (1.6V) 2/10 (1.2V) 3/10 (0.8V) 4/10 (0.4V) 5/10 (0V) 6/10 (-0.4V) 7/10 (-0.8V) 8/10 (-1.2V) 9/10 (-1.6V)

0.5

0.0

-0.5

0

10

20

30 Time[s]

40

50

60

Fig.3 The effect of the duty ratio (applied voltage) on the changing behavior of the IPMC displacement under the application of 100Hz polarity reversal PWM pulse. (Au-N117 IPMC)

Displacement[mm]

4

Duty Ratio 1/10 (1.6V) 2/10 (1.2V) 3/10 (0.8V) 4/10 (0.4V) 5/10 (0V) 6/10 (-0.4V) 7/10 (-0.8V) 8/10 (-1.2V) 9/10 (-1.6V)

2 0

-2 -4 0

10

20

30 Time[s]

40

50

60

Fig.4 The effect of the duty ratio (applied voltage) on the changing behavior of the IPMC displacement under the application of 100Hz polarity reversal PWM pulse. (Au-NF112 IPMC)

The results showed that the deformation behaviors to the step voltage can be classified into two types. One is the "Same Direction Type, (SDT)". In the case of SDT, the direction of both initial deformation and residual deformation are the same anode side. Au-N117 and Au-NF115 belong to SDT. The other is the "Opposite Direction Type, (ODT)". In the case of ODT, the direction of the initial deformation is the cathode side, it was same to SDT. The direction of the residual deformation, however, is the opposite anode side. Pt-N117 and Au-NF112 belong to ODT. The quantity of the residual deformation is increased with the increase of average applied voltage. That is to say, the initial strain of ODT is not simply attenuated but it changes the deformation mode to the residual deformation. Therefore, there is a possibility of positioning control when we use the residual deformation of IPMC in both types.

5. FEEDBACK POSITIONING CONTROL OF IPMC 5.1 Positioning control of SDT-IPMC Above mentioned investigation suggests that there is a possibility of the positioning control of IPMC, especially to the SDT-IPMC. It was confirmed as a preliminary experiment that if the duty ratio of the applied PWM pulse was changed manually, the end of the SDT-IPMC can be moved by changing the duty ratio.

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Therefore, a feedback positioning control experiments were done by using the outputs of the laser displacement meter. First, proportional control was applied. SDT-IPMC, however, cannot be controlled its position by proportional control. The problem is that, in the case of proportional control, if the generated deformation quantity was larger than the target value, the controller applied the opposite polarity. This makes the large reversal deformation and causes vibrations. It makes positioning control unstable. Next, an integral control (an integral component of PID control) was applied and positioning control was done successfully. Figs.5 and Fig.6 show examples of feedback experiments of Au-NF115 IPMC. The target values are ± 0.5mm amplitude sine wave. The frequencies of the target sine waves are, 2Hz (Fig.5) and 0.01Hz (Fig.6). Average control deviations of various frequencies are summarized in Fig.7. It shows that the positioning control can be done within 0.5Hz.

Displacement Target Value Deviation

Displacement (mm)

1.0

2Hz

0.5 0.0 -0.5 -1.0 0.0

0.1

0.2

0.3

0.4

Time (s) Fig.5 Examples of the positioning control experiment of Au-NF115 IPMC. Target value is a 2Hz ± 0.5mm sine wave. In the case of 2Hz, there is a large phase delay.

0.6 Displascement Target value Deviation

Displacement (mm)

0.4 0.2 0.0 -0.2 -0.4 -0.6

0

20

40

60

80

100

Time (s) Fig.6 Examples of the positioning control experiment of Au-NF115 IPMC. Target value is a 0.01Hz ± 0.5mm sine wave. In the case of 0.01Hz, deviation is very small and good positioning control was done.

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Average control deviation (mm)

0.7 0.6 0.5 0.4 0.3 0.2 0.1 2

0.01

3

4

5

6 7 8 9

2

0.1 Frequency (Hz)

3

4

5

6 7 8 9

1

2

Fig.7 A summary of the average control deviations in each frequency. Target value is ± 0.5mm sine wave. Deviation increases from about 0.5 Hz.

5.2 Positioning control of ODT-IPMC In the case of ODT-IPMC, the deformation behavior is so complex that it makes the positioning control very difficult. Final residual deformation quantity, however, increase / decrease by the average applied voltage. The authors thought that positioning control may be achieved by applying this property. First, the applied duty ratio was changed manually to know the deformation properties as preliminary experiments. If the changing speed of the applied PWM duty ratio is quick, IPMC first react initial deformation, and then the residual deformation generates to the opposite side. If the changing speed is very slow, initial deformation does not appear and the end of the IPMC can move by changing the duty ratio. Therefore, positioning control may be possible if the changing speed is regulated. Fig.8 is an example of the positioning control of ODT by the same control method of SDT (integral control). In this experiment, the target position is the 0mm displacement. You can see the generation of initial deformation at 0-20s and about 650s. 3

Offset Displacement Digital Output

2

14 12

1

10 0

8 6

-1

Digital Output

Offset Displacement [mm]

16x10

4 -2

2 0

200

400

600 800 1000 1200 Measurement Time [s]

1400

1600

0 1800

Fig.8 An example of the positioning control experiment of Au-NF112 ODT-IPMC by normal integral control method. Target value is 0mm constant. Rapid change of the duty ratio causes the initial deformation component.

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Next, lamp responses of Au-NF112 IPMC were investigated. The summary of the results showed that if the changing rate of the PWM duty ratio is smaller than 4.9x10-4s-1 (equivalent DC voltage is 2.0x10-4 V/s), the initial deformation component does not generate. Therefore, the maximum changing speed of the output PWM duty ratio was restricted under 4.9x10-4 s-1and a feedback positioning control experiment was examined again by using integral control method. The target value is ± 1mm amplitude sine curve. The direction of the residual deformation is opposite to the SDT, the polarity of the integral coefficient of ODT was reversal to the case of SDT. Fig.9 is an example of the positioning control. Its frequency of the target value is 9.2x10-5Hz. The following frequency limit is about 2.0x10-4Hz and if the frequency is lower than this value, ODT-IPMC can be controlled its position. 9600 Digital Output Target Value IPMC Displacement

0.5

9200 8800 8400

0.0 8000 -0.5

7600 7200

-1.0 0.0

Digital Output

Offset Displacement (mm)

1.0

1.0

2.0

3.0

4.0

5.0 6.0 Time (s)

7.0

8.0

3

6800

10.0x10

Fig.9 An example of the positioning control experiment of Au-NF112 ODT-IPMC. Target value is ± 1mm 9.2x10-5Hz sine wave.

6. THE EFFECT OF THE COUNTER ION ON THE DIRECTION OF RESIDUAL DEFORMATION As mentioned above, positioning control of IPMC was achieved in both types. The following frequency limit of ODTIPMC, however, is too low to find the application. Therefore, to know the factor to divide the deformation type is very important to develop the more practical IPMC for positioning control. Using the standard manufacturing method in this study as mentioned section 2, if we compare in the same gold plating IPMC, The thinnest Au-NF112 is ODT and Au-NF115 and Au-N117 are SDT. Au-NF115, however, was smaller than Au-N117 comparing with the rate of residual deformation quantity / initial deformation quantity. Therefore, Au-NF115 stands the nearest point to the diverging point of the deformation type. The authors found that if Au-NF115 is used for a long time in the purified water, the deformation type of Au-NF115 changes from SDT to ODT. Fig.10 indicates the step responses of Au-NF115 IPMC in the condition of reputation of 60s step response experiments using same test peace (repeat the 1/10(-1.6V) and 9/10(1.6V) duty ratio). You can see the transition of the deformation type.

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Displacement (mm)

2.0 1.0 DutyRatio 1/10 (1.6V) 9/10 (-1.6V)

0.0 -1.0 0

10

20

30 40 Time (s)

50

60

Displacement (mm)

(a) Step response in the first experiment

4

DutyRatio 1/10 (1.6V) 9/10 (-1.6V)

2 0 -2 0

10

20

30 40 Time (s)

50

60

(b) Step response after long time usage Fig.10 Changes of the direction of the residual strain by the reputation of use. Au-NF115 IPMC first shows the SDT deformation and it changes to the ODT deformation after long time usage.

The most changeable part in the processing method may be the introduced counter ion (Na+ in this study). Na+ may flow out to the purified water. Therefore, ODT Au-NF115 that had been used for a long time was re-introduced the Na+ ion by the process 8) and measured its step response again. The result shows that re-introduced Au-NF115 shows SDT deformation again. Fig.11 is an example. The re-introduced Au-NF115 shows almost the same reaction to the original one. The deformation quantity, however, is slightly decreased.

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Displacement (mm)

0.8 0.6 0.4 New test peace Reuse test peace

0.2 0.0 0

10

20

30

40

50

60

Time (s) Fig.11 Step responses of the Au-NF115 IPMC in the new test peace and the test peace that was re-introduced the Na+ counter ion after long time usage. Au-NF115 can recover the SDT deformation from ODT condition.

Next, many Au-NF115 test peaces by producing various density NaOH solutions in process 8) were prepared and found that Au-NF115 shows ODT deformation in the first step response measurement if the NaOH solutions are thinner than 2.62x10-4 mol/l. In the case of Au-N117, it was confirmed that the Au-N117 also showed the ODT deformation after long time use, and the type changed again to SDT by the re-introduction of Na+ ion. In the case of Au-NF112, the standard IPMC in this study shows ODT. However, if the density of NaOH was 2.27mol/l (twice denser than standard density), Au-NF112 shows the SDT deformation in the first step response measurement. Fig.12 indicates the results. First, the experiment of 1/10 duty ratio (equivalent to DC 1.6V) was done and then the experiment of 9/10 (-1.6V) was done. Therefore, you can see in Fig.13 that this Au-NF112 test peace shows SDT deformation in the first experiment and ODT deformation in the next experiment. 0.8

Displacement (mm)

0.6 0.4 0.2 0.0 -0.2 Duty Ratio 1/10 (1.6V) 9/10 (-1.6V)

-0.4 -0.6 -0.8 0

10

20

30 Time (s)

40

50

60

Fig.12 The step response of Au-NF112 IPMC. This IPMC was given counter ion introduction treatment using twice denser NaOH solution. In the first experiment (duty ratio is 1/10), this IPMC shows SDT deformation. In the next experiment (duty ratio is 9/10), it shows ODT deformation. This indicates the rapid outflow of the counter ion.

All of these results suggest that the decision of the deformation type is related not the thickness of the Nafion film but the density or the quantity of the counter ion.

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7. CONCLUSION This study confirmed that the positioning control of IPMC can be done by using integral control method. SDT type deformation was necessary for the high speed positioning control. The decision of the deformation type is closely related to the density or the quantity of the counter ion. The thinner IPMC generates larger deformation quantity. However, it is very difficult to make thin IPMC like Au-NF112 as SDT-IPMC. In the future, the method to keep SDT deformation has to be clarified by investigating the variety and the suitable quantity of the counter ion, chemical composition of the solution of the environment, prevention methods of the outflow of the counter ion.

REFERENCES 1. K. Oguro, et.al., J. Micromachine Soc., 5, pp.27-30, (1992). 2. Y. Bar-Cohen, Robotics2000 and Space2000, pp.188-196 (2000). 3. Sugano, et.al., 74th Annual meetings of the Japan Society of Mechanical Engineers, IV, pp. 329-330, (1996). 4. K. Asaka, "Soft Actuators" NTS Books ISBN4-86043-063-8 C3050, Section2, p83.

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Optical driving of actuator using Poly-Vinylidine DiFluoride cantilever Y. Mizutani, S. Nishimura, Y. Otani, N. Umeda Tokyo University of Agriculture & Technology, 2-24-16 Nakacho Koganei, Tokyo, 184-8588, Japan ABSTRACT Optically driven actuators are a non-contact method for the remote application of light energy. We propose a new method for optically driving actuators which uses three polyvinylidine difluoride (PVDF) cantilevers as the legs and a polymer film as the body. The PVDF cantilevers are coated with silver on one surface. PVDF is a ferroelectric polymer that has both pyroelectric and piezoelectric properties. When one side of the cantilever is irradiated by a laser beam, an electric field is produced along cross-section of the cantilever and mechanical displacement occurs by the piezoelectric effect. We measured the response time and the generated force of the cantilever. Optically driven actuator move via the slip-stick effect. Keywords: optical driven actuator, photo-thermal effect, Poly-Vinilidine DiFluoride, pyroelectricity effect

1.

INTRODUCTION

In recent years, optically driven actuators have attracted considerable attention because they can be operated remotely without the need for wires1). Previous studies of optically driven actuators have indicated their potential usefulness in various situations, such as environments having intense electromagnetic fields2). They can also be used as a non-contact method for the remote application of light energy3,4). They are thus particularly useful in environments such as space and environments have high-intensity radioactive fields. In a previous paper by us, we investigated actuators that are operated using light energy. The displacement mechanism of such actuators is principally the photothermal effect. However, the response time of these actuators is strongly dependent on their size. Finding a method for reducing the response time is a problem that has yet to be solved theoretically. The purpose of the present study is to construct an optically driven actuator using polyvinilidine difluoride (PVDF) cantilevers. Polyvinilidine difluoride is a ferroelectric polymer that has both pyroelectric and piezoelectric properties. Thus, it has fast response times. In previous studies, it has been used in various optical devices5,6,7). However, there have been several attempts to construct optical actuators from PVDF. In this paper, we briefly describe our experimental results for PVDF cantilevers and then describe an actuator based on PVDF cantilevers, along with the experimental results we obtained using such a system.

2.

MOVING PRINCIPLE OF PVDF CANTILEVER AND ITS MECHANISM

The concept of an optically driven actuator using PVDF cantilevers is illustrated in Fig. 1. It is an actuator having multiple legs; the PVDF cantilevers are the legs of the actuator. It can be moved by irradiating it with light from various directions.

Li

t gh

Light

t gh Li

PVDF cantilevers

Fig. 1 Optical driving of actuator using PVDF cantilevers.

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 637404, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.687505

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Polyvinylidine difluoride is a ferroelectric polymer. It thus has considerable promise as a material that responds rapidly to optical irradiation. It is possible to construct a cantilever from PVDF. Figure 2 shows the principle behind the displacement of a PVDF cantilever. One surface of a PVDF film is coated with Ag. After irradiation by light, it is polarized by the pyroelectric effect in the cross-sectional direction (Fig. 2(1)). Next, conduction electrons are generated and dispersed on the surface of the Ag coating (Fig. 2(2)). As a result, the electric field in the cross-sectional direction of the PVDF film is inhomogeneous and the PVDF cantilever bends in the cross-sectional direction of the PVDF film (Fig. 2(3)). Since the pyroelectric effect is faster than the photothermal effect, the PVDF cantilever is expected to have a fast response time.

light

light

light

PVDF Ag

displacement cross-sectional view of PVDF cantilever

(1) Polarization of pyroelectric effect

(2) dispersion of (3) bending by inverse surface electrical charge piezoelectric effect

Fig. 2 Moving principle of PVDF cantilever.

The PVDF cantilever used in the present study was 28 m thick, 8 mm wide and 10 mm long. Figure 3 shows a photograph of a PVDF cantilever bending in response to laser irradiation. Figure 3(1) shows its cross-sectional profile before laser irradiation and Fig. 3(2) shows its profile after laser irradiation. We used a He-Ne laser as the light source and it had a power of 10 mW. The displacement of the cantilever after laser irradiation was about 250 m.

PVDF

displacement

laser

500µm (1) Before laser irradiation

(2) After laser irradiation

Fig. 3 Photograph of moving of PVDF cantilevers. It is cross sectional view.

To analyze the bending mechanism of a PVDF cantilever, the time dependent response of the PVDF cantilever was measured using a displacement sensor. The Ag-coated surface of the cantilever was irradiated by He-Ne laser pulses that were 0.8 msec in duration and had powers of 5, 7, 9 and 11 mW. Figure 4 shows a plot of the cantilever displacement as a function of time. Large displacements were obtained for irradiation by laser powers of 7, 9 and 11 mW. There is a slight plateau in the curve at 0.1 msec followed by a gradual rise. This fast response is caused by the combination of the pyroelectric and piezoelectric effects. The second response is caused by the photothermal effect in combination with the bimetal effect. However, there is no response due to the pyroelectric effect for the case of

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irradiation with a laser power of 5 mW. Therefore, in subsequent experiments we used laser irradiation having a duration of 0.2 msec and a power of 7 mW for operating the PVDF cantilever. irradiation time

400 13mW

displacement [µm]

11mW

300

9mW 7mW

5mW

200

100

0 0.0

0.5

1.0

1.5

2.0

time [s] Fig. 4 Time behaviors of displacement of PVDF cantilever by irradiation light.

displacement [µm]

500 400 15mm

300

10mm

200 100

8mm 5mm

0 0.0

0.5

1.0 time [s]

1.5

2.0

Fig. 5 Time behavior of the displacement of PVDF cantilevers depended on length of Ag coating.

The area of the Ag-coated region is a key parameter for the pyroelectric and piezoelectric effects. Therefore we measured the dependence of the displacement on the area of the Ag-coated region. Figure 5 shows a plot of the displacement as a function of time of PVDF cantilevers which had Ag-coated regions that were 5, 8, 10 and 15 mm in length. Figure 6 shows the relationship between the maximum displacement and the length of the Ag-coated region. Above a coating length of 8 mm, the maximum displacement was the same after irradiation for 0.2 msec. For coating lengths shorter than 8 mm, the maximum displacement decreased. Therefore, it is necessary to coated the PVDF films with Ag for lengths of 8 mm or longer to obtain the greatest displacement.

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60 displacement [µm]

50 40 30 20 10 0

0

4 8 12 lentgth of Ag coating [mm]

16

Fig. 6 Dependence of the displacement of PVDF cantilever on length of Ag coating

0

gain [dB]

-10 -20 -30 -40 0.1

1.0 10.0 frequency [Hz]

100.0

Fig. 7 Frequency response of vibration amplitudes for PVDF cantilever.

The frequency response of a PVDF cantilever is higher than that for mechanisms of other optically driven actuators since the mechanism of the PVDF cantilever relies on the pyroelectric and piezoelectric effects. Figure 7 shows the frequency response of the PVDF cantilever. The resonant frequency of the PVDF cantilever is about 20 Hz. One of the most important parameters for constructing optically driven actuators is the generative force of the PVDF cantilever. We measure it by using a glass cantilever the stress parameter of which was known. Figure 8 shows the relationship between the generative force of the cantilever and the laser power. The generative force is proportional to the laser power.

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generative force [µN]

1600 1200 800 400 0 0.0

5.0 10.0 laser intensity [mW]

15.0

Fig. 8 Generative force of PVDF cantilever depended on laser intensity.

3.

OPTICALLY DRIVEN ACTUATOR USING PVDF CANTILEVERS

Figure 9 shows the construction of an optically driven actuator based on PVDF cantilevers. It consists of three PVDF cantilevers that form the legs of the actuator joined to a polyethylene film body.

light

moving direction Fig. 9 Unit of optical driving actuator using PVDF cantilever.

Figure 10 is a schematic illustration of the principle of movement of the actuator. These figures show the crosssectional profile of the actuator. Figure 10(1) shows the initial position of the actuator. The position marked 0 is the initial position of the rear leg and 0’ represents the position of the front leg. In Fig. 10(2), the front leg is irradiated by light and it bends due to the pyroelectric and piezoelectric effects. The cantilever slides on the base because of the first response. Then, after laser irradiation (Fig. 10(3)), the front cantilever stops at the point indicated by 1’ which is in front of the initial point 0’ because the frictional force of the front leg exceeds the restorative force of the front cantilever. Furthermore, the back leg slides on the base because the frictional force of the back leg is smaller than the restorative force of the actuator. Finally, in Fig. 10 (4), the actuator can be stabilized.

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PVDF cantilevers

light

driving force floor

0

0'

1. before laser irradiation

2. laser irradiation

driving force

displacement

displacement

0

1'O'

4. finishing of movement

3. after stopping laser irradiation

Fig. 10 Moving principle of optical actuator.

light

1mm movement direction

Fig. 11 Photograph of optical driven actuator using PVDF cantilever.

displacement [mm]

3

2Hz 76.7mm/s

2

1 1Hz 33.3mm/s 0

0

5

10

15 20 time [s]

25

30

Fig. 12 Displacement of optical driven actuator with various frequency of irradiation light.

Figure 11 shows a photograph of an actuator on an acrylic surface; it shows the cross-sectional profile. The actuator is 5 mm wide and 10 m high. Light is irradiated from the left of the figure and the direction of movement of the actuator is towards the left. A He-Ne laser was used as the light source and an irradiation power of 10 mW was used. Figure 12 shows the displacement of the actuator irradiated at frequencies of 1 and 2 Hz. Both displacements increase almost linearly with time. The velocities of the actuators are 33.3 mm/sec at 1 Hz and 76.7 mm/sec at 2 Hz.

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4.

CONCLUTIONS

We investigated optical driving of an actuator constructed from PVDF cantilevers. The PVDF cantilever uses the pyroelectric and piezoelectric effects and has a response time of less than 0.2 msec. The actuator travels at a velocity of 33.3 mm/sec when irradiated at a frequency of 1 Hz. In the future, we intend to extend the control of the actuator’s displacment to two-dimensions.

5.

ACKNOWLEDGEMENT

We investigated optical driving of an actuator constructed from PVDF cantilevers. The PVDF cantilever uses the pyroelectric and piezoelectric effects and has a response time of less than 0.2 msec. The actuator travels at a velocity of 33.3 mm/sec when irradiated at a frequency of 1 Hz. In the future, we intend to extend the control of the actuator’s displacment to two-dimensions.

REFERENCES 1. 2. 3. 4. 5. 6. 7.

Y. Otani, Y. Matsuba, N. Umeda, T. Yoshizawa, "Micromanipulator by photothermal effect," Proc SPIE 5264, 150153 (2003). K. Fukushima, Y. Otani, T. Yoshizawa "An Optical Driving of a Moving Machine Consisting of Piezoelectric Elements and Temperature Sensitive Ferrite," JSPE 64(10), 1512-1516 (1998). (in Japanese) K. Uchino, "Recent topics of ceramic actuators. How to develop new ceramic devices," Ferroelectrics 91, 281-292 (1989). K. Uchino, "Photostrictive Actuator," Proc IEEE Ultrason Symp 2, 721-723 (1990). S. S. Sarkisov, M. J. Curley, A. Fields, "Photomechanical effect in films of polyvinylidene fluoride," J. Appl. Phys. 85(14), 2747-2749 (2004). Y. Otani, Y. Mizutani, "Next-Generation Actuators Leading Breakthroughs Actuators for Special Environments Light-driven actuators using optical fiber and PVDF," Proc Int Symp Next-Gener Actuators Lead Breakthr Mext Grant-in-Aid Sci Res Prior Area No.438 2006, 165-168 (2006). S. S. Sarkisov, M. J. Curley, L. Huey, A. Fields, G. Adamovsky, "Light-driven actuators based on polymer films," Opt. Eng. 45(3), 034302.1-034302.10 (2006).

Proc. of SPIE Vol. 6374 637404-7

Two-dimensional magnetic force actuator using temperature sensitive ferrite driven by light beam Y. Mizutani, Y. Otani, N. Umeda Tokyo University of Agriculture & Technology, 2-24-16 Nakacho Koganei, Tokyo, 184-8588, Japan ABSTRACT A two-dimensional actuator has a feature of a non-contact for applying light energy remotely. It consists of a magnet as a movement, an acrylic plate and the temperature sensitive ferrite mounted on two-dimensional array on the plate. A curie temperature of the ferrite is set about room temperature. For moving the magnet, two ferrites in the opposite direction are irradiated by the laser. The magnetic force decreases by photo-thermal effect. For generating more strong force, a thickness of the plate and ferrite are optimized by analyzing static magnetic field. As a result, the movement is controlled in the two-dimensional area. Moreover, we attempt to control magnetic levitation. Keywords: temperature sensitive ferrite, photo-thermal effect, two-dimensional actuator

1. INTRODUCTION In recent years, optically driven actuators have attracted considerable attention because they can be operated remotely without the need for wires1). Previous studies of optically driven actuators have indicated their potential usefulness in various situations, such as environments having intense electromagnetic fields2). They can also be used as a non-contact method for the remote application of light energy3,4). They are thus particularly useful in environments such as space and environments have high-intensity radioactive fields. In a previous paper by us, we investigated actuators that are operated using light energy. The displacement mechanism of such actuators is principally the photothermal effect. However, the generative force is slightly lower. In this study, a magnetic force is focused on to controlled by optical energy. To control the magnetic force, a temperature sensitive ferrite has attracted much attention because of its magnetic property. Fig.1 shows a variation of its magnetic susceptibility with its temperature. Generally, magnetization changes ferrimagnetism from ferromagnetism at Curie temperature. Curie temperature of this ferrite is low about room temperature. Therefore it is easy to change its magnetism by Photo-thermal effect. And this ferrite is partially useful for optical control.

magnetic susceptibility

Curie temperature

ON

room temperature

OFF

temperature

Fig. 1 Principle of optical switching using temperature sensitive ferrite and permanent magnet.

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 637405, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.687513

Proc. of SPIE Vol. 6374 637405-1

2. TWO-DIMENSIONAL ACTUATOR 2.1 Principle of two-dimensional controlling Two temperature sensitive ferrites in an opposite direction of moving direction are irradiated by laser. Magnetic susceptibility of ferrites are decrease by photothermal effect.A movement is moved by magnetic force of movement direction. Furthermore, the movement can be controlled by changing of irradiation position.

movement direction

movement

ate — r1 — — = =iii — L LJ LJ (Parmanet magnet)

aciylic ,1

C—__

ferrite

(1) initial position

(2) laser irradiation

(3) finish

Fig. 2 Moving principle of two-dimensional magnetic force actuator using temperature sensitive ferrite

00000 00000 00000 00000 00000 00000 00000 00000

00000 00000 KG 00 0O0 00000 00 00 0 00 00000 coo o 0 00 00 00000 Fig. 3 Moving method of the movement magnet in the two-dimensional area

2.2 Experimental results Figure 4 shows a two-dimensional magnetic force actuator using temperature sensitive ferrite. The actuator consists of a Nd magnet as a movement, an acrylic plate (t0.8mm) and the temperature sensitive ferrite mounted in two-dimensional array on the plate. For shaping form easily, the temperature sensitive ferrite is crushed and mixed with silicon grease. The shaping ferrites are set in a reticular pattern.

..e..i)S$)D .••..

movement (Nd magnet)

. 11)) temperature

4) sensitive ferrite Fig. 4 Two-dimensional magnetic force actuator using temperature sensitive ferrite

Table 1 shows the magnetic field analysis of the actuator in various thickness of temperature sensitive ferrite. A magnetic force between the movement and temperature sensitive ferrite depends on the thickness of the ferrite. Therefore the thickness is optimized by magnetostatic field analysis and experimental results. Fig.5 shows a magnetic force and the thickness of the temperature sensitive ferrite. The magnetic force increased with decreasing the thickness to a maximum value. Consequently, the optimal thickness for magnetic force is determined 0.2mm.

Proc. of SPIE Vol. 6374 637405-2

'pa

Table 1 The magnetic field analysis of the actuator in various thickness of temperature sensitive ferrite

1.0mm

thickness

0.5mm

parmanent magnet 永久磁石 line of magnetic force

0.1mm

0.1mm

temperature sensitive 感温フェライト ferrite

magnetic flux density laser レーザ

magnetic force [N]

0.06 0.05

simulation experimental value

0.04 0.03 0.02 0.01 0 0.0

0.5

1.0

1.5

2.0

thickness of temperature sensitive ferrite [mm] Fig. 5 Magnetic force and the thickness of the temperature sensitive ferrite

Figure 6 shows the displacement of the movement magnet in two-dimensional area. The displacement increases almost linearly with time.

displacement [mm]

25

light source: LD laser 450mW

20 15 10 5 0

0

10 20 30 40 50 60 time [s]

Fig. 6 Displacement of the two-dimensional magnetic force actuator using temperature sensitive ferrite

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3. THREE-DIMENSIONAL ACTUATOR 3.1 Principle of three-dimensional controlling In the case of the two-dimensional actuation, it can not be controlled stable because of friction between the movement and the floor. Therefore, the movement magnet floated using a characteristic of diamagnetism such as graphite. Furthermore, the floated movement magnet is controlled by photothermal effect using temperature sensitive ferrite. In this study, we pay attention to levitate a magnet by using diamagnetic material. A polar of the diamagnetic material changes toward disturbing to change a relative position of these two objects. To use this characteristic, we levitate a magnet. Specifically, the movement magnet put between two diamagnetic materials. Therefore we make a buffer for keeping balance. Figure 7 shows a schematic illustration of a magnetic levitation using temperature sensitive ferrite. We use graphite as diamagnetic material. And the movement magnet is put between graphite and using assist magnet put on temperature sensitive ferrite. By using this magnet, the movement magnet can be levitated. Furthermore, to control in three-dimensional, a staring magnetic field can be changed by changing magnetic susceptibility of temperature sensitive ferrite. In this study, the movement magnet is Nd magnet (φ3mm, t2mm), a light source is laser diode with 300mW and a diamagnetic material is graphite. assist magnet

leinperature sensitive

P.—

Iernte

movement

(magnet) •

__j

graphite

Fig. 7 Magnetic levitation using temperature sensitive ferrite

Figure 8 shows a moving principle of the levitated magnet in three dimensions. Fig.1 (1) shows an initial position. To move toward vertical position, a temperature sensitive ferrite located immediately above is irradiated. Then a magnetic force toward this direction is weak. So we can control the magnet for vertical position. To move horizontal position, a temperature sensitive ferrite set on opposite side is irradiated. A magnetic force of a request direction is larger than that of opposite direction. Then the movement magnet can be moved toward horizontal direction. To uses these method, the levitated magnet can move in three-dimensions.

F- _.J

U.

:i:i- 1 (I )initial position

(2) vertical

(3) horizontal

Fig.8 Moving principle of the levitated magnet in three-dimensional area

3.2 Experimental results To levitate magnet, the position of the assist magnet is adjusted. Fig.9 shows a photograph of the levitated magnet. In this figure, the magnet can be levitated stability.

Proc. of SPIE Vol. 6374 637405-4

graphite

movement (Nd magnet)

2.0 mm

graphite

Fig. 9 Photograph of the magnetic levitation

For confirmation of the principle, we simulated a static magnetic field analysis. Fig. 10 shows typical results of the static magnetic field analysis. In the case of vertical control (Fig.10 (2)), a magnetic field is almost same in vertical direction. Therefore a gravity of the magnet is greater than the magnetic force. Hence the movement magnet can be moved toward vertical position. In the case of horizontal control (Fig. 10 (3)), the magnetic field is homogeneous toward horizontal direction. Therefore the movement magnet can be moved in horizontal direction. Hence it is indicated to be able to control the movement magnet using temperature sensitive ferrite.

(1) initial position

(2) vertical moving

(3) horizontal moving

Fig. 10 Magnet static analysis for three-dimensional actuator using temperature sensitive ferrite

position of movement from lower graphite[mm]

ネオジウム磁石の位置 [ mm]

Figure 11 shows a position of the movement magnet against the position of the assist magnet. The position of the movement magnet drops sharply between about 1mm. However to use micrometer for moving the assist magnet, the movement magnet can be controlled stable. 1.0 0.8 0.6 0.4 0.2 0.0 45.5

46.0 46.5 47.0 [ mm] [mm] positionフェライト磁石の位置 of ferrite magnet from lower graphite

Fig. 11 Position of the movement magnet against the position of the assist magnet

Proc. of SPIE Vol. 6374 637405-5

Figure 12 shows a photograph of the movement magnet to control in horizontal direction. Fig.12 (1) shows an initial position and (2) shows the moved magnet after 60sec. An irradiated ferrite is overhead of the movement magnet toward opposite side direction. The movement magnet can be moved in the distance of ∆x toward horizontal direction.

Fig. 12 Photograph of the movement magnet to control in horizontal direction

Figure 13 shows a photograph of the movement magnet to control in vertical direction. Fig.13 (1) shows an initial position and (2) shows the moved magnet after 60sec. An irradiated ferrite is directly overhead of the movement magnet. After 60sec, the movement magnet drops down and keeps its position. The movement magnet can be moved in the distance of ∆x toward vertical direction.

•

jax

(I) initial positon

Fig. 13 Photograph of the movement magnet to control in vertical direction

position of Nd magnet

form lower graphite [mm][ mm] ネオジウム磁石の位置

Figure 14 shows the time dependent of behavior of the movement magnet for controlling toward vertical position. The vertical position of the movement magnet depends on laser power. Therefore we irradiated to control the levitated magnet in vertical position. 0.5

50mW 100mW 150mW 200mW 250mW

0.4 0.3 0.2 0.1 0.0

0

60 120 時間 sec] time [[sec]

180

Fig. 14 Time dependent of behavior of the movement magnet for controlling toward vertical position

Proc. of SPIE Vol. 6374 637405-6

4. CONCLUSIONS The magnetic force actuator using temperature sensitive ferrite driven by light beam has been developed. It consists of crashed temperature sensitive ferrite mounted in two-dimensional array and acrylic plate and Nd magnet as movement. The magnetic force is optimized by magnetostatic field analysis. It can be controlled in two-dimensional area. Moreover, we applied for three dimensional controlling of levitation magnet.

REFERENCES 1. 2. 3. 4. 5. 6.

Y. Otani, Y. Matsuba, N. Umeda, T. Yoshizawa, "Micromanipulator by photothermal effect," Proc SPIE 5264, 150153 (2003). K. Fukushima, Y. Otani, T. Yoshizawa "An Optical Driving of a Moving Machine Consisting of Piezoelectric Elements and Temperature Sensitive Ferrite," JSPE 64(10), 1512-1516 (1998). (in Japanese) K. Uchino, "Recent topics of ceramic actuators. How to develop new ceramic devices," Ferroelectrics 91, 281-292 (1989). K. Uchino, "Photostrictive Actuator," Proc IEEE Ultrason Symp 2, 721-723 (1990). S. S. Sarkisov, M. J. Curley, A. Fields, "Photomechanical effect in films of polyvinylidene fluoride," J. Appl. Phys. 85(14), 2747-2749 (2004). Y. Otani, Y. Mizutani, "Next-Generation Actuators Leading Breakthroughs Actuators for Special Environments Light-driven actuators using optical fiber and PVDF," Proc Int Symp Next-Gener Actuators Lead Breakthr Mext Grant-in-Aid Sci Res Prior Area No.438 2006, 165-168 (2006).

Proc. of SPIE Vol. 6374 637405-7

Analysis of mechanical characteristics by birefringence microscope Mizue Ebisawa*, Yukitoshi Otani, Norihiro Umeda Department of Mechanical Systems Engineering, Tokyo University of Agriculture and Technology Koganei, Tokyo, 184-8588, Japan; ABSTRACT The mechanical characteristics of polymer materials are of interest to the chemical industry. There are requirements for observation of changes of internal structure to stress. A number of samples under various stress conditions have provided interesting information upon analysis by microscopic birefringence measurement. In the present paper, we propose a birefringence measurement method for observation of the internal structure of polymer materials and analysis of the relationship between a given stress and the corresponding birefringence distribution. The proposed measurement system consists of a He-Ne laser, polarizers, a half-wave plate and a quarter-wave plate. The birefringence distributions of gelatin, such as the phase difference and azimuthal angle, are shown for the case of applied uniaxial and biaxial stress. Keywords: birefringence, biaxial tensile test, mechanical characteristic

1. INTRODUCTION The mechanical characteristics of polymer materials are of scientific and practical interest. Previous studies have demonstrated that the mechanical characteristics of polymer materials are different from those of metals. The mechanical model of a polymer material’s response to stress requires information on the microscopic deformation behavior of the materials[1]. Although there have been several macroscopic investigations of the behavior of a polymer under stress, such as mechanical experiments using load cells, few microscopic observations of this deformation behavior have been reported. Birefringence measurements are widely adopted for inspecting strain occurring as a result of processing, because the distribution of strain reflects the residual stress and molecular orientation. Therefore, the present study was performed in order to verify the applicability of birefringence measurement to the analysis of the mechanical characteristics of polymer materials.

2.

PRINCIPLE OF BIREFRINGENCE MEASUREMENT

2.1 Experimental setup Figure 1 shows a schematic diagram of the birefringence microscope [2]. An He-Ne laser with a wavelength of 632.8 nm is used as a light source. The laser beam passes through a polarizer (P) with a 0º orientation to horizontal (with respect to the azimuthal angle), a half-wave plate (H) with a θ1 orientation to horizontal, and a quarter-wave plate (Q) with orientation a θ2, in order to establish the initial polarization states. The light transmitted from the sample (S) is detected by a charge-coupled device (CCD) camera after passing through an analyzer (A) with a θ3 orientation. The phase difference and azimuthal angle of birefringence are analyzed based on the known polarization states and the detected light intensity.

*[email protected]; phone +81-42-388-7372; fax +81-42-385-7204

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 637407, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.687428

Proc. of SPIE Vol. 6374 637407-1

CCD camera θ

Image formation lens

3

A Object lens θ

1

θ

S 2

He-Ne laser Illumination lens Mirror P H Q Polarization generator Fig.1

Birefringence microscope

2.2 Birefringence measurement The detected light intensity is calculated using Mueller matrices and Stokes parameters. The Mueller matrices denote half-wave plate H with set direction θ1, quarter-wave plate Q with set direction θ2, sample X with birefringence (phase difference ∆, azimuthal angle φ), and analyzer A with set direction θ3. With a linearly polarized light beam (0°) as the incident light, the polarization state at the detector (S’) is obtained from the Stokes parameter S as follows: (1)

S' = A θ 3 ⋅ X ⋅ Q θ2 ⋅ H θ1 ⋅ S

The light intensity I detected by the detector is given by

I = I o [1 + cos{4θ1 − 2θ 2 }cos(2θ 3 − 2θ 2 ) − ∆ sin{4θ1 − 2θ 2 }sin( 2θ 3 − 2φ )

(2)

provided that ∆<<1. By applying the prerequisite that θ2 = θ3, Eq. (2) can be rewritten as follows with phase difference δ and phase Φ:

I ≅ I 0 [1 + cos(δ − Φ )]

δ = 4θ 1 − 2θ 2 Φ = tan -1{∆ sin( 2θ 3 − 2φ )}

(3)

Phase component Φ is required in Eqs. (3). This phase component is determined by the local-sampling phase shifting method [3]. The phase differences δ given by the rotation angle of polarization devices are assumed to be divided into N intervals in 0 ~ 2π. When the error margin between the measured light intensity and the theoretical light intensity is minimized, the phase change can be obtained using a least-squares fitting. Phase change Φ is thus determined as follows:

Proc. of SPIE Vol. 6374 637407-2

Φ=

⎛ ( 1 ∑ cos δ i ∑ sin δ i −1 ⎜ N 2 − tan ⎜ ⎜ ( 12 ∑ cos δ i ∑ sin δ i ⎝ N

− N1 ∑ cos δ i sin δ i )(

1 ∑ Iˆi ∑ cos δ i N2 1 cos δ i sin δ i )( 12 ∑ Iˆi ∑ sin δ i N ∑ N

− N1 ∑ Iˆi cos δ i )

−

− N1 ∑ Iˆi sin δ i )

− ( N12 (∑ cos δ i ) 2 − N1 ∑ cos 2 δ i )( N12 ∑ Iˆi ∑ sin δ i − N1 ∑ Iˆi sin δ i ) ⎞ (4) ⎟ − ( N12 (∑ sin δ i ) 2 − N1 ∑ sin 2 δ i )( N12 ∑ Iˆi ∑ cos δ i − N1 ∑ Iˆi cos δ i ) ⎟⎠ The birefringence phase difference and azimuthal angle of the sample are obtained from Φ0, Φπ/4, Φπ/2 and Φ3π/4, and from the phase change according to the rotation angle of the analyzer (θ3) at the points 0, π/4, π/2, and 3π/4:

∆=

1 2

φ=

1 ⎛ Φπ / 2 − Φ 0 ⎞ ⎟ tan⎜ 2 ⎜⎝ Φ π / 4 − Φ 3π / 4 ⎟⎠

(Φ 0 − Φ π / 2 )2 − (Φ π / 4 − Φ 3π / 4 )2 (5)

2.2 Biaxial tensile machine Figure 2 shows the biaxial tensile machine used to apply the sample stress[1]. The tensile machine consists of two micrometers and two pairs of linear guides to provide displacement to a sample fixed in the center of this machine. Each of the micrometers applies a tensile stress in the 45º and -45º directions. The uniaxial or biaxial stress state is applied and controlled by the displacements. The method of fixing a sample is shown Figure 3. The sample is attached to the guide at a number of points so as not to avoid restricting the deformation of the sample. This machine is fixed to a stage of the birefringence microscope.

Micrometer 45°

Sample

Sample

Sample

-45° 30 mm Fig.2

Biaxial tensile test machine

Fig.3

Proc. of SPIE Vol. 6374 637407-3

Method of fixing a sample

3.

BIREFRINGENCE MEASUREMENT RESULTS OF UNIAXIAL AND BIAXIAL TENSILE TESTS

3.1 Birefringence measurement results of uniaxial tensile test An isotropy sample was subjected to a displacement in the direction of one axis (45º) by the tensile machine, and the birefringence was detected at the same time. In this experiment, a gelatin sheet, which was a gelled 10% gelatin solution, was used as a sample. The sheet had a length of 10 mm, a width of 10 mm, and a thickness of 2 mm. Figure 4 shows plots of the measurement results of phase difference and azimuthal angle with respect to displacement. The phase difference is seen to increase nonlinearly with an increase in the displacement. The azimuthal angle indicates the direction of displacement. 3.2 Birefringence measurement results of biaxial tensile test Birefringence of the sample in the biaxial stress state was detected using the same sample as that used in the uniaxial tensile test. The axis (-45º) of one side had a fixed initial displacement, and the displacement of the axis (45º) of another side was changed. Figure 5 shows the plots of the measurement results of the phase difference and the azimuthal angle with respect to displacement at the 45º axis. The phase difference decreased with an increase in displacement until the stresses of the two axes, (45º) and (-45º), are evenly balanced, and then increased with an increase in displacement. The azimuthal angle agrees with the direction of the principal stress. The correspondence of birefringence and the mechanical characteristics was confirmed by the above results.

Phase difference, Azimuthal angle[゜]

80 60

Azimuthal angle

40 Phase difference

20 0

0

20 40 60 Displacement[µm]

Fig. 4 Phase difference and azimuthal angle plotted against displacement under uniaxial stress

Proc. of SPIE Vol. 6374 637407-4

80

Fixed Displacement

20 Phase difference

45 0

0

200 100 Displacement[mm]

300

-45

0

Phase difference[゜]

Azimuthal angle[゜]

90

Azimuthal angle -20

-90

Fig.5 Phase difference and azimuthal angle plotted against displacement under biaxial stress

4.

CONCLUSIONS

The gelatin sheet as an isotropic sample was subjected to a displacement by a biaxial tensile machine. The mechanical characteristics of an isotropic sample under uniaxial and biaxial stress were analyzed by the phase difference and the azimuthal angle of birefringence. The birefringence incidental on stress is detected by a birefringence microscope. As a result, in the case of uniaxial stress, the phase difference increased nonlinearly with an increase in the displacement, and in the case of biaxial stress, the azimuthal angle agreed with the direction of principal stress. The correspondence of birefringence and mechanical characteristics was confirmed by these results.

REFERENCES 1. 2. 3.

S. Kanehiro et al.: Proceedings of 17th Bioengineering Conference (2005)285-286 (in Japanese). M. Ebisawa et al.: Proceedings of SPIE, 6048(2005), 604807-1-6. Y. Otani et al.: Optical Engineering, 33, 5 (1994) p.1604-1609.

Proc. of SPIE Vol. 6374 637407-5

Simultaneous measurement of nanometric longitudinal displacement and micrometric lateral displacement by using one line CCD camera Masaaki Adachi*a, Yasuto Nishideb a

Graduate school of natural science and technology, Kanazawa University, Kakuma-machi, kanazawa, 920-1192 JAPAN; bShibuya Kogyo Co.,Ltd, Mamedahon-machi, kanazawa, 920-9681 JAPAN

ABSTRACT This paper proposes a simultaneous measurement technique of 2 displacement components by using a laser beam and one high-speed line CCD camera. The laser beam is divided to two beams. One beam is reflected by a corner reflector attached on an object and the reflected beam is superimposed with the other beam. The superimposed beam is expanded by a microscope objective lens and then passed through both a wedge-shape birefringent plate and a polarizer making a fringe pattern. This pattern has a light intensity distribution like a sinusoidal shape whose envelope curve has one peak. The pattern is captured by the line CCD camera and is used to extract nanometric longitudinal displacement and micrometric lateral displacement measurement. Keywords: displacement measurement, laser, line camera, 2-dimensional displacement

1. INTRODUCTION The Michelson interferometer using a dual-frequency laser is known as an optics system to accomplish a heterodyne detection technique of nanometric displacement. This system accurately measures displacement over a wide range with a long working distance and is used in many kinds of precision engineering field. However, this system measures only one component of displacement. The development of control technologies requires more-dimensional displacement sensing technologies. When longitudinal displacement and lateral displacement are required to be measured simultaneously, two heterodyne-detection systems should be used. P. Sandoz proposed nanometric position and displacement measurement of six degrees of freedom1). W. Gao et al. proposed multi-axis position measurement2). Those paper described the technologies for multi(>2)-dimensional measurement. However, they do not have a long working distance. This paper proposes a displacement measurement technique of 2 components by using a frequency-stabilized laser and one high-speed line CCD camera. This technology works with a long working distance as a laser heterodyne displacement measurement technique. In one of two directions, measurement range is extremely narrow compared with the other. Even with the narrow range of displacement measurement output could be combined with a servo-controled system. Servo-control systems combined with multidimensional displacement sensing technologies make possible to develop more reliable precision technologies. In the proposed technique a laser beam is divided to two beams as the Michelson interferometer. One beam is reflected by a fixed corner reflector working as a reference mirror, and the other beam is also reflected by another corner reflector attached on an object moving mainly along the beam direction. The reflected two beams are superimposed and expanded by an objective lens. Then, the expanded beams pass through both a wedge-shape birefringent plate and a polarizer making an interference pattern has lateral fringes. This fringe pattern has a single peak in an envelope curve * [email protected]; phone & fax 81-76-234-4922

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 637408, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.686633

Proc. of SPIE Vol. 6374 637408-1

Polarizing beamsplitter Fringe pattern captured by line camera He-Ne laser

Mirror Corner cube mirror Z direction

Line CCD camera Polarizer

1/4 λ wave plate Corner cube (reference) mirror

X-Z table X direction

Birefringence crystal of a wedge shape and polarizer making a fringe pattern

Figure 1: An optical layout for simple and accurate measurement of 2-dimensional displacement. The object for displacement measurement is a X-Z table at right side.

of light intensity distribution. With this optical layout longitudinal displacement (along the beam: Z direction) of the object changes fringe phase while keeping the envelope curve, and lateral displacement (along perpendicular direction to the beam: X direction) of the object moves the envelope curve laterally while keeping fringe phase. Therefore, capturing the fringe pattern with a high-speed line camera and extracting phase change and the peak position of the envelope curve, we can simultaneously measure nanometric Z-displacement and micrometric X -displacement with a long working distance. From our experiments using 2048-pixel line CCD camera with a frame rate of 9KHz, Z-displacement of the object was measured with nanometric resolution and X-displacement was measured with micrometric resolution with every mili-sec time interval.

2. SIMPLE OPTICAL LAYOUT FOR 2-DIMENSIONAL DISPLACEMENT MEASUREMENT In Fig.1 we show an optical layout for displacement measurement for two dimensions by using one line CCD camera. A laser beam is divided by a polarizing beam splitter to two beams as the Michelson interferometer. One beam is then reflected by a corner reflector working as a reference mirror, and the other beam is reflected by another corner reflector attached on a measurement object (X-Z table) moving mainly along the beam direction (Z direction). The reflected two beams are superimposed with the beam splitter and expanded by an objective lens. The expanded beams pass through both a wedge-shape birefringent plate and a polarizer making an interference pattern has laterally changing fringes. Z=Z0-Δ Z=Z0 Z=Z0+Δ intensity

X=X0-Δ X=X0 X=X0+Δ intensity

x (pixel)

(a)

x (pixel)

(b)

Figure 2: Changes of fringe pattern due to displacement. (a) Displacement along Z (longitudinal) direction changes phase of fringe, (b) Displacement along X (lateral) direction changes position of the envelope curve. Δ means a small amount.

Proc. of SPIE Vol. 6374 637408-2

This fringe pattern has a single peak in an envelope curve of light intensity distribution. With this optical layout Z-displacement (along the beam) of the X-Z table changes optical path difference and changes fringe phase while keeping the envelope curve as shown in Fig.2(a). X-displacement (along perpendicular direction to the beam) of the X-Z table moves the reflected beam position and then moves the envelope curve laterally while keeping fringe phase as shown in Fig.2(b). In Fig.2 these changes are shown as ideal cases. By capturing the fringe pattern with a highspeed line camera and by extracting phase change and the peak position of the envelope curve, we can simultaneously measure precision Z-displacement through fringe-phase change and slightly rough X-displacement through the peak position change of the envelope curve with a long working distance. With this optical layout fringe space is very stable, because difference in angle between the two interfering beam directions is mainly determined by wedge-angle of the birefringent plate. This stability makes possible an accurate measurement of fringe phase.

3. NANOMETRIC DISPLACEMENT MEASUREMENT IN A LONGITUDINAL DIRECTION 3.1 Basics of displacement measurement in a longitudinal direction With the optical layout shown in Fig.1, Z-displacement (in a longitude direction) of the X-Z table changes fringe phase, but maintains a reflected beam position in lateral direction and results in keeping the envelope curve same. To measure Z-displacement accurately, phase should be measured accurately. In phase measurements, phase shifting techniques are well known. With these techniques, at least three fringe patterns are however required to be recorded with shifting a pre-determined phase interval. From recorded patterns, phase information can be extracted at each pixel using some mathematical operations. In the displacement measurement proposed here, the table is assumed to be moving freely and fringe pattern is changing too. Then, the three fringe patterns cannot be captured with shifting the pre-determined phase interval. Another phase extraction method should be used. 3.1.1 Phase extraction from a changing fringe pattern As one of phase extraction techniques for changing fringe pattern, we here use a pattern product technique. In the optical layout in Fig.1, two beams reflected by corner cube mirrors are both gaussian and are expanded by a microscope objective lens. One wave front of the expanded beam is then slightly tilted against the other by the birefringence crystal and two wavefronts are interfered though a polarizer. Then interference pattern has approximately a sinusoidal intensity change along the tilt direction. Let us this pattern be expressed by the next equation,

I(x) = a ( x ) + b ( x ) cos ( kx + ϕ 0 ) ,

(1) where x (small letter) means coordinate along the tilt direction and corresponds to pixel position, a(x) is offset, b(x) is modulation, ϕ0 is phase at x=0, and k is wave number in the tilt direction. When the table moves slowly in Z direction, light intensity changes slowly through ϕ0. By continuously recording these changes over one-wavelength in displacement we can obtain maximum and minimum intensities at each pixel position. Using average data of the obtained intensities we can calculate a(x). Then, we can calculate Ic(x) given by next, Captured pattern

Σ

x x (pixel) After finding Max & Minimum intensities at each pixels, subtract the average of them

Re Im

Σ

x

Z

r

Zθ

Phase

Re means real part, Im means imaginary part, Z means complex value, and θ means angle of Z in complex plane

Operator of integration Operator of product

Basic cosine pattern

Basic sine pattern x (pixel)

x (pixel)

Figure 3: Phase extraction using pattern products. A pattern captured by line camera is taken to the products with a basic cosine pattern and with a basic sine pattern. Two products are calculated for each integral. The integrals are used to extract phase.

Proc. of SPIE Vol. 6374 637408-3

I C (x) = I(x) − a ( x ) = b(x)cos ( kx + ϕ 0 ) .

(2) This involves a strong feature of cos(kx+ϕ0). Let us call IC(x) a basic cosine pattern. This is one of patterns which are taken the product with I(x) given in Eq.(1). From the continuously recorded patterns another pattern should be selected as a basic sine pattern whose phase is shifted π/2 from ϕ0 (π/2 shift are estimated by the method given in the next section). The basic sine pattern is given as the next equation,

I S (x) = b(x)cos ( kx + ϕ 0 + π / 2 )

= −b(x)sin ( kx + ϕ 0 )

(3)

.

When we capture a new fringe pattern whose phase should be estimated, the captured pattern is thought to be given by,

IW (x) = a ( x ) + b ( x ) cos { kx + ϕ 0 + φW ( t )} ,

(4) where φW(t) is phase change required. To obtain φW(t), we calculate an integral of product of IW(x) and IC(x) by next equations, 2 nπ

PC =

∫

IW (x) ⋅I C (x)dx

0

2 nπ

≈ b(x) ⋅ 2

∫ cos {kx + ϕ

0

+ φW ( t )} ⋅ cos ( kx + ϕ 0 ) dx

0

=

1 b(x)2 ⋅ 2

2 nπ

∫ ⎡⎣ cos {2kx + 2ϕ

+ φW ( t )} + cosφW ( t ) ⎤⎦dx

0

0

= nπ b(x)2 ⋅ cosφW ( t )

, (5) where upper bar means an average, n means integer. Similar to the above derivation, we calculate the next integral of product of IW(x) and IS(x), 2 nπ

PS =

∫

IW (x) ⋅I S (x)dx

0

2 nπ

≈ −b(x)2 ⋅

∫ cos {kx + ϕ

0

+ φW ( t )} ⋅ sin ( kx + ϕ 0 ) dx

0

−1 = b(x)2 ⋅ 2

2 nπ

∫ ⎡⎣sin {2kx + 2ϕ

0

+ φW ( t )} − sinφW ( t ) ⎤⎦dx

0

= nπ b(x)2 ⋅ sinφW ( t )

.

(6)

From Eq.(5) and Eq.(6), required phase φW(t) is calculated by the next,

φW ( t ) = arg ( PC + iPS ) .

(7) The above procedures are shown in Fig. 3. As φW(t) is calculated not from an intensity change at one pixel, but from the intensity pattern along many pixels on CCD array, signal to noise ratio is thought better than that calculated from the change at one pixel. Beside, intensity change of offset a(x) has no effect on phase calculation given by Eq(7). We can calculate phase at any moving position by using Eq.(5),(6),(7). Then, with repeating this calculations of newly captured patterns, we can obtain final displacement of the table by summing up change of the calculated phase. 3.1.2 Extraction of the basic cosine pattern IC(x) and the basic sine pattern IS(x) Here we describe the extraction method of the two basic patterns mentioned above. Only the requirement of the basic patterns is that the basic patterns are π/2 different in phase from each other. Then, basic cosine pattern IC(x) is selected

Proc. of SPIE Vol. 6374 637408-4

under no limitation and is easily obtained. But the basic sine pattern IS(x) is difficult to obtain, because the sine pattern must be accurately shifted π/2 from IC(x). Therefore, we are required to extract phase change of continuously recorded interferogram. To extract phase change we use a Max-Min algorithm3,4). From Eq.(1) we can use light intensity signals whose phase depends on pixel position x. When the table moves, these signals change their phase and changing amount of phase are same regardless of their position. From interferograms recorded during the first portion of moving we can obtain maximum and minimum light intensities at some pixels. From the obtained intensities we can calculated timedependent intensity changes whose modulation are normalized to unity. Let us the normalized changes at two positions N1,N2 be given by,

I N 1 (t) = cos { m ( t ) + ϕ N 1 }

I N 2 (t) = cos { m ( t ) + ϕ N 2 } ,

(8) where m(t) is the phase changing with time t, but independent of position x. We calculate sum and difference of these normalized intensities. They are given as follows,

2m ( t ) + ϕ N 1 + ϕ N 2 ϕ − ϕN 2 cos N 1 2 2 2m ( t ) + ϕ N 1 + ϕ N 2 ϕ − ϕN 2 I N 2 (t) − I N 1 (t) = 2 sin sin 1 2 2 .

I N 2 (t) + I N 1 (t) = 2 cos

(9)

When these changes along time are normalized again, we can obtain the next values,

2m ( t ) + ϕ N 1 + ϕ N 2 2 2m ( t ) + ϕ N 1 + ϕ N 2 Nor [ I N 2 (t) − I N 1 (t)] = sin 2 , Nor [ I N 2 (t) + I N 1 (t)] = cos

(10)

where Nor[..] means the normalized signals. Therefore, we can obtain changing phase m(t) by the next equation, Fringe pattern

Nor means normalizing operation x (pixel)

t

Nor t

Nor

t

+

-

Nor

Nor

t

intensity changes along time

r Re θ Im Phase extraction from complex value

Z

Z

t

Figure 4: Extraction method of phase change to obtain a basic sine pattern. First: two pixel points whose phase difference is roughly π/2 are selected. Second: modulations of time changes at those point are normalized. Third: added change and subtracted change for normalized changes are calculated. Fourth: calculated changes are normalized again. Fifth: time change of phase is extracted from the angle of the complex value for re-normalized changes.

Proc. of SPIE Vol. 6374 637408-5

m ( t ) = arg { Nor [ I N 2 (t) + I N 1 (t)] +i ⋅ Nor [ I N 2 (t) − I N 1 (t)]} −

(ϕ

N1

Fringe pattern

+ ϕN 2 ) 2 .

x (pixel)

(11) These procedures are shown in Fig.4. As the result we can select the interferogram whose m(t) is just π/2 and can extract the basic sine pattern IS(x) given by Eq.(3). 3.1.3 Window function to obtain the phase independent of integrational borders In Eq. (5), (6) integration is supposed to be done with 2nπ in phase change. There is no assurance that we can find such integrational borders accurately. In addition, pixel positions are discrete numbers which have less possibility in corresponding to just 2nπ phase difference. Error in integrational borders might cause one of problems in this phase extraction. To resolve this problem we introduce a window function which has less intensity at side areas than a center area. There are many window functions in literatures. Among them we chose the Hamming window WH(x) defined by the next,

⎧⎪ ⎛ 2π ( x − xsart ) ⎞ ⎫⎪ WH ( x ) = 0.5 ⎨1 − cos ⎜ ⎟⎬ ⎝ xstop − xstart ⎠ ⎪⎭ , ⎪⎩

(12) where x is coordinate of the integration area. This function takes unity at center position and takes zero both in integration borders xstart and xstop. Fig. 5 shows the Hamming function. W H(x) is not required to be windowed to I W(x) given in Eq.(4) which may be changing during measurement. What should be windowed are IC(x) and IS(x). Because, the integration given in Eq.(5), (6) involve IC(x) and IS(x) respectively. 3.1.4 Extraction of the phase independent of nonlinear response of photo array Output response of photo array on input light intensity is known to be slightly nonlinear. As this nonlinearity causes errors in phase extraction, many researches to correct this type of errors have been done. In the phase extraction proposed here photo array of the used line CCD might have non-negligible nonlinearity to measure nanometric displacement. Then we try to extract the phase independent of nonlinear response. In the phase extraction described in 3.1.1, the required phase is calculated by Eq.(7). The real part and the imaginary part in Eq.(7) are calculated by Eq.(5) and (6) respectively. The nonlinearity has usually bigger error at higher input intensity as shown in Fig.6. When IW(x) has a nearly same pattern as IC(x), the nonlinearity affects more on PC because bright parts overlapping between them have square of error

1.0

Hamming function

0.0

x (pixel)

Windowed cosine

x (pixel)

Windowed sine

x (pixel)

Figure 5: Window function and windowed basic cosine and sine functions to obtain the phase independent of integrational borders. output

1.0 0.8 0.6 0.4 nonlinear response like tangent curve linear response nonlinear response like sine curve

0.2

0.

0.2

0.4

0.6

0.8

1.0

input

Figure 6: Examples of nonlinear response of photo detector simply calculated phase corrected phase enlarged residual error output pahse

2 1 -6

-4

-2 -1

input

2

4

-2 -3

Figure 7: Phase calculated from intensities of nonlinear response and phase corrected. Enlarged (1000 times) residual errors are also showed

Proc. of SPIE Vol. 6374 637408-6

in contribution. On the other hand, IW(x) has a different pattern as IC(x), the nonlinearity affects less. Then, we try to calculate the real part with another basic cosine function IC’ (x) which has π different phase from IC(x), 2 nπ

PC ′ =

∫

IW (x) ⋅I C ′ (x)dx

0

2 nπ

≈ b(x)2 ⋅

∫ cos {kx + ϕ

0

+ φW ( t )} ⋅ cos ( kx + ϕ 0 + π ) dx

0

1 = b(x)2 ⋅ 2

2 nπ

∫ ⎡⎣ cos {2kx + 2ϕ

0

+ φW ( t ) + π } + cos {φW ( t ) − π } ⎤⎦dx

0

= −nπ b(x)2 ⋅ cosφW ( t )

. (13) Then, the real part should be used in Eq.(7) is given by Pc -Pc’. In addition, we calculate the imaginary part with another basic sine function IS’ (x) which has π different phase from IS(x), and let the imaginary part should be used in Eq.(7) be given by Eq.(6) minus new value calculated with IS’ (x). We estimate errors by the above procedure with computer simulation. First we assume a nonlinear output response of photo array is expressed as the sine curve in Fig.6. Fig.7 shows the results, where the solid curve means the extracted phase after the correction and broken curve means before the correction. The solid curve looks to have little errors. So 1000 multiplied errors are also shown as dotted curve. Here we used sine output as an example of nonlinear response. We also assume tangent output as another nonlinear response. With the tangent output simulation results like Fig.7 is given. 4. MICROMETRIC DISPLACEMENT MEASUREMENT IN A LATERAL DIRECTION 4.1 Displacement measurement in a lateral direction In Fig. 1 the X-Z table displacement in the lateral direction leads the position change of the reflected-beam center. As the line CCD camera is set for its photo-array direction parallel with the changing direction, the change makes the envelope curve of intensity distribution shift in the pixel direction. An amount of the shift depends not only on the lateral displacement but also on magnification of the objective lens and the distance between CCD camera and the lens. A much magnification and a longer distance increase the displacement sensitivity. But they cause that an interference pattern expands beyond a detection area of CCD photo array and light intensity detected by one pixel decreases. In our displacement measurement in Z direction, both sides of the intensity pattern I(x) would affect their integrations. The both sides of the pattern might affect the shift measurement of the envelope curve. Then, the pattern windowed by WH(x) should be used to the shift measurement. Fig.8 shows this measurement process. The windowed pattern is divided to two parts by a center pixel position. Then total light intensities are calculated for each part. Difference of the total intensities between in a left part and in a right part is thought to roughly give the lateral displacement. But it position of center pixel Fringe pattern

x (pixel)

x (pixel)

x Hamming window

right area

left area

Σ

Σ x (pixel)

-

Difference of total intensities between in the left area and the right area

Figure 8: Lateral displacement could be measured from the distribution of interference amplitude along the camera pixel. As interference amplitude is difficult to estimate from the interference pattern, the distribution of intensity pattern is used.

Proc. of SPIE Vol. 6374 637408-7

is thought to be strongly affected by also a fringe position around the center pixel. Because the fringe has a high peak intensity and is divided into two parts by the position of the center pixel. By studying the dividing effects, we think that the effect is synchronous with the phase change by Z displacement. Therefore, we can estimate the dividing effect from Z displacement data and can delete the effect from the difference of the intensities between in the left part and in the right part.

Light intensty 300

Z=Z0 Z=Z0 + λ/2

X:fixed

200 100 0

400

0

800

1600

1200

x (pixel)

Figure 9: Captured intensity patterns at two different displacement positions for Z direction. 80

60

Measured displacement/μm

The experiments are carried out under next conditions. In the optical layout shown in Fig.1 the objective lens of lateral magnification of 20 is used. The distance between the CCD camera and the objective lens is set around 200mm. The used CCD camera is BASLER L101-2k which has 2048 pixels, 8bit analog/digital converter, and frame rate of 9k/s. Frequency stabilized He-Ne laser having 1mW in output power is used. X-Z stage for the object of displacement measurement is made of PI piezo-stage (100-µm stroke in X and 100-µm stroke in Z direction) having few-nm resolution. Its hysteresis is estimated less than 0.015% by a maker. Input analog signal (from 0 to 10V) to the piezo-stage is controlled by an output of 16bitdigital/analog converter of a computer used in experiments. In the displacement measurement along the Z direction, fringe images are continuously captured by linearly changing input signal of PI piezo-stage with 0.0002V/ frame. Fig.9 shows 2 light-intensity patterns at certain displacement positions. Two positions differ from each other with a quarter of the laser wavelength. The results of displacement measurement are shown in Fig.10. The measured results can be compared with input signals of the piezo-stage. Assuming the piezo-stage works correct, errors are calculated along Z displacement over 80μm. The calculated errors are shown in Fig.11. The hysteresis of 0.015% means 12nm in this figure. In the displacement measurement along the X direction, as the first step 1000 fringe images are continuously captured by changing Z input signal of PI piezo-stage with 0.0002V/frame. As the second step 40000 images are continuously captured by linearly changing X input signal of PI piezo-stage with 0.0002V/frame. Fig.12 shows 2 light-intensity patterns at certain displacement positions for X direction. The positions differ from each other with around 40µm. Raw displacement measurement results for X direction are shown in Fig.13. The measured results for X displacement show bigger errors compared with Z displacement results in Fig.10. But monotonic decrease can be observed over a certain wide range. This monotonic decrease is considered to make possible the servo-control

40

20

0 0

20

40

80

60

Input displacement /μm

Figure 10: Measured displacement results for Z direction. Error of displacement measurement/nm

5. EXPERIMENTS

100 50 0 -50 -100 0

20 60 40 Input displacement /μm

80

Figure 11: Errors of displacement measurement for Z direction.

Light intensty 300

X=X0 + 30μm X=X0 - 30μm

Z:fixed

200 100 0

0

400

800

1200

1600

x (pixel)

Figure 12: Captured intensity patterns at two different displacement positions for X direction.

Proc. of SPIE Vol. 6374 637408-8

60

6. DISCUSSIONS AND CONCLUSIONS

40

Measured displacement/arb. unit

of X-direction displacement of an object.

20 This paper proposes a simultaneous measurement technique of 2 displacement components by using one high-speed line CCD 0 camera. This technique has a long working distance as few meters. For Z-displacement measurement few tens of nm precision was -20 performed. For X-displacement measurement, monotonic decrease result was observed. -40 Measurement speed of the technique depends not only the frame rate of used line camera but also an amount of data processed. -60 In the above results using the camera of frame rate of 9kHz and 0 20 40 80 60 2048 pixels, measurement speed is around 1 mili-sec/ frame. If a Input displacement /μm camera having fewer pixel number can be used in this technique, Figure 13: Measured displacement results for X direction. measurement speed is thought to become higher. Then we estimate the precision of using cameras having fewer pixel. We extract virtual interference patterns composed of fewer pixel data from 2048 pixel data used in the experiments, and then apply the same calculation program to extracted data. Regarding extracted 1024, 512 pixel data, measurement precision for X, Z displacements are the same as those using 2048 pixel data. Regarding fewer pixels for Z displacement, 256, 128, 64 pixels increase measurement errors as 15,20,25 nm in 3 σ (standard deviation). Regarding fewer pixels for X displacement, 256, 128, 64 pixels considerably increase measurement errors. In both displacement measurements origins of errors should be considered.

REFERENCES 1. P. Sandoz, “ Nanometric position and displacement measurement of the six degrees of freedom by means of a patterned surface element”, Applied Optics 44, 1449-1453 (2005) 2. W. Gao, T. Arai, S Kiyono,Y. Okazaki, M. Yamanaka, ” Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder”, Precision Engineering, 27, 289-298 (2003) 3. X. Chen, M. Gramaglia, and J.A.Yeazell, ” Phase-shifting interferometry with uncalibrated phase shifts”, Appl. Opt., 39,585-591 (2000) 4. K.G.Larkin,” A self-calibration phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns”, Optics Express, 9, 5, 236-353 (2001)

Proc. of SPIE Vol. 6374 637408-9

MEMS ACOUSTIC SENSOR USING PMN-PT SINGLE-CRYSTAL DIAPHRAGM a1

Sung Q Lee, aHye Jin Kim, aKang Ho Park, bYong K. Hong, b2Kee S. Moon Nano-Sensor Team, ETRI 161 Gajeong-Dong, Yuseong-gu, Daejon, 305-700, S. Korea a

b

Dept. Of Mechanical Engineering, San Diego Stage University 5500 Campanile Dr. San Diego, CA 92182, U.S.A. ABSTRACT

The MEMS (micro-electro-mechanical systems) microphone enables the manufacturing of small mechanical components on the surface of a silicon wafer. The MEMS microphones are less susceptible to vibration because of the smaller diaphragm mass and an excellent candidate for chip-scale packaging. The PMN-PT materials itself exhibit extremely high piezoelectric coefficients and other desirable properties for an acoustic sensor. In this paper, we present a piezoelectric MEMS microphone based on PMN-PT single crystal diaphragm. The fabrication process including dry etching conditions and scale-factored prototype is presented. In particular, this paper introduces the design of a PMN-PT single crystal diaphragm with interdigitated electrode. Keywords: Acoustic Sensor, Microphone, PMN-PT, Dry etching, MEMS

1. INTRODUCTION As the telecommunication technology grows, a mobile terminal such as cellular phones requires a higher quality of images, videos, and sounds. Traditional electret condenser microphones (ECMs) have reached moderately small sizes. However, they are approaching the size limits and are unlikely to shrink much further. A new microphone technology, the MEMS (micro-electro-mechanical systems), enables the manufacturing of small mechanical components on the surface of a silicon wafer. The MEMS microphones are less susceptible to vibration because of the smaller diaphragm mass and thus an excellent candidate for chip-scale packaging. The MEMS microphones are widely investigated and promising in many areas, including consumer electronics, military and industrial uses. Recently several kinds of MEMS microphone technologies have been proposed, such as condenser [1-4], electret [5-6], piezoresistive [7-9], and ferroelectric microphones [10-11]. However, condenser and ferroelectric microphones are popular ones due to their excellent performances. In the case of condenser microphones, a back plate and a diaphragm are built on the surface of a wafer along with the necessary electrical connections. The diaphragm is chemically etched so it can vibrate freely with incoming sound. The changing capacitance of the charged capacitor formed by the back plate and diaphragm changes acoustic signals into electrical signals. It is also known that the type of microphones requires relatively high bias voltage and has a limited sound frequency range. The condenser microphones show the highest sensitivity among all candidates. However they suffer a fabrication complexity in forming a narrow air-gap between two comparatively large surfaces, which form a variable capacitor for sound signals detection. This structure is easily damaged by surfaces sticking and dust clamped between the air-gap. Ferroelectric thin film 1 2

[email protected]; phone 82 42 860 1142 [email protected]; phone 1 619 594 8660 Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 637409, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.686007

Proc. of SPIE Vol. 6374 637409-1

MEMS microphones, which are based on the piezoelectric effect of a ferroelectric thin film, have a more robust fabrication process. Furthermore, they do not need external bias for signal readout and have a wider dynamic range [12]. In this paper, we present a PMN-PT single crystal diaphragm for piezoelectric MEMS microphones. The PMNPT based microphones can offer the ability to passively sense without the power requirements. Furthermore the new generation oxide material exhibits extraordinary piezoelectric properties. The material, the single-crystal solid-solutions (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-PT), has been shown to possess piezoelectric coefficients and electromechanical coupling responses significantly larger than conventional ceramics. A four times enhancement in piezoelectric coefficients and much higher efficiencies in electrical to mechanical energy conversions have been found. In this paper, we report on the design concept, the fabrication of a single crystal piezoelectric PMN-PT based diaphragm with an interdigitaed electrode. Since there is little research for the dry etching of PMN-PT, In particular, the dry etching condition of PMN-PT is introduced.

2. DESIGN OF PMN-PT DIAPHRAGM In the paper, we describe the design and fabrication of a single crystal piezoelectric PMN-PT based diaphragm. For a passive piezoelectric microphone, the diaphragms are made of silicon and a piezoelectric material is coated on the diaphragms. There are several options for the sensor materials including ZnO, AlN, and lead zirconate titanate (PZT). Our research focused on developing a PMN-PT single crystal diaphragm microphone. The material has a large piezoelectric coefficient and a low dielectric loss compared to conventional piezoelectric materials. The recent development of ultra-efficient single crystal piezoelectric materials lead zinc niobate-lead titanate (1-x)Pb(Zn1/3Nb2/3)O3xPbTiO3, (PZN-PT) and lead magnesium niobate-lead titanate (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3, (PMN-PT) has attracted considerable attention because of their potential use in a new generation of piezoelectric transducers and actuators. The attractiveness of these materials lies in the fact that their piezoelectric coefficients (d33>1500pC/N), dielectric constant (kRT~3000) and electromechanical coupling factor (k33~92%) and strain levels are significantly higher than those of the lead zirconate titanate Pb(Zr1-x, Tix)O3, (PZT). Furthermore, their hysteresis is much lower. The single crystal also gives more desirable and predictable resonance characteristics [13-15]. A prototype diaphragm design with two different types of electrode patterns is shown in Fig. 1. A circular electrode configuration consisting of metallic area distributed over the PMN-PT surface can lead to efficient acoustic sensing. Acoustic sensing in the proposed configuration is the result of surface contraction across the diaphragm. It can be noted from the figure 1 that the diaphragm designs include the interdigitated electrode pattern (Fig. 1 upper left). Another piezoelectric diaphragm design uses the d31 mode of a piezoelectric film (Fig. 1 upper right). In case of the interdigitated electrode design (Fig. 1 upper left), an external stress applied to the diaphragm results in output charge or voltage by d33 mode. In many perovskite ferroelectric materials, the d33 coefficient is two or more times larger than d31, and hence our interest is in the d33 mode with interdigitated electrode pattern. In addition, it can be noted that the d33 mode design requires a simpler one-side electrode fabrication process. Ferroelectric materials develop surface charges when subjected to stress, and alternatively exhibit mechanical deformation by applying an electric field. A piezoelectric diaphragm is a sensor that transforms mechanical vibration of membrane into electrical signal using piezoelectric effect. The deformation and stress distribution is important factor in microphone. In order to estimate the deformation, stress distribution, and modal analysis, numerical analysis using ANSYS is conducted. Several parameters for the numerical analysis are depicted in following table1. Based on above parameters, we used a modal analysis to determine the vibration characteristics of the diaphragm design of Fig. 1. The maximum deformation is occurred at its center (Fig.2 upper). The deformation is about 2.419E-3. The natural frequencies and mode shapes are also important parameters in the design of a microphone diaphragm for dynamic loading conditions. The modal analysis to determine the fundamental vibration mode shapes and corresponding frequencies was conducted using ANSYS finite element analysis software. The first and the second modes natural frequency of the diaphragm structure are 84,317 Hz (Fig. 2 middle) and 159,896Hz (Fig. 2 bottom), respectively. The diameter of the circular diaphragm is 500 µm. And the thickness of the diaphragm is 5 µm. The applied pressure is 5 Pa. Still, however, we need to adjust the mechanical properties and model based on the experimental results

Proc. of SPIE Vol. 6374 637409-2

d33 IDT design

d31 design

Fig. 1 Design of PMN-PT piezoelectric diaphragms (upper left: d33 mode interdigitated electrode design; upper right: d31 mode circular electrode design; below: three-dimensional view of the diaphragm design)

Table 1. Material parameters for numerical analysis Parameters Thermal conductivity Young’s Modulus Poison ratio

[

value

K : 0.0026 W

]

→ 0.26 E 6 cm ⋅ K E : 20 ~ 25 [GPa ] → 20 ~ 25 E 3 υ : 0.39

Thermal expansion coef.

α : 9.5E − 6 [K −1 ]

Density

ρ : 8.2 ⎡ g

⎤ → 8.2 E − 15 ⎢⎣ cm 3 ⎥⎦

Proc. of SPIE Vol. 6374 637409-3

Fig. 2 Vibration characteristics of the diaphragm design of Fig. 1

3. FABRICATION PROCESS OF PMN-PT DIAPHRAGM Figure 3 shows the steps required to fabricate a PMN-PT diaphragm. We have two different type of electrode: Interdigitated electrode pattern and top/bottom electrode. Each fabrication process is shown in figure 3. We use <001>-oriented and poled 500um-thick PMN-PT single crystal plates mounted on a Si substrate. The sample undergoes a mechanical polishing down to 20~30µm-thick film and Cr evaporation processes for the top side to have fine primary Au and Cr electrode layers. The interdigitated electrode pattern is micromachined by typical photolithography processes to have precisely 10µm-gap periodic electrode for the d33 mode design. The back side of the film is then exposed by a back-side wet etching process of Si substrate. Either a chemically assisted ion beam etching (CAIBE) technique or an inductively coupled plasma (ICP) etching process can be used to thinning down the film up to 5µm.

Proc. of SPIE Vol. 6374 637409-4

Single crystal PMN-PT (20µm-thick) + Si substrate

Electrode pattern (circular interdigitated electrode)

Wet etching of silicon Thinning PMN-PT film to 5 µm using CAIBE or ICP

(a) The d33 mode design

Single crystal PMN-PT film + Silicon substrate Electrode pattern (plain circular electrode) Wet etching of silicon Thinning PMN-PT film to 5 µm using CAIBE or ICP

(b) The d31 mode design Fig. 3 Fabrication processes of PMN-PT piezoelectric diaphragm

In this paper, we also report the experimental results of dry etching characteristics of PMN-PT single crystal thin film. We used an inductively coupled plasma (ICP) etching process with various gas combinations [16]. A <001>factory-oriented and PMN-PT single crystal 0.5mm-thick plate was used for this research. The material is purchased from IBULE Photonics and has the dimension of 20×20×0.5mm3. In order to obtain a thin film, a bulk sample is polished down to the thickness of 30 µm. The further thinning down of the circular diaphragm area to the thickness of 5 µm can be produced by standard photolithography and the inductively coupled plasma (ICP) etching process. The focus of this study is to study the dry etching properties of the PMN-PT thin film and to obtain the optimum gas combination to maximize the etching rate in the ICP process. The gas mixtures used in this experiment were the combination of Cl2, BCl3, and CH4. The substrate temperature was maintained at 20o and the bias power of the ICP was 200W. The etch rate was measured using a surface profilometer (alpha step). Figure 4 shows the etch rates of the PMN-PT thin film as a function of BCl3/Cl2 gas mixture. When the PMNPT thin films were etched using pure gas of Cl2 was less than 500 Å /min. As BCl3 was added into the gas mixture, the etch rate increased up 1800Å/min. Additional experiments were carried out to investigate the effect of Cl2/ CH4 gas mixture on the etch rate. As shown in Fig. 5, the etch rate using the pure CH4 gas was less than 800Å/min. With the increase of Cl2, the etch rate increased up 1800Å /min at 60% of Cl2 mixture. And further increase of Cl2 decreased the etch rate.

Proc. of SPIE Vol. 6374 637409-5

2000 1800

Etch rate (A/min)

1600 1400 1200 1000 800 600 400 200 0

20

40

60

80

100

BCl3 / (BCl3+Cl2 ) (%)

Fig. 4 Etch rate of PMN-PT film using an inductively coupled plasma (ICP) etching process with BCl3/Cl2 gas mixture

2000 1800

Etch rate (A/min)

1600 1400 1200 1000 800 600 400 200 0

20

40

60

80

100

Cl2 / (Cl2+CH 4) (%)

Fig. 5 Etch rate of PMN-PT film using an inductively coupled plasma (ICP) etching process with Cl2/ CH4 gas mixture

4. SENSITIVITY MEASUREMENTS Figure 6 shows fabricated prototype PMN-PT single crystal diaphragms. The sizes of the prototypes are larger than the design of Fig. 1 (2mm diameter). We can get a feasibility of PMN-PT microphone through this scaling factor of 4. The final thinning process was not applied for these prototypes. To fabricate the prototype, we used <001> oriented and poled 500um-thick PMN-PT single crystal plates. The samples were purchased from TRS Ceramics, Inc. For the electrode patterning, a 50nm-thick gold film is sputtered on the surface and patterned using standard photolithography. The interdigitated electrode patterns were micro-machined by photolithography processes to have a100µm-gap periodic electrode for d33 mode design. By using wire cutting followed by electrode patterning, the films were shaped into a square-shaped acoustic sensor as shown in Fig. 1.

Proc. of SPIE Vol. 6374 637409-6

Fig. 6 Fabricated PMN-PT single crystal diaphragms

Amplifier

Oscilloscope

Signal generator

Speaker

Fig. 7 Experimental setup for sensitivity measurement

In this study, we carried out experimental measurements to compare the d33 and d31 mode designs shown in Fig. 6. The experimental setup for the sensitivity measurement is given in Fig. 7. Before the poling process, the PMN-PT films had very weak factory <001> poling. The additional poling process establishes a remnant polar domain configuration in the films and a consequent strong piezoelectric response. The proper poling process is critical to maximize the output from the device. Figure 8 shows the voltage output (peak-to-peak), Vpp, from the diaphragms as the function of different poling conditions. It shows that the output voltage increases and saturates around 0.25 mV as the poling voltage increases. The poling process has been conducted under room temperature. The acoustic input for this experiment was given by a small commercial speaker attached to an amplifier and a signal generator. It can be noted from Fig. 8 that the d33 mode design generates no output voltage at 0V poling condition. Then the sensitivity of the design rapidly increases as the poling voltage increases. The phenomenon may be explained from the fact that the d33 mode design requires a different electric field distribution while the d31 mode design needs the electric filed distribution of <001> poling [15,17]. The frequency responses of the prototypes are shown in Fig. 9.

Proc. of SPIE Vol. 6374 637409-7

(mV)

£ d31 rre

OF

• d33rrode

I

21i:0o. 0

50

r 150

100

200

250

Poling voltage ('

Fig. 8 Voltage output (peak-to-peak), Vpp, from the diaphragms as the function of poling voltage

(mV)

—1

25

>a

20

ci)

0) 15

C >

= 10 a =

0

5 0 10

—.—a

1000

100

Hz

Fig. 9 Frequency responses of the PMN-PT diaphragm prototypes

Proc. of SPIE Vol. 6374 637409-8

I

10000

4. CONCLUSIONS Piezoelectric MEMS acoustic sensors have a wide variety of applications in hearing aids, surveillance, heart monitoring, etc. In this paper, we have presented a piezoelectric MEMS microphone based on PMN-PT single crystal diaphragm. The proposed diaphragm design includes an interdigitated electrode pattern that could be a pioneering effort in the area. The dry etching condition is researched for the future patterning and fabrication of various acoustic sensor structure. From the scaling-factored miniaturized PMN-PT single crystal diaphragms, we can conclude the PMN-PT thin film microphone designs have a potential to show excellent acoustic characteristics, reliability.

ACKNOWLEDGEMENTS The authors thank Dr. S. M. Wang and D. S. Kim for the numerical analysis, and also thank the Ministry of Information and Communication Grant.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

M. Jianmin, L. Rongming, C. Longqing, Z. Quanbo, L. S. Yee, and S. S. Hee, “Design considerations in micromachined silicon microphones,” Microelectronics Journal 33, 21–28 (2002). S. Bouwstra, T. Storgaard-Larsen, P. Scheeper, J. O. Gullov, J. Bay, M. Muellenborg, and P. Rombach, “Silicon microphones—a Danish perspective,” Journal of Micromechanics and Microengineering 8(2), 64–68 (1998). D. Hohm and G. Hess, “A Subminiature Condenser Microphone with Silicon Nitride Membrane and Silicon Back Plate,” J. Acoust. Soc. Am. 85, 476–480 (1989). P. R. Scheeper, A. G. H. van der Donk, W. Olthuis, and P. Bergveld, “A Review of SiliconMicrophones,” Sens. Act. A 44,1–11 (1994). F. W. Fraim and P. V. Murphy, “Miniature Electret Microphones,” J. Audio Eng. Soc. 18,511–517 (1970). J. Sprenkels, R. A. Groothengel, A. J. Verloop, and P. Bergveld, “Development of an Electret Microphone in Silicon,” Sens. Act A 17, 509–512 (1989). R. Schellin and G. Hess, “A Silicon Subminiature Microphone based on Piezoresistive Polysilicon Strain Gauges,” Sens. Act. A 32, 555–559 (1992). R. Shellin, M. Strecker, U. Nothelfer, and G. Schuster, “Low Pressure Acoustic Sensors for Airborne Sound with Piezoresitive Monocrystalline Silicon and Electrochemically Etched Diaphragms,” Sens. Act. A 46–47, 156–160 (1995). D. Arnold, S. Gururaj, S. Bhardwaj, T. Nishida, and M. Sheplak, “A Piezoresisitive Microphone for Aeroacoustic Measurements,” Proc. 2001 ASME Intern. Mech. Eng. Cong. Expos., New York, Nov. (2001). M. Royer. J. O. Holmen, M. A. Wurm, O. S. Aadland, and M. Glenn, “ZnO on Si Integrated Acoustic Sensor,” Sens. Act A 4, 357–362 (1983). R. Reid, E. Kim, D. Hong and R. Muller, “Piezoelectric Microphone with On-Chip CMOS Circuits,” J. MEMS 2, 111–120 (1993). P. Ried Robert, Kim Eun Sok, M. Hong David, and S. Muller Richard, “Piezoelectric Microphone with OnChip CMOS Circuits,” Journal of Mi- croelectromechanical Systems 2(3), 111–120 (1993). H. Fu and R. E. Cohen, “Polarization rotation mechanism for ultrahigh electromechanical response in single- crystal piezoelectrics,” Nature 403, 281-283 (2000). N. W. Hagood, R. Kindel., R. Ghandi, R. Gaudenzi, “Improving transverse actuation of piezoelectrics using interdigitated surface electrodes,” SPIE paper No. 1975-25, Proceedings of the 1993 North American Conference on Smart Structures and Materials, Albuquerque, NM, (1993). R. R. Vanga, M. Levy, K. S. Moon, and Y. K. Hong, “Single-Crystal Relaxor Ferroelectric Piezoactuators with Interdigitated Electrodes,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 51(12), 1593-1599 (2004).

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16. J.W. JangU, Y.H. Lee, Y.J. Lee, J. Lee, G.Y. Yeom, “Etching characteristics of lead magnesium niobate lead titanate PMN]PT relaxor ferroelectrics,” Surface and Coatings Technology (131), 252-256 (2000). 17. Y. K. Hong and K.S. Moon, “Interdigitated Single Crystal Piezoelectric Actuator,” Proceedings of the SPIE International Conference on Optomechatronic Actuators and Manipulation, SPIE, ISOT 2005, Sapporo, Japan, Vol. 6048, pp. 6048K-1-7, December (2005).

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Invited Paper

PMN-PT PIEZOELECTRIC NEAR FIELD OPTICAL PROBE FOR DATA STORAGE a

Yong K. Hong, bSung Q Lee, bEun Kyoung Kim, bKang Ho Park, a1Kee S. Moon a

Dept. Of Mechanical Engineering, San Diego Stage University 5500 Campanile Dr. San Diego, CA 92182, U.S.A. b Nano-Sensor Team, ETRI 161 Gajeong-Dong, Yuseong-gu, Daejon, 305-700, S. Korea ABSTRACT

This paper presents the fabrication process of a novel aperture which allows near field optical data storage. We use PMN-PT ((1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3) single crystal material - a new generation oxide material known as relaxor ferroelectrics that exhibits extraordinary piezoelectric properties - to fabricate microlenes using photolithography and dry etching techniques. In this paper, we describe the fabrication processes of a PMN-PT single crystal material microlens prototype with a miniature aperture for near field optical data storage. PMN-PT has the merits of transparency for optical usage and also has a high dielectric coefficient that is suitable for actuator and sensor applications. It provides an advantage of manufacturing both aperture and actuator/sensor with the same material. The thermal reflow technique is used to fabricate photoresist microlenses on a freestanding single crystal PMN-PT film as a mask. The PMN-PT lenses are fabricated by a chemically assisted ion beam etching (CAIBE) technique. Finally the focused ion beam (FIB) machining process is used to place a miniature aperture at the apex of the microlens. We were able to successfully fabricate the 10µm PMN-PT microlenses with less than 100nm apertures. From the experimental measurement, we were able to obtain the optical throughput of 1.83x10-7 from a 50nm aperture. Keywords: PMN-PT, Aperture, Data storage, Near field

1. INTRODUCTION It has been well known that the storage density of the conventional optical data storage using far field optical systems cannot be increased significantly due to the limit of the wavelength of the laser source and the numerical aperture of the objective lens [1,2]. One of the new technologies to overcome the limitation is the near field optical microscopy. Near field scanning optical microscopy (NSOM) has been intensively studied for optical writing. The most crucial part of the NSOM optical writing is a sub-wavelength size aperture at the apex of the probe. Currently, tapered optical fiber probes are most widely used for the NSOM. The conventional tapered optical fiber probes have a few negative aspects. The opening angle of the fiber tip is small. Therefore, most of the light is absorbed at the metal wall, which leads to a low optical transmission efficiency. Moreover, it is very difficult to fabricate the fiber NSOM probe in a mass production because the shape of the tip and the size of the metallic aperture of the fiber tip are not reproducible [3]. Recent attempts using AFM cantilever-style probes have shown improved transmission efficiency as well as AFM-like gap control between the probe and the surface. Figure 1 shows our near field optical storage design using an AFM cantilever-style NSOM probe. So far silicon based AFM cantilever-style probe design has been most popular [4]. Most of the cantilever-style probe designs have a high-throughput aperture patterned on the silicon cantilever directly. In this paper, by the use of an advanced relaxor ferroelectric material ((1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3, PMN-PT) with the thermal reflow and dry etching process, we present a piezoelectric cantilever-style probe having a microlens with an aperture at the apex of it. The material, the single-crystal solid-solutions PMN-PT, has been shown to possess piezoelectric coefficient and electromechanical coupling response significantly larger than conventional piezoelectric 1

[email protected]; phone 1 619 594 8660 Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740A, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.689527

Proc. of SPIE Vol. 6374 63740A-1

ceramics [5-8]. Furthermore, PMN-PT single crystal thin films have the merits of transparency for optical usage [9]. Therefore, PMN-PT single crystal materials are suitable for actuator and sensor applications and provide an advantage of manufacturing both aperture and actuator/sensor with the same material [10]. This paper focuses on the fabrication process of a PMN-PT single crystal optical microlens and a miniature aperture.

Optical fiber Lens

Lens Z motor

PMT(PD) Splitter CCD

Fig. 1. Schematic of the near field optical data storage head system.

2. FABRICATION OF PMN-PT APERTURE In the near field optical data storage device design, the most critical component is the piezoelectric cantilever-style NSOM probe that leads to higher resolution optical writing capability. The integration of an AFM style cantilever with an aperture allows more reliable and better control of the aperture-sample distance than that obtained by traditional NSOM shear-force detection method. The design of the proposed NSOM probe is depicted in Fig. 2. As shown in the figure, an interdigitated electrode is implemented on the PMN-PT cantilever to provide an embedded sensing capability. To construct a near field optical data storage head, a PMN-PT cantilever is also fabricated and a microlens is attached to the end of the cantilever. An aperture is place at the top of the microlens.

Focused UV light

Sensor electrodes

PMN-PT cantilever Sub 100nm aperture

Built-in microlens

Al coating

Fig. 2. Design of piezoelectric cantilever style near field optical probe.

Proc. of SPIE Vol. 6374 63740A-2

Photoresist coating

————

a

Photolithography and wet etching

300

a

Thermal reflow

10! h

Dry etching (CAIBE) Metal deposition

— .-. 'a, a' .

Focused ion beam machining

Cross sectional view

Fig. 3. Fabrication processes of PMN-PT microlens array with aperture.

This paper focuses on the fabrication of PMN-PT microlenses with an aperture. The prototype is fabricated through the fabrication of freestanding single crystal PMN-PT films and patterning them by photolithography, chemically assisted ion beam etching (CAIBE) and focused ion beam (FIB) machining processes. Figure 2 illustrates the required processes. We prepared a mechanically polished PMN-PT single crystal film with the thickness of 20µm. We used <001>-factory-oriented and poled 0.5mm-thick PMN-PT single crystal plates. The samples were purchased from TRS Ceramics, Inc. Then a photoresist is used to make circular plates on the PMN-PT film by using photolithography process. For the thermal reflow treatment, the sample was heated on a hot plate, with the heating rate of 1oC/min until the working temperature of 170oC was reached. The spherical shape of photoresist is given in Fig. 4. After the thermal reflow process, a chemically-assisted-ion-beam system (CAIBE, Ribetch 160 ECR LL) is used for the formation of PMN-PT microlenses by controlled dry etching of the sample. Figure 4 shows SEM images of a PMN-PT microlens obtained by the CAIBE process. It can be seen from the figure that the shape of the microlenes is pointed. This means that the etching rate of PMN-PT is slightly faster than that of the photoresist. By controlling the CAIBE etching time, we were able to change the microlens to a round shape. The SEM image of the round shaped microlens is shown in Fig. 5. The CAIBE system could produce 10um-thick lenses in about 3-4 hr etch time without any etch gas mixture. After the CAIBE process, a Cr and Au films with the thickness of about 100 nm was entirely deposited onto the surface of the microlenses. Finally, a focused ion beam (FIB, Hitachi FB-2000A) was used for patterning of a small hole on the tip of the lens. The FIB milling enables not only accurate control of the aperture size, but also provides a means of producing specific aperture shapes with nanometer-scale precision. The FIB system uses a beam of focused high-energy (30kV) gallium ions to remove material in a very controlled manner. Note that the actual inner size of the aperture is much smaller than the outer diameter of the aperture observed by scanning electron microscopy (SEM). The SEM images of the fabricated probes and a close up view of the apertures with about 50 nm diameter (inner) are shown in Fig. 5.

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~100um

:.

4

(a)

(b)

(c)

(d)

Fig. 4. (a) Photoresist mask after the thermal reflow process (b) PMN-PT microlens microlens fabricated by standard photolithography and chemically assisted ion beam etching (CAIBE)

(c) Zoom image of (b) (d) Aperture (outer diameter: 300nm; inner diameter: 100nm); Gold has been deposited on the surface and an aperture was made by focused ion beam (FIB).

S47005.OkV 132 6O.OkSE(U)

Fig. 5. SEM image of a 10 µm PMN-PT microlens (left). An aperture (outer diameter: 150 nm; inner diameter: 50nm) was made by focused ion beam (FIB) (right).

3. MEASUREMENT OF OPTICAL THROUGHPUT Although minimizing the size of the NSOM probe tip aperture is a primary factor in achieving high image resolution, a sufficient diameter to provide the desired optical signal output level must be maintained. In particular, for the purpose of recording, optical throughput is very important. Optical throughput is the ratio of the near field and corresponding far

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field photon intensities. It is well known that the throughput of an aperture NSOM probe is drastically decreased by decreasing the size of the aperture. To evaluate the throughput of the fabricated aperture probe we used a measurement setup as shown in Fig. 6. A photodiode is used to sense the near field laser beam. A laser diode of 405 nm wavelength is focused on the probe. The throughput of the prototype PMN-PT probe was somewhat low. A 50 nm diameter aperture of PMN-PT probe shows an approximately 2x10-7 throughput. The throughput result is similar as that of the conventional optical fiber NSOM probe. Finally, Figure 7 shows the prototype near field optical data storage head. The fabricated NSOM aperture array is attached at the end of a PMN-PT cantilever with interdigitated electrode. The interdigitated electrode provides deflection sensing capability required to control the gap between the probe and the media surface.

Optical chopper

BS

Lens Probe Lens Lens Pin hole

Fig. 6. Optical throughput measurement setup: Laser is delivered to the aperture probe and detected by a photodiode. A lock in amplifier and a chopper are used to enhance sensitivity.

TpII

Fig. 7. PMN-PT cantilever with embedded sensor and aperture.

Proc. of SPIE Vol. 6374 63740A-5

4. CONCLUSIONS One of the main goals of this research is to fabricate an aperture NSOM probe made of single-crystal piezoelectric materials (PMN-PT and investigate the performance. We used a bulk sample of PMN-33%PT to produce a free standing single crystal film. Then, we were able to successfully fabricate 10µm PMN-PT micro-lenses with less than 100nm apertures using the photolithography, thermal reflow, dry etiching and focused ion beam techniques. We have conducted an optical throughput measurement test. The throughput result is similar as that of the conventional optical fiber NSOM probe. This may be from several reasons. We expect that the throughput of the PMN-PT probe will be improved by higher surface quality of the microlens. We would need to improve the shape of the microlens to minimize the intensity loss inside the lens.

ACKNOWLEDGEMENTS The authors thank the Ministry of Commerce, Industry and Energy (S. Korea) Grant.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

Y. Mitsuhashi, “Optical storage: Science and technology: Part 1: Regular Papers & Short Notes & Review Papers,” Japanese Journal of Applied Physics, 37(4B), 2079,1998. T.D. Milster, “Near-field optics: a new tool for data storage,” Proceedings of the IEEE, 88(9), 1480, 2000. P.N. Minh and T. Ono, “Nonuniform silicon oxidation and application for the fabrication of aperture for nearfield scanning optical microscopy,” Applied Physics Letters, 75(26), 27, 1999. K.-B. Song, E.-K. Kim, S.-Q Lee, J. Kim And K.-H. Park, “Fabrication of a High-Throughput Cantilever-Style Aperture Tip by the Use of the Bird’s-Beak Effect,” Jpn. J. Appl. Phys. 42 , 4353, 2003. S. E. Park and T. R. Shrout, “Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals,” J. Appl. Phys., 82, 1804, 1997. H. Fu and R. E. Cohen, “Polarization rotation mechanism for ultrahigh electromechanical response in singlecrystal piezoelectrics,” Nature, 403, 281, 2000. S.-F. Liu, S.-E. Park, T. R. Shrout, and L. E. Cross, “Electric field dependence and piezoelectric properties for rhombohedral 0.955Pb(Zn1/3Nb2/3)O3 – 0.045PbTiO3 single crystals,” J. Appl. Phys., 85, 2810, 1999. E. M. Sabolsky, A. R. James, S. Kwon, S. Trolier-McKinstry, and G. L. Messing, “Piezoelectric properties of <001> textured Pb(Mg1/3Nb2/3)O3–PbTiO3 ceramics,” Appl. Phys. Lett., 78, 2551, 2001. Y. Lu, M. Cronin-Golomb, S.-W. Liu, H. Jiang,F.-L. Wang, J. Zhao, S.-Q. Wang, and A.J. Drehman, “Fabrication and optical characterization of Pb(Mg1/3Nb2/3)O3-PbTiO3 planar thin film optical waveguides,” Applied Physics Letters, 72(23), 2927, 1998.

10. M. Levy, R. Vanga, K.S. Moon, H.K. Park, Y.K. Hong, “Single-crystal relaxor ferroelectric piezoactuators with interdigitated electrodes”, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, , 51, 1593, 2004.

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Real-time high-displacement amplified bimorph scanning mirror Paul E. Pattersona, b, Jason M. Zarab a Department of Electrical Engineering and Computer Science, United States Military Academy, West Point NY 10996; b Department of Electrical Engineering and Computer Science, The George Washington University, Washington DC 20052 ABSTRACT This paper provides an overview of recent research in the use of microelectromechanical systems (MEMS) actuators for beam steering applications, including optical coherence tomography (OCT). Prototype scanning devices have been fabricated out of polyimide substrates using conventional integrated circuit technology. The devices utilize piezoelectric bimorphs to mechanically actuate the torsion mirror structure made of polyimide. The material properties of the polyimide allow very large scan angles to be realized in the devices while using low voltages. Prototype devices have demonstrated optical scan angles of over 80 degrees with applied voltages of only 40V. Different device sizes have also been demonstrated with resonant frequencies between 15-60Hz (appropriate for real-time imaging). Analytical models have been developed that predict resonant frequency of the device as well as the angular displacement of the mirror. Further finite element modeling (FEM) has been done using ANSYS. These models closely reflect measured scan angles of the prototype devices. Based upon these models, further refinements can be made to the design to produce specific resonant frequencies for use in a multitude of applications. These models are currently being used to design and fabricate multiple devices on a single wafer with minimal post processing requirements. The ability to fabricate these devices in bulk will reduce their cost and potentially make them disposable to reduce the cost of their use in numerous applications, including patient care when used in biomedical imaging applications. Keywords: Micromirror, Polyimide, Piezoelectric, MEMS 1. INTRODUCTION The field of optical MEMS or MOEMS has seen an explosive growth over the last few years. This growth is expected to continue for the foreseeable future. Emerging Opportunities in Optical MEMS: 2003-2007, a report from the Communications Industry Researchers, Inc. (CIR) states that the growth of MOEMS subsystems will grow from $560 million in 2003 to $1.7 billion in 2007 [1]. Numerous methods have been explored for beam steering applications in the field of MOEMS, and several categories have been developed to classify these micromirrors [2]. A majority of the micromirrors to date have relied on electrostatic actuation. In general, micromirrors that rely on electrostatic actuation require large drive voltages (>50V). Electrostatically actuated micro-mirrors have been fabricated that are capable of achieving rotational angels of 90°with drive voltages of 47V[3]. Other electrostatically actuated micromirrors have demonstrated scans of 21° at 3.6kHz with a driving voltage of 75 V[4]. Recently MEMS flexure lead zirconate titanate (PZT) actuated scanners have been demonstrated which achieve optical angles of up to 40° in static operation and 10° in resonance at 17.4kHz [5]. Micromirrors, which utilize comb-drives for electrostatic actuation, have also been demonstrated. These devices are capable of 8.5° of mechanical deflection at 19.55kHz with an applied voltage of 100V [6]. Similar devices to those described in this paper have also been fabricated out of polyimide and actuated electrostatically. These devices are capable of scanning up to 146° at 50V [7,8]. Most micromirrors utilize silicon hinges that are too stiff to achieve the large scan angles desired in medical imaging systems. The processing required for many of the aforementioned micromirror structures is very specialized and is not a viable means to mass produce such devices for use in medical imaging applications. The micromirrors presented in this paper are prototype scanning devices that have been fabricated out of polyimide substrates using conventional patterning and etch technology and are appropriate for real time imaging.

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740B, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.686383

Proc. of SPIE Vol. 6374 63740B-1

2. METHODOLOGY The micromirror device is comprised of a table (with attached mirror) suspended by two small torsion hinges. These torsion hinges are fixed at one end to the supporting structure of the device. A gold-coated silicon mirror is then attached to the table of the device. Figure 1a is a schematic of a prototype device without a mirror attached. No dimensions are given, as this is a general schematic that depicts the typical layout of any of the devices. Figure 1b is an exploded view of the hinge structure. Initially 6 different prototype designs were fabricated.

(Torsion Hinges)

Hinge Thickness

Table (without mirror attached) Support cutaway

Hinge Width

Table cutaway

Hinge Length

Support Structure

(a)

(b)

Fig. 1. (a) Schematic of polyimide support structure without mirror. (b) Exploded view of the torsion hinge schematic Table 1 details the dimensions of these prototype devices. Four different gold coated silicon mirrors were fabricated for attachment to the six prototype devices (0.875mm, 1mm, 1.5mm, and 2mm). The mirrors are all 400µm thick. Initial testing of the devices revealed that the device best suited for real-time imaging applications (around 30Hz) a device with a large support structure and 135µm hinges with a 1.5mm mirror attached. The remainder of this paper will focus on devices with those dimensions. Table 1. Table of different prototype devices and their dimensions.

Support Structure Size

Table Size (mm)

Hinge Width (µm)

Hinge Thickness (µm)

Hinge Length (µm)

Large Large Large Small Small Small

2 x 2.25 2 x 2.25 2 x 2.25 1 x 1.125 1 x 1.125 1 x 1.125

90 135 180 60 90 120

3 3 3 3 3 3

250 250 250 250 250 250

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Figure 2 is a schematic of the prototype device design selected as the most suitable for use in a real time imaging system. Figure 3 is a picture of an actual prototype device. The entire support structure of the device is made of polyimide. The mirrors are fabricated on a separate wafer of gold-coated single crystal silicon (400µm thick). The mass of the mirror and the dimensions of the hinges can be varied to develop devices with the desired scan deflections and frequency responses for a multitude of real time imaging applications. The mirror pivots about the torsion hinges when the whole structure is subjected to a forced vibration. This forced vibration is generated by a commercially purchased piezoelectric bimorph that is 2mm in width and 25mm in length (piezo.com) and is attached to the base of the device. The support structure of the device has a relatively low resonant frequency (approximately 15-60Hz). This enables us to drive the entire structure at a frequency well below the bimorph resonant frequency of 215Hz. The small tip displacement of the bimorph at low voltages is enough to excite the device when operated at the device’s resonance. The motion it causes in the polyimide structure amplifies the small tip displacement of the bimorph into a large optical scan angle.

(2.25mm) (1.5 mm x1.5 mm)

(Torsion Hinges)

(25 mm)

Gold Coated silicon mirror Polyimide Fig. 2. Schematic of torsion mirror device with a hinge width of 135µm and a mirror that is 1.5mm x 1.5mm Once in motion the mass of the mirror and its moment of inertia cause the hinges to twist. This develops a restoring torque in the hinges. The restoring torque is realized as the bimorph tip displaces in the opposite direction of travel. In a perfect oscillator this motion would continue indefinitely. However, in the case of our device there are numerous factors that cause the oscillating motion of the device to stop rather quickly when no force is applied. Some of the factors that cause the device to stop oscillating are the effect of air damping and the stiffening of the torsion hinges as they twist. Operating the bimorph at the resonant frequency of the support structure allows us to overcome some of these effects. This forced vibration causes the device to behave more like a perfect torsional pendulum or oscillator.

Proc. of SPIE Vol. 6374 63740B-3

(2.25mm)

Polyimide structure

PZT Bimorph (piezo.com)

Fig. 3. Picture of actual torsion mirror device with the same dimensions as those in 2. The mirror and support structures were modeled using one-dimensional beam theory and fundamental vibration mechanics. The resonant frequency of the structure can be predicted using equation 1 [9].

fr =

1 2π

JG l I 2

(1)

Where J is the polar moment of inertia of the hinge, G is the shear modulus of the hinge, I is the moment of inertia of the mirror, and l is the length of the hinge. The torque applied to the hinges causes a twisting motion. This motion is related to an angle in the hinge. The angle at which a hinge twists is the same angle that the mirror attached to the hinge is displaced. The angle of displacement can be predicted using equation 2.

θ=

TL JG

(2)

Where T is the torque applied, L is the length of the torsion hinge, J is the polar moment of inertia of the torsion hinge and G is the shear modulus. The torque is generated by the tip displacement of the piezoelectric bimorph accelerating the mass of the table and mirror. The structures were also modeled and simulated using finite element analysis program (ANSYS, Inc., Canonsburg, PA). These simulations allow us to alter certain dimensions of the device to achieve the optimal resonant frequencies for use in imaging systems prior to manufacturing the devices. Figure 4a shows the ANSYS modal analysis of the device with 135µm wide hinges. Figure 4b shows the model used for the harmonic analysis. Table 2 shows the material properties used to simulate the device.

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b

a

Fig. 4. (a) ANSYS modal animation of the device (b) Device used for ANSYS harmonic analysis of a 135um hinge device with 1.5mm mirror attached. Table 2. Table of key material properties used for ANSYS modeling.

Material

Modulus (GPa)

Density (kg/m3)

Polyimide Silicon PZT

2.5 160 63

1470 2330 7500

Piezoelectric strain coefficient (d31) N/A N/A 1.8e-10 m/V

A harmonic analysis was also done using ANSYS. The results of this analysis can be seen in Figure 5. From the graph it is easy to see that the largest displacements of the mirror occur at approximately 24Hz.

Fig. 5. ANSYS harmonic analysis of a 135um hinge device with 1.5mm mirror attached.

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3. RESULTS

The initial prototype mirror assemblies were fabricated at North Carolina State University in the Biomedical Microsensors Laboratory (BMMSL) using a three-layer process on five-inch silicon wafers. A sacrificial silicon oxide layer was deposited on the wafer prior to processing to release the polyimide structures from the wafer. This sacrificial layer was later etched away using hydrofluoric acid (HF). To form the thin hinge layer, a 3 µm layer of polyimide (PI2723, HD Microsystems, Wilmington, DE) was spun onto the wafer and then patterned. Figures 6a and 6b show the cross section of this process and a top-down view. The thicker supports and tables were made of a 30µm thick patterned polyimide layer (Durimide, Arch Chemicals, Norwalk, CT). See figures 6c and 6d. The mirrors are made of gold plated single crystal silicon in a separate process on a separate wafer. Once the devices were released from the wafer using the HF etching solution, the mirrors were mounted. The mirrors were glued to the polyimide table using a fast drying epoxy. The entire device is then mounted to the bimorph using double stick tape. This was a sufficient bonding method as the mass of the device was very small (less than 3mg). Several different device configurations were fabricated Figure 7 shows several of the devices on a wafer prior to being released. Silicon Wafer 3µm Polyimide 30µm Polyimide Silicon Oxide

Si

a b

Si

c d Fig. 6. (a) Cross-section of mirror support structure with first layer of polyimide. (b) Top down view of first layer of polyimide. (c): Cross-section of second layer of polyimide for mirror support structure. (d) Top-down view of second layer of polyimide for mirror support structure.

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Fig. 7. Picture of devices before being released from the wafer. The optical displacement of the mirror was determined by using a calibrated target with a grid printed on it. This target was placed a known distance from the mirror. A 3mW HeNe laser was reflected off of the mirror and scanned across the target. Displacements were measured by tracing the path of the beam across the calibrated target as the bimorph was driven at frequencies between 0 – 140 Hz and 10 – 100 volts peak to peak. Figure 8 is an image of a scanned HeNe beam on the target. 1cm

Fig. 8. Scanned HeNe beam on target. Mirror is 25 mm from the target. Large support structure with 135µm hinges. Driving voltage was 40Vpp. Resonant frequency was 33Hz. Approximate scan angle is 85o. A device with a 1.5mm mirror attached and 135µm wide hinges has a predicted resonant frequency of 24.2Hz. The modal analysis by ANSYS predicted a resonant frequency of 22.6Hz. The measured resonant frequency varied between 28Hz-33Hz with multiple devices of the same hinge width and mirror size (1.5mm mirror and 135µm wide hinge). The variations between predicted and actual resonance can be attributed to several unknown device characteristics such as the actual piezoelectric coefficient of the bimorph, the actual modulus of the polyimide being used and the damping coefficient of the device. The variation in resonant frequencies can also be explained by variations in the mass of the mirrors attached to the devices due to non-uniform amounts of epoxy being applied. Prototype scanning mirrors have demonstrated optical scan angles up to 97° at frequencies ranging from 15-60 Hz and drive voltages ranging from 15-40 V. Variations of drive voltage and scanning ranges result from modifying the hinge dimensions and the mirror masses of the structures.

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Reliability testing has been conducted on the devices. Multiple devices have been operated for over 1 million cycles with no signs of plastic deformation of the hinges. This would allow for the device to be operated continuously for a 24-hour period without failure of the hinges. This further improves the devices application for real time imaging applications. The structure was also tested in various orientations to ensure that there was minimal if any loss of scan range based upon orientation. Figure 9a and 9b show the device in operation. 1mm

1

(a)

(b)

Fig. 9. (a) Device at rest. (b) Device in motion

4. CONCLUSIONS We have modeled, fabricated, and tested an amplified bimorph scanning mirror for use in numerous imaging applications. The prototype devices have been used in the lateral scanning arm of an optical coherence tomography system. The results from our modeling and testing of the device have shown the devices capable of optical scan angles of up to 97 degrees using applied voltages of 15-40 V at frequencies of 15-60Hz. These figures show that this device is appropriate for real time imaging. We have also modeled the devices using ANSYS. Our ANSYS models accurately allow us to predict changes in the structures behavior based upon changes in the size of the mirror that is used. The results of our various ANSYS models closely predict the measured values we have obtained in the lab. There are several sources of error that explain the discrepancies between our modeled devices and our actual devices. The mass is slightly different in each device due to the unknown quantity of epoxy applied to each device to attach the mirror. There was also some difficulty in modeling the PZT bimorph. The bimorph parameters are unknown since the bimorph was purchased from a third party. These unknown parameters contributed significant error to our dynamic models. A new device fabricated on a single wafer (to include the PZT) will allow us to much more closely model the device since the properties of the PZT being used will be known. Additional sources of error in the models can also be attributed to not knowing the exact damping coefficient. The coefficient used for the ANSYS harmonic analysis was determined using the quality factor of one of the prototype devices. This is a good approximation of the damping factor but most likely contributed to some error in the harmonic analysis. Finally, the bulk properties of the polyimide (specifically, Young’s modulus) were used in the models. In the future, tensile testing will be done to determine the actual modulus of the polyimide being used. We are developing methods to fabricate the entire device on a single silicon wafer using standard processing techniques. This will allow for a more uniform and stable device. These devices can also very easily be tailored to suit specific imaging application needs. Simply changing the size of the mirror or the dimensions of the hinges allows us to choose the resonant frequency of the micro-scanner. Again this has been demonstrated through our ANSYS models and

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in experimental data collected from actual devices. Currently new prototype devices are being fabricated on a single wafer using a nine step process. The process includes the deposition of a thin film PZT sol-gel to act as the actuator for the device. The new fabrication process enables an entire device to be made on the same wafer with no post processing requirements. The small size of the device and the large optical scan angles that it can achieve make this device ideally suited for use in various imaging system configurations, including real-time imaging applications.

REFERENCES 1. “New Opportunities for Optical MEMS are emerging outside of Telecom, says new CIR report - Market Intelligence - Communications Industry Researchers Inc”, Fiber Optics Weekly Update, 7 March 2003. 2. Z F Wang et al “Development of scanning micromirror with discrete steering angles” Journal of Physics: Conference Series 34 410-416 (2006). 3. Y S Yoon et al “A low voltage actuated micromirror with an extra vertical electrode for 90° rotation” J. Micromech. Microeng. 13 922-926 (2003). 4. Zhou, LX, Kahn, JM, Pister, KSJ “Scanning micromirrors fabricated by an SOI/SOI wafer-bonding process” J MICROELECTROMECH S 15 (1): 24-32 FEB 2006 5. Johannes G Smits, Koji Fujimoto, and Vladimir Kleptsyn, “Microelectromechanical flexure PZT actated optical scanner: static and resonance behavior”, J. Micromech. Microeng. 15(2005) 1285-1293. 6. Chang-Hyeon Ji et al "An alectrostatic Scanning Micromirror with Diaphragm Mirror Plate and Diamond Shaped Reinforcement Frame," J. Micromech. Microeng. 16 1033-1039 (2006). 7. J. Zara and S. Smith, “Optical Scanner Using a Micromachine Actuator”, Sensors and Actuators: A: Physical, 102 (1-2), pp. 176-184, 2002. 8. Zara, J., S. Yazdanfar, K. Rao, J. Izatt and S. Smith, “Electrostatic MEMS Actuator Scanning Mirror for Optical Coherence Tomography,” Optics Letters, 28(8), pp. 628-630, 2003. 9. K.E. Petersen, Silicon Torsional Scanning Mirror, IBM Journal of Research and Development 24, 631-637 (1980)

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OPTIMIZATION OF ELECTROSTATIC SIDE-DRIVE MICROMOTOR TORQUE USING A NEW ROTOR-POLE-SHAPING TECHNIQUE Mohamed A. Basha and S. Safavi-Naeini Electrical and Computer Engineering, University of Waterloo, University Ave. West, Waterloo, Ontario, Canada N2L 3G1 ABSTRACT In this paper we report a new design technique to optimize the driving torque of electrostatic side drive micromotors based on a new technique of rotor-poles-shaping. By reshaping the rotor pole from it regular pie shape, we can modify the distributions and directions of electric ﬁeld in the gap between rotor and stator poles. Hence, the tangential electrostatic force component exerted on the rotor poles, responsible for driving torque, is maximized. A 2D parametric ﬁnite element model using ANSYS APDL programming language is developed for the optimization of the rotor pole shape. The ﬁnite element model uses a potential periodic boundary condition to simulate only one micromotor sector. Simulation results show an increase of the driving torque up to 48.75%. Keywords: : Micromotor, rotor-pole shaping, FEM, periodic boundary condition

1. INTRODUCTION The inial design of a functional electrostatic micromotor at Berkeley1 was fabricated using surface micromachining process. The electrostatic excitation of the micromotor is achieved through a sequence of high voltage pulses (100V − 400V ) supplied to diﬀerent stator poles depending on the stator and rotor poles conﬁgurations. Design and fabrication of ultrasonic2, ,3 magnetic4,5 , piezoelectric2 , electrostatic6,7 , and thermally actuated8,9 micromotors have been achieved in the last two decades. The small size of micromotors made micromotors an eﬀective candidate for several emerging applications. Micromotors have been used in precision surgical and medical applications10,11 , optical scanners12,13 , optical switching and routing of wavelengths in optical back bone networks14,15 , high density data storage16 , and constructing a micro-robot.17,18 Electrostatic forces are not signiﬁcant in the macro scale and not comparable to magnetic forces. Resizing down to microscale, electrostatic forces become signiﬁcant, more powerful and capable of driving and actuating micromotors. The use of standardized fabrication processes and the small size-scale are advantages of electrostatic micromotors over other types of micromotors. LIGA19 and DRIE of Silicon-On-Insulator (SOI) wafers12 are the two main fabrication methods for micromotors with a high aspect ration rotor. Surface micromachining with two structural layers20 process was used successfully to fabricate planer micromotors with rotor diameters ranging from 100µm − 1200µm6,7,12 for various applications. In this paper, we present a new design technique to maximize the micromotor driving torque for the same driving voltage and dimensions. The new technique is based on reshaping the rotor-poles to optimize the driving torque of the micromotor. The analysis is based on a 2D ﬁnite element analysis of the electric ﬁeld and electrostatic forces on rotor poles. By reshaping rotor poles, we can modify the direction and distribution of induced electric ﬁeld in the gap between rotor and stator poles and hence the electrostatic force on the rotor poles. As a result, we were able to maximize the driving torque. The organization of the paper is as follows: In section 2, we discuss theoretical design aspects of the micromotors, the new rotor-pole shaping technique, and 2D ﬁnite element analysis of the micromotor. In the following section, we present the simulation results from 2D ﬁnite element analysis of various micromotors.

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740C, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.687698

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g

ro

∆r

spp spw

rpw rpp

Figure 1. A schematic drawing of the micromotor design parameters.

2. DESIGN OF ELECTROSTATIC MICROMOTORS 2.1. Classical Micromtors Design Figure 1 depicts the electrostatic micromotor design parameters. Table 1 lists the deﬁnitions of the design parameters. The ratio of rotor to stator poles is 2 : 3 for maximum average generated torque and minimum torque ripples.21 The aim of micromotor design is to produce enough driving torque to override the friction between rotor bushings and ground. The micromotor driving torque is a result of the application of a potential diﬀerence between rotor and stator poles. The potential diﬀerence will generate an electric ﬁeld in the gap between rotor and stator poles. As a result, an electrostatic force is exerted on the rotor poles causing the rotor to move. The generated torque is usually calculated using the so called stored electrical co-energy concept which is deﬁned as 12 CV 2 , where C and V represent the capacitance and the voltage diﬀerence between the driving electrodes of the rotor and stator poles, respectively. The exerted torque is deﬁned as the rate of change of the stored electrical co-energy with respect to a change in the rotor angle θ (i.e. direction of rotation) and is expressed as: T =

V 2 dC 2 dθ

(1)

An other way of calculating the driving torque in an electrostatic micromotor is using Maxwell stress tensor method to calculate the generated electrostatic force on the rotor poles surfaces from a ﬁnite element analysis. Integrating the electrostatic force over the surface of the pole to ﬁnd the driving torque. Analytical21 and ﬁnite element formulations22 were previously used to analyze and optimize micromotors for optimum driving torque. All previously designed and fabricated micromotor has the regular pie shape for rotor poles with angular width of ”rpw” as shown in Fig. 1. Electrostatic force is inversely proportional to the gap distance g. Hence, we kept the gap parameter, g, at the minimum allowed by the fabrication process and is 2µm in MUMPs process for maximum driving torque. The optimization process is based on sweeping the micromotor parameters, i.e. r, r, rpw,.....etc, and calculating the resultant driving torque. The rotor pole angular width, rpw, is changed while maintaining the regular shape of the rotor poles in almost all designed and fabricated micromotors.

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Table 1. Design parameters of electrostatic micromotors and optimized parameters using analytical formulation.21

P arameter rpp rpw spp spw ro ∇r g Nr Ns

Def inition rotor pole pitch rotor pole width stator pole pitch stator pole width rotor radius rotor tooth height gap between rotor and stator poles number of rotor poles number of stator poles

Optimization 2π/Nr π/Nr 2π/Ns π/Nr speciﬁed by the design requirements ro × rpw lower limit of the fabrication 2Ns /3 3πro /20g

2.2. Rotor Pole Shaping Technique We will study the behavior of the electric ﬁeld in the gap between rotor and stator poles in the micromotor and the generated electrostatic forces on the rotor poles by solving the basic electrostatic equation (∇2 V = 0)using FEM solver with the appropriate boundary conditions. Electric ﬁeld between two conductors is directed from higher to lower potential conductor. The electric ﬁeld is normal to the surface of a conductor and can be derived from the potential distribution in the gap region by the simple gradient formula (E = −∇V ), Fig. 2a. The electrostatic forces, calculated by Maxwell stress tensor, acting on the rotor poles have three components: tangential, radial, and axial force components. The upward axial component will reduce the rotor weight and hence has the eﬀect of reducing the friction between the rotor and substrate by levitating the rotor. This force component is ignored in the 2D ﬁnite element analysis. The tangential force component acting on the rotor poles is responsible for the driving torque. Because of the micromotor symmetry, a radial force component will be balanced by a similar component in the opposite direction on the other side of the rotor. Radial and tangential force components are shown in Fig. 2b. Generated forces on the rotor pole edges facing the stator pole are usually in the radial direction and have no eﬀect on the driving torque. The tangential force component is usually generated on the side edges of the rotor poles. The shape of the rotor poles, control the distribution and direction of the generated electric ﬁeld. By changing the shape of the rotor pole, we can modify the electric ﬁeld direction and distribution to maximize the tangential component of the electrostatic force and hence maximizing the driving torque. The new shape of the rotor poles is a simple trapezoidal shape, Fig. 3. The proposed rotor pole shape is simple and will show the eﬀectiveness of the new design technique. A new design parameter will be introduced

High edge nodes

High edge nodes

High edge nodes

(a)

Low edge nodes

(b)

Figure 2. (a) The electric ﬁeld in the gap region and (b) the electrostatic force generated on the rotor pole in one micromotor sector.

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spp spw

∆θsh

∆r

rpw rpp

Figure 3. A schematic drawing of the micromotor design parameters with the new rotor pole shape.

(θsh ) that speciﬁes the rotor pole shape. Other rotor shapes are possible and will be investigated in future work. By modifying the rotor pole shape from the regular pie shape to the new proposed simple trapezoidal shape, distribution and direction of electric ﬁeld are changed. As a result, the generated electrostatic force in the tangential direction, with respect to rotor poles, in the rotor pole edges will increase. The driving torque will reach an optimum value that corresponds to an optimum shape of the rotor.

2.3. Finite Element Model Finite element analysis (FEA) is used to calculate the potential and electric ﬁeld distributions in the gap between rotor and stator poles. The driving electrostatic force and torque on the rotor poles can then be calculated to compare among diﬀerent rotor pole shapes. The micromotor has an angular symmetry; hence only one sector of the micromotor, Fig. 4, is analyzed. With the rotor to stator poles ratio of 2 : 3 and the number of rotor poles Nr , the micromotor sector angle is θsec = 2rpp = 4π/Nr with a total number of sectors Nsec = Nr /2. In our analysis we exploited the periodicity of the micromotor sectors and considered only one sector for the micromotor in the ﬁnite element analysis, thereby signiﬁcantly minimizing the analysis time especially for large micromotors comprised of many such sectors.The periodic potential boundary conditions are applied between all nodes at one edge of the sector and the corresponding nodes on the other side of the sector and then enforces a potential relationship between both edges of the micromotor sector. The periodic potential boundary conditions (PPBC) between two nodes from low and high edges of the micromotor sector is expressed as V (r, θ)|right edge = V (r, θ + θsec )|lef t edge

(2)

The boundary condition applies between all nodes from the lower and higher edges of the micromotor sector. The uses PPBC accounts for the eﬀect of the potential from other attached sectors at the lower and higher edges of the simulated sector. Rotor and stator poles are modeled as perfect conductors (a very good approximation of polysilicon based on its conductivity). Hence, only air will be meshed with eight-node quadrilateral elements. Figure 5 shows a meshed micromotor sector. The Electric ﬁeld should be continuous in the air region surrounding the micromotor and can not be terminated by a ground plane. Inﬁnite elements from ANSYS (IN F IN 110) are used to terminate the air region and account for extended free space (Fig. 2). In some cases, by calculating the distance the potential decays away and becomes nonsigniﬁcant to the source potential, the zero potential line technique can be used to terminate air region and truncate the electric ﬁeld. However, inﬁnite element technique is more suitable for parametric models and more accurate representation of the ﬁeld continuity. To apply the periodic potential boundary conditions in the ﬁnite element model between nodes of two edges in a micromotor sector, care should be taken when meshing the air region to generate similar elements on both edges of the micromotor sector to have eﬃcient formulation of the periodic potential boundary conditions. Each

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θsec Higher edge

Lower edge

Figure 4. 3D Schematic drawing of the micromotor sector to be used for FEA in ANSYS with the sector angle sec and total number of sectors Nsec = Nr /2.

Infinite Elements

Figure 5. A meshed micromotor sector with eight node element ended with inﬁnite elements to account for the free space extension.

pair of nodes from both edges will have the same radial distance from the center of the micromotor and will be coupled by equation (2)(Fig. 6b). The ﬁnite element model of the electrostatic micromotor is written using ANSYS parametric design language (APDL). This model gives a ﬂexible way to automate the meshing as well as changing the micromotor parameters for rotor and pole-shaped optimization to maximize the driving electrostatic force and torque. Maxwell stress tensor method is used to calculate the electrostatic forces on the rotor pole nodes. The driving torque is calculated by integrating the tangential force component along the perimeter of the rotor poles. Figure 7 shows a 2D simulation of the potential distribution in one micromotor sector under a PPBC. A solution for the whole micromotor can be constructed from replicating the solution of the simulated sector. For veriﬁcation purposes of our 2D ﬁnite element model,a micromotor with physical dimensions from [23] are used in our ﬁnite element model and the calculated driving torques are compared to those obtained in [23]. The micromotor has a rotor radius of 50µm and gap or 1.5µm and 2.5µm. The calculated driving torques for this micromotor are 11.6pN.m and 7.0pN.m for g = 1.5µm and 2.5µm respectively. The driving torques from our 2D ﬁnite element model with the potential periodic boundary condition (PPBC) for the same micromotor

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Left edge nodes PBC

Right edge nodes PBC

(a)The red line shows the nodes on both sides of the (b)The green lines between each nodes couple represent micromotor sector that will be used to specify the the constraint equation for the periodic potential periodic potential boundary conditions. boundary conditions. Figure 6. Element nodes distribution in the meshed micromotor sector.

Figure 7. Potential distribution in the air region of the micromotor sector. Note the potential has the same values at both edges of the sector. The potential did not decay to zero at the end of air region because of the inﬁnite element (INFIN110) termination.

dimensions are 11.63pN.m and 7.02pN.m for g = 1.5µm and 2.5µm respectively. The results show a very good agreement.

3. SIMULATION RESULTS Two micromotors with rotor diameters of 400µm and 800µm and air gap of 2µm will be simulated and optimized for driving torques using the rotor pole shaping techniques. The optimization of the driving torque will be based on changing rotor pole shaping parameter θsh from 0 to rpw/3. The corresponding driving torque for each value of θsh is calculated and compared with the case of regular rotor pole shape (i.e. θsh = 0). Figure 8 shows the driving torque of the ﬁrst micromotor as a function of rotor pole shaping parameter θsh . The curves in the ﬁgure correspond to diﬀerent number of rotor poles. Table 2 lists the optimized dimensions of the micromotor for diﬀerent number of rotor poles. The simulation results show an increase in the driving torque between 30 − 48.75% from the original driving torque with regular rotor pole shape. The second micromotor example has a rotor diameter of 800µm. Table 3, shows the optimized micromotor dimensions for diﬀerent number of rotor poles. The rotor pole is again reshaped to optimize the driving torque of the micromotor. Figure 9 shows the driving torque of the micromotor versus the rotor pole shaping parameter

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θsh . The new driving torque of the optimized micromotor represents an increase of the driving torque of with regular rotor pie shape. Further optimization of the driving torque of the micromotor can be achieved for diﬀerent shapes of the micromotor rotor poles. The proposed shape of the rotor, although simple, proves the concept of rotor pole shaping to increase the driving torque of electrostatic micromotors with the same physical dimensions and driving voltage. Hence, lower driving voltage is required to generate the same driving torque to rotor the same micromotor.

300

280 E

260 ci)

=

0 2 240 0)

= >

0

0.1

0.2

0.3 0.4 0.5 Rotor-pole shaping angle 0sh

0.6

0.7

0.8

Figure 8. Driving torque versus the rotor-pole shaping parameter θsh for diﬀerent number of rotor poles with a gap and rotor diameter of 2µm and 400µm, respectively.

Table 2. The optimized design parameters of electrostatic micromotor for diﬀerent number of rotor poles (Nr ).

P arameters rpp rpw spp spw Optimum θsh Optimized driving torque Increase of driving torque

Design1 2.4o 1.2o 1.6o 1.2o 0.35o 295 pN.m 47.50%

Design2 3.0o 1.5o 2.0o 1.5o 0.312o 299 pN.m 48.75%

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Design3 3.6o 1.8o 2.4o 1.8o 0.45o 289 pN.m 35.0%

Design4 4.0o 2.0o 2.67o 2.0o 0.583o 277 pN.m 30.0%

0 ci)

=

0

01

H 0) = >

0

0.05

0.15 0.2 0.25 Rotor-pole shaping angle 0sh

0.1

0.3

0.35

0.4

Figure 9. Driving torque versus the rotor-pole shaping parameter θsh for diﬀerent number of rotor poles with a gap and rotor diameter of 2µm and 800µm, respectively. Table 3. The optimized design parameters of electrostatic micromotor for diﬀerent number of rotor poles (Nr ).

P arameters rpp rpw spp spw Optimum θsh Optimized driving torque Increase of driving torque

Design1 1.4o 0.72o 0.95o 0.72o 0.18o 1200 pN.m 29.17%

Design2 1.5o 0.75o 1.0o 0.75o 0.155o 1180 pN.m 32.84%

Design3 1.8o 0.9o 1.2o 0.9o 0.255o 1140 pN.m 35.55%

Design4 2.0o 1.0o 1.33o 1.0o 0.255o 1100 pN.m 29.56%

Design4 2.25o 1.125o 1.5o 1.125o 0.234o 1030 pN.m 25.01 %

4. CONCLUSIONS We have presented a new technique for increasing the driving the torque of electrostatic side drive micromotors with rotor to stator poles ratio of 2:3 based on rotor pole shaping. In this technique, rotor poles are reshaped to change the electric ﬁeld in the gap between rotor and stator poles to increase the driving tangential electrostatic forces acting on the rotor. A 2D parametric ﬁnite element model was used to simulate only one micromotor sector using periodic potential boundary conditions. The ﬁnite element simulations show an increase of the driving torque of up to 48.75% for micromotor with rotors of 400µm and 800µm.

ACKNOWLEDGMENTS The authors would like to acknowledge of the support of the Canadian Microelectronic Corporation (CMC).

REFERENCES 1. L.-S. Fan, Y.-C. Tai, and R. Muller, “Ic-processed electrostatic micromotors,” Sensors and Actuators 20, pp. 41–48, November 1989. 2. S. Dong, S. P. Lim, K. H. Lee, J. Zhang, L. C. Lim, , and K. Uchino, “Piezoelectric ultrasonic micromotor with 1.m mm diameter,” IEEE Trans. Ultrasonic, Ferroelectric, And Frequency Control 50, April 2003.

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3. V. J. Snitka and V. Mizariene, “State-of-the-art ultrasonic micromotors and their future applications,” Proceedings of SPIE 4236, pp. 330–338, March 2001. 4. B. Wagner, M. Kreutzer, and W. Benecke, “Permanent magnet micromotors on silicon substrates,” J. Microelectromechanical System 2, March 1993. 5. H. Gucckel, K. J. Skrobis, T. R. Christenson, J. Klein, S. Han, B. Choi, E. G. Lovell, and T. W. Chapman, “Fabrication and testing of the planar magnetic micromotors,” J. Micromech. Microeng. 1, pp. 135–138, 1991. 6. M. Mehregany, P. Nagarkar, S. D. Senturia, and J. H. Lang, “Micromotor fabrication,” IEEE Trans. Electron. Devices 39, pp. 2060–1069, Sept 1992. 7. M. Baltzer, T. Kraus, and E. Obermeier, “Design and fabrication of surface micromachined micromotors with large dimensions.,” J. Micromech. Microeng 7, pp. 196–199, 1997. 8. J. H. Comtois, M. A. Michalicek, , and C. C. Barron, “Electrothermal actuators fabricated in four-level planarized surface micromachined polycrystalline silicon,” Sensors and Actuators A. 70, pp. 23–32, 1998. 9. J.-S. Park, L. L. Chu, A. D. Oliver, and Y. B. Gianchandani, “Bent-beam electrothermal actuators-part ii: Linear and rotarymicroengines,” Journal of Microelectromechanical Systems 10, pp. 255–263, June 2001. 10. W. Xinli, C. Shumei, and C. Shukang, “Advantages of electrostatic micromotor and its application to medical instruments,” Industry Applications Conference 4, pp. 2466–2468, 2002. 11. D. Polla, A. Erdman, D. Peichel, R. Rizq, Y. Gao, and D. Markus, “Precision micromotor for surgery,” 1st Annual International, Conference On Microtechnologies in Medicine and Biology , pp. 180–183, 2000. 12. A. A. Yasseen, J. N. Mitchell, D. A. Smith, and M. Mehregany, “High-aspect-ratio rotary micromotor scanners,” Sensors and Actuators 77, pp. 73–79, 1996. 13. A. A. Yasseen, S. W. Smith, F. L. Merat, and M. Mehregany, “Diﬀraction grating scanners using polysilicon micromotors,” IEEE J. Selected Topics Quantum Elec. 5, p. Jan./Feb., 1999 1999. 14. M. Simard, Z. Khalid, and A. Kirk, “Digital optical space switch based on micromotor grating scanners,” IEEE Photonic Technology Lerr. 18, pp. 313–315, Jan. 2006. 15. J. Klemic, A. Yasseen, J. Mitchell, and D. Smith., “A rotary electrostatic micromirror 1 8 optical switches,” IEEE J. Selected Topics Quantum Elec. 5, pp. 26–32, Jan./Feb. 1999. 16. L. Fan, “Design and fabrication of micromotors for high density data storage,” IEEE Trans. Magnetics 32, May 1996. 17. P. Dario, M. C. Carrozza, C. Stefanini, and S. D’Attanasio, “A mobile microrobot actuated by a new electromagnetic wobble micromotor,” IEEE/ASME Transction on Mechatronics 3, March 1998. 18. H. Lu, J. Zhu, and Y. Guo, “Development of a slot-less tubular linear interior permanent magnet micromotor for robotic applications,” IEEE Transaction on Magnetics 41, Oct. 2005. 19. V. D. Samper, A. J. Sangster, R. L. Reuben, and U. Wallrable, “Multistator liga-fabricated electrostatic wobble motors with integrated synchronous control,” J. Microelectromechanical System 7, June 1998. 20. D. Koester, A. Cowen, R. Mahadevan, M. Stoneﬁeld, and B. Hardy, PolyMUMPs Design Handbook. MEMSCAP, MEMS Business Unit (CORONOS), Research Triangle Park, N.C., USA, revision 9.0 ed., 2001. 21. I. Dufour, E. Sarraute, and A. Abbas, “Optimization of the geometry of electrostatic micromotors using only analytical equations,” J. Micromech. Microeng. 6, pp. 108–111, 1996. 22. T. B. Johansson, M. V. Dessel, R. Belmans, and W. Geysen, “Techniques for ﬁnding the optimum geometry of electrostatic micromotors,” IEEE Trans. Industry Applications 30, pp. 912–919, July/August 1994. 23. T. B. Johansson, M. V. Dessel, R. Belmans, and W. Geysen, “Techniques for ﬁnding the optimum geometry of electrostatic micromotors,” IEEE Trans. Industry Applications 30, pp. 912–919, July/August 1994.

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Liquid crystal optics for laser beam modulation M. Kuriharaa, N. Hashimotob a Citizen Displays Co.,Ltd, Nishi-tokyo-shi, Tokyo, JAPAN b Citizen Watch Co.,Ltd, Tokorozawa-shi,Saitama, JAPAN [email protected] , [email protected] ABSTRACT Liquid crystal devices are one of the suitable devices for wave-front modulation since its extra low operating voltages such as 1~3Vrms. In this paper, we will present about liquid crystal active prisms for laser beam steering and its characteristics to the temperature change which causes an undesired optical power. Further more, we will present a recent result of a variable focus lens using quantized GRIN lens technology. Keywords: Liquid crystal, beam steering, optical power, active prism, GRIN lens

1. INTRODUCTION As recent progress of opt-mechanical engineering, active optics such as active prisms, lenses or phase compensators will play an important role to an optical apparatus. To realize active optics, LCDs are one of the suitable devices since its half-wave voltages are only a few volts and can be driven by COMS ICs. To apply LCDs to optical devices has an old history for example in Kent state or Akita univ1)2). We have demonstrated real-time holography systems using highresolution LCD panels in 19913) and in 2000, we have started math-production of LC active phase compensators for DVD pickups4). Recently, we presented liquid crystal active prisms for laser beam steerings. To steer laser beams, two methods should be considered such as diffraction and refraction. Diffraction can achieve wide angle of steering5), but it is difficult to obtain continuous steering phenomenon. To focus liquid crystal prisms, two methods are exist such as continuous ramp phase modulation6) and stair-case phase modulation7). We have selected the latter case since we can use conventional math-production methods. In this paper, we will present about liquid crystal active prisms for laser beam steering and its characteristics to the temperature change which causes an undesired optical power. Further more, we will present recent results of a variable focus lens using a quantized GRIN lens technology8).

2. LIQUID CRYSTAL WAVE-FRONT MODULATOR9) Figure 1 shows schematic diagram of Liquid crystal devices for laser beam modulations. LC molecules are homogeneous aligned to the ITO coated glass substrates. To assume that ITOs are divided into two areas (upper and lower), while we apply voltages to the lower ITO area, LC molecules will reoriented to Z axis (electric fields). In this case, effective refractive index of lower area should be no and upper area is still ne. So the optical path difference between upper and lower area is (ne-no) d. To control applied voltages precisely, we can control the tilt angle of LC molecules continuously and then effective refractive index neff becomes no
Liquid crystal layer

Input

Output

YA

A

—I-

po1ariza

2

Beam

I

coated glass

Figure 1: Phase modulation using a liquid crystal device

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740D, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.689108

Proc. of SPIE Vol. 6374 63740D-1

3. THE BEAM DEFLECTOR 3.1 The quantized prism using LC cells Figure 2 (a) shows a side view LC cell structure for the beam steering device. Lower ITO layer is patterned like a grating and each line is connected with high-resistive electrode each other as shown in Figure 2(b). Another side of the ITO layer used as the common electrode is a flat pattern. LC molecules are aligned along the rubbing direction of a polyimide surface formed on the ITO layer. When a linear polarized light was illuminated to LC cell, the output light is divided into two optical phenomena, the refraction and the diffraction. Now, we will discuss the refraction phenomenon. When the voltage is applied to the ITO electrode, it can be seen the LC molecules are reoriented according to applied voltages. When the voltage "V1" is larger than the voltage "V2", the distribution of the LC molecular orientation becomes like a schematic in Figure 2(a), and the staircase shaped distribution of phase delay is obtained as shown in Figure 2 (c). This distribution acts as a quantized prism and input polarized light is steered according to applied voltages. Phase delay (D) is defined as a difference of the retardation between applied voltage "V1" and "V2" and the width of a grating electrode is defined as "w". So, the deflection angle can be expressed as θ r = tan -1 (D/w). On the other hand, the diffraction is occurred from the saw-teeth grating distribution indicated the upper area of the dotted line in figure 2 (c). (c)

(a) Glass substrate

θr = tan

Phase delay (V1>V2)

-1

(D/w)

Refracted beam

ITO layer(common)

I

Alignment layer LC layer Alignment layer ITO layer V1

V2

θ

r

Phase delay : D

Position Electrode’s width : w

Glass substrate

Incident polarization

Incident beam

(b)

High resistive electrode V1

V2

Figure 2 : Side view of the LC beam deflector with grating - structure ITO(a), ITO patterns connecting with high-resistive electrode(b) and its phase distribution patterns (c).

Pattern width : w

Pattern pitch

Pattern space

２５℃ ４５℃

Retardation (nm)

3000

3.2 The characteristics of the retardation The retardation versus applied voltage measured using the rotation analyzer method at the wavelength of 650nm is shown in Figure 3. The isotropy of the refractive index of LC molecules become decrease when a temperature becomes high, since the retardation at 45°C is small than the one at 25°C . But the shape of the retardation is similar to each other.

2000

1000

0 0.0

0.5

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Applied voltage (Vrms)

Figure 3 : Phase retardation vs applied voltage.

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4. EXPERIMENTAL RESULTS 4.1 The deflection characteristic of an LC cell We observed the beam spot deflection using CCD camera. F=300mm lens is set before LC cell and CCD camera is set at a focal point of the lens. Figure 4 shows deflected beam profiles. We use a circular aperture of 1.3mmΦ. White line shown in the Figure 4 is the reference line. Applied voltage "V2" is adjusted from 1.2Vrms to 3.0Vrms and "V1" is fixed to 1.2Vrms. We can see from the figure that the beam spot is moving according to the applied voltage "V2". The shape of the beam spot is kept to 2.2Vrms (not photograph), but after that the shape became gently elliptic. The phenomenon is cased by none linearity characteristic of the retardation curve and then cause the optical aberration.

(b)

(a)

(c)

(d)

d

Figure 4: Photographs of the deflected beam spot . V1=1.2Vrms(a), 1.8Vrms(b), 2.4Vrms(c) and 3.0Vrms(d). V2 is fixed to 1.2Vrms. Figure 5 shows the deflection angle versus applied voltage. The measurement data of the deflection angel, θm, is calculated from the following equation θm = tan -1 (f/d), where "f" is the focal distance, "d" is the distance of between white line and the beam spot. The theoretical data of the deflection is calculated from the retardation characteristic, shows in Figure 3, and equation of θr = tan -1 (D/w), "D" is the phase delay between the point "V1" and "V2". We use "w" of 1.5mm. We can see from the figure that measurement data is almost equal to the theoretical data. To achieve larger deflection angle, we have used larger retardation of "D", or narrow effective width of "w". Larger retardation cause is low response time at same LC material.

Deflection angle (mrad)

1.2 1.0 0.8 0.6 0.4

measurement data

0.2

calculated data

0.0 1.0

1.5

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Applied voltage (Vrms)

Figure 5 : Deflected angle vs applied voltage at beam width of 1.5mm.

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4.2 The deflection efficiency To achieve high deflection efficiency, we have to reduce the diffraction efficiency and a dead pattern space. But minimum pattern space is fixed 3µm. We have to find optimized number of the grating lines in the fixed space of "w". Because, if number of the grating lines become large, the diffraction efficiency becomes low, but total dead space becomes large. To estimate these phenomena, we prepare three types of LC cell shown in the Table1. Figure 6 shows the transmittance of the deflected light (a) and the diffracted light (b) versus applied voltage. The transmittance of the deflected light is over 95% both 30 and 64 lines, which present enough high performance. The first order diffracted light is under 1.5%, and second order one is under 0.5%. The characteristic of 50 lines is average between 30 lines and 64 lines (not in figure). These are enough low to influence the deflected light. We use an LC cell of 64 grating lines since the diffracted light is separated wider compare to 30 grating lines. Table 1 : Comparison of three types of grating number using LC cells. Line number Pattern pitch (µm) Pattern space (µm) 64 23.4 3 50 30.0 3 30 50.0 3 100%

(b)

30 lines

Diffraction efficiency

Deflection efficiency

99%

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0.0%

1.0

2.0

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1.0

2.0

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Applied voltage (Vrms)

Applied voltage (Vrms)

Figure 6 : Transmittance ratio of deflected (a) and diffracted light (b),Square is the first order beam and triangle is the second order.

4.3 The influence of LC cell impedance An LC cell require high transmittance and its low fluctuation which cause from thin film structures and refractive index change of LC molecules while driving. We select the optimized ITO layer which has a very thin film structure, so that impedance of the ITO layer is very high compare to conventional LC cells. Usually we can neglect the impedance of the ITO layer since the impedance of the LC layer is extremely high. But, in this case we have to consider the impedance of the ITO layer since the impedance of the LC layer depends on driving frequency. The impedance of ITO is a function of the geometric structure such as pattern length "Lp" and pattern width "wp", we select a shorter length of "Lp" to achieve low impedance. Figure 7 shows the phase distribution pattern of the LC cell under the uniform voltage pattern. Figure 7(a) is the previous case of LC cell structure, and we can see undesirable phase distribution pattern. Figure 7(b) is the case of new structure and an uniform phase distribution pattern is obtained. Length of "Lp" is quarter compare to previous one.

Figure 7 : Photographs of the interference images of LC cells sandwiched between crossed polarizers. (a) the previous case of LC structure; the interference image is non-uniform (b) new structure case; the interference image is uniform. Applied voltage and frequency is 2.0Vrms and 1kHz, respectively.

(a)

(b)

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4.4 Inflation of LC cells under the temperature change To apply LC cell to optical systems, the influence of the temperature change such as the inflation of LC cell sometimes become a problem. When LC cell is heated, the glass substrates start up the inflation of the LC layer which causes optical power (see Figure 8). Optical power is change the focus of the deflective beam and sometimes it become a problem in the focusing systems. To investigate the property of the temperature dependency of the power, we measure various sizes of LC cells for DVD pickups we are now doing mass production. Figure 9 shows the power fluctuation coefficient versus LC cell sizes. Definition of coefficient is ratio between the power change and the temperature change. From the figure, we can see the larger cell size, smaller the influence of the temperature to the power change. Usually, to consider the space effect, it is better to use the cell which the efficient area is equal to cell size. But, to consider temperature effect, we have to use the enough large cell.

LC layer

LC layer

Figure 8 : The inflation of LC cell while heating which came an undesirable optical power.

Power coeffient (wave/°C)

0.0010

0.0008

0.0006

0.0004

0.0002

0.0000 0

5

10

15

20

25

LC cell size (mm)

Figure 9 : Optical power coefficient vs LC cell size at measuring area of 3mmΦ.

5. LC LENS WITH QUANTIZED GRIN The LC active prism can deflect the beam perpendicular to the optical axis. On the other hand, an active focusing lens can adjust the beam on the optical axis. To achieve an active focusing lens, we present LC lens with quantized GRIN structure. Because, we can use a flat structure of LC cell and utilize conventional mass production method. Figure 10 shows ITO patterns and its phase distribution profiles which shows the quantized GRIN lens. In GRIN lens, the phase distribution is defined as N(r) = N0 – a × r2, where "N0" is the refractive index at the optical axis, "a" is a constant.

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This structure is well known as a waveguide. Radius of the L-th number zone (rL) is given as rL = R × ( L / M ) , where "R" is radius of pupil and "M" is the divided number. Figure 11 (a) shows a beam spot image at the focal point when the LC lens acts as a positive focus lens. Figure 11(b) shows a beam spot profile when the LC lens acts as a negative focus lens. Of course, when V1 = V2, the LC device acts as an optical flat. We can change a focal length from -400mm to 400mm at 2.5mm diameter.

N(r) (a)

rL V1

I

(b)

R

V2 Figure 10 : ITO patterns of a quantized LC-GRIN lens and its phase distribution profiles.

Figure 11 : Photographs of the beam spot images of a quantized LC GRIN lens. Positive focus (V1V2) (b).

6. CONCLUSION We have presented liquid crystal active prisms for laser beam steerings. Though it has staircase phase distributions, diffraction noise is quite low. The influence of temperature change which will cause undesired optical power to LC cell has precisely examined. This data present design guide to apply this device to optics without focus correction systems. We have also presented liquid crystal GRIN lens which can apply auto-focus systems. These devices have a simple structure so that we will do math-production using conventional process. Our next project is to achieve higher modulation and also combine with nano-structure technology.

REFERENCES 1)http://www.lci.kent.edu/ 2)http://www.ee.akita-u.ac.jp/~sato-www/ 3)N. Hashimoto and S. Morokawa, Proc. SPIE1461, Practical Holo. V(1991) 4)S. Ohtaki et. al., Jpn. J. Appl. Phys. 38 (1999) 1744 5)Paul F. McManamon, Jianru Shi, Philip J. Bos, Optical Engineering, 44(12), pp, 12804-1(2005) 6)Andrii B. Golovin et. al., Proc. SPIE5741, pp, 146(2005) 7)S. Satoh, N. Hashimoto, Proc. SPIE5003, pp, 138 (2003) 8)M. Kurihara, N. Hashimoto, Proc. of the 31th kougaku Symposium (Japan), pp, 53 (2006) 9)N.Hashimoto et. al , L. Vicari edit. "Optical Applications of Liquid Crystals" IOP publishing. ISBN:0750308575

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Reconfigurable microfluidic chip based on a light-sensitive hydrogel Khaled Al-Aribea, George K. Knopfa, and Amarjeet S. Bassib a

Department of Mechanical & Materials Engineering Department of Chemical & Biochemical Engineering The University of Western Ontario, London, Ontario, Canada, N6A 5B9 b

ABSTRACT Glass is often used as a substrate material for developing microfluidic chips because it is hydrophilic (attracts and holds moisture), chemically inert, stable over time, optically clear, non-porous, and can be fabricated at low cost. However, the size and geometry of the various components, flow channels and fluid reservoirs are all fixed on the substrate material at the time of microfabrication. Recent advances on the development of a light driven microactuator for actively changing the size and geometry of micro features, based on a photo-responsive hydrogel, are described in this paper. Each discrete microactuator in the platform structure is a bi-layered hydrogel that exploits the ionic nature of the pH sensitive polymer blend of polyethylenimine (PEI) and poly(vinyl alcohol) (PVA), and the proton pumping ability of the retinal protein bacteriorhodopsin (bR). When irradiated by a light source with a peak response of 568 nm the bR molecules in the (bR-PVA) layer undergo a complex photocycle that causes protons to be pumped into the adjoining pH sensitive (PEI-PVA) layer. The diffusion of similarly charged ions through the second actuating layer generates electrostatic repulsive and attractive forces which alter the osmotic pressure within the cross-linked polymer network. Depending upon the type of electrostatic forces generated, the pH sensitive hydrogel layer will swell or, alternatively, collapse. The fabrication of the (bR-PVA)-(PEI-PVA) hydrogel microactuator is described and the experimental results from preliminary tests are presented. The application of the light sensitive hydrogels to developing a reconfigurable microchip platform is briefly discussed. Keywords: PVA hydrogel, bacteriorhodopsin, pH sensitivity, smart gels, microfluidics.

1. INTRODUCTION Microfluidic chips are highly integrated devices that permit very small quantities of fluid to be transported and manipulated in a precise manner. Often these devices perform several functions on the same substrate material including fluid transport, directional flow, pumping, sample preparation, separation, mixing, detection, and in situ chemical reactions. Common substrate materials include glass, silicon and polymers. Glass is often used as the substrate and building material because it is hydrophilic (attracts and holds moisture), chemically inert, stable over time, optically clear, non-porous, and low cost. Unfortunately, the design features embedded in a glass or silicon microfluidic chip, Fig. 1, are largely passive elements because the geometry of the various channels, chemical reactors, and fluid reservoirs are all fixed in the material at the time of microfabrication. The most common approach to constructing complex microfluidic systems is to fabricate the individual components separately and then assemble them on the solid substrate or, alternately, insert them in a silicon substrate using photolithography [1,2,3,4]. The process of assembling micro-scale components on the substrate is not a trivial task because the presence of electrostatic and surfaces forces make the component manipulation very difficult [1]. One area of research is to create an active microfluidic substrate that would permit changes and controlled modifications to the chip configuration while performing the analysis. For example, the dynamic control of the microchannel geometry and pathway would enable the analyst to regulate both the volume and amount of time it takes for the fluid to be transported from the reservoir to the mixer or diffusion chamber. Furthermore, microfluidic systems that use light sensitive components would eliminate many of the microfabrication and microassembly problems. Optical driven and controlled microfluidic chips have several advantages over thermal and electrically operated designs. There are no additional electrons introduced to chemical process because the stream of photons from the impinging light source provides both the energy into the system and control signal used to initiate the desired response. Optical systems are free from current losses, resistive heat dissipation, and friction forces that greatly diminish the performance and efficiency of conventional electronic or electro-mechanical systems. The negative effects Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740E, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.686211

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of current leakage and power loss are greatly amplified as design engineers strive for product miniaturization through the exploitation of micro- and nano-scale technologies. Reservoir

Microchannel

Microvalve

(a) Apparatus for conducting microfluidic experiments (Micralyne Microfluidic Toolkit™).

(b) Features of a standard microfluidic chip built on a glass substrate.

Fig. 1 Typical experimental setup and basic design of an off-the-shelf microfluidic chip.

Polymer materials, such as light sensitive hydrogels, represent a suitable alternative to glass or silicon based substrates. Hydrogels are composed of hydrophilic and/or hydrophobic cross-linked polymeric networks with a fluid filling the interstitial spaces of the network. The cross-linking can be conducted physically by forming physical entanglements or chemically by using cross-linking chains that can react permanently with active groups on the monomer chains. Due to their hydrophilic, hydrophobic, and elastic nature these hydrogels are primarily used for drug delivery systems and biomedical instrumentation. Light driven hydrogels have been studied by a number of researchers. Ishihara et al [5] investigated the swelling properties of 2-Hydroxyethyl methacrylate with azobenzene molecules as the side groups. The azobenzene molecule is a UV sensitive molecule that can make a 180° rotation around a carbon double bond. The rotation of the azobenzene group around the carbon double bond induces structural rearrangement. The maximum volume change that was observed with this structural rearrangement was 14% in 6 hours at 25°C [5]. Another approach that utilized the light ionizable molecules to trigger the microgel networks was introduced by Ishikawa and Kitamura [6]. The researchers used polyacrylamide microgels that contain the UV ionizable molecule, triphenylmethane leuco cyanide. When light ionizes these molecule repulsive forces between similarly charged molecules are generated, these forces drive the hydrogel to swell. It was reported that the photo-dissociation of this light sensitive chromophore occurs in less than 60 seconds. The equilibrium time for an 11µm particle is about 1 hour, while for a 180µm particle it takes more than 55 hours [6]. A third approach was exploiting the heating abilities of light to induce swelling or collapse of N-isopropylacrylamide, the ionic hydrogel networks [6]. The N-isopropylacrylamide hydrogel is studied by number of researchers to demonstrate the photo-thermal effect in activating ionic hydrogels. This particular hydrogel has a transition temperature of around 32°C. Suzuki and Tanaka [7] developed a synthesized hydrogel that contained N-isopropylacrylamide as the main constitute and trisodium salt of copper chlorophyllin as a light sensitive chromophore. Discontinuous volume transition was observed around 31.5°C. The diameter of the sample shrank from about 240µm to about 100µm in response to a temperature increase from 25°C to 40°C. Mamada et al [8] investigated the response of a N-isopropylacrylamide gel with the photosensitive molecule bis(4-(dimethylamino)phenyl) (4-~inylphenyl) methylelucocyanide as a side group. Juodkazis et al [9] studied the effect of laser radiation on the temperature responsive hydrogel N-isopropylacrylamide. The experiments confirmed that radiation forces can alter the phase transition process by shifting back the volume transition temperature in the range of 10°C. Sershen et al [10] incorporated gold colloid and gold nanoshells, the strong optical absorption particles in drive the temperature responsive hydrogel poly(N-isopropylacrylamide-co-acrylamide). The gold-colloid nano-composites hydrogel that collapse when illuminated under green light and gold nanoshell hydrogel that collapses in response to near IR light. Both hydrogel composites exhibited fast responses and can reach

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final state in 5s when fabricated in micro scale. Al-Aribe et al [11] presented an alternative technology that exploits the proton pumping abilities of bacteriorhodopsin and the ionic nature of gel networks. The system is driven by an optical effect where the light source is used to drive ionic hydrogels without changing the gel composition or altering the surrounding temperatures. This paper describes how the simple bi-layered (bR-PVA)-(PEI-PVA) hydrogel can be controlled by a directed light source and, if embedded properly within a reconfigurable microchip platform, function as an array of spatially distributed microactuators that permit local displacements and mechanical forces. A reconfigurable microchip platform would permit the constituent components to be repositioned and reshaped as the requirements change. In addition, this capability would also permit active control of the fluid flow through the microchannels by dynamically varying the channel geometry and enable active mixing of microfluids on the chip surface. Two common design features for creating a reconfigurable microchip are illustrated in Fig. 2. The first design involves regulating the speed of flow in the channel whereas the second approach is concerned with the volume of fluid flowing through the channel. The following section describes the fundamental mechanism for microactuation and summarizes fabrication considerations. Some preliminary results of an individual hydrogel actuator are presented in Section 3, and concluding remarks are summarized in Section 4. Separation membrane Fluid flow

Actuating PEI-PVA hydrogel Light sensitive bR-PVA hydrogel Light source (λ, I)

(a) Swelled and deswelled hydrogel micro-actuators used to push fluid along a channel. Actuating PEI-PVA hydrogel Light sensitive bRPVA hydrogel Light source (λ, I) (b) Deswelled and swelled hydrogel micro-actuators used to regulate flow in a channel.

Fig. 2 Illustrations of hydrogel micro-actuators used to reconfigure the flow channel of fluid on a microchip.

2. BI-LAYERED HYDROGEL MICROACTUATOR The bi-layered light sensitive hydrogel is introduced as a micro-device that controls the liquid flow on a reconfigurable microfluidic chip. The first layer of the hydrogel actuator converts a light signal into a pH gradient that induces the second pH layer to generate a physical displacement for performing mechanical work. The photo-responsive polymer contains the retinal protein bacteriorhodopsin (bR) and poly(vinyl alcohol) (PVA). When exposed to the light with a wavelength of 568nm, the bR molecules undergo a photocycle that causes protons to be pumped into the surrounding medium. The diffusion of these similarly charged ions through the adjoining layer fabricated from a blend of (PVA) and a pH sensitive polymer, polyethylenimine (PEI). This second pH sensitive hydrogel layer will either swell or collapse due to the osmotic pressure within the cross-linked polymer network. The photosensitive and pH sensitive layers are described below.

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2.1 Bacteriorhodospsin (bR) Bacteriorhodopsin (bR) is the light-harvesting protein naturally found in the plasma membrane of Halobacterium salinarium [12,13]. Arrays of bacteriorhodopsin protein are arranged in the form of a hexagonal two-dimensional crystalline lattice, making purple colored membrane (PM) fragments. The function of a bR molecule is to convert light into chemical energy by transporting protons from the cytoplasm side into the cell exterior. Each bR molecule consists of 248 amino acid residues arranged in seven α-helices. PM exhibits good stabilities against time for several years, and against temperature at 80°C as a wet, and up to 140°C, when it is used dried. The bR molecules are stable over a wide range of pH values from 0 to 12, in the presence of high ionic concentrations (up to 3 M NaCI) [13]. The geometrical distribution of the bR molecules with lipid in the PM fragments provides bR array high level of chemical and thermal stability; making is ideally suited for application within artificial devices, even in micro and nano scales applications. The PM is a thin irregular shaped membrane, with diameter in the range of 0.5µm, and thickness of about 5nm. Each bR protein is centered with retinal bounded between the amino acid membrane helices. The retinal is the chromophor that triggers the protein’s photo-cycle, inducing a very precise and compatible series of dependent photoelectro-chemical transitions, called intermediates, Fig. 3. The photo-cycle intermediates start when, irradiating the oriented protein with visible light in the range of 400-600nm, and with optimum around 568nm [14, 15]. When the retinal is hit by a photon, the protein goes conformational changes from all-trans to 13-cis followed by four spectral intermediates (L-M-N-O), inducing proton transport from the cytoplasmic side to the exterior side before it returns back to its ground state take place. These photo-induced cyclic intermediates physically are activation, proton dissociation, proton translocation, proton association, and relaxation [16]. During these primary deformations, the proton transport in this protein is performed with small movements of groups of atoms by 1Aº or less, in less than 16ms [15].

5 bR570 0640

1LS

5mS((

\

560

5

11(590

4'

550

ts

Fig. 3 Schematic representing the basic photocycle of bR in the bulk aqueous phase where the proton transfer starts with the release of a proton during the L→M transition and end with a proton uptake during the M→N transition.

2.2 (bR-PVA) photosensitive layer The two photosensitive layers are comprised of bio-proton pump and a neutral polymer network. The proton pump is created by the bR molecules embedded in the neutral polymer networks poly(vinyl alcohol) (PVA). PVA is a stable polymer that has a relatively simple chemical structure with a hydroxyl pendent group [17,18]. Consequently, the polymer has minimal effect on the protein orientation. The bR-PVA hydrogel layers are fabricated by freezing and thawing a mixture of aqueous PVA solution and bR suspension. The role of the freeze-thaw process is to create the physical polymerization of the mixture by entangling the PVA polymer chains without having chemical or thermal reactions that might cause overheating and, therefore, damage to the polymer fibers. The entangled PVA polymer networks hold the bR protein molecule, in the oriented positions in the interstitial spaces of the network. The number of the freeze-thaw cycles used during fabrication influences the tightness of the resultant networks.

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Upon irradiation by visible light, the bR-PVA uses photons to induce the flow of hydrogen ions. The transported hydrogen ions diffuse through the gel causing a pH gradient across the interface between the bR-PVA layer and the second hydrogel layer Fig. 4. In response this causes an osmotic pressure difference. The generated osmotic pressure difference causes the protons to diffuse into the pH responsive layer. The pH differences causes the interior layer to undergo mechanical deformation and, thereby, microactuation. Forces generated by expanding pH sensitive hydrogel Actuating PEI-PVA hydrogel

Hydrogen protons bR purple membrane fragment

Light sensitive bR-PVA hydrogel (a) Before exposure to light.

Light (λ, I) Light source (λ, I) (b) After bR layer is exposed to light.

(c) Mechanism at interface between the two layers.

Fig.4 Illustration showing the transfer of hydrogen ions across the interface and resulting swelling phenomenon.

2.3 (PEI-PVA) pH sensitive layer The actuating mechanism, or shell, is a second hydrogel layer that responds to the changes in pH caused by the diffusion of ions released from the first photosensitive bR-PVA layer. The hydrogel layer is a blend containing the ionic polymer polyethylenimine (PEI) and the neutral backbone polymer PVA, cross linked by the freeze-thawing fabrication process. In this layer the diffused ions change the ion concentration, which shifts the point of equilibrium and thereby induces the PVA hydrogel to enlarge or swell. The swelling phenomenon is an ionic driven phenomenon. The co-polymer PEI was utilized in this design because it is a highly positive charged polymer that forms a positive charged hydrogel network. The functional role of the PVA in the blend is to enhance the mechanical properties of the microactuator. PVA is a suitable backbone for the pH responsive polymer PEI because of its rubbery and elastic nature. When hydrogen ions are released from the bR-PVA layer and diffused into the pH sensitive PEI-PVA layer, repulsive forces between similar charges are generated. The generated repulsive forces drive the network polymers to move far away from each other. The polymer movement is determined by the interaction of the osmotic pressure forces, the network's stored elastic forces, and the ionic attractive and repulsive forces. The balance between these forces will eventually bring the actuator into the equilibrated swollen phase. 2.4 Actuating mechanism Since the bR-PVA hydrogel layer transports protons from the cytoplasmic side to extracellular side of the protein, the bR-PVA gel layer is assembled such that the extracellular side of each bR-PVA layer is in direct contact with the pH sensitive layer. As there is osmotic pressure difference between points in continuous medium (gel networks, and surrounding fluid), protons will continue diffusion approaching zero osmotic pressure difference. Once the gel gets zero osmotic pressure difference in all axes local deformations (swelling, collapsing) vanish. Deformation mechanics is controlled by controlling the dynamics of the osmotic pressure difference, which is generated by the pH gradient across the actuator structure.

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2.5 Fabrication considerations The fabrication process consists of three sequenced stages: immobilizing the bR into the PVA gel; fabrication of the pH sensitive gel; and assembly of the bR-gel with the pH sensitive layer. The critical factor for fabrication is the formation and characterization of the cross-linkers used in the gel networks. The bi-layered hydrogel requires the physical crosslinking of the contributing polymers in order to exhibit better mechanical properties than either chemically or optically cross-linked gels [18]. This method exploits the advantages of the small relative movements of the polymer chains during the transition between frozen and thaw states. The quantity of heat that is either gained or released from the system is accompanied by mechanical work that is performed by the network or delivered to the network. The performed mechanical work is observed as displacements of the polymers chains. The functional performance of the gel structure is directly affected by a number of factors that can be controlled during the fabrication. The pH of the bR-PVA gel should be maintained around 7, and it should not go below the isoelectric point. The isoelectric point is the pH at which the protein has no net electrical charge. Orientation and alignment of proteins at this neutral point can not be achieved with the available techniques. Extraction of the bR protein from the Halobacterium salinarium can be performed by the most common method [12,19]. Orientation of the extracted bRprotein can be achieved by applying an electric field of 30V/cm [11]. Furthermore, the number of freeze-thaw cycles directly influences the tightness and pore size of the gel networks and, therefore, the response time of the system [18]. The more freeze-thaw cycles, the longer the bR protein will remain in its oriented position. Unfortunately, this also slows down the system response and reduces the magnitude of any geometrical changes. For these reasons it is important to keep the number of the freeze-thaw cycles for the bR-PVA at the highest possible number while those for the pH sensitive PEI-PVA sensitive layer to the lowest number. As well, increasing the number and duration of the cycles for the bR-PVA gel causes significant amount of water to evaporate and, consequently, negatively effecting the orientation of the bR protein. The concentration of the polymer in the photosensitive layer must be carefully determined to the protein molecules can be oriented and tighten. However, the greater the concentration of PVA the more opaque the hydrogel blend will become and the amount of light reaching deeper bR molecules will be reduced. Therefore, it is important to correlate the gel thickness to the appropriate concentrations of bR and PVA. The ionic strength of the gel filled solution is an important factor for the pH sensitive (PEI-PVA) network performance. Although low ionic strength solutions will give large volume changes, it is necessary to load the bR-PVA gel with ionic solution such as 0.15 M KCL [16] to work as a source of protons. This solution should be kept around pH 7. In this sense determination of the working point of the ionic strength, where the bR-PVA and the pH sensitive layers can work both gets the gel into the functioning point. All fabrication stages are recommended to be carried out away from intensive light so that the system bR molecules are kept inactivated along the fabrication processes.

3. RESULTS AND DISCUSSION The photosensitive bR-PVA layer created for the experiments was prepared using an aqueous solution containing 0.1 ml of 4% PVA and 0.1 ml of 18 mg/ml bR. The PVA solution was obtained by dissolving the PVA monomer at 90˚C for 6 hrs, then cooling it down to room temperature. The bR protein was extracted from the Halobacterium salinarium by the most common method [12,20]. The extracted bR protein was purified from the contaminating ions until it assumed low conductivity, less than 5µS/cm. The purified protein was mixed with the PVA aqueous solution and put between two electric field electrodes of 20V/cm. The negative electrode was in contact with the bR-PVA blend to attract the cytoplasm side of the protein. With this orientation, the direction of the light source beam can be provided perpendicular to the negative electrode, from the cytoplasm surface to the extracellular surface. The mixture was cooled to -20˚C. After about 40 min, the sample solidified. At this point the electric field was discontinued. The first freezing cycle was 12 hr at -20˚C and 2 hrs at 23˚C. The sample was treated with two other freeze/thawing cycles, each cycle consisted of 4 hrs freezing and 2 hrs thawing. The PEI-PVA actuating layer contained a blend of 0.4 ml 4% PVA aqueous solution and 0.025 ml of PEI 50% aqueous solution. Both polymers were purchased from Sigma-Aldrich Chemicals Co. This blend was poured on the top of the bR-PVA making the two layer structure. The combined layers were put into a cooler at -20˚C for 12 hrs and at 23˚C for

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4 hrs; then exposed to two other cycles of 4 hrs freezing and 2 hrs thawing. The electric field was connected at the end of each thaw cycle for about 30 min and disconnected once the sample froze. The functional performance of the proposed photosensitive (bR-PVA)-(PEI-PVA) hydrogel structure was evaluated by observing the swelling and deswelling (shrinking) characteristics under long-term constant illumination. A 500 mW and 514 nm light source was used to perform the experiments. The volume change of the original 625mm3 actuating gel, Fig. 5, was experimentally determined by measuring weight and monitoring the pH level. Measurements of weight and pH were taken at over a 17 hour period. The preliminary measurements are summarized Fig. 6. The observations confirm that the volume of the bi-layer photosensitive hydrogel structure will expand to more than 3.2% over a 2.5 hour exposure period. However the test data indicates that long-term exposure to the light source will cause the expanded hydrogel to collapse by more than 28% decrease from its original volume. The experimental observations also confirmed that the diffusion of the released ions from the light activated bR molecules caused a measurable change in pH, and that the pH change in the actuating PEI-PVA hydrogel triggered the volume expansion and contraction.

Swelled PEI-PVA actuator

Photosensitive bR-PVA hydrogel

Fig. 5 Photographs of a "swelled" microactuator prototype.

The changes in mass, pH and % volume over a 7.5 hr period are graphically shown in Fig. 6. The data suggests that two different stages occur in the hydrogel response. The initial pH of the gel was 6.4. When the bR-PVA layer was exposed to the light source for up to 2.5 hours the PEI-PVA actuating layer swelled resulting in a 3.2% volume change. At the same time the pH level of this gel decreased to 5.7. The second stage in the response occurred when the pH of the actuating hydrogel fell below the threshold around 5.5. At this point the volume of the original hydrogel started to collapse resulting in a maximum shrinkage of 28.69% at 18 hrs. During the period of continuous shrinkage the pH of the outer medium increased to a value near the neutral point of 7. It was also observed that the change in outer medium pH was delayed with respect to the changes in actuator volume. This suggests that the pH first changes inside the crosslinked networks of the actuating layer because of proton transfer from the bR protein molecules, and then these protons transfer into the outer medium. It is important to note that during microfluidic operation the wavelength, intensity, and duration of light exposure are all control variables. The objective of these initial experiments is to demonstrate the ability of the (bR-PVA)-(PEI-PVA) hydrogel device to generate sufficient ions to cause a significant change in pH and thereby a measurable increase/decrease in the actuating hydrogel layer. The response time of the actuator dynamics is also a critical design parameter. The current micro-actuator prototype is 625 mm3 and requires over 2.5 hours to fully expand. One of the fastest pH sensitive hydrogels reported in the literature is the p(HEMA-DMAEMA) and it has been used successfully in a number of microfluidic systems and drug release applications [3,20]. However, the 375 mm3 p(HEMA-DMAEMA) hydrogel test sample took more than 41 hrs to respond [20]. It is likely that the current (bR-PVA)-(PEI-PVA) hydrogel structure will respond quicker once the physical scale of the device is significantly reduced for specific microchannel configurations.

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1

Weight (g)/ Change in pH

Change in pH

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% Change in Volume

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1

2

3

4

5

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Time (hrs)

-5

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(b) Percentage change in volume of the specimen over time. Fig. 6 Experimental observations of the (bR-PVA)-(PEI-PVA) hydrogel microactuator over a 7.5 hr time period.

The experimental results indicate that the design of the bi-layer hydrogel structure (Fig. 4) can function as a discrete microactuator. In this context, individual hydrogels can be incorporated into an array of discrete actuators that form a reconfigurable microchip platform as illustrated in Fig. 7a. Each microactuator acts as a small piston that deforms the outer surface of the platform. A variety of fabrication technologies may be used to create the necessary holes and cavities, and deposit the hydrogel material into the substrate. The basic design consists of a highly transparent glass for maximum transmission of light to the (bR-PVA) gels, a semi-rigid substrate that holds the hydrogels in place and constrains the (PEI-PVA) gel motion to only one direction. In addition, each hydrogel actuator is surrounded by a liquid reservoir with a porous separation barrier. The cylindrical holes with the hydrogel inserts are covered by a flexible nonporous membrane that separates the hydrogel liquid from the fluid being transported on the surface of the microchip. The flexible membrane must be molded such that disc shaped protrusions (ie. bosses) rest over the hole entrance (Fig. 7b). When the bR-PVA is exposed to the directed light it causes the actuating PEI-PVA to swell and push the disc insert to create local displacement. The discrete array design enables local geometric changes to occur on the surface.

4. CONCLUSIONS The proposed (bR-PVA)-(PEI-PVA) microactuator is constructed from two adjoining hydrogel layers. The first layer is photosensitive (bR-PVA) hydrogel that generates hydrogen ions in response to directed light exposure. The diffusion of the ions across the interface generates a pH gradient that influences the cross-linked monomer networks in the actuating layer. The pH sensitive (PEI-PVA) hydrogel expands or contracts due to the repulsive or attractive forces produced.

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Preliminary tests demonstrate that this bi-layered hydrogel structure will respond to light. Although the response appears slow, it is comparable to other light-responsive hydrogels described in the literature. Under constant illumination the prototype showed an expansion of 3.2% and a contraction of 28.7% volume change. The mass of the sample increased and decreased respectively. Evidence also demonstrated that the pH changed during this process. Future studies will investigate the range of control of the fabrication factors and the impact of that on the system response. Effect of the system geometry on its response will be studied and investigate the effect of different polymer ratios on the mechanical properties. In addition, studies are needed to determine whether a smaller prototype will respond faster. As well, tests need to be conducted on depositing the (bR-PVA)-(PEI-PVA) devices on a variety of patterned arrays. Issues to be examined include whether the hydrogel forms a suitable seal and how best to activate the micro-device with a directed light source. Flexible separation membrane with cylindrical inserts Insertion of deswelled hydro gels Substrate with holes

Transparent glass

(a) Construction of a reconfigurable microchip platform. Flexible membrane

Displacement

(PEI-PVA) layer Liquid reservoir with porous enclosure (bR-PVA) layer Glass Light source (λ, I) (b) Behaviour of an individual (bR-PVA)-(PEI-PVA) microactuator. Fig. 7 Simplified drawings of a reconfigurable microchip platform and an individual microactuator.

ACKNOWLEDGMENT This work has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). The authors also wish to acknowledge the academic scholarship provided to K. Al-Aribe from the Higher Institute of Electrical and Electronic Technology (Libyan Cultural Section).

REFERENCES 1.

Beebe, D., Moore, J., Yu, Q., Liu, R., Karft, M., Jo, B., Devadoss, C. (2000). Microfluidic tectonics: A comprehensive construction plate form for microfluidic systems. Proceedings of the National Academy of the Sciences of the United States of America 79: 13488-13493.

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2. 3. 4. 5. 6.

7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

Liu, R., Yu, Q., Beebe, D. (2002). Fabrication and characterization of hydrogel-based microvalves. Journal of Microelectromechanical Systems 11(1): 45-5. Beebe, D., Moore, J., Bauer, J., Yu, Q., Liu, R., Devadoss, C., Jo, B. (2000). Functional hydrogel structures for autonomous flow control inside microfluidic channels.” Nature 404(6): 588-590. Luo, Q., Mutlu, S., Gianchandani, Y., Svec, F., Frechet, J. (2003). Monolithic valves for microfluidic chip based on thrmoresponsive polymer gels. Electrophoresis, 24:3694-3702. Ishihara, K., Hamada, N., Kato, S., Isao (1984). Photoinduced swelling control of amphiphilic azoaromatic polymer membrane. Journal of Polymer Science, 22: 121-128. Ishikawa, M., Kitamura, N. (1994). Photoinduced volume change of polyacrylamide microgels; micrometer size effects and kinetic analysis. Microchemistry, Spectroscopy and Chemistry in Small Domains, edited by H. Masuhara, Elsevier, 373-386. Suzuki, A., Tanaka, T. (1990). Phase transition in polymer gels induced by visible light. Nature 346: 345-347. Mamada, A., Tanaka,T., Kungwatchakun, D., Irie,M. (1990). Photoinduced phase transition gels. Macromolecules. 23:1517-1519. Juodkazis, S., Mukal, N., Wakakl, R., Yamaguchi, A., Matsuo, S., Misawa, H. (2000). Reversible phase transition gels induced by radiation forces. Nature. 408:178-181. Sershen, S., Mensing, G., Ng, M., Halas, N., Beebe, D., West, J. (2005). Independent optical control of microfluidic valves formed from optomechanically responsive nanocomposite hydrogels. Advanced Materials. 17: 1366-1368. Al-Aribe, K., Knopf, G.K., Bassi, A.S. (2006). Photo-responsive hydrogel for controlling flow on a microfluidic chip. Proc. of SPIE Vol. 6343 pp. 63432R-1-9. Oesterhelt, D., Stoeckenius, W. (1971). Rhodopsin-like protein from the purple membrane of Halbacterium. Nature. 233(39):149-152. Hampp, N. (2000). Bacteriorhodopsin as a photochromic retinal protein for optical memories. Chem. Rev. 100:17551776. Lanyi, J. (2004). Bacteriorhodopsin. Annu. Rev. Physiol. 66: 665-688. Kuhlbrandt, W. (2000). Bacteriorhodopsin – the movie. Nature. 406:569-570. Eroglu, I., Aydemir, A., Turker, L., Yucel, M. (1994). Photoresponse of bacteriorhodopson immobilized in polyacrylamide gel membranes. Journal of Membrane Science. 86:171-179. Peppas, N.A., Huang, Y., Torres-Lugo,M., Ward, J.H., Zhang, J. (2000). Physicochemical foundations and structural design of hydrogels in medicine and biology. Annu. Rev. Biomed. Eng. 2: 9-29. Hassan, C.M., Peppas, N.A. (2000). Structure and applications of poly(vinyl alcohol) hydrogels produced by conventional crosslinking or by freezing/thawing methods. Advances in Polymer Science. 153: 37-65. Saneipoor, P. (2003). Investigation of the Growth and Bacteriorhodopsin (bR) Production by the Archaea Halobacterium Salinarium. MESc Thesis, The University of Western Ontario. Brahim, S., Narinesingh, D., Guissepi-Elie, A. (2003). Release characteristics of novel pH-sensitivity p(HEMADMAEMA) hydrogel containing 3-(trimethoxy-silyl) propyl methacrylate. Biomolecules 4:1224-1231.

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Low-Cost Deformable Mirror for Laser Focusing W. Gregera, T. Hösela, T. Fellnerb, A. Schotha, C. Muellera, J. Wildeb, H. Reineckea, a Laboratory of Process Technology b Laboratory of Assembly and Packaging Technology University of Freiburg, IMTEK - Department of Microsystems Engineering Georges-Koehler-Allee 103, 79110 Freiburg, Germany, Email: [email protected] ABSTRACT This paper presents a new concept of low degree-of-freedom deformable mirrors. The application of the mirror is the focusing of a laser beam, featuring a variable focal length. The deformation shape, which is in this case a circular parabolic and an elliptical parabolic respectively, is achieved by a local variation of the mirror’s thickness. The paper explains the analytical treating of the mirror’s thickness distribution as well as an iterative approximation procedure using FEM simulation. The mirrors were fabricated using hot embossing and injection molding technology. The molds required are made from steel whereas the structuring is done by conventional milling. The fabricated mirrors were coated with a reflective gold layer. For deformation measurements a functional demonstrator consisting of the coated mirror, assembly plates and an electromagnetic actuator was produced. The deformation of the mirror was measured using a 3D coordinate measuring machine. The optical function was characterized by a CCD laser measurement setup. Deviation between the measured and the optimal deformation function was sufficiently small. The spot size of the focused laser beam was up to 470 µm whereas the focal length could be varied in a range of 250 mm to 1000 mm. Due to the use of polymeric material, the long time behavior in respect of creep was researched using FEM simulations as well as endurance tests. Keywords: deformable mirror, adaptive, variable focal length, polymer, laser focusing

1. INTRODUCTION Deformable mirrors are being used in a broad range of applications. Some application examples of high degree-offreedom mirrors are the correction of blurred wave fronts for ground-based telescopes [1] and the wave front correction of laser beams [2,3]. These mirrors usually require expensive actuator arrays and closed loop control systems for proper deformation of the mirror. In addition to the applications mentioned above, there are many others like spherical correction [4], focusing [5], or beam shaping. Here, low degree-of-freedom mirrors are much more suitable than high degree-of-freedom mirrors, because these types of mirrors are mostly cheaper and don’t need a complex control-loop system. In this paper we present a new approach for low degree-of-freedom deformable mirrors considering a laser-focusing mirror with a variable focal length as an example. Due to its application - the focusing of a laser beam - the mirror’s surface must keep a parabolic shape for all focal lengths. This is achieved by a local variation of the mirror’s section thickness. In order to keep costs low, the mirrors are fabricated in polymer.

2. THEORY For the special case of an angle of incidence of 0° the mirror’s surface must remain a parabolic shape, which can be described by the following equation:

O(r) =

1 2 r 4f

(1)

where r is the radial distance to the mirror’s centre and f is the focal length. For most applications the angle of incidence differs from 0°, therefore the surface shape is not circular symmetric. Himmer and Dickensheets have demonstrated that Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740F, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.685206

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the ideal surface function for an angle of incidence higher than 0° can be found by transforming the circular symmetric parabolic [6]. However, this surface function has only single axis symmetry. Using a centre-coupled actuator, a two-axissymmetry with origin in the center is needed. A possible solution is an elliptical parabolic which is given by:

O(x, y) = ax 2 + by 2

(2)

where a and b is depending on the focal length f and the angle of incidence α:

a=

1 1 ; b= cos α 4 f cos α 4f

(3)

Figure 1 shows physical optics propagation (POP) intensity simulations of a focussed laser beam using the transformed parabolic (left) and the elliptical parabolic surface function (right) with a focal length of 200 mm and an angle of incidence of 45°. The elliptical parabolic surface function leads to small aberrations of the spot size, called coma, resulting of the asymmetric shape of the mirror’s surface. However, regarding the application of laser focussing, the elliptical parabolic surface function is still suitable. 8761.73

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989 93

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Fig. 1. POP intensity simulations using the transformed parabolic (left) and the elliptical parabolic (right). The focal length is 200 mm and the laser diameter is 10 mm. The laser total power is 1 W. The irradiance chart is denoted in Watt/mm2. The deformation of the circular mirror is given by the plate theory [7]. The following differential equation describes the deformation of a simply supported circular plate:

Mr +

dM r r − M t + Qr = 0 dr

(4)

where Mr denotes the bending moment acting along circumferential sections and Mt denotes the bending moment acting along the diametral section and Q denotes the deformation force given by: r

2Qπr = 2π ∫ qr dr

(5)

0

where q is the acting pressure. Defining the surface function as a parabolic (1) and substituting Mr, Mt and Q in (4) leads to: r Erh(r) 2 h ′(r) = − ∫ qrU s[Rc − r] dr 8 f (υ −1) 0

(6)

where E denotes the Young’s modulus, h(r) the plate thickness, υ the Poison’s ratio, Rc the radius of the actuator tightening device and Us[n] a step function which is 1 for values n ≥ 0 and 0 for n < 0 and which is needed to apply a

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center limited loading. Defining the boundary plate thickness h(r=R) = 0 gives the following solution for the differential equation: 1

⎛ ⎛ ⎛ r ⎞⎞⎞⎞ 3 2 fq(1 − υ ) ⎛ 2 ⎜⎜ r + U s[r − Rc ]⎜ Rc 2 − r 2 + 2Rc 2 log e ⎜ ⎟⎟⎟⎟⎟⎟ h ( r) = 3 3⎜⎜C1 + E ⎝ Rc ⎠⎠⎠⎠ ⎝ ⎝ ⎝ C1 =

⎛ R 2 fq(υ − 1) ⎛⎜ 2 Rc + 2 Rc 2 log e ⎜⎜ ⎜ E ⎝ Rc ⎝

⎞⎞ ⎟⎟ ⎟ ⎟ ⎠⎠

(7)

(8)

Figure 2 shows the calculated thickness distribution of a simple supported center actuated mirror with a Poisson’s ratio of 0.417, an actuator force of 1 N, a focal length of 100 mm, an actuator tightening device radius of 0.5 mm and a mirror radius of 10 mm.

Fig 2. Thickness distributions using different Young’s modulus. An increasing Young’s modulus leads to decreasing thickness profile while focal length, Poisson’s ratio and actuator force is constant. The resulting plate thickness at the boundary of zero is not realizable. Furthermore this differential equation only describes a circular symmetric mirror with an angle of incidence of 0°. Another method to determine the plate thickness is the combination of a finite element simulation (FEM) and a thickness optimization tool. The FEM tool simulates the mechanical deformation of the mirror device whereas the optimization tool generates a proper thickness distribution. This is done by calculating the difference between the optimal deformation function and the simulated deformation function using the following relation:

w ( r) ∝

1 h(r) 3

(9)

where w(r) is the deflection at the radius r. Figure 3 shows the functional principle of the automatic design optimization using the combination of a FEM mechanical simulation and the optimization tool “Optimize”. First, there has to be defined the optical target function (in this case a paraboloid), the boundary conditions, including the geometry of the mirror, the material properties, the actuator force and most important the effective aperture. Using a smaller aperture as the mirror’s diameter, will lead to a boundary thickness greater then 0.

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Furthermore, an initial value for the mirror’s thickness has to be defined. Subsequently, an ANSYS Classic macro is automatically generated by “Optimize” and executed by ANSYS. After that, the FEM model is simulated and the deformation results are transferred back to “Optimize.”

Fig. 3. Schematic view of the automatic design optimization, consisting of a closed loop system of an optimization algorithm and a mechanical FEM simulation. “Optimize” plots the current simulated deflection path as well as the target deflection. Using the deviation between the simulated and the target deflection, “Optimize” calculates the new optimized thickness variation. Then, the optimization loop starts again. After about 50 iterations, taking a computing time of about 2 h on a 2.0 GHz Pentium processor, the mean deviation between simulated and target deflection is typically smaller than 300 nm. Figure 4 shows the comparison between the thickness profile calculated using equation 7 and the profile determined by the automatic design optimization.

Fig. 4. Comparison of the iterative and analytical determined thickness profile. In this case, the effective aperture is 14 mm, and the mirror’s diameter is 20 mm. Using the reduced aperture leads to a boundary thickness greater than 200 µm. The thick center part of the iterative solved thickness profile, which serves as an actuator coupling device, is needed for uniformly coupling the actuator force into the mirror. To verify the calculated thickness profile, mechanical simulations have been carried out. The FEM model consists of a circular or an elliptical base geometry (depending on the angle of incidence), a strengthening ring in the boundary region (for claming the mirror), and a thick center part. To avoid asymmetric deformation of the FEM model, circularly aligned

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cubic elements, were used. The strengthening ring is constrained to the vertical direction, the thick center part in the lateral direction. To achieve a realistic mechanical simulation, the number of elements in height is at least four layers. Figure 5 shows the deformation and stress results of a mechanical FEM simulation of a thickness optimized mirror model. With regards to the computing time and symmetry conditions, the model only consists of a quarter piece of the whole mirror. The maximum mechanical stress is located at the boundary of the mirror device; however, its value is below the elastic limit.

Fig. 5. Simulated FEM model of an optimized mirror consisting of a thick center part, the actual mirror part and the strengthening ring for clamping the mirror. Using the FEM model above, mechanical simulations with different tractive forces were applied. Figure 6 shows the simulated deformation profiles (legend points) for different tractive forces. The dotted lines represent the corresponding parable fits. The difference between the simulated deformation and the corresponding parable fits is negligible. This means that for every actuator force below the elastic limit the mirror deforms according to the desired circular parabolic and to the elliptic parabolic respectively. The maximum deflection of about 250 µm is equivalent to the minimum focal length of 100 mm (equation 1).

Fig 6. Deflection of the optimized mirror using different tractive forces. The legend points show the simulated deflection path, the solid line shows the corresponding parable fit. Due to the mirror’s application, the focusing unit of a barcode scanner, the dynamic of the adaptive mirror should be at least 60 Hz. The determination of the dynamic behaviour was made by FEM modal analysis. Among the mass and elastic properties of the mirror device also the mass and the mechanical properties of the used solenoid actuator core have to be

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considered. Figure 7 shows the topview of the mirror for the first three modes with the corresponding frequencies using a standard solenoid actuator core made of steel.

220 Hz

455 Hz

5438 Hz

Fig. 7. Topview of the deflected mirror for the first three modes with the corresponding frequencies. The frequency of the first mode is significant smaller than the required dynamic of the adaptive mirror. A cross-section view of the first and the second mode shows convex and concave parabolic shape, respectively.

3. FABRICATION OF THE ADAPTIVE MIRROR In order to minimize costs of the mirrors, polymer technology is used for fabrication. For concept testing and design evaluation, hot embossing technology was used. Furthermore, the injection molding process was evaluated for the fabrication of the adaptive mirror. Both technologies usually use thermoplastic polymers. Requirements of the polymers used regarding the fabrication processes are: good processability with respect to both process technologies, good demoldability, and low shrinkage. Further requirements regarding the application of the deformable mirror are: low temperature dependence of the Young’s modulus, low expansion coefficient, low water absorption, and low creep modulus. Two polymers that fulfill these requirements are Cyclo-olefincopolymer (COC) and Polycarbonate (PC). The embossing mold was fabricated using a conventional five axes milling machine, followed by a post processing polishing step. The mold was made from steel. To optimize the fabrication process with regard to low warpage, a DOE investigation (design of experiments) was made. Only the four process parameters embossing temperature, dwell pressure, dwell and cooling rate have an effect onto the warpage of the fabricated mirror. Following, the hot embossing process will be described more in detail, considering PC as example. After evacuating the embossing machine, the mold and the polymer is heated to the embossing temperature of 175° C. The mold and substrate are pressed together with an embossing force of 5 kN for a process time of typically 10 minutes. Afterwards the sample is cooled down to room temperature. During this period an embossing force of 20 kN is applied to compensate the resulting shrinkage. Subsequently, the machine aerates and opens. In a last step the polymer part is demolded from the embossing tool. The total embossing process time is about 100 minutes. Due to the optimization using DOE, the evenness of the mirror’s surface, a quality index of warpage, could be reduced from 60 µm to 4 µm. For the injection molding process, hot runner technology was used. The important advantage of hot runner systems is that the dwell can be applied for a longer time, compared to the conventional injection molding process. This gives a better control of shrinkage and warpage. In our experiments a manifold hot runner system with two molds was used. The cycle time was about 30 seconds. Our experiments indicate that the mold temperature has the strongest effect on the warpage of the mirror whereas an increasing temperature leads to a decreasing warpage. Prior to optimization, the evenness of the molded mirrors was about 120 µm; afterwards, a value below 10 µm was measured. In a post-processing step, the embossed mirrors were metallized using a standard vapor deposition process. According to the application’s wavelength of 670 nm and 633 nm respectively, the metallization was made from gold. In order to obtain high reflectivity and for a minimum impact onto the mechanical behavior of the mirror, the coating is about 100 nm thick. Figure 6 shows an embossed, uncoated mirror made from PC.

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Fig. 8. Picture of an uncoated, embossed mirror mad from PC.

4. RESULTS AND DISCUSSION For deformation measurements a functional demonstrator was fabricated. This demonstrator consists of the gold-coated mirror device made from PC, assembly plates, and an electromagnetic actuator for deforming the mirror. Applying the maximum power of 3 Watt (supply voltage 12 V), the actuator reaches the maximum tractive force of about 2 N. In order to verify the actual deformation function for different focal lengths, the actuator current was varied between 0 and 200 mA. The deformation of the mirror was measured using a Werth multi-sensor 3D coordinate measuring machine.

Fig. 9. Deflection versus radius using different actuator currents. The solid lines correspond to the measured deflection profile, the dotted lines accords to the corresponding parabola fit). Figure 9 shows the deflection profile for different actuator currents. It can be seen that the measured deflection profile (solid line) and the corresponding parabola curve fits (dotted line) are almost congruent. Furthermore, it can be seen that the thick center part has no effect on the deflection profile. The actuator current of 200 mA corresponds to a focal length of about 150 mm. An actuator current of 220 mA would decrease the focal length to the minimum of 100 mm. The characterization of the optical function was made using a laser measurement setup (figure 10). This setup consists of the functional demonstrator (including the coated mirror device, the actuator and some assembly plates), a HeNe laser source, a beam expander, some apertures, some neutral gray filters and a CCD camera. The beam expander collimates

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the laser beam to a diameter of about 14 mm whereas the neutral gray filters reduce the intensity. The laser beam is focused by the adaptive mirror into the CCD camera. The signal of the CCD camera is analyzed by a personal computer.

Fig. 10. Laser measurement setup, consisting of a HeNe laser source, a beam expander, some apertures, some neutral gray filters, the functional demonstrator and a CCD camera. The angle of incidence of the laser beam to the adaptive mirror is at least 7°. The minimum distance between mirror and camera is about 250 mm. Due to length of the optical setup, a distance larger 1 m is not possible without using tilted mirrors. Figure 11 shows the measured spot size versus the focal length using an adaptive mirror that is designed for an angle of incidence of 0.

Fig. 11. Spot size of the focused laser beam versus the mirror’s focal length. For a focal length of 250 mm, a spot diameter of 470 µm is achieved. At the minimum focal length of 250 mm, the spot diameter is 470 µm, whereas the radius is defined by 1 sigma of the Gaussian beam. With increasing focal length, the spot diameter increases almost linear. At a focal length of 1 m, the spot size is still below 1000 µm. Due to use of a mirror with a rotation-symmetric paraboloid and an angle of incidence larger 0°, the spot diameter of is limited. To find this limit, we have measured the spot size using a rotation-symmetric paraboloid reference mirror with a fixed focal length of 444.5 mm and a surface accuracy of lambda/8. The spot size of

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the reference mirror was about 200 µm. However, further decrease of the spot size could be achieved by the use of a polymer mirror designed for an angle of incidence of 7°. One of the critical properties of polymer is that a loaded polymer part tends to creep. In the case of a constant load, the strain will increase over the time. With regard to the adaptive polymer mirror, the deformation function would change over time, so that the spot size would increase. Furthermore, in the case of strong creeping, the maximum focal length could be limited by self-deflection (the deflection under force of gravity with connected solenoid actuator core). To determine the effect of creep we have applied a variation stress test to five mirrors. The amplitude of the deflection is 250 µm, which corresponds to the minimum focal length of 100 mm. The variation frequency of the sine signal was 3 Hertz. The evenness, the self-deflection, the maximum deflection and the spot diameter where measured over time, using the Werth multi-sensor 3D coordinate measuring machine and the laser measurement setup respectively. Figure 12 shows the evenness and self-deflection of the adaptive mirror over the time and variation stress cycles.

Fig. 12. Evenness and self-deflection over time of a variation stressed mirror. Positive values correspond to convex deflection, negative values to concave deflection. At the beginning of the variation stress tests, the surface shows a convex shape. This corresponds to a positive evenness value. With increasing time and load cycles, the deflection also increases in the direction of loading. The surface shape is changing from convex to concave. After 600 hours (25 days) which accords to 6.5·106 loading cycles, the evenness is about 4 µm, and the self-deflection about 11 µm. The corresponding maximum focal length has changed from 5 m to 2.3 m. Figure 13 shows spot diameter and focal length over time of a mirror with an actuator current of 130 mA. The spot diameter starts at about 850 µm, the focal length at about 400 mm. With increasing loading time and cycles, the focal length decreases. The shift of focal length can be explained by increasing strain, which results from the polymer’s creep. The spot diameter also decreases with increasing time. A possible explanation is the relaxation of internal stress, for example induced during the fabrication process, so that the deviation between the optimal and the real deformation function becomes smaller. After 600 hours (25 days) or 6.5·106 loading cycles the spot diameter is only about 580 µm, which is about 35 % smaller compared to initial value before testing. However, with further increase of loading time, an increasing spot diameter is expected. For typical applications a durability of 3 years is required. To determine the long-time behavior of the mirror for different loadings and/or temperatures, we have modeled the polymer’s creep using FEM simulations with nonlinear material models. One of the results of our simulations is that a closed loop system is needed to compensate the shift of focal length based on polymer’s creep. Furthermore, the change of the deformation function is very small, so that the spot diameter will not increase too much.

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Fig. 13. Spot diameter and focal length over time of a deflected mirror with an actuator current of 130 mA.

5. CONCLUSION AND OUTLOOK A new approach for low degree-of-freedom deformable mirrors is presented. The deformation function is achieved by a local thickness variation of the mirror backside. The mirror reported in this paper supports a circular parabolic deformation function with a variable focal length, but other deformation functions are feasible as well. The mirror is fabricated from polymer material using the hot embossing process and the injection molding process. Due to the reduction of the process-based warpage of the mirror’s surface, process optimizations for both fabrication technologies were carried out. For characterization, a functional demonstrator with an electromagnetic actuator was fabricated. The deviation between the theoretical and the obtained deformation is small. The focal length could be varied within a range from 250 mm to 1000 mm. The spot diameter of the focused laser beam was in the range of 470 µm to 1100 µm (depending on the focal length) whereas the diameter of the collimated laser beam was 14 mm. Due to the use of polymers, the long time behavior with respect to creep was also investigated using endurance tests. The change in focal length of mirrors loaded with 6·106 deformation cycles was 1.8 cm. The spot diameter decreases with increasing loading cycles from 850 µm to 580 µm. Furthermore, FEM simulations with non-linear material models using different loading forces or temperatures show that the deformation function of the mirror’s surface does not change much. Future work will focus on the fabrication of a mirror designed for an angle of incidence up to 45°. Also, the mirror will be characterized for focal lengths larger than 1 m.

REFERENCES 1. Goncharov A V, Owner-Petersen M and Andresen T 2002 Adaptive optics schemes for future extremely large telescopes Opt. Eng. 41(5) 1065-72 2. Hooker C J, Divall E J, Lester W J, Mountzouris K, Reason C J and Ross I N 1999 A closed-loop adaptive optical system for laser wavefront control CLF Annual Report 1998/99 199-200 3. Buske I, Heuck H-M, Huve J, Zimer H and Wittrock U 2001 Master-oscillator-power-amplifier laser with adaptive aberration correction Summaries of papers presented at the Conference on Lasers and Electro-Optics. Conference Edition (IEEE Cat. No.02CH37337). Opt. Soc. America 1 291-2

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4. Himmer P A and Dickensheets D L 2005 Spherical aberration correction using a silicon nitride deformable membrane mirror IEEE/LEOS International Conf. on Optical MEMS 2005 185-6 5. Himmer P A and Dickensheets D L 2004 Dynamic behavior of high-speed silicon nitride deformable mirrors SPIEInt. Soc. Opt. Eng. Proc. of Spie - the International Society for Optical Engineering 5348-1 150-9 6. Himmer P A and Dickensheets D L 2003 Off-axis variable focus and aberration control mirrors Proc. of Spie - the International Society for Optical Engineering 4985 296-303 7. Timoshenko S and Woinowsky-Krieger S 1996 Theory Of Plates And Shells McGraw-Hill 51-78

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The simple and practical variable optical attenuator using a piezoelectric sheet containing an optical fiber Seungtaek Kim*, Heuiseok Kang, Sungbok Kang, Won Kim, Hoon Jeong, Youngjune Cho Mechatronics Lab., Korea Institute of Industrial Technology 35-3 Hongchen Ibjang ChenAn ChungNam ROK 330-825 ABSTRACT In this letter, we proposed a new method for a variable optical attenuator (VOA) through controlling a mechanical misalignment between 2 single mode fibers using a piezoelectric sheet. A piezoelectric sheet with 3 electrodes is adopted in our proposed structure. We can change amount of the bend of the PZT sheet by controlling the applied voltage on the inner electrode of the PZT sheet, which causes the optical loss to be dependent on the applied voltage. The numerical analysis about the optical loss related to the various mechanical offsets is also investigated. From our experimental results, the dynamic range of the proposed structure is about from 0 to 56 dB when the applied voltage range is from 0 to 22 V DC. In our previous work using the piezoelectric tube, the dynamic range is about from 0 to 25dB when it is from 0 to 600V DC. The required voltage to get the same attenuation is dramatically reduced. It can make it more practical in the optical communication field. Keywords: Voltage Controlled Optical Attenuator, Variable Optical Attenuator, Fiber Optic Components and Piezoelectric Bender.

1. INTRODUCTION A variable optical attenuator (VOA) is an indispensable component in fiber optic communication system, providing gain equalization in optical amplifiers, signal attenuation for detector saturation protection as well as power management for varying numbers of active channels. Various types of VOAs have been developed such as microelectromechanical systems (MEMS) [1, 2], planar lightwave circuits (PLC) [3], acoustooptics modulators (AOM) [4], or thermooptics modulators (TOM) [5]. Despite these prior technologies, a simpler, more compact and more cost-effective VOA is still necessary for the access network such as AON or PON systems expanded in the near future because it is very important to maintain a constant power at the receiver with each different transmission length for each end-point user. For all of these applications, the VOA should meet certain specifications such as low insertion loss, low polarization dependence loss, low return loss, a fast time response in order to follow rapid network changes, and low electrical consumption but unfortunately, focusing on the feasibility of the VOA using the PZT sheet, we didn’t take all of the required things above mentioned into account. The remaining requirements will be pursued by authors. In this paper, we utilized the electromechanical bend of the piezoelectric sheet. A single PZT sheet containing the 3electrodes, can generate displacements according to the applied voltage. The optical fiber on the PZT sheet also moves along together. To make the PZT sheet bend, the positive voltage is applied only on inner electrode and the ground voltage is on the 2 outer surfaces. The deflection of the sheet changes according to the applied voltage. As a result, it reduces the coupling powers between the fibers. The numerical analysis about the optical loss shows the dependence on mechanical disturbance. We categorized the causes of the optical loss by the deflected tube into 3 fundamental misalignments such as a lateral, a longitudinal and an angular misalignment. We also develop the computer interface GUI, the optical alignment system including the vision system and high voltage DC-DC converter as a PZT driver.

2. METHODOLOGY We look into the possibility that the PZT sheet plays a role as the optical attenuator. Some numerical analysis can make it clear. We investigate the estimation of optical power loss at a joint between 2 single mode fibers. Most loss at the joint Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740G, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.685676

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between 2 fibers result from 3 causes: the longitudinal separation, the angular misalignment, and lateral displacement. After considering the 3 components graphically, the total loss analysis at the connection region will be followed including the above-mentioned 3 fundamental reasons plus reflections compositively. The proposed structure as the VOA will be mentioned in detail, and the experimental setup will be introduced below. Let’s take the 3 optical loss mechanism into account separately. The three fundamental types of misalignments between fibers are a lateral offset, a mechanical gap, and an angular mismatch. Firstly, lateral displacement results when the axes of the two fibers are separated by a distance d like Fig. 1. Core

Cladding

d

Fig. 1 Conceptual view of lateral misalignment S

Fig. 2 Conceptual view of longitudinal misalignment Secondly, longitudinal separation occurs when the fibers have the same axis but have a gap s between their end faces like Fig. 3.

Fig. 3 Conceptual view of angular misalignment Thirdly, angular misalignment results when the two axes forms an angle so that the fiber end faces are no longer parallel like Fig. 5 From the previous work [13], the angular misalignment can generate the large optical loss easily. It will be applied to VOA to create the optical loss mainly. In practice, all of the things including the 3 fundamental loss causes should be considered compositively. Based on the Gaussian-beam model of single mode fiber filed [7], Nemota and Makimoto [8] derived the following coupling loss between single mode fibers that have unequal mode-field diameters and lateral, longitudinal and angular offsets plus reflections. The equation from the study of [8] is below

LSM

⎡ 16n12 n32 4σ ⎛ ρu ⎞⎤ ⎜⎜ − ⎟⎟⎥ = −10 log⎢ exp 4 ⎝ q ⎠⎦ ⎣ (n1 + n3 ) q

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········································· Eq. (1)

where

ρ

= (k W1 )2 q = G2+( σ +1)2 u = ( σ +1) F2+2 σ F G sin θ + σ (G2+ σ +1) sin2 θ 2

F = d / (k W1 ) 2

G = s / (k W1 )

σ

= ( W2 / W1 )2

k = 2 π n3/ λ n1 = core refractive index of fibers n3 = refractive index of medium between fibers λ = wavelength of source d = lateral offset s = longitudinal offset θ = angular misalignment

W1 = 1/е mode-field radius of transmitting fiber W2 = 1/е mode-field radius of receiving fiber This general equation gives us very good correlation with experimental investigations [9]. Using the Eq.(4), the 3 graphs are generated in Fig. 4, 5, and 6. In the Fig. 7, the s and the angle are fixed at 1㎛ and 1°. Then, the range of d is from 1 to 20㎛. In the Fig. 8, the d and the s is fixed at 1㎛ and 1㎛. The range of the angle varies from 1 to 80°. In the Fig. 9, the theta and d is fixed at 1° and 1㎛. The range of the s varies from 1 to 20㎛.

tht 1

IthI, d 'a

Separation,s (a)

Fig. 4 Optical loss vs. d

Fig. 5 Optical loss vs. theta

Fig. 6 Optical loss vs. s

From the analysis about the optical loss from the mechanical misalignment, the main insertion loss is separation s and lateral offset d. Then, the large dynamic loss can be achieved from the angular mismatching between the fibers. Using the numerical analysis, let’s apply it to our structure. Before considering the proposed structure, we look into our previous work briefly. We used the deflection of a piezoelectric tube with quartered electrodes in Fig. 7. The understanding of the basic mechanism and performance of tube manipulation are required to its design and application. The treatment of the z displacement is clear from the study [10]. Fig. 8 is the real view of the PZT tube that is used in the experiment from PI Ceramics.

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'<1

0 C

-4

ru

Fig. 8 Real view of the PZT tube

Fig. 7 Deflection of a tube

Our previous proposed VOA module is like Fig. 9. The module is composed of the fiber and the tube. The 2 fibers are a common single mode fiber like SMF-28 and the PZT tube has quartered electrodes. The fiber is inserted into the tube. Then, if the tube bends with the applied voltage, the fiber also bends coincidently. It makes the angular misalignment between the fibers and results in the optical loss. Optical Fiber

PZT tube Electrpde AN

Cladding

Core

stage

H Fig. 9 Previous VOA module 30

25

Voltage Increase Voltage Decrease

15

10

5

Fig. 10 Previous experimental results using a PZT tube

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0

0

59

0

57

0

Voltage (V)

55

0

53

0

51

0

49

0

47

0

45

0

43

0

41

39

0

0

37

0

35

0

33

31

0

0

27

29

0

0

25

0

23

0

21

0

19

0

17

15

0

0

13

90

11

70

0 50

Loss (dB)

20

As Fig. 10 shows the experimental results from our previous work, the dynamic rage is about 25 dB and the applied voltage is about 680V DC. Because it needs the high voltage to make 25dB-attenuation, the special high-voltage DC-DC converter is necessary for the practical usage in the field. To resolve this problem, we adopt the PZT sheet instead of the PZT tube.

Ground Positive Voltage

Ground Fig. 11 Structure for the PZT sheet Fig. 11 is the structure for the piezoelectric sheet. It consists of 2 thin PZT strips and 3 electrodes. In the middle of the PZT strips, there exists the metal sheet to improve the mechanical properties of the PZT bender. The surface electrodes were usually set to ground. For bilateral motion, a bipolar signal was applied to the middle contact. In our experiment, we considered the positive single polar signal as the applied voltage to simply demonstrate the feasibility of the PZT sheet as the VOA. TmIJ

dIinuiit

rtg Pdnt

'V I I

p

I

)

Fig. 12 Operation condition Fig. 12 is the operation condition to make a displacement when one side fix and one side free

Optical Fiber

PZT Sheet

Fig. 13 Brief view for the proposed VOA structure Fig. 13 is the proposed VOA structure. The PZT sheet including the optical fiber is fixed by the 6-axis stage. The other fiber is arranged horizontally and vertically. Fig. 14 shows the experimental setup. It contains the optical source, optical detector, the alignment system, high voltage generator and GUI. The DFB laser diode and the optical power meter were used to make the light and to detect the power of the light, respectively. The wavelength and the optical power for the light source were 1550 nm and 5dBm, respectively. The optical alignment system was composed of the 2 6-axis precision stages for the various mechanical movements and 2 vision cameras for macro optical alignments. The DC-DC converter was made to generate the DC voltage range from 0 to 200 V DC and had the USB interface to communicate with the computer. The GUI to control the voltage from the DC-DC converter was made using the LabWindows CVI.

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Fig. 14 Experimental Setup Fig. 15 is the magnified view of the connection area. Using the 6-axis stages, the insertion loss is reduced to the 7 dB. At the previous work, it’s about 16 dB.

Fig. 15 Magnified view of the connection area

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a) image from side camera

b) image from upper camera

Fig. 16 Image from the vision cameras Fig. 16 a) and b) were the image from the side camera and the upper camera. Both the images were for the macro vision alignment and the observation for the air gap between 2 optical fibers. To monitor the air gap using the image from 2 cameras, we increased the applied voltage.

3. RESULTS We continuously increase the applied voltage from 0 to 20 V DC. At each step, the increased voltage is about 0.5V DC, and the optical power is checked and recorded in the computer. To reduce the error and to stabilize the module, we added the enough extra time to finish the PZT sheet movements and to check the light power and to record. Because most of PZT components have inherently hysteresis, we decrease the applied voltage at the same step from 20 to 0 V DC. We could observe the hyseresis curve. After calculating the measured results, optical loss curve is drawn like Fig. 17. From the graph, the dynamic range of the VOA is about 25 dB. 60.00

50.00

Optical Loss (dB)

40.00

30.00

20.00

10.00

0. 00 6. 5

8. 5

10

12

14

15.5

17

Applied Voltage (V DC)

Fig. 17 Loss curve vs. applied voltage

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19

20. 7

4. CONCLUSIONS We have proposed the simple and practical VOA using the PZT sheet. In out experiments, the dynamic range is about 45dB and the driving voltage range is dramatically reduced to the about 20V DC. The PZT sheet is commercially available one from PI Ceramics. One of the problems is to attach the optical fiber to the PZT surface. In this experiment, we used the normal epoxy to fix the optical fiber to the PZT sheet. Therefore, the temperature change could affect the characteristics. To resolve this kind of problem, we’re designing the small and thin V-groove. From the experimental results, the strong feasibility for the PZT sheet to function as the VOA is demonstrated numerically and experimentally.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

R.R.A. Syms, H. Zou, J. Stagg, D.F. Moore, “MEMS variable optical attenuator with a compound latch”, Microelectronic Engineering, pp.423-428, 2004 Zhonghui Cao, X. Wu, “A micro-machining-based digital variable optical attenuator”, Sensors and Actuators, pp.181-186, 2001 T.V. Clapp, S. Day, S. Ohja, R.G. Peall, “Broadband variable optical attenuator in silica waveguide technology”, ECOC’98, Madrid, Spain, pp. 301-302, 1998 Q. Li, A.A. Au, C.H. Lin, E.R. Lyons, H.P. Lee, “An efficient all-fiber variable optical attenuator via acoustooptic mode coupling”, IEEE Photon. Technol. Lett. 14, pp.1563-1565 S.S. Lee, Y.S. Jin, Y.S. Son, T.K. Yoo, “Polymeric tunable optical attenuator with an optical monitoring tap for WDM transmission network”, IEEE Photon. Technol. Lett. 11 1999 590-592 D. Marcuse, D. Gloge, E.A.J. Marcatili, “Guiding properties of fibers”, Optical Fiber Telecommunication, Academic, New York, 1979 D. Marcues, “Loss analysis of single mode splices” Bell Sys. Tech. J., vol. 56, pp. 703-718, May, 1977 S. Nemota, T. Makimoto, “Analysis of splice loss in single mode fibers using a Gaussian field approximation” Optical Quantumm Electron., vol. 11 no. 5 pp. 447-457, Sept, 1979 W.C. Young, D.R. Frey, “Fiber connectors” Optical Fiber Telecommunications II, Academic, New York, 1988 M. Locatelli, G. Lamboley, Rev. Sci. Instrum, 59, 661, 1998 T. Tiedge, A. Brown, J. Appl. Phys. 68, 649, 1990 C. Julian Chen, “Electromechanical deflections of piezoelectric tubes with quartered electrodes”, Appl. Phys. Lett. 60, (1), 6 January 1992 S. Kim, H. Kang, S.B. Kang, W. Kim, H. Jeong, Y.J. Cho et al “The simple and cost-effective method for the voltage controlled variable optical attenuator using the piezoelectric ceramic tube with the electrodes on the surface”, Proceedings of SPIE Volume 6048, 5 December 2005

* [email protected]; phone 82 41 589 8451; fax 82 41 589 8408; www.kitech.re.kr

Proc. of SPIE Vol. 6374 63740G-8

A NOVEL CAPACITIVE TYPE MINIATURE MICROPHONE WITH A FLEXURE HINGE DIAPHRAGM 1

Hye Jin Kim, Sung Q Lee, Kang Ho Park

Nano Convergence Sensor Team, ETRI 161 Gajeong-Dong, Yuseong-gu, Daejon, 305-700, S. Korea ABSTRACT This paper presents a novel, highly sensitive condenser microphone with a flexure hinge diaphragm. We used the finiteelement analysis (FEA) to evaluate the mechanical and acoustic performance of the condenser microphone with a hinge diaphragm. And we fabricated the miniature condenser microphones with area of 1.5 mm x 1.5 mm. From the simulation and measurement results, we confirmed that the maximum displacements at the center of flexure hinge diaphragms are several hundred times, compared with flat diaphragms. Moreover, the miniature microphones have obtained -3 dB bandwidth of nearly 20 kHz by proper design of the flexure hinge diaphragms. Keywords: acoustic sensor, condenser microphone, MEMS

1. INTRODUCTION Recently, as it rapidly supplies the portable/mobile terminals including the cellular phone, PDA (personal digital assistant, PMP (portable multimedia player), etc, the demand about sound and audio technology is continuously increased. So far, a lot of research has been published in order to achieve high performance acoustic sensors with higher sensitivity and broader frequency range. Especially, MEMS technology enables the manufacturing of small mechanical components on the surface of a silicon wafer so that have been successfully applied to miniature silicon capacitive microphones [1-3]. Generally, most miniature microphones for the portable terminals are adopted by diaphragm-based capacitive type, i.e., condenser microphones and electret microphones because they have the flat frequency response in broad bandwidth, high SNR (signal-to-noise ratio) and high sensitivity, as compared with other types of microphones as like piezoelectric or piezoresistive microphones. The electret microphones have been introduced to replace the external bias voltage which been required by typical capacitive microphones and to reduce the power consumption [4-5]. The sensitivity of a capacitive microphone is determined by the electrical field strength exerting across the capacitor gap and the deformation (deflection) of diaphragm. Thus, to achieve higher sensitivity in broad bandwidth, the membranes of condenser microphones have to be designed to be flexible more. A important number of corrugated diaphragms have been introduced in order to release the residual stress in the diaphragm so that achieve higher sensitive condenser microphone [6-7]. This paper presents a novel high sensitive miniature condenser microphone with a flexure hinge diaphragm, which have not been introduced in the presented reports.

2. STRUCTURE AND FABRICATION This paper presents that a miniature condenser microphone with a flexure hinge diaphragm can obtain higher 1

[email protected]; phone 82 42 860 6152 Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740H, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.686008

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sensitivity, compared with other condenser microphones. A schematic view of a condenser microphone with a flexure hinge diaphragm is shown in Figure 1. The cross-sectional structure is seen along the A-B line, passing through the center of a diaphragm. The device consists of a rigid perforated backplate with a large amount of holes and an aluminum diaphragm etched by hinge pattern using RIE technique. The fabrication sequences are shown in Figure 2. First, the grooves for acoustic holes are formed on the upper side of a 5” SOI wafer by Deep-RIE technique (Figure 2a, 2b). The etching depths for holes with diameters of 5 µm, 10 µm and 15 µm are 10 µm, respectively. And after patterning of silicon oxide layer as an insulating layer (Figure 2c), the rigid backplate electrodes of 0.2 µm are coated by aluminum sputtering and the silicon nitrides of 0.3 µm are also deposited by PECVD equipment (Figure 2d). Next, we use the sacrificial layer to realize the devices in one single chip (Figure 2e). The sacrificial layers of about 2.5 µm were defined by silicon oxide and SOG (spin-on-glass). Silicon oxides of 3 µm are deposited by PECVD equipment at low temperature. And SOG (211) are coated and cured in furnace at 300 oC. Then dry etch-back process was conducted to smooth the surface until 2.5 µm-thick sacrificial layers were left. Figure 3 shows scanning electron microscope (SEM) images measured after SOG coating and curing process. Actually, this method makes a large cavity in holes, respectively. However, the sacrificial layers including silicon oxide and SOG film can be etched all during the backside etching process (Figure 2h) so that the cavities formed by SOG coating process can be neglected. Then, the sacrificial layers were patterned to the design as well (Figure 2e). Next, the aluminum membranes of 0.8 µm are deposited and etched with the flexure hinge pattern using reactive ion etching technique (Figure 2f). And, the contacts of the backplate electrodes and diaphragm electrodes are patterned and aluminum pads of 0.8 µm are also deposited (Figure 2g). Finally, these miniature condenser microphones are completed by Deep-RIE backside etching and by sacrificial layer releasing in BHF (Figure 2h).

Bridge Hinge diaphragm

B

A

Backplate

Figure 1.

Acoustic holes

A schematic cross-sectional view of the condenser microphone with a flexure hinge diaphragm

Proc. of SPIE Vol. 6374 63740H-2

(a)

SOI wafer

SiO2

(b)

(c) Al

Si3N4

(d)

SiO2 / SOG sacrificial layer

(e) Al diaphragm

(f)

___ _ _ _ ___I Al pad

(g)

r r--------------------------------(h)

Figure 2.

H

HH

HH

— H

A Schematic view of the fabrication process (the cross-section along line AB in Figure 1)

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I,

—

r -ci-—

V

--

Dot WD I AccV Spot Moqn 10-0 kV 3-0 2000x SE 20-4 ETRI

Figure 3.

Dot WD I 1 9M kV 3M 1 tttto SE 19-5 ETRI

I it pm

AccV Spot Moqn

I 2 pm

Scanning electron microscope (SEM) images measured after SOG coating and curing process

3. NUMERICAL ANALYSIS It is well known that the sensitivities of condenser microphones are very dependent on the stress distribution and deformation of diaphragms. In this paper, we used the finite-element analysis (FEA) using ANSYS to evaluate the mechanical and acoustic performance of the condenser microphone with a hinge diaphragm. Several parameters for the numerical analysis are depicted in TABLE I. Based on above parameters, we conducted a modal analysis to determine the vibration characteristics of the flexure hinge diaphragm (Figure 4, Figure 5). A reference microphone with a flat diaphragm was used for a comparison. Figure 4 shows the stress distributions of the flat diaphragm (Figure 4a) and the flexure hinge diaphragm (Figure 4b) with input sound signal. And Figure 5 shows the deformation characteristics of the flat diaphragm and the flexure hinge diaphragm. The diameters of hinge diaphragm and flat diaphragm are 500 µm, respectively. And the thickness of the diaphragm is 1 µm and the applied sound pressure is 100 Pa. The maximum deformations per a pressure occurred at center of the hinge/flat diaphragms are 0.01826 µm/Pa and 0.7314E-4 µm/Pa, respectively. It means that the sensitivity of a flexure hinge diaphragm can be improved about 250 times higher than a flat diaphragm. TABLE I Material parameters for numerical analysis

Parameters

value

[W

]

Young’s Modulus

→ 237 E 6 m ⋅K E : 70 [GPa ] → 70 E 3

Poison ratio

υ : 0 . 33

Thermal conductivity

K : 237

Thermal expansion coeff.

α : 23 [µ m ⋅ m

Density

ρ : 2700 ⎡ kg ⎢⎣

-1

⋅K

−1

]→

23 E − 6

⎤ → 2 . 7 E − 15 m 3 ⎥⎦

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(a)

(b)

Figure 4. The stress distributions of the flat diaphragm (a) and the flexure hinge diaphragm (b) with input sound signal

Figure 5. The deformation characteristics of the flat diaphragm (left) and the flexure hinge diaphragm (right)

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It is also known that the natural frequency and mode shapes are very important factors for condenser microphones with broad bandwidth. Figure 6 shows the vibration mode shapes and corresponding frequencies for a flexure hinge diaphragm. The first and second modes occurred at 14,905 Hz and 23,191 Hz, respectively. Actually, the first resonance occurs in the audio frequency range (2 ~ 20 kHz), but we can obtain broader bandwidth by proper design of the flexure hinge diaphragm, i.e. wide bridge pattern.

1st 14,905 Hz

2nd 23,191 Hz

3rd 23,219 Hz

4th 66,432 Hz

Figure 6. The vibration mode analysis for a flexure hinge diaphragm

4. SENSITIVITY MEASUREMENTS Figure 7 shows miniature condenser microphones with hinge diaphragm fabricated with silicon-based MEMS technology. The areas of the devices are 1.5 mm x 1.5 mm. We measured the displacements in the center of a hinge diaphragm and a flat diaphragm with LDV (Laser Doppler Vibrometer) in the audio frequency range (Figure 8). First, we measured that the diaphragm sticks to the backplate when the bias voltage was about 25 V. With the driving voltage of 15 Vo-p, the maximum displacements at the center of a diaphragm are about 0.2 µm in the flat frequency range, and the first resonance mode occurs at nearly 20 kHz. From the simulation and measurement results, we confirmed that the sensitivity of a flexure hinge diaphragm can be improved about several hundred times higher than a flat diaphragm. In addition, the condenser microphones with a flexure hinge diaphragm can be expected to obtain the broader frequency range including the audio frequency by proper design revision with bridge widths.

Proc. of SPIE Vol. 6374 63740H-6

Figure 7. Optical microscope images of fabricated miniature condenser microphones

2.5

the flexure hinge diaphragm the flat diaphragm

Displacement (µm)

2.0

1.5

1.0

0.5

0.0

-0.5 0.1

1

10

Frequency (kHz)

Figure 8. Displacements at the center of the flexure hinge diaphragm and the flat diaphragm in the audio frequency range

5. CONCLUSIONS This paper reports on a miniature condenser microphone with a flexure hinge diaphragm with area of 1.5 mm x 1.5

Proc. of SPIE Vol. 6374 63740H-7

mm. We conducted finite-element analysis (FEA) using ANSYS to evaluate the mechanical and acoustic performance of the condenser microphone with a hinge diaphragm. The maximum displacements at the center of the hinge diaphragms are about 0.2 µm in the flat frequency range, and the first resonance mode occurs at nearly 20 kHz. In summary, the fabricated condenser microphones have higher sensitivity in wide frequency range including the audio frequency range. Thus, we expect that the devices will be well applied for mobile terminals.

ACKNOWLEDGEMENTS We would like to thank Dr. S. M. Wang and D. S. Kim for their numerial analysis assisting.

REFERENCES 1. 2. 3. 4. 5. 6. 7.

Q. Zou, A. Li, L. Liu, “Theoretical and experimental studies of single-chip-processed miniature silicon condenser microphone with corrugated diaphragm,” Sens. Act. A, vol. 63, pp. 209-215 (1996). Y. B. Ning, A. W. Mitchell, and R. N. Tait, “Fabrication of a silicon micromachined capacitive microphone using a dry-etch process,” 1995 Proc. IEEE Transducers & ’95 EUROSENSORS IX, pp. 704–707. D P. R. Scheeper, B. Nordstrand, J. O. Gullov, B. Liu, T. Clausen, L. Midjord, and T. Storgaard-Larsen, “ A new measurement microphone based on MEMS technology,” J. Microelectromech. Sys., vol. 12, pp. 880-891 (2003). F. W. Fraim and P. V. Murphy, “Miniature Electret Microphones,” J. Audio Eng. Soc., vol. 18, pp. 511-517 (1970). J. Sprenkels, R. A. Groothengel, A. J. Verloop, and P. Bergveld, “Development of an electret microphone in silicon,” Sens. Act. A, vol. 17, pp. 509-512 (1989). J. Chen, L. Liu, Z. Li, Z. Tan, Y. Xu, J. Ma, “On the single-chip condenser miniature microphone using DRIE and backside etching techniques,” Sens. Act. A, vol. 103, pp. 42-47 (2003). R. Kressmann, M. Klaiber, G. Hess, “Silicon condenser microphones with corrugated silicon oxide/nitride electret membranes,” Sen. Act. A, vol. 100, pp. 301-309 (2002).

Proc. of SPIE Vol. 6374 63740H-8

Liquid pressure varifocus lens using a fibrous actuator Ryoichi Kuwano*a, Yasuhiro Mizutanib, Tsuyoshi Tokunagac, Yukitoshi Otanib a Mechanical Engineering Section, Fukuyama Polytechnic College, 4-8-48 Kitahonjo, Fukuyama, Hiroshima, Japan 720-0074; b Department of Mechanical Systems Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei, Tokyo, Japan 184-8588; c Precision Engineering, Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino, Chiba, Japan 275-0016 ABSTRACT A liquid pressure varifocus lens has been developed that employs a fibrous actuator which contracts on application of a current or on heating. The focal length of the convex lens can be varied continuously between 90 mm to 300 mm. The shape of the lens changes smoothly and the construction of the lens is extremely simply. It requires a low electric power to drive it. In this study, the optical characteristics and the response time of the liquid pressure varifocus lens were measured. The time constant of the fibrous actuator was 1.0 s for the rise time when electric power was initially supplied. A fibrous actuator having a length of 370 mm was used, and a voltage of 9.5 V was applied. Keywords: Variable focus lens, liquid pressure, polymer film, fibrous actuator

1. INTRODUCTION We have proposed a variable focus lens, the focal length of which is controlled by liquid pressure1,2). Other types of variable focus lenses have also been proposed3)-10) and they can be categorized based on their driving mechanism, their arrangement of lens components, and their applications. The mechanism for varying the focal length can be divided into principally either electrical or mechanical mechanisms. The drive device can be characterized based on the dynamic range of displacement, electric power consumption, response speed and size. We have employed a method which uses a syringe to inject liquid into the lens. However, this mechanism can be discontinuous due to frictional resistance to piston packing, making it unsuitable for applications in which the direction of movement needs to be reversed. Since an actuator that employs a shape memory alloy has a large displacement magnitude, it is suitable as a drive device. In this report, we propose a liquid pressure varifocus lens that uses a fibrous actuator. The optical characteristics and the response time of the liquid pressure varifocus lens are given.

2. PRINCIPLE OF LIQUID PRESSURE VARIFOCUS LENS The focal length of the liquid pressure varifocus lens that we developed is varied by deforming the shape of the lens. This is done by varying the pressure of the liquid enclosed in the lens. Figure 1 shows the principle of the liquid pressure varifocus lens and its structure. It consists of a polymer film, an acrylic plate and a liquid as shown in Fig. 1(a). The plan view shown in Fig. 1(a) shows the layout of the four pistons which vary the liquid pressure via fibrous actuators. Fibrous actuators contract on application of a current or heat. The plan view shown in Fig. 1(b) shows the fibrous actuator in its contracted state and the pistons aligned in the four directions shown, so that the pressure inside the lens is high. Conse*[email protected]; phone +81 84 923-6391; fax +81 84 923-6581; http://www.tuat.ac.jp/~otani/ Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740I, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.689330

Proc. of SPIE Vol. 6374 63740I-1

Piston

: Contraction force : Movement direction of piston

Top view Fibrous actuator

Electrode Polymer film

Cross section

Liquid Acrylic plate (b) Convex lens (a) Initial state Fig. 1 Principle of liquid pressure varifocus lens and its structure

quently, the internal pressure of the lens increases, and the lens surfaces expands into the convex shape shown in the cross-section given in Fig. 1(b). The focal length of the lens can thus be controlled by varying the pressure of the liquid in the lens. The refractive surface of the lens is analyzed using a bending model of a flat plate. If a symmetrical load is applied to the center of the film, the deflection w of the film is given as2), w=

p (a 2 − r 2 )⎛⎜ 5 + ν ⋅ a 2 − r 2 ⎞⎟ , 64 D ⎠ ⎝ 1 +ν

(1)

where ν is Poisson's ratio. The deformation w of the film is proportional to the liquid pressure p, and the displacement depends on the fourth power of the radius r.

3. EXPERIMENTAL RESULTS Figure 2 shows the experimental setup for measuring the characteristics of the fibrous actuator and the liquid pressure varifocus lens. This system consists of an actuator controller, a laser displacement meter, a personal computer (PC) for acquiring data and the liquid pressure varifocus lens. The fibrous actuator is driven by a pulse width modulation (PWM) wave generated by a one-chip microcomputer (the actuator controller). The actuator controller controls the time period of the electric pulse applied to the fibrous actuator. A function generator is used for changing the duty ratio. The output voltage from the function generator is converted to A/D by the actuator controller and the duty ratio is set. The maximum electrical power is 100 % of the duty ratio. The frequency of the PWM wave is 488 Hz. Thus the construction of the liquid pressure varifocus lens system is extremely simply. Figure 3 shows the static characteristics of the fibrous actuator. The fibrous actuator has a diameter of 100 mm and a length of 150 mm. A load of 80 g and a voltage of 3 V was applied to the fibrous actuator in this measurement. We measured the relationship between the applied current and the contraction length while keeping the duty ratio constant. Since the movement of the fibrous actuator depends on the current and the temperature, the contraction length will depend on the square of current or voltage. However, the current produced by the PWM drive has a linear dependence on the duty ratio. Figure 3(b) shows the step response. The movement of the fibrous actuator is stable for duty ratios below 60 % and over 80 %. The time constant was 1.0 s for the rise time when electric power was initially supplied. Unstable movement was observed for duty ratios between 60% and 80%.

Proc. of SPIE Vol. 6374 63740I-2

Laser displacement meter

DC power supply Function generator

A/D unit Liquid pressure

Vref

PC

One chip microcomputer

PIC16F873

varifocus lens Fibrous actuator Fig. 2 Experimental setup.

4.0 3.0 2.0 1.0 0 0

10

20 30

40 50 60 70 Duty ratio % (a) Static characteristics

160 140 120 100 80 60 40 20 0 80 90 100

5.0 Contraction ratio %

: Contraction ratio : Current

Current mA

Contraction ratio %

5.0

4.0 3.0 2.0 1.0 0

L 0

5

-

10 15 time s (b) Time response

20

:

Duty ratio 100% 90% 85% 80% 75% 70% 65% 60% 50% 40% 30% 20% 10%

25

Fig. 3 Stactic and dynamic characteristics of fibrous actuator.

Figure 4 shows the gain curvature of the liquid pressure varifocus lens. The displacement of the lens center was measured when the sine wave was input to the actuator controller as a reference voltage. A fibrous actuator having a length of 370 mm was used, and a voltage of 9.5 V was applied. The resonance frequency was 5 Hz, and the amplitude stabilized to 0.07 mm at frequencies of 10 Hz or higher. Figure 5 shows the relationship between the duty ratio and the focal length. Since the pressure in the liquid pressure varifocus lens increases with an increase in the duty ratio, the focal length also changes. The fabricated liquid pressure varifocus lens exhibits smooth operation, and the focal length changes continuously from 90 mm to 300 mm. To demonstrate the variable focus function, we captured sample images using a CCD camera. Figure 6(a) shows the optical arrangement for capturing the sample images, and Fig. 6(b) shows the images. The refractive surface at a duty ratio of 0 % is flat. The sample images are magnified as the duty ratio is increased, demonstrating the change in the optical characteristics of the lens.

4. CONCLUSION A liquid pressure varifocus lens that uses a fibrous actuator driven by current or heat was proposed. The fabricated liquid pressure varifocus lens changes its shape smoothly and its focal length can be controlled over a wide range. The system

Proc. of SPIE Vol. 6374 63740I-3

Focal length mm

Gain dB

0 5 -10 -15 -20 -25 -30 -35 -40 10-2

10-1 100 101 Frequency Hz

102

Fig. 4 Gain curvature of liquid pressure varifocus lens.

350 300 250 200 150 100 50 0

0 10 20 30 40 50 60 70 80 90 100 Duty ratio %

Fig. 5 Relationship between duty ratio and focal length.

120

Sample image

65

Liquid pressure varifocus lens

Duty 0%

Duty 20%

Duty 40%

Duty 60%

Duty 80%

Duty 100%

Fibrous actuator CCD

(b) Captured images

(a) Optical arrangement for capturing images using a CCD.

Fig. 6 Effect varying duty ratio on the focal length.

can be constructed extremely simply. It can be driven using a low electric power. A rapid response should be achievable by optimizing the structure of the lens and the layout of the fibrous actuator. We will use the lens as an optical component in a high powered laser, and attempt laser processing for three-dimensional fabrication.

REFERENCES 01. 02. 03. 04. 05. 06. 07. 08.

R. Kuwano, T. Tokunaga : Optics Japan'97, (1997) 85 (in Japanese). R. Kuwano, T. Tokunaga, Y. Otani and N. Umeda : Opt. Rev. 12, 5 (2005) 405. M. C. King and D. H. Berry : Appl. Opt. 9, (1970) 2035. S. Sato : Jpn. J. Appl. Phys. 18 (1979) 1679. T. Tatebayashi, T. Yamamoto, and H. Sato : Appl. Opt. 30, 34 (1991) 5049. N. Sugiura and S. Morita : Appl. Opt. 32, 22 (1993) 4181. T. Kaneko, H. Suzuki, T. Hattori, T. Higuchi : JSPE semestrial meeting spring, (1993) (in Japanese). M. Kasahara, S. Onizawa, H. Akabane, M. Agu, K. Ooi and Y. Osada : Jpn. J. Opt. (KOGAKU), 26, 9 (1997) 485 (in Japanese). 09. D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi and Y. H. Lo: Appl. Phys. Lett, 82, 19 (2003) 3171. 10. B. H. W. Hendriks, S. Kuiper, M. A. J. van As, and C. J. Renders : Opt. Rev. 12, 3 (2005) 255.

Proc. of SPIE Vol. 6374 63740I-4

Sol-Gel based 1ⅹ2 power splitter for a plastic optical fiber H.Jeong1, Y.J.Cho2, S.T.Kim3 Korea Institute of Industrial Technology 35-3 Ibjang Hongcheon CheonAn, ChungNam KOREA

ABSTRACT This paper presents a sol-gel based 1ⅹ2 power splitter for an optical communication based on the plastic optical fiber. To find out optimum parameters of a power splitter, mode propagation along the splitter was theoretically analyzed using BPM (Beam Propagation Method) and the results show that the distance between two arms at the output port of a splitter should be kept below 100μm in order to increase the output power. The planar lightwave circuit device was fabricated by a nano imprint lithography process followed by a spin coating process. The core size and the length of a power splitter were 230 μmⅹ230 μm and 2 cm, respectively. The measured surface roughness of core/cladding using the AFM (Atomic Force Microscope) was under 100nm.

The characteristics of a fabricated power splitter were conducted

using an 850nm VCSEL (Vertical Cavity Surface Emission Laser) source and 50:50 power splitting performance was obtained.

1. INTRODUCTION The expansion of high-capacity optical transmission techniques into telecoms, datacoms, and access networks provides unique opportunities for sol-gel optical waveguide devices because of their low cost compared to the classical technologies [1-4].

The sol-gel technique is a low temperature method for the

preparation of optical waveguides from a liquid phase and allows to fabricate waveguides in a few steps with a low cost equipment.

In this paper we propose a sol-gel based 1ⅹ2 power splitter for an optical communication based on the plastic optical fiber (POF). In the residential networks (the infrastructure needed to bring the fiber to the home) component cost is critical and performance is secondary. Until now, however, in previous studies the power splitter with highly multi-mode POF has not been fully investigated so far. In this paper, we

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740J, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.685669

Proc. of SPIE Vol. 6374 63740J-1

propose a power splitter for highly multi-mode POF. Based on BPM (Beam Propagation Method) software, a three-dimensional semivectorial calculation was carried out. To reduce the radiation loss, the dependence on the splitting angle and the distance between two output arms was simulated.

The

splitters were designed and fabricated using imprinting method for the 850 nm wavelength region.

2. Fabrication : Sol-gel Hybrid organic-inorganic silicon(ORMOCER®) waveguides were obtained by using organically modified silicon dioxides where the organic groups are not only modifiers but also formers of the network [5-9]. Acid catalyzed silica sols were prepared from the hydrolysis and polycondensation reaction of organically functionalized alkoxysilanes. HCl was used as catalyst, ethanol(EtOH) as solvent, and bidistilled H2O for hydrolysis.

Table 1 shows the characteristics of fabricated sol-gel solution. The refractive indices

of the solution were measured at the wavelength of 632.8 nm.

The measured refractive index of the core

and that of the cladding was 1.4581 and 1.4792, respectively. Table 1. Characteristics of fabricated sol-gel solution Cladding Chemical name

Core

Organic modified polyorganosilane (Diluted in organic solvent)

Appearance

Slightly milky white liquid

Refractive index

1.4581

1.4792

Viscosity (@ 20 °C)

2.6 cPs

4.3 cPs

Specific gravity (@ 20 °C)

0.91

0.89

Solvent (wt%)

70

70

Type of solvent

Ethanol

Iso-propanol

Surface resistivity

2.6E8

-

3. BPM Simulation The conventional Y-splitter suffers severe radiation loss when the splitting angle is larger than 2° [10]. To reduce the radiation loss, the splitting angle must be small and the splitter length is therefore increased. To find out optimum design of a splitter, angle, splitter length and distance between two arms at output were simulated within the splitter using beam propagation method (BPM).

Proc. of SPIE Vol. 6374 63740J-2

BPM is the most widely

used propagation technique for modeling integrated and fiber optic photonic devices, and most commercial software for such modeling is based on it. In this work, the optimum configuration of a splitter is simulated with the BPM using BeamPROP software of the RSoft Design Group, Inc. Figure 1 shows the simulation parameters of a splitter. The thickness of waveguide and the length of a splitter are fixed to 210 µm and 2 cm, respectively. d

W

d L2 L

Fig. 1 Parameters of a Y-splitter To improve the performance of a splitter, the splitting angle (or distance between two arms at output of a splitter) must be optimized and Fig. 2 shows the simulation results of relative output power with respect to the distance between two arms and the splitting angle. The length of splitting zone, L2, is fixed to 1.5 cm because simulation result shows that the radiation loss is negligible above the length of 1.5 cm. Figure 2 (a) shows that the relative output power shows maximum value at 50 ~ 100 µm and decreases dramatically above 100 µm of distance between two arms at output of a splitter, w.

In the same way, the

relative output power shows maximum value at 0.2 ~ 0.45° and decreases dramatically above 0.45° of the splitting angle, as shown in Fig. 2 (b). These results mean that the output power deceases as the distance increases because the route of beam propagation changes severely as the distance increases. we fixed the distance between the output arms to 100 µm for fabrication of waveguide.

Proc. of SPIE Vol. 6374 63740J-3

Therefore

O'P E

RMi

oap: Rthth!

(a)

(b)

Fig. 2 Relative output power with respect to (a) distance, w, between output arms of a splitter, (b) splitting angle Figure 3 shows the simulated beam propagation through a splitter. We assume that the field of input beam is the Gaussian shape and the FWHM(Full Width Half Maximum) of a Gaussian beam is same with the thickness of a splitter.

As shown in Fig. 3, there is no leaky mode through a splitter except the center

region which introduces additional loss. And the optical power is distributed to all allowed guided mode not confined to fundamental mode in a highly multi-mode waveguide.

Fig. 3 Simulated beam propagation through a splitter (L = 2 cm, w = 100 µm)

4. Fabrication and Characteristics of a Y-splitter We have fabricated multi-mode optical power splitters by using imprint method based on the PDMS stamp and UV curable property of the sol-gel solution. Figure 4 schematically shows the fabrication process.

First, poly(dimethylsiloxane) (PDMS) molds were prepared by casting PDMS on a

photolithographically generated silicon master with the desired waveguide pattern. Then PDMS molds

Proc. of SPIE Vol. 6374 63740J-4

were attached with pre-formed an under-cladding layer. In the next step, waveguide core ridges were patterned directly by UV exposure through a waveguide pattern PDMS molds. After that, waveguide pattern PDMS master was removed and, finally, the core ridges were embedded in an over-cladding layer.

Wngid.________________ I_JtrtrtrtrLJ

c.rPDMI nth. muhy

FDMS mold

FDMS mold

Fill the IIV curable resh'

Under claddi

Apply to a subshate

H

flflflp]fl

Remove the FMDS mold &

oatthecladding

Fig. 4 Basic fabrication steps of a optical waveguide Figure 5 and 6 show the fabricated Y-splitter with s-bends structure and cross-section of the fabricated power splitter, respectively.. The thickness of the under-cladding layer was 30 µm, and the dimension of the core layer was 230 µm ⅹ 230 µm.

To estimate the smoothness of the imprinted surfaces, we

performed atomic force microscope (AFM) analysis. Figure 7 shows AFM results of the surfaces, and smooth surface can be formed by the imprint process. The imprint process gives the average values of 29.034 nm for cladding surface and 148 nm for core surface.

Proc. of SPIE Vol. 6374 63740J-5

Fig. 5 Fabricated Y-splitter on a silicon wafer

Fig. 6 Optical microscopic image of fabricated waveguide (ⅹ10)

Proc. of SPIE Vol. 6374 63740J-6

i L\c: .

.

(a)

(b) Fig. 7 Measured surface roughness of (a) cladding, 29.034 nm, and (b) core, 148 nm. For optical testing, both ends of the splitter were cleaved. Light from a VCSEL (Vertical Cavity Surface Emission Laser) at 850 nm wavelength was coupled into the splitter via a POF of 250 µm diameter and transmitted light was focused on a camera to observe the mode field profile and on a PD (Photo Diode) to measure its output power.

The measured losses were relatively high because of processing imperfection

caused by a limited imprint resolution at the Y-junction. The spectral insertion loss (fiber-splitter-fiber) of a Y-splitter with best score was 6.9 dB and, for comparison, the insertion loss of a straight waveguide with 2 cm length was 3.4 dB. The excess loss due to the Y-splitter, therefore, is in the range of 0.5 dB.

5. CONCLUSIONS

Proc. of SPIE Vol. 6374 63740J-7

We have introduced a process of UV-imprint fabrication of multi-mode waveguide in hybrid organicinorganic sol-gels that offer the feature of a simple waveguide fabrication process. Y-splitters have been fabricated to utilize in the optical communication using the plastic optical fiber. Simulation based on BPM is presented, which presents optimum design parameters of a splitter. While the measured excess loss due to Y-splitter is relatively high, we confirm that the UV-imprint fabrication method and sol-gel material have high potential for optical device components.

REFERENCE [1] S. I. Najafi, Ed., Proc. Critical Review Conference on Glass Integrated Optics and Optical Fiber Devices, SPIE Vol. CR 53, 1994. [2] R. V. Ramaswany and R. Srivastave, J. Lightwave Technol. 6 (1998) 984. [3] J. Schmudtchen, A. Splett. B. Schuppert, K. Petermann, and G. Birbach, Electron. Lett. 27 (1991) 1486. [4] T. Kominato, Y. Ohmori, H. Okazika, and M. Yasu, Electron. Lett. 26 (1990) 327. [5] Y. Sorek, R. Reisfeld, I. Finkelstein, and R. Rushin, Opt. Mater. 4 (1994) 99. [6] Y. Sorek, R. Reisfeld, A.M. Weiss, Chem. Phys. Lett. 244 (1995) 371. [7] M. Zevin, R. Reisfeld, Opt. Mater. 8 (1997) 37. [8] S. Motakef, T. Suratwala, R.L. Roncone, J.M. Boulton, G. Teowee, and D.R. Uhlmann, J. Non-Cryst. Solids 178 (1994) 37. [9] H. Schmidt, H. Krug, R. Kasemann, and F. Tiefensee, in:Submolecular Glass Chemistry and Physics, SPIE, vol. 1590, 1991, p. 36. [10] H. Sasaki and N. Mikoshiba, “Normalized power transmission in single mode optical branching waveguide,” Electron. Lett., vol. 17, pp. 136–138, Feb. 1981.

Proc. of SPIE Vol. 6374 63740J-8

Invited Paper

Liquid Crystal Laser Manipulation System for Controlling Microscopic Particles Marenori Kawamura*, Mao Ye and Susumu Sato Department of Electrical and Electronic Engineering, Akita University, 1-1 Tegtagakuen-cho, Akita 010-8502, Japan *E-mail: [email protected]

A novel optical manipulation system for controlling three-dimensional positions and rotation of trapped microscopic rods is proposed by using a liquid crystal (LC) device with unique functions such as an anamorphic lens property in addition to both variable-focusing and deflection properties. Arranging the control voltages of the LC optical device, the laser beam can be focused with any elliptical cross section. The trapped slender object is aligned along the rotatable major axis of the elliptically shaped laser beam spot and can be shifted three-dimensionally. keywords: optical manipulation, liquid crystal optical device, variable-focal length, beam deflection, anamorphic lens property, elliptically shaped laser beam

1. Introduction Optical trapping, as a manipulation technique for controlling microscopic particles such as biological samples and transparent dielectric particles suspended in a solution are widely studied in biological research applications by using a strongly focused Gaussian beam.1-3 These particles are trapped into most intense part of the beam due to the optical gradient force. Recently, electro-optic devices with optical properties that are controllable electrically using nematic liquid crystal (LC) materials have been demonstrated and appeared promising for use in the optical system, for example, LC lenses,4-7 LC micro-lenses,8-9 LC gratings10 and other optical devices.11 The focal length of the LC lens and LC micro-lens can be tuned by applying a voltage. We reported the 3D microscopic particle manipulation by using a composite lens of an objective lens with a high numerical aperture and an LC lens that has two functions of variable focusing and beam deflection by applying a control voltage.12 The trapped microscopic particles such as polystyrene balls (11µm) can be shifted in the longitudinal direction as well as the transverse direction without any use of mechanical parts. In this study, we propose and demonstrate an optical manipulation system for controlling the positions and rotations of the trapped slender particles suspended in the water using the LC optical device with eight-divided circularly hole-patterned electrodes. 2. Experimental Figures 1(a) and 1(b) show the side and top views of the LC optical device with eight-divided circularly hole-patterned electrodes for rotating the electric field, respectively. A thin LC (E44, Merck) layer with a positive dielectric anisotropy of the thickness d LC=110 µm is sandwiched between two glass substrates (d g1= d g2=1.1 mm). The lower glass substrate is coated with a transparent indium tin oxide (ITO) film and its surface with the ITO faces the LC layer. The outer surface of the upper substrate is coated with eight-divided circularly hole-patterned aluminum (Al) thin film electrodes (diameter: 6.7 Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740K, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.688882

Proc. of SPIE Vol. 6374 63740K-1

mmφ). The surfaces of the substrates which face the LC material are coated with polyimide (PI) film and are rubbed unidirectionally to align the LC directors homogeneously. Each voltage of V1 ~ V8 can be independently applied across the eight-divided circularly hole-patterned electrodes and the lower ITO electrode. The optical properties in the hole-patterned region were measured by using a He-Ne laser (633 nm), polarizing microscope and a charge coupled device (CCD) array camera. Figure 2 shows the schematic diagram of the 3D controllable and rotatable manipulation system of microscopic particles by using the LC optical device. The manipulation system consists of a laser source (Coherent Japan, Verdi) operated at 532 nm, two convex glass lenses, LC optical device and condenser lens (40x, NA=0.45). The circularly or elliptically patterned laser beam passing through the LC optical device and the condenser lens is focused to the glass receptacle containing the slender glass rod particles (length: 30~50 µm, diameter: 11 µm) suspended in the water. The trapped microscopic particles are monitored by using the microscope system. The band-pass filter (550~750nm) and interference filter at a center wavelength of 589 nm are used to cut off the very intense laser beam for protecting the CCD array camera. 3. Results and discussion Figures 3(a) ~ 3(h) show the interference fringe patterns of the circularly hole-patterned region at various applying voltages to the eight-divided electrodes of the LC optical device under crossed polarizers. They are observed using the CCD camera connected with the polarizing microscope. Since there is a phase difference of 2π between the neighboring fringes, the phase difference properties of exiting ray from hole-patterned region can be estimated. It is seen from Figs. 3 ((a) V1~8=45 Vrms, (b) V1~8=50 Vrms, (c) V1~8=70 Vrms and (d) V1~8=80 Vrms) that almost circular fringe patterns can be observed while the same voltage (1 kHz) is applied to each divided electrode and the phase difference profile varies with the applied voltage. When the voltages are applied across the electrodes, the electric field intensity is maximum at the edge area and becomes minimum at the center of the hole-pattern in the circularly hole-patterned region. Then the parabolic profile of the effective refractive index distribution is attained. Since the LC directors in the center of the hole-pattern rotate to the electric field as increasing the voltage, the rotation of the directors near the boundary of the hole-pattern tends to saturate at the high voltage. As changing the control voltages of each divided electrode, the elliptical interference fringe patterns are obtained as shown in Figs. 4(a) V1=V5=80 Vrms, V2= V4=V6= V8=57 Vrms, V 3=V7=40 Vrms, 4(b) V4=V8=80 Vrms, V 1= V3=V5= V7=57 Vrms, V2=V6=40 Vrms, 4(c) V3=V7=80 Vrms, V2= V4=V6= V8=57 Vrms, V 1=V5=40 Vrms and 4(d) V2=V6=80 Vrms, V 1= V3=V 5= V 7=57 Vrms, V4=V8=40 Vrms. It is seen that the directions of major and minor axes of the fringes can be rotated. The LC director distributions, that is the profile of phase retardation in the hole-patterned region can easily be arranged by the external voltage. The phase retardations within the area of about 6.0 mm in diameter are shown in Fig. 5. The open and solid circle symbols are the measurement values from the interference fringe patterns along the major and minor axes, and the solid lines are the regression curves using a quadratic equation. The optical property seems to be an anamorphic lens-like distribution of the refractive index. Figures 6(a) and 6(b) show the focal length and the normalized astigmatic focal distance as a function of applied voltage Vc, where each applied voltage to eight-divided electrodes is arranged to be Vmajor = Vc 2 , Vminor = Vc corresponding to the major and minor axes of the elliptical interference fringe and Vside = Vc 2 to other directions. Both the focal length and astigmatic properties can easily be adjusted by changing the applied voltage to the divided electrodes. The focusing ranges in the major and minor axes are covered from 55 cm (at 80 Vrms) to 93 cm (at 60 Vrms) and from 24 cm (at 90 Vrms) to 29 cm (at 60 Vrms), respectively. Figures 7(a) ~ 7(g) show a demonstration of the trapped microscopic glass rod trapping and rotating in the clockwise direction. Since the trapped slender particle aligns along the major axis of the elliptical intensity profile at the focusing point, the particle can be rotated by controlling each applied voltage to

Proc. of SPIE Vol. 6374 63740K-2

the divided electrode and setting the major axis direction of the ellipse. The trapped particle can also be rotated in the anticlockwise direction. Figure 8 shows the voltage-controllable shift of the trapped glass rod particle, while the applied voltages (V3~7) to the electrodes 3~7 are constant values (80 Vrms) and the control voltages V1 , V2 = V8 = V1 2 are arranged from V1 =20 to 80 Vrms. Since the trapping beam is deflected in two transverse directions as shown in the schematic diagram (Fig.2) by controlling the appropriate voltage application to the divided-electrodes, the trapped particle can be shifted about ±90 µm. 4. Conclusion We have proposed a laser manipulation system with 3D controllable and rotatable trapping the microscopic particles using an LC optical device with a function of adjustable laser spot profile. The trapped slender particles can be rotated clockwise or anticlockwise by arranging the control voltage applying to the eight-divided circularly-hole patterned electrodes of the LC optical device. Furthermore, the positions of the trapped particles can be shifted by using beam–steering the function of the LC optical device.

References 1. A.Ashkin, J.M.Dziedzic and T.Yamane, “Optical Trapping and Manipulation of Single Cells Using Infrared Laser Beams”, Nature (London), 330, pp.769-771 (1987). 2. W.H.Wirght, G.Jsonek and M.W.Berns: “Parametric Study of the Forces on Microspheres held by optical Tweezers”, Appl. Opt. 33, pp.1735-1748 (1994). 3. D. Cojoc, V. Emiliani, E. Ferrari, R. Malreanu, S. Cabrini, Z. R. Proietti and E. D. Fabrizio, “Multiple Optical Trapping by Means of Diffractive Optical Elements”, Jpn. J. Appl. Phys., 43, pp.3910-3915 (2004). 4. S.Sato, “Liquid-Crystal Lens-Cells with Variable Focal Length”, Jpn. J. Appl. Phys, 18, pp.1679-1684 (1979). 5. S.Sato: “Applications of Liquid Crystals to Variable-Focusing Lenses”, Opt. Rev., 6, pp.471-485 (1999). 6. M.Ye and S.Sato, “Optical Properties of Liquid Crystal Lens of Any Size”, Jpn. J. Appl. Phys., 41, L571L573 (2002). 7. M.Ye, B.Wang and S.Sato, “Liquid-Crystal Lens with a Focal Length that is Variable in a Wide Range”, Appl. Opt., 43, pp.6407-6412 (2004). 8. T.Nose and S.Sato, “A Liquid Crystal Microlens Obtained with Non-Uniform Electric Field”, Liq. Cryst., 5, pp.1425-1433 (1989). 9. S.Masuda, S.Takahashi, T.Nose, S.Sato and H.Ito, “Liquid Crystal Microlens with Beam Steering Function”, Appl. Opt., 36, 4772-4778 (1997). 10.Z.He, T.Nose and S.Sato, “Polarization Properties of an Amplitude Nematic Liquid Crystal Grating”, Opt. Eng., 37, pp. 2885-2898 (1998). 11.T.Yamanaka, R.Yamaguchi and S.Sato, “In-Plane Switching Micro Optical Devices Using Weak Anchoring Effects”, Abstr .Int. Liquid Cryst. Conf., 25D-29P, p.302 (2000). 12.M. Kawamura, M. Ye and S. Sato, “Optical Trapping and Manipulation System by Using a Liquid Crystal Lens with Focusing and Deflection Properties”, Jpn. J. Appl. Phys., 44, pp.6098-6100 (2005).

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Fig. 2 Schematic diagram of a laser manipulation system by using an LC optical device.

Proc. of SPIE Vol. 6374 63740K-4

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Fig. 3 Interference circular fringe patterns of the hole-patterned region.

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(a) V1=V5=80 Vrms, V2= V 4=V6= V8=57 Vrms, V3=V7=40 Vrms,

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Fig. 4 Interference elliptical fringe patterns of the hole-patterned region.

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40 Phase retardation (2π)

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Fig. 6 Optical properties of the LC optical device.

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IMAGING TECHNOLOGY OF THREE DIMENSIONAL DISTRIBUTION FOR SUGAR CHAIN ON SINGLE LIVING CELL-MEMBRANE

Kazuya Yamamoto*, Ichirou Ishimaru, Yoshiki Fujii, Toshiki Yasokawa, Katsumi Ishizaki, Makoto Yoshida, Kaoru Takegawa, Naotaka Tanaka, Shigeki Kuriyama, Tsutomu Masaki, Seiji Nakai Faculty of Engineering, Kagawa University, 2217-20, Hayashi-cho, Takamatsu, 761-0396, Japan ABSTRACT We study on the imaging technology of three-dimensional distribution for sugar chain on single living cell-membrane. This technology can observe the entire cell surface. To observe the cell surface, the local area image of cell-membrane is taken by TIRF (total internal reflection fluorescence) microscopy. And by scanning the whole cell surface area, we can obtain the image of the entire cell membrane. These observed local area images can be converted into an entire surface image by the pattern matching processing. For this scanning technology, we propose the proximal two beam optical tweezers to rotate the single floating cell. This proximal two beam optical tweezers can rotate the floating single cell in the nutrient medium by light pressure. Two beams illuminate the single cell at proximal two points from below and above. The cell is trapped at the center of these two focal points. At the same time, light pressures that are generated at two focal points are made to act as rotational torque. Conventionally TIRF microscope is well known as the observation technology for the cell-membrane using the evanescent light as the exciting light. We can observe the local area images of the fluorescently labeled sugar chain that binds the glycoprotein. Using the proposed optical system, we can obtain the fluorescent distribution images on the cell-membrane. Keywords: evanescent light, fluorescent, cell-membrane, non-contact, light pressure, living cell, normal correlation, pattern matching

1. INTRODUCTION Recently, it has been discovered that specific sugar chains appear on the cell membrane when a cell becomes cancerous. It is also known that ion permeation of a cell membrane is related to cell activity. Thus, it is thought that highly sensitive monitoring of the entire cell membrane will assist to elucidate the cell function. However, information on the cell membrane cannot be obtained using a bright field microscope because the cell is transparent, and the signal from the cell membrane can not be distinguished from the signal from the cell contents. In order to observe phenomena on the cell membrane, we stained specific molecules on the cell membrane using a fluorescent dye. In addition, since we only wanted to excite the fluorescence on the cell surface, we decided to use evanescent light as the exciting light. Evanescent light can be generated on the surface of a cover glass when a light beam undergoes total internal reflection at the cover glass surface. Evanescent light produces a thin layer of light which is only several hundred nanometers in thickness. Thus by using the thin evanescent field as the illumination source allows us to observe just the cell membrane in high sensitivity. However, the contact area between an evanescent field and a spherical cell is narrow, which means that this method cannot be used to observe the entire cell membrane. To realize observation of the entire cell membrane, we propose a method for measuring the three dimensional distribution of only the fluorescent dye located in a cell membrane. As shown in Fig. 1, in this method, the cell membrane is excited by evanescent light, and the entire cell surface is scanned using a non-contact method for rotating the cell. In this letter, we describe the precise positioning system that we designed to bring the cell membrane into contact with the evanescent field and we also describe the experimental results.

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740L, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.685893

Proc. of SPIE Vol. 6374 63740L-1

Be am 1

Evanescent light

Cover glass

Fig. 1. The conceptual diagram for a three-dimensional distribution imaging method for glycoprotein in a cell membrane. This imaging optical system is comprised of a method that excites the cell membrane using evanescent light and a method that rotates the cell without contact by using light pressure from two beams. The surface of the cell membrane can be scanned by rotating the cell.

2. PROXIMAL TWO-BEAM OPTICAL TWEEZERS In this study, in order to scan the entire cell surface, we rotated single living cells using proximal two beam optical tweezers [1-2]. This optical tweezers use the light pressures. The principle of light pressure generated by light absorption is shown in Fig.2. When a beam enters the target object, it is absorbed and travels straight from the incident point to the outgoing point. At this time, a transfer of momentum from the photon to the target object takes place, and light pressure is generated in the direction of the photon movement. This light pressure F is expressed by the equation (1). α is the absorption constant. L is the distance between the incident point and the outgoing point. n is the refractive index. P is the light intensity. c is the velocity of light. F= (1-e-αL) × nP/c.

(1)

To harness this light pressure as a rotating torque, we illuminated a point slightly away from the center of gravity, as shown in Fig. 2. The rotating torque T generated by the light pressure is expressed by equation (2). d is the distance from the center of the cell to the optical axis. T=F×d.

(2)

Beam Photon

L

Cell Fig. 2. The direction of the light pressure generated by light absorption. L is the distance between incident point and out going point.

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However, if just one beam illuminates the cell, the cell is pulled to the focal point. In this case, rotating torque cannot be generated. Therefore, we proposed using proximal two-beam optical tweezers to generate rotating torque. The procedure of rotating the cell is as follows. First, beam 1 illuminates the cell from below, as shown in Fig.3 (a). The cell is trapped at the focal point. Next, beam 2 illuminates the cell at the proximal right-hand point from above, as in shown Fig.3 (b). The cell is trapped at the center of two focal points. In each beam, the light pressure is generated by light absorption, as shown in Fig.3 (c). The light pressure F1 is generated by beam 1 and light pressure F2 is generated by beam 2. In this case, the distance from F1, F2 to the center of gravity is not 0. So, a rotating torque T is generated and the cell is made to rotate in a clockwise direction.

Beam 1 Beam 2

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Fig.3. Procedure of proximal two-beam optical tweezers. Beam 1 and Beam 2 illuminate the single cell from below and above. The cell is trapped at the midpoint between the two focal points. Hence, a rotating torque T is generated and the cell is made to rotate.

3. OPTICAL SYSTEM THAT INTRODUCE PROXIMAL TWO BEAM OPTICAL TWEEZERS INTO TIRF MICROSCOPE We employed this rotational method in conjunction with a total internal reflection fluorescence (TIRF) microscope that was used for observing the cell surface [3-4]. A TIRF microscope can easily generate evanescent light on a cover glass surface that is the observation face. However, because the TIRF microscope employs an infinity correction lens, the cell can not be rotated. As shown in Fig. 4, when the proximal two beam optical tweezers rotational method is incorporated in the TIRF microscope, the beam that illuminates the cell through the TIRF objective lens is focused on the cover glass surface. Since the cell is pressed onto the cover glass surface by the trapping force F, it cannot rotate. In order to rotate a single living cell, the focal point must be shifted from the cover glass surface to the center of the cell. Also, in order to use evanescent light as the exciting light for the cell membrane, a precise positioning method that can position the cell membrane in the thin evanescent field is required. To achieve this, we inserted a concave lens in the light path. The principle of displacing the focal position using concave lens is shown in Fig. 5. The beam that passes through the concave lens is focused at a point that is slightly displaced from the cover glass surface towards the sample. The distance S’ between the focusing point of the beam and the TIRF objective lens can be expressed by equation (3). f is the focal length of the TIRF objective lens. S is the distance between the front focus of concave lens and the TIRF objective lens. S’ = Sf/(S-f).

(3)

In the case of the TIRF objective lens (Olympus, PlanApo 100 × OTIRFM, focal length: 2 mm), when the distance between the focal position and cover glass surface is 10 µm, a change in S of 1 mm will result in a 25-nm change in S’. Therefore, using this precise positioning method for the focal position of the beam, the cell membrane can be positioned in the evanescent field.

Proc. of SPIE Vol. 6374 63740L-3

Beam 1 Beam2

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Cover glass

Fig. 4. When one of the focal points is located at the cover glass surface, the cell is pressed onto the cover glass by the trapping force F. In this case, the cell is prevented from rotating.

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Figure 6 shows the experimental optical system of the three dimensional imaging on the cell-membrane. This optical system is composed of the TIRF microscopy unit and the proximal two beam optical tweezers unit. At the TIRF microscopy unit, to generate the evanescent field on the cover glass surface, the He-Ne laser illuminates the cover glass through the TIRF objective lens. At the proximal two beam optical tweezers unit, to rotate the single cell, two beams that is separated by the B.S. illuminate the cell through each objective lens from bellow and above. And, to bring the cell membrane into contact with the evanescent field, we operate precisely a beam focusing point by displacing the concave lens. The excited fluorescent light on the cell-membrane with rotating the single cell is detected by a cooled charge coupled device (CCCD) camera through the imaging lens. Then, by inserting the fluorescence cube in the light pass of the fluorescent light, the exciting light that was totally reflected at the cover glass surface is filtered out.

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Fig.6. Optical system for measurement of the fluorescent distribution on the cell-membrane.

4. EXPERIMENTAL RESULTS OF SCANNING FLUORESCENT DISTRIBUTION ON CELL-MEMBRANE We verify that the fluorescence distribution of a cell membrane can be scanned by rotating the cell. We used a breast cancer cell (YMB-1-E) whose diameter was approximately 20 µm as a sample. We stained the glycoprotein in the cell membrane using a fluorescent dye that is the lectin labeled (Invitrogen, Alexa Fluor 633). The peak excitation wavelength of this fluorescent dye is 633 nm. Hence, we generated the evanescent light using a He-Ne laser (Sigma koki, 05-LHP-925, wavelength: 632.8 nm). However, the excited fluorescent light had low intensity, thus we measured the fluorescently labeled cell by using a CCCD (Andor, X-1558). Figure 7(a) shows the bright field image of the breast cancer cell in the nutrient medium. This figure was obtained by focusing on the cell surface, but the cell membrane and cell interior cannot be discriminated. Figure 7(b) shows the local area image of the breast cancer cell’s membrane that was obtained by TIRF microscopy. The light from the fluorescent dye that is attached to the glycoprotein in the cell membrane was observed. The image shown in Fig. 7(c) was obtained by scanning the cell surface through one rotation. This image was manually produced by stitching together single images by matching areas having high fluorescent intensities. In this figure, the same fluorescent distributions appear in the two black circles.

Proc. of SPIE Vol. 6374 63740L-5

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2Ojim (c) Fig. 7. (a) Bright field image of a cancer cell in a nutrient medium; (b) the local area fluorescence image of the cancer cell is observed by TIRF microscopy; (c) the image of the cell scanned during one rotation. The same fluorescence distribution can be observed in the black circles.

5. PATTERN MATCHING PROCESSING USING NORMAL CORRELATION COEFFICIENT Figure 8 shows the program flowchart of the pattern matching processing for converting the continuously obtained local area images into an entire image on the cell-membrane. The parallel displacement values, ∆ xi, ∆ yi between the former frame image and the next frame image are calculated by pattern matching method. These values are obtained by heuristic search that find the maximum value of the matching degree. We can obtain the (n-1) numbers of displacement values from the n number of images. The n number of images can be merged into a whole image of the cell-membrane, based on these obtained displacement values.We adopt the normal correlation coefficient as the matching degree. The feature of the normal correlation is that the coefficient is not affected by deference of the average light intensity between the images. The normal correlation coefficient R is expressed by the equation (4). xi is the intensity at i pixel of the former frame image. yi is the intensity at i pixel of the next frame image. n

n

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Proc. of SPIE Vol. 6374 63740L-6

(4)

Read the former frame image

Read the next frame image Displace ∆xi, ∆yi the former frame image

Calculate the matching degree No Find the maximum value? Yes

No All data read?

Yes Convert images into an entire image Fig. 8. The program flowchart of the pattern matching processing.

As shown in Fig. 9(a), this scatter diagram shows the each pixel light intensity relationship between the images. The correlation coefficient is defined as the dispersion from the regression line. The range of R is from -1 to 1. When two images become to be similar, the absolute value of R gets closer to 1. In this case, all data locate on the regression line. And, the inclination of this regression line describes the ratio of the average light intensity between two images. So, the similarity can be estimated, not in accordance with the difference of the average light intensity as shown in (b).

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Fig. 9. The relationship between the light intensity of frame image and light intensity of next frame image. Scatter diagram (a) shows the each pixel light intensity relationship between the images. Scatter diagram (b) shows that the correlation coefficient does not in accordance with the difference of the average light intensity.

Proc. of SPIE Vol. 6374 63740L-7

6. NORMAL CORRELATION COEFFICIENT DISTRIBUTION IN SEARCH SPACE For clarifying the issues of heuristic search, we examine the normal correlation distribution in the search space. 3 typical patterns of the processed images are shown in the upper side of Fig.10. Right hand side image is the former frame image. Left hand side image is the next frame image. The graphs at the lower part of Fig. 10 show the relationship between the parallel displacement values, ∆ xi, ∆ yi and the correlation coefficient. The (a) images have the clear texture. It is expected that the maximum value can be obtained easily. The texture of these (b), (c) images are vague. And the light intensity of (c) image is very low. As the result, in all patterns, the coefficient distributions have the single-peak pattern. And, the peak coefficient of the (c) images is 0.97. So, we can adopt the simple heuristic search to find the global maximum.

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Fig. 10. The correlation coefficient distribution between the former frame image and next frame image of 3 typical textures. The (a) images have the clear texture. It is expected that the maximum value can be obtained easily. The texture of these (b), (c) images are vague. And the light intensity of (c) image is very low.

7. EXPERIMENTAL RESULTS OF PATTERN MATCHING Figure 11 shows a merged image from the continuously obtained images among one rotational period of the cell. The same texture of fluorescent distribution is observed in the white circles that are marked in Fig. 11. However, the interval between the circles is not equal to the perimeter of the cell.

Fig.11. The merged image of the fluorescent distribution among the one rotational of the cell.

Proc. of SPIE Vol. 6374 63740L-8

Hence, we analyze the displacement of the texture between the frame images. Figure 12 shows the relationship between the elapse time of capturing images and the displacement of the rotational direction. In the sections between the 9 to 14 seconds, the inclination is varied. The proximal two beam optical tweezers rotates the cell at approximately constant speed. So, the images in this region are not merged well. This is because the texture of the images in this section is not clearly. Therefore, we will improve the optical system or the image processing for enhancing the image quality.

. 70 60 50 0

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16

Elapse time of capturing images [sec]

Fig. 12. The relationship between the elapse time of capturing images and the displacement of the rotational direction.

8. CONCLUTION We have proposed a method for measuring the three-dimensional distributions of fluorescent dye located only in the membrane of a cell. Using this method on a breast cancer cell, we were able to verify that the surface distribution of a fluorescent dye in a cell membrane can be scanned. In addition, the proximal two beam optical tweezers can rotate the cell in multiple directions by steering the two beams using a galvanometric mirror. Therefore, by extending this technique, it should be possible to measure the entire cell membrane.

ACKNOWLEDGMENTS This study was supported by the 2005 industry-university co-operation official collaboration development business from Kagawa industry support foundation.

REFFERLENCE 1. T.Yasokawa, I.Ishimaru, F.Oohira, R.Hyodo, H.Kobayashi, A.Hayashi,Y.Inoue, K.Ishizaki, “Proposal of spectroscopy-tomography of single-cell,” Optomechatronic Micro/Nano Components, Devices, and Systems, Proceedings of SPIE, Vol. 5604, pp.108-117 (2004). 2. H.Kobayashi, I.Ishimaru, R.Hyodo, T.Yasokawa, K.Ishizaki, S.Kuriyama, T.Masaki, K.Takegawa, and N.Tanaka, “Aprecise method for rotating single cells,” Appl.Phys.Lett, 88, 131103 (2006). 3. Axelrod, D., “Total internal reflection fluorescence microscopy,” Method in Cell Biology, 30, pp.245-270 (1989). 4. REICHERT W M, TRUSKEY G A (Duke Univ., NC, USA), “Total internal reflection fluorescence (TIRF) microscopy. I. Modelling cell contact region fluorescence,” REICHERT W M J Cell Sci Vol.96, No.2, Page219-230 (1990)

Proc. of SPIE Vol. 6374 63740L-9

Laser Irradiation induced Vibrations in Solids Bodo Richert, Hideki Okamura International Christian University, 3-10-2 Osawa, Mitaka, Tokyo, 181-8585, JAPAN contact: [email protected]

ABSTRACT Pulsed Laser beam irradiation induced nm peak to peak resonant vibrations in solids were generated, detected and analyzed. For the evaluation of the induced vibrations, transducers and optical methods were used. The enhancement effect of vibrational amplitude by resonance and other methods was confirmed. The existence of vibrations of picometer amplitude induced by mechanical means in solids are visualized by use of synchronous illumination and optical manipulation. Keywords: Vibration, Resonance, Vibration Measurement, Vibration Visualization, Laser Generation, Laser Induction

1. INTRODUCTION Studies show, that pulsating laser irradiation can induce acoustic waveforms in solids. [1] Though, laser irradiation induced vibrations by well-known methods such as heat deposit and ablation do not offer a sufficiently efficient conversion rates of light into mechanical energy. To the authors knowledge the largest observed laser induced vibrations on a bulk substance are of picometer amplitudes. [1,5] However, there is room to improve the efficiency and enhance vibrational amplitude through new mechanisms and techniques. Recently the feasibility of vibration generation on micro scale objects was confirmed. For instance, a recent study examined a new technique of radiation pressure induced vibration modes of micro-toroids (micrometer scale) for which high Q factors could be determined. [2,3] Along with theses experimental results also theoretical research is conducted to examine the possibility of SAW generation by laser pulses in solids. [4] Laser beams have a definite wavelength, repetition frequency and beam properties. For instance Surface Acoustic Waves (SAW) find applications in non destructive testing (NDT). Also other vibrational wave forms such as bulk and shear waves can be used for propulsion purposes and other actuations. The above described characteristics of laser beams bear a vast potential to refine and improve methods to generate and fine adjust vibrational waveforms without direct contact to the excited bulk substance. This studies goal is to develop and evaluate novel techniques to enhance vibrational amplitudes in bulk substances by adjustments to the above mentioned laser beam characteristics. One idea is to direct a pulsating laser onto a bulk substance at its resonant frequency. Excitation at a resonant frequency with a high Q factor of the excited bulk substance can allow to achieve high amplitude vibrations. Further manipulations on the laser beam to enhance the vibrations amplitude are to be investigated as well. Shen et al for instance predicted in his theoretical study that high energy density laser beams such as focused laser beams can create higher vibrational amplitudes compared to less dense but same energy laser beams. Also the understanding of the process of laser irradiation induced vibrations and the vibrational wave distribution is indispensable to gain control over the vibrations finally and use them in applications. Therefore another objective of this study is to develop and introduce an evaluation technique for the vibrations generated.

2. MATERIALS AND METHODS The analysis of laser irradiation induced vibrations in solids was conducted by sensors and visual means. The excitation in the solid was done with a Q-sw Nd:YAG laser (Spectra Physics Laser Inc. Model J40-BLGS, wavelength 1064 nm, pulse duration ~10ns) whose laser beam was impinging onto the surface of the targets. The laser beams pulse frequency, energy and energy density was changed. To generate the laser pulses a four channel digital delay/pulse generator (Stanford research systems, INC., Model DG535 was used) was used.

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740M, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.688582

Proc. of SPIE Vol. 6374 63740M-1

In this paper, the term front side is meant to be the side at which the excitation laser impinges onto the target surface. Consistent with that, the term back side describes the side opposite to where the excitation laser impinges onto the target. Targets which were used in the experiments were 1. small copper ring of the dimensions: outer/inner radius 48,1 mm/38.7 mm, thickness 2.0 mm. 2. big copper ring of dimensions: outer/inner radius 120mm/100.6 mm, thickness 2 mm 3. absorptive glass disc of dimension: radius 25mm, thickness 2 mm 4. silicon plate The targets were fixed with nylon threads or tape to a fixed stand to allow free vibrations in the target. 2.1. Transducer Measurement 2.1.1. Appliances The mechanical measurement of the vibrations in the excited solids was conducted with transducers (piezoelectric sensors) which were glued onto the surface of the vibrating object. When a vibrational wave passes or stands at the transducers position it will cause the transducer to bend. The transducers used gained a 4V output from bending them 10µm peak to peak.

4V

10µm

5mm

Fig.1

15mm

Fig. 2

Fig. 1 Side view of a transducer as used to measure vibration frequency and amplitude in the target solids. Fig. 2 View of a target (copper ring) with a transducer glued onto the surface. The darkened area on the surface is to enhance the excitation laser beams energy absorption.

2.1.2. Transducer experiment setup The excitation laser beam was directed with a mirror onto the targets surface. Adding of a focal lens allowed to increase and decrease the energy density of the laser beam. Change of settings in the computer allowed further laser beam energy change. The pulse frequency of the excitation YAG-laser was increased in increments gradually from 1kHz to 200kHz. Inspection on the transducers trace in the oscilloscope allowed to observe the reaction in the target from the change in frequency, energy and energy density.

Proc. of SPIE Vol. 6374 63740M-2

laser beam irradiated target with transducer motion sensor/s attached

optional focal lens

Oscilloscope

Q-sw Nd:YAG LASER

frequency generator Fig. 3. Schematic arrangement of the transducer measurement experiment. The focused and unfocused laser beam is directed onto the target solid. Setting of the YAG Laser pulse frequency to a resonant frequency, leads to vibrations in the target. An oscilloscope connected to the frequency generator running the Q-sw Nd:YAG Laser, and the motion sensors (transducers) glued onto the target shows the vibrational frequency.

2.2. Vibration Visualization Experiment A second series of experiments was conducted with the use of a technique introduced by Duncan [5] in a theoretical study on visualization of vibrations by synchronous illumination to a vibration frequency. Duncan’s technique is very sensitive, demands high precision adjustments to the setup and a smooth reflective surface for the illumination beam. To generate sufficiently high amplitude vibrations, a piezoelectric speaker was glued onto a silicon plate which has good reflective surface characteristics. As described in Fig. 7, the blue illumination laser beam was directed through a system of pinhole, lenses and spatial filter into a camera. The reflected blue laser light from the vibrating surface was manipulated by a spatial filter and directed into a camera where a pattern of light fringes gives information about the vibrational wave. The spatial filter used was a manipulated pinhole with an annular region to pass the +1 or -1 diffraction term. An opaque area in the center of the spatial filter was to reduce the relatively high intensity of the 0th diffraction term. The pulse frequency of the illumination laser is synchronized to the vibrational frequency in the silicon wafer which was measured with a transducer. For further investigation of the changes in the vibrating material and to draw conclusions on the propagation pattern the illumination pulses could be delayed relative to the excitation pulses. This feature allows to observe changes between two or more excitation pulses.

Proc. of SPIE Vol. 6374 63740M-3

pin hole

blue Laser

Monitor

10/15/20 µm

ccd-camera

f=9mm

f=50mm

f=400mm

frequency generator

spatial filter laser beam irradiated vibrating target (silicon wafer)

piezoelectric speaker

f=200mm

Oscilloscope

Fig. 4. A schematic sketch of the experiment setup to visualize vibrations in the solid by synchronous amplitude modulated illumination inspired by Duncan. The excited vibrational waves in the solid cause a phase-modulation of light that is reflected from its surface. Correct manipulation and spatial filtering of the reflected light, leads to light fringes due to the vibrations which can be visualized and filmed with a camera.

3. RESULTS 3.1. Transducer Measurements 3.1.1. Detection of waveforms Many eigenfrequencies of the targets were found by changing the excitation laser beams frequency in small increments between 1 kHz to 200 kHz. One Eigenfrequency of the small copper ring target was found at 9.66 kHz. (Fig. 5.a)

Proc. of SPIE Vol. 6374 63740M-4

Transducer trace in Oscilloscope when laser beam impinges on target

Transducer trace in Oscilloscope when laser beam is blocked from Target

I

I

I

YAG-laser pulse

YAG-laser pulse

5.a

5. b.

Fig. 5. a shows an oscilloscope trace of the transducer (ochre) and the pulse generator (red) with spikes each instant when the laser beams hit onto the target at a frequency of 9.66 kHz.. Fig. 5 b shows the oscilloscope traces when the laser beam was blocked from the target, while the laser was still in operation.

By inspection of the oscilloscope traces it can be confirmed, that the vibrations in the solid measured with the transducer are generated by the laser, because blocking the laser beam from the target, leads to the extinction of the vibrations. Giving way to the laser beam to hit the target again resulted in a reestablishment of the vibrations in the solid. Therefore we could confirm, that the vibrations were solely induced by laser beam irradiation 3.1.2. Analysis of waveforms To further analyze the characteristics of the vibrational waveforms in the solid, a second transducer was glued onto the backside (ochre/middle trace Fig.6.) of the target ring in addition to the one on the front side (blue/upper trace Fig. 6.). The transducers were offset approximately at 1/3 of the rings circumference.

Hi

I. j

Table. 1 Amplitudes of vibrations measured with the traces in Fig.3. Frequency

.

16660 Hz (C1 back, ochre/ middle trace) 16660 Hz (C3 front, blue/ upper trace) 79000Hz (C3 front, blue, upper trace)

Amplitude ≈14 nm

≈9 nm ≈2nm

Fig. 6. Shows three oscilloscope traces taken while the YAG Laser beams impinge onto the surface of the target solid with a pulse frequency of 16.660 kHz. The pulse generator trace (red/lower trace) shows the instant in which the laser pulse is generated, the traces show the reading of the transducer on the backside of the target (ochre/ middle trace) and front of the target (blue/ upper trace).

Analyzing the trace in Fig. 6. we can detect several waveforms, amplitudes and frequencies. The main vibration is at 16.66 kHz on both sides and of similar magnitude. In particular ≈14nm on back and ≈9nm on the front. In addition we can observe a second vibration, which is only existent on the front side. This vibration is of small magnitude (≈2nm) and much higher frequency of approximately 79kHz. Further observation of this small amplitude, high frequency vibration leads to the conclusion that the vibration is out of phase, because the last vibration phase before the excitation laser pulse is much shorter than the other vibrational phases.

Proc. of SPIE Vol. 6374 63740M-5

3.1.3. Characteristic of measured resonant vibrations Series of measurements in which the excitation laser pulse frequency was changed in increments where the laser beam energy and energy density were kept constant allowed us to compare vibrational amplitude to laser excitation frequency, determine the Q-factor and half-width. 16

4 12

10

S

6 4

20.2 20.4 20.6 20.S 21 2L2 21.4 21.6 21.S

Frequency (kHz) Fig. 7. Resonance curve of an absorptive glass disc vibrating at and near a resonant frequency.

Figure 7. shows a typical resonance curve for an absorptive glass disc. The transducer trace indicated vibrational amplitude of 6.5nm at 20.4 kHz. Increase of frequency in 200 Hz increments lead to a steep increase in amplitude with a maximum vibrational amplitude of 15.7nm at 20.9 kHz. Increasing the frequency further the amplitude decreased steeply again and was only 5.9 nm at 21.5 kHz. The measured data allowed to determine Q to be 26 with a half width of 0.8 kHz. An unfortunate side effect of the laser irradiation was that due to the heat gradient in the material, tensions caused cracks in the glass disc even for an unfocused low energy YAG Laser beams.

35

Resonance unfocused 10.25 mJ/pulse

30

focused 10.25 mJ/pulse

Amplitude (nm)

25

focused 20.34 mJ/pulse

20

unfocused 20.34 mJ/pulse

15 10 5 0

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 .8 .9 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 .0 .1 .2 .3 .4 16 16 17 17 17 17 17 17 17 17 17 17 18 18 18 18 18

Frequency (kHz)

Fig. 8. Resonance curve of a copper ring excited with focused and unfocused YAG Laser beam at and near a resonant frequency with different laser power settings.

Proc. of SPIE Vol. 6374 63740M-6

The graph in figure 8 shows the resonance curve of the big copper ring (inner/outer radius 100.6/120 mm, thickness 2mm). The experiment was conducted with focused and unfocused laser beams of power 10.25 µJ/Pulse and 20.34µJ/Pulse. The pulse frequency was changed in 50Hz increments between 16.85kHz and 18.45 kHz. We can recognize an increase in amplitude when the YAG-laser pulse frequency approaches the Eigenfrequency of 17.70~17.75 kHz. Also, an irregularity in the amplitude change can be identified in the range of 17.05~17.35 kHz due to additional vibrations similar to those visible in Fig. 6. With a focused high power YAG Laser beam of 20.34µJ/Pulse we could achieve a maximum amplitude of 31.1nm. The half width was measured 0.5kHz and the Q-factor was calculated to be 35.4. For a beam of 10.25 µJ/Pulse the maximum amplitude was found to be 9.8 nm (focused) and 9 nm (unfocused). The qfactors could be determined to be 32.2 for focused and 39.4 for unfocused irradiation. 3.1.4. Amplitude and Laserenergy and Energydensity To examine how laser energy and energy density influence vibrational amplitude of the targets we directed focused and unfocused laser beam at the targets Eigenfrequency onto the surface and measured the amplitude with a transducer. 30

focused

Amplitude [nm]

25

unfocused

20 15 10 5

22

20

18

16

14

12

10

8

6

4

2

0

0 Laser Power [µJ/Pulse] Fig. 9. Vibrational amplitude of a copper ring excited at a resonant frequency of 17.72kHz with a focused and unfocused laser beam at several laser energy settings.

From the measurements and the graph documented in Fig. 9. we can see that vibrational amplitudes are dependent on the energy and energy density of the laser beam. At an energy of 21.84 µJ/Pulse an unfocused laser beam could achieve amplitudes of 12.9nm, while for a focused beam of high energy density amplitudes of 24nm could be achieved. 3.2.

Visualization of vibrations

For vibrations induced by a piezoelectric speaker glued onto a Si plate we could measure vibrations of amplitude 1 µm with the oscilloscope and observe changes in the spatial filtered light pattern when the speaker was switched on and off. (Fig. 10 a, b)

Proc. of SPIE Vol. 6374 63740M-7

Fig. 10 a piezoelectric speaker off

Fig. 10 b piezoelectric speaker on

Fig. 10 shows the image of the reflected and spatial filtered light. The image patterns changed when the vibrations were existent and when not.

It was confirmed that the image change was due to the vibrations by repeatedly switching on and off the piezoelectric speaker and having the identical pattern change repeatedly. In Figure 11 we can see the spatial filtered light reflected from the silicon plate vibrating at a frequency of 17060 Hz with an amplitude of 1µm peak to peak. The images a,b,c,d show the light of the reflected blue illumination laser beam with 0, 10, 20 and 30 µs delay relative to the excitation moment. For a frequency of 17,060kHz we have a phase length of 58.6 µs, what means that we see images of different moments between two excitations. The change in light pattern and images at the delay instants were identical each time.

00 µs delay

Fig. 11a

10 µs delay

Fig. 11b

20 µs delay

Fig. 11c

30 µs delay

Fig. 11d

Fig. 11 A series of light reflection images taken with a delay of the illumination laser beam with respect to the moment of vibration excitation in the silicon plate.

Proc. of SPIE Vol. 6374 63740M-8

4.

DISCUSSION

The experiments could confirm, the feasibility to generate resonant vibrations in solids by laser irradiation. This resonant characteristic implies the possibility to generate high amplitude vibrations in solids. It is important to acknowledge that the vibrations generated with the excitation laser were found on the front and backside of the copper ring. Further enhancement of amplitude could be achieved, by increasing laser pulse energy and pulse energy density. A disadvantage of high energy and high energy density laser beams observed though was, that they damaged the excited vibrating target. Further investigation and development of a multiple point illumination technique and improvement on the material may lead to a solution of the problem. In Figure 8 we can observe irregularities in the resonance curve. These irregularities are due to additional smaller vibrations induced by the excitation laser similar to those in Fig, 6. These small vibrations are one reason, that an efficient conversion of light into mechanical vibrations is difficult and implies that an Eigenfrequency with no disturbing additional vibrations has to be found. Duncan’s technique to visualize vibrations works, but has to be further improved to obtain more details about the vibrations and their natural characteristic. The pictures taken in Figure 11 show clearly that the vibrations generated were no standing wave but changed the structure or surface of the solid.

5. CONCLUSION This paper proofed to the authors knowledge for the first time, that the generation of resonant vibrations in solids by pulsating laser irradiation is possible. Another finding was, that the amplitude of the vibrations is proportional to the beam power and that all vibrations found were of resonant character. All the results imply, that there is a potential to generate high amplitude vibrations in solids by pulsating laser irradiation, when conditions and the technique is further improved. To achieve this goal not only excitation beam characteristics, but also ideal material and shapes are to be identified. The study could also prove that the visualization of vibrations as introduced by Duncan [5] is possible. Further improvement of the visualization experiment setup can lead to an improvement in visualization of the vibrations, which consequently leads to a better understanding of their distribution and can open ways to understand, control and make use of the vibrations.

REFERENCES 1. Dewhurst, R.J., D.A. Hutchins, S.B. Palmer, “Quantitative measurements of laser-generated acoustic waveforms”, Journal of Applied Physics 53(6), (June 1982): 4064-4071. 2. Cameron, Tal, Hossein Rokhsari, Lan Yang, Tobias J. Kippenberg, Kerry J. Vahala, “Temporal Behavior of Radiaton-PressureInduced Vibrations of an Optical Microcavity Phonon Mode”, Physical Review Letters, 94, (2005): 223902-04. 3. Rokhsari H., T.J. Kippenberg, T. Carmon, and K.J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator”, OPTICS EXPRESS Vol. 13, No. 14 (2005): 5293-5301. 4. Shen, Yhong-hua, Shu-yi Yhang, Jian-chun Cheng, “Theoretical Study on Surface Acoustic wave Generated by a Laser Pulse in Solids”, Analytical Sciences Vol. 17 Special Issue (April 2001): s204-207. 5. Duncan, Bradley D. “Visualization of SAW waves by means of synchronous amplitude-modulated illumination”, Applied Optics Vol. 39, No. 17 (10June 2000): 2888-2895.

Proc. of SPIE Vol. 6374 63740M-9

Light-driven micromanipulator and its application for 3D fabrications Yukitoshi OTANI a), Yuji HIRAI a), Yasuhiro MIZUTANI a), Norihiro UMEDA a), Toru YOSHIZAWA b) a

Institute of Symbiotic Science and Technology, Tokyo University of Agriculture and Technology Koganei, Tokyo 184-8588, JAPAN b Faculty of Health and Medical Care, Saitama Medical University Hidaka, Saitama, 350-1241 JAPAN

ABSTRACT: An optical actuator has some interesting characteristics, such as no generation of magnetic noise and receiving the energy remotely. A novel micromanipulator by photothermal effect is proposed. It consists of three optical fiber cantilevers. One end of the fiber is cut for a bevel and painted with black color. A photothermal effect is occurred responding to the incident beam at the end of the optical fiber. It can manipulate a sample and move it in the arbitrary place in 3D space. We succeed to fabricate the 3D structures. Keywords: micromanipulator, 3D fabrication, optical fiber cantilever, optical actuator, photothermal effect

1. INTRODUCTION There are many possibility of optics such as optical measurement. However, quite a few applications of light energy are reported. An optical actuator features characteristics, such as energy supplied remotely in wireless and no generation of magnetic noise, moreover it is possible to build up simple construction. We have also considered possibility to add a sensing function with driving light, like a touch sensor. In recent days, there are many new attempts for actuating and/or driving to small object with nano to micrometers because it is too small to control by electric motor. We focus to build a novel optical actuator for a miniaturized inspection robot of extremity environment

Table1 shows example of various optically driving methods. We classify the various methods. First trial of optical movement was to use an optical radiation power. Optical trapping and tweezers are very famous for its application. To use a photo-electromotive power is one of the first trials of an optical actuator

Electrical motor

kN Gripping power

Paying attention to manipulators, there are many requirements from industry and bio-medical area. It requires for wide variety of samples, not only solid materials as mechanical parts bust also soft one as cells, and non-contact and remote control. Figure1 shows a function compared different motors as size of sample and gripping power. The conventional methods, such as electric motor, ultrasonic-motor, air actuator, and piezo actuator, have limitation of handling size until micro meters and optical trapping area such as nano meters. We focus to develop on the area of undeveloped area.

N Piezo

mN mN nN

Ultrasonic

Air pressure

Undeveloped area Optical trapping

pN nm

mm m Size of sample Fig.1 Function compared different motors as size of sample and gripping power mm

Contact author: email [email protected], http://www.tuat.ac.jp/~otani Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740N, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.689277

Proc. of SPIE Vol. 6374 63740N-1

proposed by Uchino1). This actuator was consisted of PLZT, therefore its moving sped is slow such as several tenth µm per minutes. Our first proposal is an optical actuator using piezoelectric elements and temperature-sensitive ferrite 2,3). However, size of element is a little bit large. Therefore response time is required as several tenth seconds for one movement. Then, we proposed a new type of a small optical actuator that is driven by photothermal Table 1 Conventional method of optically driving effect4,5). An optical fiber oscillator was first reported by Hane6). To method application proposed by overcome limitation of the vibration amplitude, we have proposed an Optical radiation trapping Ashikin optical fiber actuator that was cut for Evanescent photon power trapping Kawata, Umeda Photo-electromotive power actuator Uchino, Nakata a bevel to increase a spring constant. gripper Fukuda Most of them, a light converts to a motor Fukuda mechanical movement by changing Photo-thermal actuator Yoshizawa into heat. We succeeded to move a Otani, Matsuba small machine and manipulate a manipulator Otani, Knopf micro bubble Otani small particles. However, it works Photo-thermal magnetic force motor Takizawa very slowly for practical actuator Mizutani, Otani applications. Photochemical change micro-pump Fukuda manipulator In this paper, we show a micro Photo-chemical change actuator Ikeda （ Azobenzen） manipulator by photo-thermal effect and demonstrate three-dimensional fabrication for its applications.

2.

CONSTRUCTION OF MICROMINIPULATOR

Figure 2 is construction of a micromanipulator made of optical fiber cantilever(OFC). It is composed of three optical fibers jointed to a base. One of the fibers is cut for a bevel as shown in Fig.3. Figure 3 (b) is a photograph of the end part. The surface at the end of fiber is painted on black for photothermal effect. Therefore it can easily absorb light to convert to heat. A thermal expansion is occurred by photothermal effect respond to incident beam. This effect makes the end of fiber stretching to the deformation direction shown in Fig.3 (b). In case the light on, the optical fiber is bend because of thermal expansion light

(a) Shape of end of optical fiber

light deformation direction bevel painted on black

optical fiber 10 mm

sample (b) Photograph of end part

Fig.2 Optical manipulator by optical fiber cantilever

Fig. 3 Part of optical fiber feet

Proc. of SPIE Vol. 6374 63740N-2

20 30 40 50 60 [℃] (a) Deformation and temperature distribution

Power F [µN]

af t er 光入射 11sec 秒後

φ1.0/L20mm φ0.75/ L15m φ1.0/L5 m mm φ0. 75/ L3. φ1 75mm .0/ L2 .5m m φ0 . 5/ L1 0m m

200

光入射前 bef or e

m 8m 8 . 1 5/ L m 7 . experiment φ0 L2.5m 5/ φ0.

150 100 5 0

5mm φ0.5/L1.2

00

10

20

30

40

φ0.25/L5 φ0.25/L1.25 φ0.25/L0.63 50

Incident intensity [mW] (b) Force of manipulation vs incident light power

Fig.4 FEM analysis for photothermal deformation thermal expansion. If the light is off, it returns to the initial position. As the irradiation area for photothermal effect is so small that its frequency response is high because it can take short time for heat exchange. We studied theoretical analysis of the OFC by using the finite element method FEM. We used a plastic fiber with 250 micro meters of diameter. The front edge size of optical fiber is 10 mm of bevel. Figure 4 is the result of FEM analysis before and after illumination by He-Ne laser with 35 mW. The highest temperature is 60 degrees and it bended 60µm. Figure 4 (b) is a result of motion power of front edge by changing of diameters and lengths. We chose best condition of the OFC is 0.5mm of diameter and 10mm of bevel. By using these parameters, the circles in Fig.4(b) are experimental results. Both results are agreed very well.

3.

EXPERIMENTAL RESULT

Figure 5 shows an experimental setup for driving the micromanipulator. Three OFC are mounted on the xyz-stage. A laser diode with 810 nm of wavelength is used as a light source. Its maximum power is 500mW but we usually use less than 50 mW. The light comes in one of the optical fiber by lens. A material of the optical fiber is selected to plastic. We tested the deformation of plastic is 30 times than quartz glass. The size of micromanipulator is 10mm of length, 3mm of width and a diameter of 500 µm. Three optically driving pawls are driven by each laser diodes. We set the optical manipulator on an optical microscope. We control the xyz moving stage to position the manipulator and switch the laser diode to move the OFC for gripping and releasing by personal computer.

Objective lens 対物レンズ

LD+lens

LD レンズ

Z

Y

X

T

光ファイバ

OFC

Fig.5 Construction of light-driven manipulator by optical fibers

Proc. of SPIE Vol. 6374 63740N-3

Figure 6 is experimental results for handling a small plastic particle with 100 µm of diameter. The microscope was focused onto the base plate. Figure 6(a) means before illumination and (b) is just after and after illumination. After illuminating the OFC, it manipulated a micro-particle and it takes 0.3 seconds while it manipulates in case intensity of 35mW. Figure 6 (c) is after the movement to x direction and (d) is just after the release. We succeed to pick the micro-particle. This manipulator can be also utilized in the water. We succeeded to align glass beads to make characters “TUAT” in Fig.7(a).

サンプル particle

I

0

100µm 100mm

(a) Before manipulation

(b) Manipulation

0 (c)

U (d) After manipulation

Moving

After repeating this Fig.6 Manipulation process of glass beads sample process, we can fabricate the three-dimensional structure. Z Figure 7(b) demonstrates three-dimensional fabrication of micro particle with 100µm of diameter with the four layers We used UV cure adhesive on each layer. The width of this line is 300 µm. We succeed to fabricate the 3D structure.

Z Y X

Y

Z

X

100µm 100µm

(a) 2D alignment

(b) 3D structure

Fig.7 Manipulated results of glass beads

Proc. of SPIE Vol. 6374 63740N-4

4.

CONCLUSION

We developed an optical manipulator consisted of optical fiber cantilevers. We succeed to move a new type of a micromanipulator that is driven by photothermal effect. It consists of an optical fiber cantilever with the size of 3x3x10mm. It moves less than 1 second of speed. Moreover, we analyzed deformation of optical fiber cantilevers by FEM. We demonstrated particle movement and alignment of glass beads even if in water condition. Finally, we succeed to fabricate three dimensional structure of glass particles. We intend to expand to an optical robot for micro optomechatronic machine. Moreover this manipulator is powerful to handle for bio-medical sample

REFERENCES 1. 2. 3. 4. 5. 6. 7.

K.Uchino : J.Rob.Mech., 1, pp.124 (1989). K.Fukushima, Y.Otani, T.Yoshizawa : Proc.of China-Japan Bilateral Symposium on Advanced Manufacturing Engineering, pp.49 (1998). T.Yoshizawa, D.Hayashi, Y.Otani :Proc.SPIE Vol.4190, pp.212 (2001). Y.Otani, Y.Matsuba, T.Yoshizawa : Proc.SPIE Vol.4564 (2001) pp.216-219. Y.Matsuba, Y.Otani, T.Yoshizawa : Proc.SPIE Vol.4902 (2002) pp.78-82. S.Inaba, H.kumazaki, K.Hane : JJAP, 34 (1995) pp.2018. Y.Otani, Y.Matsuba, S.Chimura, N.Umeda, T.Yoshizawa : Micromanipulator by photothermal effect, Proc.SPIE Vol. 5264 (2003) pp.150-153.

Proc. of SPIE Vol. 6374 63740N-5

Optimal actuation of micro-cantilevers by a laser beam Sagnik Pal and Anjan K. Ghosh Department of Electrical Engineering Indian Institute of Technology Kanpur India-208016. Abstract Singly-clamped micron-sized cantilevers actuated by optical radiation pressure exerted by a laser are analyzed. An expression for optimum point of actuation giving the maximum amount of deflection is obtained. Introduction A beam of light can exert sufficient radiation pressure to move a micro-structure. Ref. [1], [2], [3] present experimental evidence of actuation by radiation pressure. Several applications of optically actuated MEMS cantilever, such as photodetector, optical information processing, analog computation are investigated by researchers [4], [5]. In this paper, we analyze the steady state deflection of a singly-clamped, polysilicon microcantilever on which a CW laser beam is incident normally. We assume that the microstructure is overdamped and under the action of the laser beam searches a steady deflection without any oscillations. We show, through analysis and simulations, that there exists a point of incidence of the laser beam that produces the maximum steady-state deflection of the cantilever tip. An expression for the point of incidence corresponding to maximum deflection is derived. We calculated the temperature increase due to the CW laser beam. The effects of changes in material properties due to laser heating are found to be negligible. The knowledge of the optimum deflection under optical actuation is helpful in designing opto-mechanical microsystems such as switches. Analysis The steady state deflection, v(x), of a uniform singly-clamped cantilever with a length L , width W , thickness H is described by [4]

d 2 v M ( x) = EI dx 2

(1)

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740O, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.685947

Proc. of SPIE Vol. 6374 63740O-1

where E is the elastic modulus of the cantilever material, I = WH 3 / 12 is the cross sectional-area moment of inertia and M ( x) is the total internal bending moment at position x . The boundary conditions are v = 0, dv / dx = 0 at the fixed end. The pressure exerted by a normally incident beam of light on non-absorbing objects is [4]

p =

2RS c

(2)

where S (W / m 2 ) is the modulus of Poynting vector, R is the reflection coefficient and c is the speed of light. For a Gaussian laser beam centered at x = A, y = 0 (see Fig.1 below) and normally incident on the cantilever, the intensity profile is given by, −2 (( x − A ) 2 + y 2 ) w02

S = I 0e

(3)

where w0 is the laser spot size. The pressure exerted, and hence the cantilever tip deflection, varies OPI1CAL PRESSURE CENTERED

AT: A y=O

SIDE H

VIEW

V <=0

x=.

XA

V/

t

/ / / /

y=b

W2b

x

Top VIEW

y=-b Fig. 1: Singly-clamped cantilever actuated by laser

with the center of the beam. From (2) and (3), the force per unit length exerted by a laser normally incident on the cantilever,

Proc. of SPIE Vol. 6374 63740O-2

−2 ( x − A ) 2

b

q( x) =

∫ p ( x, y)dy = Be

w02

(4)

−b

where, B=

⎛ W ⎞ 2π RI 0 w0 ⎟ erf ⎜ ⎜ 2w ⎟ c 0 ⎠ ⎝

(5)

The internal bending moment in the cantilever is, x

M ( x) = ∫ q ( x1 )( x − x1 )dx1

(6)

0

Let, l = L / w0 , a = A / w0 . The solution of (1) for the internal bending moment corresponding to the force distribution given by (4) yields

(

(

)

2 Bw04 v ( x = 0) ≈ 2 2π 1 + erf ( 2a ) l 3 − 3 2π (1 + erf ( 2a ))al 2 − 3e − 2 a l 2 24 EI

)

(7)

We assume that the length of the cantilever is greater than ten times the laser spot size, i.e., L > 10 w0 . Hence, terms containing lower powers of l have been neglected in (7). At a = a optimum , v( x = 0) is maximum. dv / da = 0 at x = 0 and thus 4 2 −2a 2 le = (1 + erf ( 2a )) 3 π

(8)

2

Since, for a ≥ 0 , e −2a is monotonically decreasing and (1 + erf ( 2a)) is monotonically increasing, the solution of (8) increases monotonically with l . For L / w0 = l ≥ 10 , (9) yields a ≥ 0.92 i.e.

erf ( 2a ) ≥ 0.93 . Putting erf ( 2a ) ≈ 1 in (8) gives a optimum =

Aoptimum w0

=

1 2 2l log e 2 π 3

Proc. of SPIE Vol. 6374 63740O-3

(9)

Simulations

A polysilicon cantilever with L = 1000µm, W = 30µm, H = 1µm , E = 160 GPa is considered. Eq. (1) is solved numerically to obtain cantilever deflection vs. A for w0 = 35.3553µm for a CW laser with power= 1W . From numerical calculations with various values of A we observe Aoptimum = 41.25µm as depicted in the plot of deflection v vs. A in Fig.2. From (9) we find, Aoptimum = 41.16 µm . Thus, analytical and numerical calculations produce almost similar results.

3/ \ N

12.57 2 i 0 = 2 0

—

o a)

N

I I I

0-

1-

= 0

I

0

0

I

I

I

I

0.1

0.2

0.3

0.4

I

0.5

0-6

F

0.7

I_

0.8

0.9

Point at which laser is incident (A microns) Fig.

2:

Cantilever

tip

deflection

vs.

A . ( L = 1000µm , W = 30µm , H = 1µm ,

10

E = 160 GPa ,

w0 = 35.3553µm , Laser power = 1Watts.) The steady state temperature profile along the cantilever length is obtained by numerical solution of the heat equation [3]. Both ends of the cantilever are assumed to be thermally insulated. 1% absorption of the incident laser power is assumed. Temperature dependence of Young’s modulus and the thermal expansion coefficient for silicon are obtained from literature [6], [7]. Change in the cantilever tip deflection due to thermal effects is found to be less than 0.5%.

Proc. of SPIE Vol. 6374 63740O-4

We repeated the calculations with a few other values of cantilever dimensions. The results of our calculation are shown in Table 1. In each calculation the analytical result of maximum deflection matches well with simulations. Sl. No.

1. 2. 3. 4.

L (microns) (a)

w0 (microns) (b)

L / w0 (c)

1000 1000 1000 1000

25 33.33 50 100

40 30 20 10

Table 1: Analytical and simulated values of

Aoptimum Simulated (d) 30.95 39.30 54.57 92.61

Analytical (e) 30.91 39.22 54.37 91.41

Aoptimum

Conclusions

Singly-clamped cantilever actuated by optical pressure from a laser beam is analyzed. It is assumed that the length of the cantilever is an order of magnitude greater than the laser spot size. The effects of changes in material properties due to laser heating are negligibly small. Analytical expression for optimum point of laser actuation is derived for normal incidence. Good agreement between simulation results and analytical expression is observed. References: 1 Ashkin, A, ‘Acceleration and trapping of particles by radiation pressure’; Phys. Rev. Lett.; vol. 24, no. 4, Jan. 1970; pp156-159 2 Gauthier, Robert C. et al., ‘Optical selection, manipulation, trapping and activation of a microgear structure for applications in micro-optical-electromechanical systems’; Appl. Optics, vol. 40, no. 6; Feb 2001; pp. 930-937. 3 Sulfridge, Mark et al., ‘Optical actuation of a bistable MEMS’; J. Microelectromechanical Systems; vol. 11, no. 5, Oct. 2002; pp.574-583 4 Dragoman, M and Dragoman, D., ‘Optical actuation of micromechanical tunneling structures’; 22nd Int. Annual Conf. Semiconductors, Sinaia, Romania; 1999; pp. 451-455 5 Dragoman, D and Dragoman, M., ‘Optical actuation of micromechanical tunneling structures with applications in spectrum analysis and optical computing’; Appl. Optics, vol. 38, no. 32; 1999; pp. 6773-6778 6 Nandapawar, M. L. and Rajagopalan, S., ‘Wachtman’s equation and temperature dependence of bulk moduli in solids’; J. Appl. Phys., vol. 49;July 1978; pp. 3976-3979 7 Bao, M. ;’Analysis and design principles of MEMS Devices’ ; New York, Elsevier, 2005.

Proc. of SPIE Vol. 6374 63740O-5

Development of PC controlled laser manipulation system with image processing functions Yoshio Tanaka*a, Akitsugu Murakamib, Ken Hiranoa, Hideya Nagataa, Mitsuru Ishikawaa a

b

AIST, AIST Shikoku, 2217-14 Hayashi-cho, Takamatsu, 761-0395 Japan Faculty of Engineering, The University of Tokushima, Tokushima, 770-8506 Japan

ABSTRACT Laser manipulation is an important technique suitable for controlling objects in liquid at length scales ranging from sub-micrometers to micrometers. However, the use of this technique by itself is not enough to dexterously or automatically manipulate objects. In this article we propose a concept for automated non-contact micro-manipulation combined with laser manipulation and advanced control system techniques, and describe the configuration of a developed system, i.e. a three-beam laser trapping system with excellent user-interfaces, real-time image processing functions and a micro-laser ablation beam. We also show the results of several demonstrations; namely the arrangement of metallic particles, the manipulation of a non-spherical object, the laser perforation of a cell, and the automated selection and transportation of colored micro beads. Keywords: laser trapping, optical tweezers, laser scanning, image processing, automatic control, laser perforation, MEMS, Lab-on-a-Chip, user-interface, non-spherical object

1. INTRODUCTION Micro/Nano manipulation technology for micro/nano electromechanical systems (MEMS/NEMS) and Lab-on-aChip is currently an area of intensive research. Laser trapping of micron-sized dielectric particles was first demonstrated by Arthur Ashkin in 1970 [1]. This technique has been further extended [2-7] and is widely used for non-contact micro/nano manipulation in various fields including physics, chemistry and biology. The ability to manipulate small transparent objects without physical contact, as opposed to the use of mechanical micro-hands [8], allows for many interesting studies of biological systems by applying pico-newton forces to objects [9,10]. However, the control system and user-interface of a conventional laser trapping system is insufficient to manipulate objects in a three-dimensional (3D) working space, if the intention is to manipulate dexterously or automatically the objects in real time. We have developed a three-beam laser trapping system with excellent user-interfaces, real-time image processing functions and a micro-surface-processing beam. In this paper, we first propose a concept of automated non-contact micromanipulation system based on laser manipulation and advanced control system techniques, and suggest suitable areas of application. Next, we describe the system configuration of the developed system. Finally, we show the results of several demonstrations; namely the arrangement of metallic particles, the manipulation of a micron-sized non-spherical object, the laser perforation of a cell, and the automated and selective transportation of colored micro beads.

2. CONCEPTUAL SYSTEM DESIGN Many powerful laser manipulation techniques have been proposed [2-7] since the first laser trapping demonstration by Ashkin [1]. Figure 1 shows the principle of laser manipulation based on geometrical optics. For a spherical particle with * Correspondence: Email: [email protected], Telephone: +81-87-869-3582, Fax: +81-87-869-3582

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740P, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.684978

Proc. of SPIE Vol. 6374 63740P-1

a high refractive index, a single-beam laser trap, known as optical tweezers, is used widely (Fig. 1(a)). The symbols of FA and FB represent the radiation forces corresponding to rays A and B, and f represents the focal point of an incident laser beam. For manipulating a metallic or low-refractive-index particle, the laser scanning technique first demonstrated by Sasaki [2] has proven extremely useful. In addition, the synchronous scanning technique of multiple beams further enhances the ability of pattern formation, not only for high-refractive-index particles [3] but also for metallic particles (Fig. 1(b)) [11]. Therefore, the complementary use of optical tweezers and laser scanning techniques enables noninvasive manipulation of all micron-sized objects with specific optical properties. However, for the following two reasons, unassisted use of these laser manipulation techniques is not sufficient to manipulate dexterously a non-spherical object in a 3D space or to automatically trap and transport objects. Firstly, in order to avoid thermal damage to biological objects, laser beams generally used are in the IR region. Thus, an operator cannot identify exactly the actual focal points of incident beams. Secondly, a non-artificial object generally has an inhomogeneous refractive index and a non-spherical shape; consequently, undesired torques as well as forces may be generated. To achieve dexterous or automatic manipulation for arbitrarily-shaped micro-objects, we propose a laser manipulation system combined with image processing and automatic control techniques. Figure 2 conceptualizes the system, and also shows suitable areas of application, such as skilled operation in the medical/biotechnology field, laser-controlled µ-TAS, micro-fabrication of MEMS and micro-liquid processes. In this hypothetical system, the control algorithms installed in a

Laser Beam

−∆P Objective Lens

B

P1

A

∆P

P2

FA

f

F

o

FB

Sphere Particle

(a) a

Laser Beam

b

Synchronous Scanning Beam 1

Objective Lens Condensed Beam

Beam 2

Fa Metallic Particle

Ft

Z Y

f Fb

X

Metallic Particle

(b) Fig. 1 Principle of laser manipulation based on geometrical optics. (a): conventional optical tweezers for a micro particle with a high refractive index. (b): synchronous laser scanning manipulation for arranging metallic or lowrefractive-index particles.

Proc. of SPIE Vol. 6374 63740P-2

drilling of particle/cell

µ-TAS

Control system technology • Image processing • Automatic control theory

Fusion / Combination

illuminator

spermatozoom, fluorescence bead non-contact injection micro pipette

micro vessel (micro reactor) xyz stage

Micro fabrication direct/indirect manipulation using laser beams

Laser Manipulation

Skilled operation under medical/biotechnology field

micro nozzles non-contact micro arrangement micro chemical reagent micro vessel/reactor

Micro-liquid process micro nozzle

Input/output interface for real time control objective lens

transportation and precise making thin film application

functional liquid organic device/IC

Three laser beams for 3D manipulation micro machine/structure

Laser beam for micro surface processing Visual information

microscope

Fig. 2 Concept of the automated micro-manipulation system and its areas of application.

personal computer (PC) determine a 3D focal position of each beam through real-time feedback signals based on visual information, such as position, color, size, and shape of the target objects. In addition, a laser beam for micro-surfaceprocessing is also set up in order to complete all tasks, such as marking, perforation and manipulation, in a microscopic closed environment without physical contact.

3. DEVELOPED SYSTEM 3.1 Optical Configuration To demonstrate the hypothetical system described above in Section 2, we have set up a three-beam laser trapping system as an additional optical structure linked to a commercially available inverted microscope. Figure 3 shows the optical configurations of the developed system. The laser trapping sources are a continuous wave (cw) Nd:YAG laser with wavelength 1064 nm and a cw Cr:Forsterite laser with wavelength 1250 nm, with the former laser beam split in two (i.e., into horizontally and vertically polarized beams). The micro-surface processing beam is the third harmonic pulse of a Q-switched Nd:YAG laser, with a wavelength of 355 nm. These three trapping beams, the surface processing beam and visible laser beams, which are made of a He-Ne laser with wavelength 633 nm and form the indicator for each trapping beam, are introduced coaxially into the optical microscope through a relay lens, a dichroic mirror and an oil-immersed objective lens. The 3D focal position of each trapping beam is independently controlled; those on the X-Y axes by a set of PC-controlled galvano mirrors and that on the Z-axis by a lens on a linear motorized stage which can be moved parallel to the optical axis. We can specify the focal positions of the trapping beams by real-time man-machine communication functions using a pointing device, that is, a PC mouse “click-and-drag” procedure. See Section 3.2 below. 3.2 User-Interfaces We have developed a PC mouse tracking system under the Windows® operating system as the user-interface, by which the focal position of each trapping laser beam on the X-Y axes follows the mouse cursor in real-time. This interface enables us to control interactively the focal positions of the corresponding trapping beams by a simple “click-and-drag” procedure. In order to better facilitate control of the focal position of each laser beam, we have attached coordinate systems rigidly to the mouse cursor in the operation-window and to the microscopic environment in the image planes. Figure 4 shows the coordinate systems of the mouse tracking system. The PC mouse is easier to operate than a conventional dial-

Proc. of SPIE Vol. 6374 63740P-3

P1

BD1

cw Nd:YAG Laser, 1064nm, 16W(max), TEM00 R1 λ/2

Z1 axis SH1 BS2 P4

P5

Z3 axis

GM3

SH2 BS1

BD3

P4

BE4 BE3

BE2

He-Ne Laser, 633nm

P0

Pulsed Nd:YAG Laser (3rd harmonic, 355nm, 4mJ)

R3 λ/2

dichroic mirror

P2

SH3

Z4 axis

relay lens

R2 λ/2

BS3

Z2 axis

GM2

BD2

BE1

cw Cr:Forsterite Laser 1250nm, 400mW(max) TEM00

GM1

Windows® NT Ver.4

CCD Camera

DA Board Image Processing Board

Microscope

Personal Computer (PC) System

P: polarizer, R: retardation plate (halfwave plate), GM: galvano mirror, BS: beam splitter, BD: beam damper, BE: beam expander, SH: shutter

Fig. 3 Optical configuration of a three-beam laser manipulation system with a processing beam and an image processor.

< operation frame >

< microscopic frame >

objective lens

z (focal axis) y

desired position object image

laser beam

Dy

image feature

object

Dx

computer

mouse cursor

monitor

Mx

Cartesian control law

My

x focal point (x,y,z)

mouse

user

Fig. 4 Coordinate systems of the mouse tracking system.

controller, because both the operation frame and the microscopic frame are defined in a Cartesian coordinate system. We have also installed real-time image processing functions using an image processing board (IP5005BD, Hitachi Inc.). All activity in the micro-environment is monitored through a color CCD camera and shown on both a TV monitor and the computer display, along with additional information such as approximate focal positions of the invisible trapping beams and scanned beam trajectories, all of which are obtained or generated using the real-time image processor.

Proc. of SPIE Vol. 6374 63740P-4

4. DEMONSTRATIONS 4.1 Arrangement of metallic particles The synchronous laser scanning technique illustrated in Fig. 1(b) was applied to the arrangement of silver particles in water. The synchronous scanning of multiple laser beams forms an “optical cage” between the scanning trajectories; consequently, the particles in the cage are arranged gradually with the passage of time. This technique enhances the ability to manipulate and form patterns [2, 11]. Figures 5(a) and 5(b) show the process of arranging silver particles in a straight line using two beams. The power and scanning frequency of each laser beam were 25 mW and 12.5 Hz, respectively. Using the image processing functions of the IP5005BD, the scanning trajectories of the invisible trapping beams were displayed on the monitor as solid white lines. As the distance between the two trajectories narrowed, the particles between the trajectories aligned themselves. Figures 5(c) and 5(d) show the process of arranging silver particles in a circle. In this case, each laser beam was 25 mW, with a scanning frequency of 7.7 Hz. In the case of coaxial circular scanning with two beams, the optical cage forms a torus like as closed doughnut. The particles between the trajectories, namely the particles in the doughnut-like cage, were arranged in the center of the torus after 30 seconds (Fig. 5(d)).

SI

(b)

(a)

S.' •

I

St 4 S

•

S.

*

.4 10µm

(c)

10µm

(d)

a

4

IIIq

4

4

I

— 10µm

4

10µm

Fig. 5 Examples of the process for arranging metallic (silver) particles using synchronous laser scanning. (a): in a straight line, (b): in a circle.

4.2 Manipulation of non-spherical object User-controlled dexterous manipulation, namely control of laser beam movements by an operator’s mouse clickand-drag procedures (mouse-controlled movements), of non-spherical micro-objects was demonstrated preliminary to their fully automated micro-manipulation by control algorithms based on visual feedback signals. A rod-shaped material (aluminum borate whisker) in water was stably trapped on the X-Y plane by simultaneous irradiations of two beams at tip positions on either side of the rod, if in the case of single-beam irradiation the trapped rod rotated in the beam axis (Z-axis). The subsequent manipulation of the trapped rod on the X-Y plane was easy to perform by the mouse-controlled laser-beam movements. Figure 6 shows a sequence of images recorded with the CCD camera showing an example of the trap and dexterous manipulation of the whisker. First, the whisker was stably trapped by simultaneous irradiations of the two beams at the tip positions on either side of the rod (Fig. 6(a)). The irradiation points are indicated by

Proc. of SPIE Vol. 6374 63740P-5

the black arrows. Second, by means of mouse-controlled laser-beam movement at each irradiation point, in the direction represented by the white arrow, the orientation of the whisker was dexterously changed in the X-Y plane, as shown from Fig. 6(a) to Fig. 6(d). Finally, when we stopped the laser irradiation at one end (tip position 1), the irradiation at the other end (tip position 2) maintained the entrapment of the whisker; however, the orientation of the trapped whisker changed from within the X-Y plane to in the Z-axis (Fig. 6(e)).

(c)

(b)

(a) 1

1

2 A

(d)

2

4

7

/

1 2

a

(e)

2

2

1 sa

Fig. 6 Dexterous manipulation of a non-spherical micro-object using a PC mouse “click-and- drag” procedure.

4.3 Laser perforation of a cell In order to explore the potential for new applications in the medical/biotechnology field, we have demonstrated the laser perforation of a specific cell using single-shot laser ablation. Figure 7 shows an example of the bursting of a specific single cell (rat brown pro-adipocyte cell). The selected cell is indicated by the arrow, and the target position of the singleshot pulse beam by the solid circle. In this demonstration, the Q-switched laser power was operated at less than 2 mJ/pulse, but the irradiation power within the microscopic environment through some optics was not measured precisely, because it was too weak to be measured directly. The plasma membrane at the specified position on the cell surface was drilled, and the subsequent bursting of the membrane after the perforation enabled us to access and manipulate its organelles, such as the nucleus in the cell (Fig. 7(b)).

(a)

(b)

10µm

10µm

Fig. 7 Example of the bursting of a specific single cell (rat brown pro-adipocyte cell) using laser perforation. (a): before laser shot, (b): after a few single-shots.

Proc. of SPIE Vol. 6374 63740P-6

4.4 Automated transportation of micro beads We carried out an automated particle transportation experiment using real-time pattern recognition techniques in order to explore the future possibilities for an advanced laser-controlled flexible ‘lab-on-a-chip’. In this demonstration, positions of all polystyrene micro-spheres, which were dyed white or blue, in an aqueous solution were first detected by real-time image processing techniques, after which the beads of a pre-specified color and size were automatically and selectively trapped and transported to the destinations one by one. Figure 8 shows a sequence of images recorded with the color CCD camera. In Figs. 8(a)-8(d), the fifteen white 5µm-squares which form the letter ‘S’ and represent the virtual destinations in the workspace, were made using an image processor board and exist in the same image plane. The relevant beads in each scene are indicated by the same numbered arrows. First, based on the pre-specified color and size information, the three blue beads that had to be transported were detected in the scene by color image processing techniques (Fig. 8(a)). Second, the three beads were trapped and transported one by one to their three destinations at the bottom of the letter ‘S’, automatically (Figs. 8(b)-8(d)). Finally, these beads were aligned in their bottom destinations. Note that the beads were released from laser entrapment after the transportation by closing the shutter; therefore, in Fig. 8(d) the particle indicated by arrow 2 has disappeared from the scene because of Brownian movement. (b)

(a) 3

0 2

S

2

1=•

1

_____ 0 (c)

0

••

(d)

I

3

I

0

• •

0

10µm

10µm

II I

2

1

1

EP 10µm

0

3

3

1

1

—

0

10µm

Fig. 8 Demonstration of the automated transportation of colored micro-beads using optical tweezers combined with image processing techniques

5. CONCLUSION We have developed a laser trapping-ablation system combined with real-time image processing techniques and mouse-controlled user-interfaces, and have carried out four demonstrations using samples with various optical properties and shapes. Although the demonstrations performed are indeed simple, the system can be used as a research tool in the various fields of research mentioned in Section 2. Furthermore, it is expected in the future that a such system combined with real-time visual-feedback control algorithms will automatically perform work equivalent to a skilled operator’s in a microscopic environment, or will be used to assemble versatile micro-devices in industrial as well as research fields.

Proc. of SPIE Vol. 6374 63740P-7

ACKNOWLEDGEMENTS We would like to thank Dr. Satoshi Fukuoka of AIST Shikoku for preparation of the rat brown pro-adipocyte cells. This work was partly supported by Grants-in-Aid for Scientific Research (C, #1756021) from the Japan Society for the Promotion of Science.

REFERENCES 1. 2.

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett., 24-4, pp.156-159 (1970). K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Optical trapping of a metal particle and a water droplet by a scanning laser beam,” Appl. Phys. Lett., 60-7, pp.807-809 (1992). 3. K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Pattern formation and flow control of fine particles by laser-scanning micromanipulation,” Optics Lett., 16, pp.1463 (1991). 4. J. E. Curtis, Brian A. Koss, D. G. Grier, “Dynamic holographic optical tweezers,” Optics Communications, 207, pp.169-175 (2002). 5. D. G. Grier, “A revolution in optical manipulation,” Nature, 424, pp.810-816 (2003). 6. P. J. Rodrigo, V. R. Daria, J. Glückstad, “Four-dimensional optical manipulation of colloidal particles,” Appl. Phys. Lett., 86-7, 074103 (2005). 7. F. Arai, K. Yoshikawa, T. Sakami, T. Fukuda, “Synchronized laser mi romanipulation of multiple targets along each trajectory by single laser,” Appl. Phys. Lett., 85-19, pp.4301-4303 (2004). 8. T. Tanikawa, T. Arai, “Development of a micro-manipulation system having a two-fingered micro-hand,” IEEE Trans. on Robotics and Automation, 15, pp.152-162 (1998). 9. J. T. Finer, R. M. Simmons, J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometer steps,” Nature, 368, pp.113-119 (1994). 10. P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cell using multiple optical trapping,” Biophysical Journal, 69-5, pp.1666-1673 (1995). 11. Y. Tanaka, H. Misawa, Y. Kinouchi, “A new arrangement method of metal particles using synchronous scanning laser beams,” Trans. Society of Instrument and Control Engineers, 36-5, pp.459-461 (2000). (in Japanese) 12. H. Misawa, M. Koshioka, K. Sasaki, N. Kitamura, H. Masuhara, “Three-dimensional optical trapping and laser ablation of a single polymer latex particle in water,” J. Appl. Phys., 70-7, pp.3829-3836 (1991).

Proc. of SPIE Vol. 6374 63740P-8

A robust vision-based technique for human arm kinematics identification Omid Talakouba and Farrokh Janabi Sharifib a Department b

of Electrical and Computer Engineering, Ryerson University, Toronto,Canada M5B 2K3, Email: [email protected]; Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada M5B 2K3, Email: [email protected] ABSTRACT

Motion, independent of forces, is described by kinematic parameters (usually using Denavit-Hartenberg convention) that have been used widely in biomechanical ﬁelds. Examples of these ﬁelds include robotics, human motion studies, and biomechanical structures’ design and control; e. g. for exoskeleton and artiﬁcial human arm. A common way to precisely measure the joints movements is by using a motion capture system. Until now, the most successful motion capture technology is optical motion capture; this is due to its highly accurate measurement of small reﬂective markers that are attached to some relevant body landmarks. This paper addresses the problem of estimating the human arm kinematics parameters from video or captured images of human arms. We introduce a new robust framework that leads to reliable and accurate estimation of shoulder and elbow center of rotations along with the arm kinematics parameters. Keywords: Arm, Kinematics, Optical Tracking, Estimation, DH parameters

1. INTRODUCTION Many research areas are interested in the human arm kinematic parameters, because of its wide range of applications from rehabilitation purposes to army power-man exoskeletons. Some clinical approaches or rehabilitation institutes are seeking for estimation of patients’ kinematic parameters over the clinical rehabilitation period in order to take the patient rehabilitation progress into the consideration. Usually a reaching task is considered to evaluate these parameters.1 For instance, Bown et al.2 combined electromyography (EMG) signals with kinematic modeling in order to distinguish between healthy cases and objects with Muscular Dystrophy. Reach and Grasp task captured as another approaches to study forearm movement.3 Although reach and grasp is not a general forearm movement, Lan and Baker validated their proposed kinematic model for that certain task by using a magnetic-sensor-based 3D motion capture system. All the researchers evaluated human kinematic parameters by capturing the body motion, to the best of our knowledge. Until now, the most successful motion capture system is optical motion capture. This is due to its high precision measurement of little reﬂective markers, attached on some relevant body landmarks. Basically the most commonly used motion capture techniques employ optical methods to record a subject’s motion. Van Bogart et al.4 gathered kinematic data of the upper extremities by 3D motion analysis system using seven infrared Charged-Coupled Device (CCD) cameras and retro-reﬂective markers in order to obtain a 3D kinematic model for the Adult Ischemic Stroke Patients. A method was proposed to dynamically assess the eﬀect of thoracic trunk posture on Scapular kinematics5 during (1) elevation of the Humerus in the Scapular plane and (2) axial rotation of the Humerus during elevation in the scapular plane. In this study, the electromagnetic tracking method was provided data with good reliability, and the root mean square errors were small for measuring Scapular and Humeral movements. This also conﬁrms the results of previous studies that showed the method provided highly reliable data.6, 7

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740Q, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.686229

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Many researchers have been working on controlling a slave robot from a remote site using a master arm which widely used in telesurgeries. A popular teleoperate technique is exoskeleton type master arm. Lee et al.8 introduced a arm-exoskeleton system in order to measure the changes in kinematic parameters to control the slave arm. Most of the exoskeleton type master arms have a similar kinematic design to that of the slave arm, with actuators, usually electric motors; thus making the master arm bulky and heavy. To over come this issue teleoperation with motion capturing devices was introduced,9 which generates the slave robots motion command from the partitioned inverse kinematics showing that the masterarm’s kinematic structure does not have to be same as the slave robot’s. The human arm mechanism, particularly shoulder joint, is the most complex mechanism in the human body. Biomechanics scientists has usually modeled the shoulder as 5-DOF mechanism with the assumption that the shoulder’s center of rotation is ﬁxed. Biryukova et al. modeled shoulder as a joint with the center of rotation ﬁxed in relation both to the scapula and the upper arm.10 The proposed model allowed a description of the human arm kinematics in terms of rotations about natural anatomical axis. However, there are many evidences showing that this model is not exact either. First, the forearm segment is not rigid because of the rotations of the radius relative to the ulna and the hand segment is not rigid because of the displacements of the carpal bones. Second, the shoulder center of rotation as well as elbow and wrist axis of rotations can move relative to the adjacent segments during the movements.11 Nevertheless, the proposed model seems to be a reasonable compromise between accuracy and simplicity of the human arm description.12 Some other researchers considered the human arm as 7-DOF manipulator to model shoulder movements completely. For instance, Okada et al. 13 addressed development of shoulder a movable center of rotation, which enables unique human-like motion in contrast to the conventional design of anthropomorphic 7-DOF manipulators that have base three joint axis intersecting at a ﬁxed point. Okada focused on the human daily motion that was, for example, drinking a cup of coﬀee to validate his humanoid robot motion. Shoulder’s center of rotation will be approximately ﬁxed if shoulder moves in a relatively small course of its workspace, while the angle between Humerus and upper body does not exceed 30 degrees. In this case, shoulder can be accurately approximated as a 3-Degree of Freedom spherical joint. This paper addresses evaluation of human arm kinematic parameters along with elbow and shoulder center of rotations while shoulder moves within mentioned partial of its workspace; otherwise evaluation of center of rotation by a motion capture system would be out of sense since the center moves in respect to other body landmarks due to the shoulder’s skeletal structure. A few markers were mounted on arm. The marker positions were tracked in order to evaluate the shoulder and elbow center of rotations along with other kinematic parameters of human arm as mentioned in section 4 and 5. In addition to this, we used a few number of markers in order to evaluate the centers robustly. Since evaluation of these parameters has been done without considering a particular application, result of this paper can be used in any of above-mentioned applications.

2. MOTION CAPTURE SYSTEMS Motion capture systems are mainly used in two applications, computer animation to increase the level of realism in the digitized the performed movements by an actor, and biomechanics to precisely measure the movements of joints. There are many approaches to track and model human body based on video sequences data, but the problem remains far from solved. This is in part because image data is typically noisy and in part because it is inherently ambiguous.14 Introducing a valid model is therefore one important practical step towards restricting motion tracking and surface measurement algorithm for human motions and conﬁgurations. This model helps reducing the search space required for the exploration, and therefore improving reliability. Another important factor in handling ambiguous data is the use of a synchronized multi-image acquisition system.15 Topological information is also of great importance during the tracking, and surface measurement approach. This topological information make the system capable of detecting the presence of occlusion and in particular self-occlusion detection.

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Monocular motion capture systems use sequences of frames acquired by a camera. To gain three-dimensional information from single video clips, knowledge of human motion required. Some systems learn from provided sample training data and estimate the performed 3-D motion based on statistical models. While other systems perform the tracking of deﬁned constrained human body models. Multi-image systems use sequences of images acquired simultaneously by two or more cameras. Until now, the most successful technology in motion capture systems is optical motion capture. This is due to its high precision measurement of reﬂective markers, observed by a number of cameras, attached to some relevant body landmarks. The capture system infers the time-varying location of each marker in space by triangulation based on the projection of the markers into each camera projection plane. High-end systems typically collects the images of many cameras in order to employ a redundant array to provide accurate information over large capture volumes. The most common passive system works with strongly retro-reﬂective markers and illumination source mounted on each camera. An active system uses LED markers that pulse in synchronize with the cameras’ digital shutters. Cameras are equipped with optical ﬁlters tuned to the wavelength of the illumination source or LEDs in both systems. An Active capture system can identify each marker at any particular moment since the active markers can uniquely communicate with the cameras by modulating their pulses, whereas passive systems must infer marker identity from continuous observation. In practice, both optical system can reliably generate accurate trajectory data of markers with only occasional gaps caused by occlusions or placing the subject out of the capture region. Although motion capture system gathers an accurate information from the markers position, it does not capture the object structure. Therefor a post-processing step, ﬁtting an articulated model or skeleton to the data, is required in the applications where visual representation of object desired. On the other hand, some systems are interested in actual motion parameters as interest of this paper. In this paper we gathered the data from a Certus OptoTrack system. This system gathered the data from its markers by resolution of 0.1mm. Certus system is line of sight system; i.e. the system only provides the marker positions which are in its line of sights. Since we used one tracking system in out experiment, the experiment setup was designed in a way that the candidate arm moves in front of tracking system and all the markers would be seen by the camera. Small number of frames was used to evaluate the shoulder and elbow center of rotation; then other arm kinematic parameters such as links length and joint angles were evaluated in each frame.

3. SHOULDER AND ELBOW CENTER OF ROTATIONS Complex and correlated movement of joints in human arm allows arm to provide suﬃcient mobility to place the arm in many diﬀerent positions and orientations. When shoulder moves within its entire workspace, shoulder center of rotation (SCR) is moving in space due to human skeleton structure. However the shoulder center of rotation will be ﬁxed if shoulder moves within a speciﬁc partial of its workspace as deﬁned in section 1. In order to evaluate shoulder center of rotation, a marker was placed on Humerus between shoulder and elbow. Position of the marker gathered in 40 randomly selected frames. All these points have an unique distance with SCR and located on a spherical. the SCR is evaluated by the fact center of rotation is located on the perpendicular bisector plane of each pair of points. Easily we can write each plane’s equation in terms of a vector inner product. Collection of these vector inner products leads to a set of linear equations. The solution to the linear equation system is center of rotation since center of rotation is the common point between all the planes. These linear equation can be rewrite in form a matrix form as AC = B. ‘C‘ determined from the orthogonal matrix QR decomposition (decomposition of the matrix into an orthogonal and triangular matrix) with pivoting and least squares. Equations 1 deﬁnes the matrixes and relationships between them. A = Pi − Pj B = diag(A × DT )

where

(i = j) (Pi + Pj ) D= 2

C = A−1 B

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(1) (i = j)

(2) (3)

In order to evaluate elbow center of rotation, another marker was mounted on Radius close to the wrist where skin has small movement in respect to the Radius. Additional constrain, that the center of rotation must located in the same plane as the points, required in elbow’s center of rotation evaluation because elbow considered as revolute joint that has only 1 degree of freedom. Without this constrain the above mentioned steps may lead to any point on axis of rotation due to the errors. Evaluation of shoulder, elbow center and axis of rotations leads to calculation of transformation matrixes, RCM and RMG , which relates center of rotations to markers’ and markers’ coordinates to a ﬁxed reference frame (global frame) respectively. Having the joints locations leads us evaluation of Kinematic parameters as described in section 4.

4. KINEMATICS MODELING In order to evaluate the arm kinematic parameters, ﬁrst kinematic model and its relation with the parameters should be obtained. We model the arm as an spherical joint, shoulder, and a revolute joint, elbow, as shown in ﬁgure 1.

I

II [email protected] [I C [UI

Isi (shoulder)

Pjow Global Frame

(1 Figure 1. shoulder joints

Denavit-Hartenberg (DH) convention is a general method to deﬁne the relative position and orientation of two consecutive links and consequently relation between any two links in the model. Table 1 shows DH parameters of the shown arm model at ﬁgure 1. Link

ai

αi

di

ϑi

0

a0

α0

d0

ϑ0

1

0

0

ϑ1

2

0

− π2 π 2

0

ϑ2

3

a3

0

d3

ϑ3

0

π 2

d4

ϑ4

4

Table 1. DH parameters. First row (Link 0) stands for convention of global frame to the shoulder center of rotation

Having the parameters ai , αi , di , and ϑi leads to evaluating the relative position and orientation of two consecutive links as shown in (4). ⎡

Aii−1

Cϑi ⎢ Sϑi =⎢ ⎣ 0 0

−Sϑi Cαi Cϑi Cαi Sαi 0

Sϑi Sαi −Cϑi Sαi Cαi 0

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⎤ ai Cϑi ai Sϑi ⎥ ⎥ di ⎦ 1

(4)

¶1•••• Figure 2. suggested locations where markers can be installed

By using the table 1 and equation 4, computation of the direct kinematics function yields to obtaining the convention matrix between any two joints or any joint and global frame. Basically the homogenous transformation matrix that expresses the position and orientation of frame j with respect to frame i is denoted by Tji and deﬁned as equation 5. if i < j (5) Tji = Aii+1 Aii−1 ...Aj−1 j Also the kinematic parameters can be evaluated as an inverse kinematic problem from the transformation matrix elements. For instance all the kinematic parameters of a spherical wrist can be evaluated from 3 elements of its transformation matrix, β13 , β23 , and β33 where β represents the transformation matrix element. Therefore, we determine the orientation and location of arm joints in respect to global frame and each other, Tji s, by RCM , RMG matrixes as described in section 3.

5. EXPERIMENT 6 markers was mounted on each examinee arm (ﬁgure 2 shows location of markers). Only gathered data from 2 of markers as mentioned in section 3 are used in evaluation of center of rotations and the rest are used to deﬁne local axis in order to evaluate other kinematic parameters; location of these 2 markers are illustrated in ﬁgure 3. Designed experiment contains 3 stages. As the ﬁrst step, examinee moved his elbow in an arbitrary trajectory with in the deﬁned workspace as described in section 1, while his Scapula was ﬁxed to the chair he

Figure 3. suggested locations where markers can be installed

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parameter

Error

Distance between Shoulder Center and global frame origin( d20 + a20 )

1.8mm

Distance between Elbow Center and global frame origin

1.4mm

upper arm length

1.1mm

Forearm length (d4 )

0.9mm

Table 2. MSE of evaluated constant parameters and link lengths.

was sitting at. The gathered coordinates of the marker located on Humerus was used to evaluate the shoulder center of rotation. After evaluation of the center, the location of center was determined in a local frame deﬁned by markers located on upper arm (shoulder, Humerus, and elbow as shown in ﬁgure 2). As the second step, the upper arm was ﬁxed to the chair as well and examinee was moving his forearm in its whole rang of motion without any rotation on his wrist; i.e. moving the marker mounted in his wrist in a 2D space. By gathering the data on this phase, the elbow center of rotation was evaluated as mentioned in section 3 and its position determined in a local frame deﬁned by markers located on the forearm and the markers on upper arm. The third experiment was done by moving the arm in an arbitrary trajectory within the deﬁned range. Since the center positions in local coordinations are known due to previously mentioned steps, the rest of arm kinematic parameter, joint angles, could be evaluated in this phase of experiment.

6. ERROR ANALYSIS Main sources of error in our experiment are skin and muscle movements between an anatomical landmark and the tracking system error. Skin and muscle movements tend to cause displacement on order of 10-20mm between a surface marker and an underlying anatomical landmark.16–18 When it comes to building the skeleton frames out of the 3D marker positions, any signiﬁcant skin movement may penalize the quality of the model reconstruction. Therefore the markers mounted as close as possible to the bones where the skin has minimum deformations and is relatively ﬁxed in respect to correspondent link/joint. For example, a marker placed close to the wrist where the muscle deformation does not have any eﬀect on the marker position in respect to the elbow center of rotation as shown in ﬁgure 2. However, we gathered the data from 40 randomly selected frames (20 pairs of frames) to evaluate each center of rotation. At least 3 frames (3 linear equations) required for the center evaluation but gathering 40 frames (20 linear equations) in evaluation of each center signiﬁcantly suppresses eﬀect of muscle deformation and skin movement in respect to the skeletal landmarks. Although selecting more frames may slightly improves the accuracy, it increases the computation time signiﬁcantly; since the real time applications was desired in our methodology, we chose 40 frames as the number of frames in the centers evaluation. Achieved MSE errors are shown in table 2; considering the illustrated errors and comparing them with previously proposed methods that evaluated the human arm kinematic parameters such as experiments done by Nussbaum and Zhang,19 our proposed method has better performance by far. Almost all the proposed researches focused on a speciﬁc task, but we asked the candidate to make an arbitrary movement. We deﬁned the experiment as an arbitrary movement and we choose the points randomly to generalize the experiment for any application. Deﬁning a speciﬁc trajectory can reduces error of our experiment since we can eliminate the redundant trajectory and choose the frames suﬃciently far from each other. Achieved errors under these conditions prove advantage of proposed method to the others in terms of its accuracy and robustness. We repeatedly evaluated the centers, particularly shoulder’s, in a long period of time in order to examine variance of evaluated center locations. Result of this experiment revealed with a very low variance in centers locations in respect to the mounted markers. This small variances in evaluated position of the center proves

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—

(a)

(b)

(c)

Figure 4. (a) histogram of the distance between SCR of subject 1 and the global frame origin evaluated in 100 trials. (b) histogram of the distance between SCR of subject 2 and the global frame origin evaluated in 100 trials (c) histogram of distance between elbow center of rotation and the global frame origin. The distances shown in millimeters.

robustness of the proposed method over the time in evaluating the kinematic parameters as well. Histograms of evaluated shoulder and elbow center of rotations resulted from 100 trial over the time taken form 2 diﬀerent subjects are shown in ﬁgure 4 as an example. Since we did not perform the same task as others, we could not compare robustness of our method with other proposed methods.

7. CONCLUSION The computer simulation result of proposed method for evaluation of human arm kinematic parameters and center of rotations, shows that this method is reliably accurate that other proposed methods to the best of our knowledge. Since we converted problem of ﬁnding center of rotation into set of linear equations which can be solved as matrix algebra, our method is computational inexpensive. So, this method can ﬁnd a candidate kinematic parameters in real time bases. This advantage of proposed method along with its robustness proves that our method can be used in applications such as teleoperate and especially telesergery. However it should be noted that Certus OptoTracking system is a line of sight system; i.e. the markers should be in line of sight of the camera(s). Therefore more than a few cameras should be used in diﬀerent angles in order to keep all the markers under consideration over the whole period of operation.

REFERENCES 1. M. W. B. A. Hingtgen, J. R. McGuire and G. F. Harris, “Quantiﬁcation of reaching during stroke rehabilitation using a unique upper extremity kinematic model,” in Proceedings of the 26th Annual International Conference of the IEEE Engineering in Medical and Biology Society, 2(7), pp. 4916–4919, 2004. 2. T. R. R. C. Bowen, R. Seliktar and M. Alexander, “Surface emg and motor control of the upper extremity in muscular dystrophy: A pilot study,” in Engineering in Medicine and Biology Society, 2, 2001. 3. N. Lan and L. Baker, “Biomechanical couplings between elbow and forearm movements,” in 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2, 2004. 4. J. M. J. Van Bogart and G. F. Harris, “Upper extremity motion assessment in adult ischemic stroke patients: A 3-d kinematic model,” in IEEE Engineering in Medicine and Biology Society, 2, 2001. 5. M. A. Finley and R. Y. Lee, “Eﬀect of sitting posture on 3-dimensional scapular kinematics measured by skin-mounted electromagnetic tracking sensors,” in Arch. Phys. Med. Rehabil, 84, 2003. 6. K. McQuade and G. Smidt, “Dynamic acapulohumeral rhythm: the eﬀects of external resistance during elevation of the arm in the scapular plane,” J Orthop Sports Phys Ther 27, 1998.

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7. P. Ludewig and T. Cook, “Alterations in shoulder kinematics and associated muscle activity in people with symptoms of shoulder impingement,” Phys Ther 80, 2000. 8. M. S. Lee, J. Lee and C. Lee, “A new master arm for man-machine interface,” in IEEE Systems, Man and Cybernetics, 4, 1999. 9. M. K. C. L. S. Lee, D. Choi and J. Song, “An uniﬁed approach to teleoperation: Human and robot integration,” in IEEE Int. Conference on Intelligent Robots and Systems, 1, 1998. 10. A. A. F. E.V. Biryukova, A. Roby-Brami and M. Mokhtari, “Kinematics of human arm reconstructed from spatial tracking system recordings,” in Journal of Biomechanics, 33(8), 2000. 11. V. Zatsiorsky, Kinematics of Human Motion, 1997. 12. E. B. R.A. Prokopenko, A.A. Frolov and A. Roby-Brami, “Assessment of the accuracy of a human arm model with seven degrees of freedom,” in Journal of Biomechanics, 34, 2001. 13. M. Okada and Y. Nakamura, “Development of a cybernetic shouldera 3-dof mechanism that imitates biological shoulder motion,” in Robotics and Automation, 21, 2005. 14. D. D. M. J. M. Rehg and T. Kanade, “Ambiguities in visual tracking of articulated objectsusing 2d and 3d models,” in International Journal of Robotics Research, 22(6), 2003. 15. G. Schrotter, “Markerless tracking and surface measurements in biomechanical applications,” in The IASTED Intl. Conf. on Robotics and Applications, 22(6), 2005. 16. A. Cappozzo, “Three-dimensional analysis of human walking: Experimental methods and associated artifacts,” in Human Movement Science, 10, 1991. 17. L. P. A. appello, P. Francesco and A. Leardini, “Optimization and smoothing techniques in movement analysis,” in International Journal of Biomedical Computation, 41, 1996. 18. B. F. L. Che‘ze and J. Dimnet, “A solidiﬁcation procedure to facilitate kinematic analysis based on video system data,” in Journal of Biomechanics, 28, 1995. 19. M. Nussbaum and X. Zhang, “Heuristics for locating upper extremity joint centers from a reduced set of surface markers,” in Human Movement Science, 19, 2000.

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A Fuzzy Adaptive PD Controller Based Microassembly System Junping Wang∗a, b, Xiaodong Taoa, Deokhwa Honga and Hyungsuck Choa a Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Guseong-dong, Yuseong-dong, Daejeon, Korea, 305-701 b School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, P R China ABSTRACT Proportional control based visual controller is the main method used in the visual serving, but small proportional gain results in the slowly response and large proportional gain will result in large overshoot or make the system instable. A PD visual controller for microassembly system is presented to acquire better dynamic response. The fuzzy logic is applied to tuning the controller gains which is a model free method. Thus, the difficulty in obtaining precise and detailed system model is avoided and we can get satisfactory performance which is robust to modeling error and external disturbances. Furthermore, image moments are selected as visual features to avoid image singularities and the Jacobian matrix is full rank and upper triangular, thus it has the maximal decoupled structure and simplified the controller. A series of simulations are performed on peg and hole assembly to investigate the feasibility and effectiveness of this method. Keywords: Microassembly, visual servoing, fuzzy adaptive PD controller

1.

INTRODUCTION

Today, as more microelectromechanical systems (MEMS) are commercially available, the cost and complexity of equipment, as well as the level of human skills required to assemble such devices has also increased. Therefor, automated assembly of MEMS has become a necessary technology in order to reduce manufacturing costs, and increase production volume [1]. Due to small size of these parts, the conventional MEMS fabrication technique can not meet these demands. Vision is a robotic sensor because it provides dense information about the task space while being a noncontact sensing modality, and thus machine vision technique has been utilized in microassembly[1][2], Especially the visual servoing technique has become a main research method [3]. Visually servoed assembly has been shown to effectively compensate for uncertainty in the calibration of camera-lens systems, manipulators, and workspaces. Our microassembly task is to insert a micro peg to a hole and the approach to visual servoing is an image-based one. The advantage of image-based visual servoing is that it eliminates the need to perform an explicit inverse perspective projection mapping [4]. For image-based systems the error is defined on the image plane, and the manipulator control input is typically defined either in joint coordinates or in task space coordinates. Therefore, it is necessary to relate changes in the image features to changes in the position of the object. The image Jacobian captures these relationships. * [email protected]; phone +82-42-869-3253; fax +82-42-869-3095 Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740R, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.686804

Proc. of SPIE Vol. 6374 63740R-1

The visual controller can derive the velocity control law based on the inverse Jacobian that will produce the desired change in the image [5]. The objective of the visual controller is to make the image error converge to zero and is the key issue in the high performance visual servoing system. Up to now simple proportional control law is used in most of the visual servoing system. However, small proportional gain results in slow response whereas large proportional gain will result in large overshoot or make the system even unstable. Therefore, it is difficult to acquire better dynamic response only with proportional control law. In this paper in order to avoid these problems we apply a PD visual controller to microassembly system. In the proposed controller the proportional part makes the system respond faster and the differential part can improve the dynamic performance. Over the years, many techniques have been suggested for tuning of the PD parameters. Among them, the model-based tuning method appears to be very encouraging [6]. In real situations, however, highly precise and detailed modeling of the system is often difficult to achieve, because various uncertainties such as modeling error and external disturbances are involved in the system. Due to these difficulties, the PD controllers are rarely tuned optimally based on the system model and the engineers need to settle for a compromise performance. To this end a fuzzy adaptive PD visual controller is designed, based on the feature position error and the change of feature error, the PD parameters are tuned on line by fuzzy rules, thus we can get satisfactory performance which is robust to modeling error and external disturbances. The proposed controller is applied to the microassembly of micro peg and hole, and simulation is performed to investigate the feasibility and effectiveness of this method. This paper is organized as follows: in Sec. 2, we introduce our microassembly system setup and task description. In Sec. 3, Fuzzy adaptive PD controller design using image moments as visual features is introduced. Sec.4 describes simulation results for the peg-in-hole task. Finally, Sec.5 provides a conclusion for the paper.

2.

SYSTEM SETUP AND TASK DESCRIPTION

Fig. 1(a) shows the configuration of the proposed system, which is equipped with a zoom lens, an auto-focusing unit, a four-axis stage and a CCD camera. The micro peg is fixed on the microgripper, while the MEMS-fabricated structure with micro hole is laid on the four-axis micro motion stage. The four degrees of freedom motion with instantaneous visual information feedback makes it possible to achieve an accurate alignment between the peg and hole. The OC

Camera X YC

XC

Camera coordinates

C

YC

ZC

Image plane

Peg

u

Hole ZW θ

W

Y

v

World coordinates O

W

W

XW θW

XW

(a) System configuration

YW

(b) Coordinates system Figure 1 Visual servoing system

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motorized zoom lens has 0.5x to 2x magnification. An auto-focusing stage is powered by a stepping motor driver and controlled by a programmable multi-axis controller. The rotation stage and the Z stage are supplied by Physik Instrumente, which is controlled by a plug-in control board. The resolution for X and Y stages is 3µm. while the resolution of Z stages is 0.03um. The resolution for the rotation stage is 32µrad. Our microassembly task is to insert the micro peg to the hole. For simplicity, the micro peg held by the griper is located on the optics axis and in the focus plan, which can be achieved by autofocusing process. The distance between the peg and hole is estimated by the depth from focus technique that is described in [2]. We assumed that the tilting angle mismatch between the peg and hole is negligibly small, during the assembly process, the stage has a constant motion along Z axis, so in this paper we only research the accurate alignment between the peg and hole. With instantaneous visual information feedback, the stage will move the micro hole towards the peg and make an accurate alignment between them. This process can be achieved by three-axis micro motion stage that are two translation axes X and Y and one rotation axis Z. The coordinates system is shown in Fig.1(b), where XW – OW – YW represents the world coordinates system and XC - OC - YC represents the camera coordinates system and u – v represents the image plane.

3.

FUZZY ADAPTIVE PD CONTROLLER DESIGN

3. Image moments as visual features for visual servoing The application of the image moments as visual features to image based visual servoing is interesting since they are generic, whatever the object shape complexity, they can be computed easily from a binary or a segmented image. They have intuitive meaning since the low order moments are directly related to the area, the centroid and the orientation of the object in the image. The most important objective of using moments in visual servoing is to try to determine features that can avoid the image singularities that may appear when conventional redundant image point features are used. The analytical form of the interaction matrix or image Jacobian matrix related to any image moments was determined in [7]. Here we briefly recall the basic definition of image moments and give a general analytical form of their interaction matrix, and then visual features using image moments are selected to align the micro peg and hole. We denote R(t) the observed object in the image at time t which defined by a set of closed contours. The origin moments mij of order i + j are defined by

mij = ∫∫

x i y j dxdy

R (t )

(1)

The centered moments of order i + j with respect to the centroid of the object are defined by

µ ij = ∫∫

R (t )

( x − xg )i ( y − y g ) j dxdy

(2)

where xg and yg are the centroid of the object. The interaction matrix or image Jacobian matrix describes the time variation of the moments with respect to the relative kinematic screw V = (v,ω)T, where v = [v x v y v z ]

T

and

ω = [ω x ω y ω z ]T

represent the translational

and rotational velocity, respectively.

m& ij = J mij V ,

µ& ij = J µ V ij

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(3)

where J m is the ij

image Jacobian matrix with respect to the origin moments and J µ the image Jacobian matrix ij

with respect to the centered moments. The details of the interaction matrix are explained in [7]. For peg and hole alignment task, three degrees of freedom stage including two translation motions and one rotation motion shown in Fig.1(a) with instantaneous visual information feedback makes it possible. Three moments based visual features are selected to provide visual information feedback. They are xg and yg which are the center of gravity of an object in the image, and the object orientation α. These three visual features are defined by origin and centered moments given as follows:

xg =

m10 m 2 µ11 1 ， y g = 01 ， α = arctan( ) m00 m00 µ 20 − µ 02 2

(4)

In our configuration the object surface is parallel to the image plane. A simple form of image Jacobian J related to the three features is given by

⎡ f / zg J = [ J xg , J yg , J α ] = ⎢ 0 ⎢ ⎢⎣ 0 T

0 f / zg 0

− yg ⎤ xg ⎥ ⎥ 1 ⎥⎦

(5)

where zg is the depth of the gravity center. The matrix presents partially decoupling properties, since it is upper triangular. So the image singularities problem is solved since the Jacobian matrix is full rank all the time. 3.2 PD controller design Fig.2 shows the principle diagram of the image based visual servoing system, the objective of the visual servoing system is to move the object to the desired position where the object position is measured by the camera. The image Jacobian is used to relate the motion of the stage systems to the variation of feature in camera image with respect to time. This relation implies that if the rate of the feature vector motion is known, the motion of the stage can be specified with respect to camera coordinates. With the known relationship between the motion velocity and the image feature change, we can determine the stage velocity at any control instant that can lead to reaching a desired image feature vector. For the case of the fixed camera system, we obtain the following relationship between the velocity of the stage motion and the feature change obtained in image coordinates.

⎡ dx g ⎤ ⎢ dt ⎥ ⎢ dy ⎥ ⎡ f / z g 0 − y g ⎤ ⎡ v x ⎤ ⎢ g ⎥ = ⎢ 0 f / zg xg ⎥ ⎢v y ⎥ ⎥⎢ ⎥ ⎢ dt ⎥ ⎢ ⎢ ⎥⎦ ⎢⎣ω z ⎥⎦ 0 0 1 ⎢ dα ⎥ ⎣ ⎢ ⎥ ⎣ dt ⎦ where

(6)

f = [ x g , y g , α ]T is the visual features using image moments with respect to the image plane,

u = [v x , v y , ωZ ]T is the velocity vector which is the defined as the control input.

Proc. of SPIE Vol. 6374 63740R-4

If we define the error function as e = fd − fc and the change of the error as ∆e, where fd is the desired feature vector and fc is the current feature vector. The PD control law is given by

u( k ) = k p J −1e ( k ) + k d J −1

∆e ( k ) Ts

(7)

where k is the kth time step. Ts is the time interval, kp and kd are the control gains which will be tuned by the following algorithm. Fuzzy Adaptive PD Controller Fuzzy inference

Reference feature

+

-

error de dt

∆Kp

∆Kd

Vx

PD controller

Vy

ωz Actual feature

Figure 2

Translation axis X Translation axis Y

Xw w

Y Rotation axis θ

Feature extractor

Coordinate transformation

Object position

θw Camera

Control diagram of the 3 DOF visual servoing system

3.3 Controller parameters tuning method using fuzzy logic The parameter of the PD controller affects the control performance, so the optimization of the parameter is important to get the satisfactory dynamic performance. In real application, highly precise and detailed modeling of the system is often difficult to achieve, so the modeling error or uncertainty exits that will affect the control performance and limit the application of model free tuning method. During the past several years fuzzy logic has emerged as one of the most effective method to deal with the effects of these uncertainties. The combination of the conventional PD controller with fuzzy logic produces the fuzzy PD controller where the fuzzy logic is used to tune the PD gains online [8]. In this paper, a fuzzy adaptive PD visual controller is applied to visual servoing, based on the feature position error and the change of feature error, the PD parameters are tuned on line by fuzzy rules, and thus we can get satisfactory performance which is robust to modeling error and external disturbances. As shown in Fig.2, the fuzzy adaptive PD visual controller comprises two parts, one is the conventional PD controller which is described by Eq.(7), and another part is the fuzzy section which has a supervisory role in tuning the gains of the PD controller during the system operation. The input vector to the fuzzy system is the error (e) and the change of error (∆e), and the output vector is the incremental values of the proportional and the derivative gains (∆kp and ∆kd). The fuzzy section of the PD controller comprises three blocks that are the fuzzifier, the fuzzy inference rules and defuzzifier block. The fuzzifier block fuzzifies the error and the change of error. In visual servoing the error and its change are in the image domain. Scaling and quantization constitute the fuzzification of the error and the change of error. The quantization of the error and the change of error require all the fuzzified values to remain within a certain range which is from Negative large (NL) to Positive large (PL). The fuzzy set “Error (e)” and fuzzy set “The change of error (ec)” have seven members that are {NL, NM, NS, ZO, PS, PM, PL}, respectively. The membership function is shown in Fig.3(a) Given the fuzzy rules, fuzzified error and change of error, a fuzzified output is produced using the compositional rule of inference. The fuzzy rules for tuning the controller gains are given in Table 1 and Table 2. The

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fuzzified output is defuzzified by the defuzzification method and then ∆kp and ∆kd are obtained. There are many types of implication functions and defuzzification methods. The max-product implication function with the centre of gravity defuzzification method is used in this paper. The max-product implication function and the centre of gravity defuzzification method are shown by Table 1 The fuzzy rules for ∆kp

N

NL NM NS ZO

Table 2 The fuzzy rules for ∆kd

ZO NS NM NM

ZO

FS ZO NS NS NMNM FS ZO NS NM NM NM NL SD ZO NM NM NM NL NL

FS

NS NL NL NL NM FS FS NS NL NM NM NS ZO ZO NS NM NM NS NS ZO ZO NS NS NS NS NS ZO Zo ZO ZO ZO ZO ZO ZO

FM

FL NS

FS

FS

FL

FL

FL FM FM FM PS

PS

FL

NS

FL FL FM FM FS ZO ZO FL FL FM FS FS ZO NS FM FM FM FS ZO NS NS

SD

FM FM FS

FS

FS

NL

NM

FM FL

NL NM NS ZO PS FM FL

PS FM FL NL NM

FS

NS

µ r ( x, y ) = µ A ( x ) ⋅ µ B ( y ) n

yo = ∑ y r µ r ( y r ) r =1

n

∑µ (y r =1

FS

FS

(8) r

r

)

(9)

where a fuzzy subset A with elements x has a membership function µA(x) and a fuzzy subset B with elements y has a membership function µB(y), µr(x, y) is the resultant of the max-product implication function, yo is the defuzzified output, y r is the mean value of the membership function µr, r (r =1,2, ... n) denote the rth fuzzy rule. The membership functions of the output variables are shown in Fig.3(b). Getting ∆kp and ∆kd, then the descaled output is added to the PD gains to readjust them by

k p (i ) = k p (i − 1) + C p ⋅ ∆k p (i )

(10)

kd (i ) = kd (i − 1) + Cd ⋅ ∆kd (i )

(11)

where i is the time instant, Cp and Cd are the descaling coefficients for the proportional and derivative gains, respectively.

4.

SIMULATION OF VISUAL SERVOING

Based on the motor-stage system in section 2, we simulate the system to evaluate the performance of the controller. The structures of these three axes are similar and so we use the same transfer function to represent these axes. The simulation diagram is shown in the block diagram as shown in Fig.2. The following transfer function is used to describe the motor-stage system in simulation.

Proc. of SPIE Vol. 6374 63740R-6

Membership function

Membership function

Error/ The change of error

∆kp /∆kd

(a) Membership function of input ( e and ∆ e)

(b)

Membership function of output (∆kp and ∆kd)

Figure 3 Membership function of input and output

G (s) =

127.4 s 2 - 2.817 ⋅ 10 4 s + 1.193 ⋅ 10 7 s 3 + 1501 s 2 + 2.0218 ⋅ 10 5 s + 1.176 ⋅ 10 7

(12)

We use four corners coordinates to constitute the object image and then the moments can be computed from the four corners. In simulation, the coordinate transformation from the world coordinates system to the image plane is shown as

⎡X w ⎤ ⎡u ⎤ ⎢v ⎥ = M M ⎢ Y w ⎥ 2 1⎢ ⎥ ⎢ ⎥ ⎢ 1 ⎥ ⎢⎣1⎥⎦ ⎣ ⎦

⎡cos ∆θ w ⎢ where M 1 = sin ∆θ w ⎢ ⎢ 0 ⎣

− sin ∆θ w cos ∆θ w 0

∆x w ⎤ ⎥ ∆y w ⎥ , 1 ⎥⎦

(13)

⎧∆θ w = θ w (k ) − θ w (k − 1) ⎡m 0 u 0 ⎤ ⎪ w w w ⎢ ⎥ ⎨ ∆x = x (k ) − x (k − 1) , M 2 = ⎢ 0 m v 0 ⎥ , ⎪ ∆y w = y w (k ) − y w (k − 1) ⎢⎣ 0 0 1 ⎥⎦ ⎩

In the above equations M1 expresses the transformation from the world coordinates system to the camera plane coordinates system, and M2 is the projection matrix which gives the relationship between the image and the pixel coordinates in the homogeneous coordinates space, m is a fixed scale factor that related to the camera parameters, (u0, v0) are the center of the pixel coordinates system. The adaptive fuzzy PD controller is applied to the microassembly systems. Given the initial gains of PD contoller kp = 10 and kd = 0.5, the fuzzy logic is applied to adjust the controller gains online which is explained in Sec.3. The simulation results are shown in Fig.4(a)~(d). Fig.5 and Fig.6 show the tuning process of gains kp and kd. The gains are adjusted using fuzzy inference according to the error and the change of error, where we do not need the system model or accuracy model. To show that the fuzzy adaptive controller is robust to modeling error and external disturbances, another simulation is performed where the disturbance is added to the system during operation and the results are shown in Fig.7(a)~(d). Fig.8 and Fig.9 show the tuning process of gains kp and kd while the disturbance exits. According to simulation results, it is shown that the fuzzy adaptive PD controller provides satisfactory performance no matter the

Proc. of SPIE Vol. 6374 63740R-7

modeling error and external disturbances exits or not. Furthermore, image moments are selected as visual features instead of point coordinates which are mostly used in visual servoing. These independent visual features can avoid image singularities that might cause control instabilities, where the Jacobian matrix is full rank and upper triangular, thus it has the maximal decoupled structure and simplified the controller. 200

380

Desired position Initial position

360

vx vy

150

ωz

100

Velocity (um/s)

340

V (pixels)

320 300 280

50 0 -50 -100 -150

260

-200

240 120

140

160

180

200

220

240

260

280

300

320

0.0

0.1

0.2

U (pixels)

(a) Image-plane feature motion 1.0

xg yg

8

0.5

0.5

α

x

θ

y

6

0.0

40

-0.5

0

-1.0

-40

-1.5

Position (mm)

4

80

Error (rad)

Error (pixels)

0.4

(b) Control input

160

120

0.3

Time (s)

2 0 -2 -4

-80 0.0

0.1

0.2

0.3

0.4

-6 -8

-2.0 0.5

0.0

0.1

0.2

(c) Image moments error

0.4

0.5

(d) Stage motion of the three axes

Simulation results based on fuzzy adaptive PD controller

50

2.0

40

1.5

30

1.0

Kd

Kp

Figure 4

0.3

Time (s)

Time (s)

0.5

20

0.0

10 0.0

0.1

0.2

0.3

0.4

0.5

0.0

0.1

0.2

0.3

0.4

Time (ms)

Time (ms)

Figure 5 Tuning process of gain kp

Figure 6 Tuning process of gain kd

Proc. of SPIE Vol. 6374 63740R-8

0.5

380

200

Desired position Initial position

360

vx 150

vy

ωz

100

340 320

Y Axis Title

V (pixels)

50

300

0 -50

280

-100

260

-150 -200

240 120

140

160

180

200

220

240

260

280

300

320

0.0

0.1

0.2

U (pixels)

(a) Image-plane feature motion

0.4

0.5

(b) Control input

160

1.0

xg yg

120

8

x

y

θ

6

0.5

α

0.0

40

-0.5

0

-1.0

-40

-1.5

Position (mm)

4

80

Error (rad)

Error (pixels)

0.3

Time (s)

2 0 -2 -4

-80 0.0

0.1

0.2

0.3

-6 -8

-2.0 0.5

0.4

0.0

0.1

0.2

Time (s)

0.3

0.4

0.5

Time (s)

(c) Image moments error

(d) Stage motion of the three axes

Simulation results based on fuzzy adaptive PD controller with disturbance

Figure 7

2.0

50 45

1.5

40

30

Kd

Kp

35

1.0

25 20

0.5

15 10

0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.0

Time (ms)

0.1

0.2

0.3

0.4

0.5

Time (ms)

Figure 8 Tuning process of gain kp with disturbance

5.

Figure 9 Tuning process of gain kd with disturbance

CONCLUSIONS

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Instead of proportional control based visual controller, a PD visual controller for microassembly system is presented in this paper to acquire better dynamic response. The fuzzy logic is applied to tuning the controller gains which is a model free method. Thus, the difficulty in obtaining precise and detailed system model is avoided. Based on the feature position error and the change of feature error, the control gains are tuned on line by fuzzy rules, therefore we can get satisfactory performance which is robust to modeling error and external disturbances. Furthermore, image moments are selected as visual features to avoid image singularities and then the Jacobian matrix is full rank and upper triangular, thus it has the maximal decoupled structure and simplified the controller.

REFERENCE 1.

D. Popa, B.H. Kang, J. Sin, J. Zou, “Reconfigurable Micro-Assembly System for Photonics Applications,” Proceedings of the 2002 IEEE International Conference on Robotics 8 Automation, Washington, DC May, pp.1495-1500, 2002

2.

S. J. Ralis, B. Vikaramadiya, B.J. Nelson, “Micropositioning of a weakly calibrated microassembly system using coarse-to-fine visual servoing strategies,” IEEE Transactions on Electronics Packaging Manufacturing, vol 23, no. 2, pp. 123-131, 2000

3.

S. Hutchinson, G. D. Hager, and P. I. Corke, “A Tutorial on Visual Servo Control,” IEEE Transactions on Robotics and Automation, vol. 12, no. 5,pp. 651-670, 1996

4.

G. Yang, J.A. Gaines, and B.J. Nelson, “Optomechatronic design of microassembly systems for manufacturing hybrid Microsystems,” IEEE Transactions on Industrial Electronics, vol. 52, no.4, pp 1013-1023, 2005

5.

H.S. Cho, “Optomechatronics: Fusion of optical and mechatronic engineering,”CRC Press, Boca Raton, FL, 2005.

6.

J.Q. Liu, “Advanced PID control and its simulation using MATLAB,”Electronics industry press,Beijing,2003

7.

F. Chaumette, “Image Moments: A General and Useful Set of Features for Visual servoing,”IEEE Trans on

8.

H.B.Kazemian, “Developments of fuzzy PID controllers,” Expert systems, vol.22, no.5, pp 254-258, 2005

Robotics, vol. 20, no. 4, pp.713-723, 2004

Proc. of SPIE Vol. 6374 63740R-10

An algorithm of calculating the scanning start angle and the scanning angle of linear array CCD panoramic aerial camera Gang Zhou a,b, Lin-Pei Zhai a Changchun Institute of Optics, Fine Mechanics and Physics, Changchun 130031; bGraduate School of the Chinese Academy of Sciences China, Beijing 100000, China

a

ABSTRACT The scanning start angle (SSA), the scanning angle (SA) and the target slope angle (SA) are important parameters of Linear Array CCD Panoramic Aerial Camera. This paper analyzes the relationship of them and suggests that the current method of calculating SA is very difficult to be realized in engineering. It proposes an algorithm of calculating SSA and SA according to TSA. Its main characteristics are, with achieving the overlap rate as a premise, to calculate SSA and SA reasonably and to try to put the target into the middle of swath coverage, making the coverage as wide as possible. The algorithm is very simple and is easy to be realized in engineering. The paper gives us the relationship graph between TSA and SA. Keywords: scanning start angle, scanning angle, target slope angle

1. INTRODUCTION The Linear Array CCD panoramic aerial camera operates as a pan-scanning system, in that it scans the ground scene perpendicular to the flight path as illustrated in figure 1. The imagery is only collected while scanning from left to right. The minimum overlap rate between two adjacent swaths should be no less than the overlap rate given. In fact, the minimum overlap is always in the place nearest to the aircraft, as shown in figure 2. The angle of camera’s field of view (FOV) is driven by the window size, which is the maximum SA and sets limit on the target acquisition. SSA is the camera’s oblique angle when it starts to scan. SA is the angle of horizon coverage. Target should be in the swath covered. TSA is the oblique angle of line CCD camera when the camera’s optical axis faces to the target. Furthermore, it will be the most desirable that the swath is as wide as possible achieving the required minimum overlap rate. SSA and SA are the most important parameters to achieve the above aim.

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740S, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.684596

Proc. of SPIE Vol. 6374 63740S-1

SCANNING END ANGLE TARGET SLOP ANGLE

SCANNING START ANGLE SCANNING ANGLE

FIELD OF VIEW

ALTI TUDE

SCAN DIRECTION OVERLAP

SWATH WIDTH START OF SCAN

FLIGHT DIRECTION

END OF SCAN

Fig.1.. The geometric relationship of panoramic camera

FIGHT DIRECTION

SCAN DIRECTION

STRI P A

STRI P B OVERLAP

Fig.2.. Overlap

In order to improve scan efficiency it is expected that SA is as big as possible. But we can’t define SA as big as the angle of FOV simply because it might produce gaps in along track coverage, which is not allowed. SA sometimes has to be smaller than the angle of FOV in order to realize the minimum overlap rate. Therefore, it is of great importance to give a reasonable SSA and an appropriate SA, which can be determined by many factors such as TSA, overlap rate, the ratio of velocity and height (V/H), and so on. Therefore, the best result is that target is near the middle of the swath covered, and the minimum overlap rate is equal to the requirement when SA is less than the angle of FOV.

Proc. of SPIE Vol. 6374 63740S-2

2. GEOMETRICAL ALGORITHM Figure 2.tells us that the minimum overlap is closest to the aircraft. According to the location of the target, there are three kinds of operating modes for camera to achieve the minimum overlap rate as illustrated in figure 3. The camera operates on the left oblique mode when the target area is on the left downward of the aircraft as shown in figure 3.(a) and in figure 3.(b) it operates on the vertical mode when the target is right under the aircraft, and it operates on the right oblique mode when the target is on the right downward of the aircraft as shown in figure 3.(c). AI RCRAFT

AI RCRAFT

2β

θ

θ

s

θ

θ

s

e

2β

e

SCAN DI RECTI ON

SCAN DI RECTI ON

( a)

( b) AI RCRAFT

θ

θ

s

e

2β

SCAN DI RECTI ON

( c)

Fig.3.. Three kinds of scanning angle:(a) left downward of the aircraft ;(b) right under the aircraft;(c) right downward of the aircraft

2.1 When the target area is on the left downward of the aircraft As illustrated in figure 2.(a), when the coverage is on the left downward of the aircraft, we can calculate SA as

2β =

Vs × K × B × (1 - ρ ) η × cos(θ e )

where

Proc. of SPIE Vol. 6374 63740S-3

(1)

2 β = SA of the camera (degree) Vs = the scan velocity (degree/second) K = the coefficient of the camera (1/meter) B = the width of swath

ρ

= the overlap rate；

η

= velocity/height (1/second)

θe

= the scanning end angle (degree)

Usually

Vs and B are defined as constant. ρ can also be supposed as a constant. K c is defined as K c = Vs × K × B × (1 - ρ )

As a result of (1) and (2),

(2)

2 β can be 2β =

Kc η × cos(θ e )

(3)

Where θ e is an unknown parameter, but it can be written as

θ e =θ s + 2β

(4)

where θ s is SSA. Even though θ s is an unknown parameter either, it can be determined by TSA. Given that ψ is a certain given angle, θ s can be written as

θ s =θ t -ψ

(5)

where θ t is TSA. Hence, combining equations (3), (4) and (5), we obtain

2β =

Kc η × cos(θ t - ψ + 2 β )

(6)

It is very difficult to get a result from equation (6). 2.2 When the target area is right under the aircraft As illustrated in fig. 2 (b), when the coverage is right under the aircraft, SA can be obtained from the equation

2β =

Kc

η

(7)

In this case, SA is related to V/H. 2.3 When the target area is on the right downward of the aircraft As illustrated in fig. 2 (c), when the coverage is on the right downward of the aircraft, the equation for SA can be written as

Proc. of SPIE Vol. 6374 63740S-4

2β =

Kc η × cos(θ s )

(8)

Combining equations (5) and (8), we obtain

2β =

Kc η × cos(θ t - ψ )

(9)

2.4 Discussion According to the above procedures, it is the most difficult to calculate SSA and SA when the target area is on the left downward of the aircraft. When the target scanning area is right under the aircraft, it is the easiest to obtain the calculating result and SA is the smallest at the same time. When the scanning area is on the right downward of the aircraft, the result is not so easy to get as it is right under the aircraft. The above algorithm has the following characteristics. In most cases, the minimum overlap rate of imagery collected is just of the given value and there is a constant relationship between SSA and TSA. But it’s very difficult to obtain the result when the target area is on the left downward of the aircraft. When the target is at the edge of FOV, there exist two possible problems. One is that SSA is out of FOV, and the other is that the scanning end angle is out of FOV. We have attempted to give solutions to such problems.

3. SOLUTION IN ENGINEERING The above algorithm provides us with a method of calculating SA geometrically. However, it is rather difficult to be realized in engineering. Hence based on the above geometrical algorithm, a new one is put forward here, which has bigger SA and makes the calculating much easier meanwhile. 3.1 Process of calculating Given that θ r is the angle of FOV defined as ± α , η is V/H ,

ρ

is the overlap rate, K c is the constant parameter of

the camera and θ t being TSA can be any point within the range of FOV, i.e. - α ≤ θ t ≤ α . Then, according to θ t , we can obtain θ s and

2β .

It is supposed that

α

=60 o, K c =2.0,

ρ =10%,

and there are three V/H , namely η 1=0.01,η 2=0.05,η 3=0.09. The

calculation is as follows. First, when the scan area is right under the aircraft, according to η , we calculate the minimum SA as

2 β min =

2.0

η

(10)

Second, if 2 β min is no less than θ r , i.e. 2 β min ≥120 o, the scan range will be out of the limitation of the window. So

θs

can be defined as

θs

= -60 o

(11)

2 β =120 o

(12)

Thus, 2βhas it’s maximum value

In this case, the setting of SSA and SA will result in slightly higher overlap than 10 percent. Third, if 2 β min is smaller than θr, i.e. 2 β min ＜120 o , but is bigger than half of θ r , θ s is defined as

Proc. of SPIE Vol. 6374 63740S-5

θ s = θ t - β min

(13)

2 β = 2 β min

(14)

Then 2 β can be obtained from the equation

Based on the result of θ s and

2 β , if the end of scan is also beyond the limitation of the window, i.e.

θ s + 2 β > 60 o

(15)

In order to improve the scan efficiency, θ s is defined newly as

θ s = 60 o - 2 β min

(16)

But the value of 2 β is not changed. And it is the biggest we can have under the condition that the minimum overlap is no less than 10 percent even though it is not in its maximum theoretically. Fourth, if 2 β min is smaller than θ r /2 , according to the position of the target slope angle θ t , there are five possibilities. (a) If θ t ＞ 60 (b) If

o

- β min , θ s and 2 β are defined as equation (16) and (14) respectively.

β min ＜ θ t ≤ 60 o - β min , θ s

is defined as equation (13),

2β =

2 β is obtained from

2 β min cos(θ s )

(17)

If the end of scan goes beyond the limitation of the window also, i.e. if inequation (15) comes into existence, θ s is not changed,

2 β is defined newly as

2 β = 60 o - (θ t - β min ) (c) If - β min ≤ θ t ≤ β min , (d) If

θs

is defined as equation (13),

2 β is obtained from equation (14).

- 60 o + β min ＜ θ t ＜ - β min , 2 β is calculated according to θ e , which is written as

θ e = θ t + β min Then,

(19)

2 β is calculated by 2 β min cos(θ e )

(20)

θ s = θ e - 2β

(21)

2β =

θs

(18)

is written as

If θ s is less than -60o, θ s is defined newly as -60o. And then combining equation (19),

2 β = 60 o + θ t + β min

Proc. of SPIE Vol. 6374 63740S-6

2 β is defined newly too as (22)

(e) If θ t

< -60 o + β min ， 2 β is set as 2 β min , and θ s is defined as -60o.

3.2 Graphs When η is 0.01, 0.05 and 0.09 respectively, according to TSA, we can get the graphs of TSA, SA, SSA by the above algorithm. Fig. 4 shows the relationship graph of TSA and SA. And the relationship between TSA and SSA is illustrated in figure 5. If η is small enough, i.e. η ≤0.01, SA will reach it’s maximum value 120o with the overlap rate higher than the value appointed. Furthermore, the smaller η is, the higher the minimum overlap rate is. It has to be admitted that when the target is near the edge of FOV, SA might not be the theoretical maximum angle with the minimum overlap higher than the value appointed. However, so long as the target is not near the edge, the algorithm in the paper is excellent which puts the target near the middle of swath covered and makes SA in maximum theoretically achieving overlap rate appointed. of Ut .nd a with dffiutt ii 120

Iii =0.01

100

80

60

40 q3=O.O9

20

6O

-40

-20

0 input value 8t

20

40

60

Fig.4.. The relationship of TSA and SA Graph of et and es with diffrent p 40

20

0

-20

,=O.O5 Iii =0.01

-BC

-60

I

-40

-20

I 0 input value Bt

I

I

20

40

Fig.5.. The relationship of TSA and SSA

Proc. of SPIE Vol. 6374 63740S-7

60

4. CONCLUSION It is really a hard nut to crack in the controlling system of panoramic aerial Camera to give the reasonable SSA and the appropriate SA. In this paper an algorithm suitable for engineering is put forward, in which the overlap rate is no less than the value appointed. Yet it might not be the most perfect and is to be studied further especially when the target is near the edge of FOV.

Proc. of SPIE Vol. 6374 63740S-8

Mark Position Measurement by Visual Feedback with Laser S. Nara† and S. Takahashi† †

Department of Intelligent Mechanical Systems Engineering, Kagawa University, 2217-20, Hayashi-Cho, Takamatsu-City, Kagawa 761-0396, JAPAN ABSTRACT

In this paper, we develop an observation device to measure a 3D position for a moving object by using a laser range ﬁnder and a CCD camera. Then, we propose a new method for the object recognition and the tracking control, respectively. As for the recognition, we use a special mark which is called the cross mark. For the tracking control, we construct PID control with an extended Kalman ﬁlter to realize control system without delay. Through some experiments, we verify performance of observation device and show availability of our proposed method. Keywords: Visual Feedback, Extended Kalman Filter, Cross Mark Recognition

1. INTRODUCTION Recently, many researchers are working on visual feedback which controls robot based on image information from attached camera.3–5 Today, the research is applied to various ﬁelds of industrial, thus, it contributes to an automation of various works. However, there are many works that automation is still diﬃcult. In the above work, there is a measurement of a working radius of a crane truck. The working radius means the distance between rotation center and hook of the crane. The measurement is diﬃcult because of the following matters. First, because the measurement is conducted in unknown environment, it is diﬃcult to recognize target objects which include the rotation center and the hook. Next, the crane has many kinds of types, so the working radius changes from few to 100m. Finally, now that the hook is moved by an operation, the movement should be observed. For these problems, camera is the eﬀective sensor, so some research including position measurement based on image processing and stereo camera6 is accomplished. In this paper we develop an observation device to realize the measurement. The observation device is equipped with a CCD camera and a laser range ﬁnder (LRF) and AC servo motors. In addition, the camera has a zoom function and each motor has an encoder. Using the camera, we propose a recognition method. Because a shape of the hook is not unique, it is diﬃcult to recognize it. In order to simplify the recognition, we attach a speciﬁc mark on the hook and the rotation center. Moreover the position of the mark is measured instead of the hook and the rotation center based on the information of the camera, the LRF and encoders. Furthermore, the observation device has to track the moving mark, in order to take the mark on the camera image. Therefore, we conduct a control system which controls the posture of the observation device. This paper is organized as follows. The section 2 introduces the observation device which we developed. The section 3 explains proposed methods of the mark recognition and position measurement. The section 4 expresses the tracking control based on image information. The section 5 veriﬁes the availability of the observation device by results of some experiments. Finally, the section 6 makes a summary. The corresponding author is S. Takahashi S. Nara: E-mail: [email protected], Phone: +81 87 864 2374 S. Takahashi: E-mail: [email protected], Phone: +81 87 864 2329

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740T, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.685749

Proc. of SPIE Vol. 6374 63740T-1

Figure 1. The cross mark

2. OBSERVATION DEVICE This section introduces the observation device which we developed. This device is equipped with power-zoom CCD camera FCB-EX480B (SONY), laser range ﬁnder DME-3000 (SICK) and AC servo motors with incremental encoder FHA-8C-100 (HARMONIC DRIVE SYSTEMS). In addition, the camera can 216x zoom, combining 18x optical zoom and 12x digital zoom. In this paper, we use the mark (shown in Fig. 1) which is attached to the crane. The mark has a speciﬁc ﬁgure in a circle which has diameter of 30cm. In this paper, cross is treated as the speciﬁc ﬁgure. The details of mark recognition will be described below.

3. METHOD OF MEASUREMENT This section explains about the mark recognition and the position measurement. As for the mark recognition, we explain about the cross mark. Additionally we control zoom lens in order to keep the mark size constant on the image.

3.1. Mark recognition based on image processing We explain about mark recognition based on image processing. In this paper, the mark recognition aims to recognize the cross mark. Mark recognition for the whole image needs huge process time. Therefore, in order to narrow the search area of the mark and decrease process time, we detect circle area. 3.1.1. Detection of the circle area First we make binary image using binary process. However it is diﬃcult to obtain an optimal binary image using general binarization which use constant threshold under the environment where illumination is changed. Also as for the variable threshold method like the moving-average method,2 it needs enormous process time. Then, in order to optimal binary image, we propose the binary method which improved on moving-average method for the mark. Let (i, j) be the coordinate of an any pixel on the image. And the brightness of the pixel is deﬁned as f (i, j). When any pixel is binarized, an average of brightness aij is calculated in a region which has size of M ×M by following equation. aij =

1 M2

f (x, y)

(x,y)∈Rij

(x, y) is position of pixel which constitutes the region Rij , and M is set optional value experimentally. In addition, a variance of brightness Vij in the region Rij is given using the average of brightness aij . Vij =

1 M2

(aij − f (x, y))2

(x,y)∈Rij

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Then using the average of brightness aij and the variance of brightness Vij , target pixel is binarized by following conditions. ⎧ 255 if Vij < VT h ∩ f (i, j) ≥ aT h ⎪ ⎪ ⎨ 0 if Vij < VT h ∩ f (i, j) < aT h B(i, j) = 255 if Vij ≥ VT h ∩ f (i, j) ≥ aij ⎪ ⎪ ⎩ 0 if Vij ≥ VT h ∩ f (i, j) < aij where, B(i, j) means binary image (shown in Fig. 2(b)). VT h is threshold of variance which is set experimentally. Further aT h means threshold of brightness, and this value is given by histogram of input image. This paper deﬁnes that brightness value 0 is black and brightness value 255 is white.

(a)

(b)

(c)

(d)

Figure 2. (a)Input (b)Binary (c)Labeling (d)Detected circle

Next median ﬁlter smoothes the binary image. Then, labels are attached to connecting regions which has white pixel based on a Scan Line Seed Fill Algorithm (shown in Fig. 2(c)). As for the labeling process, an area S and a boundary length L of a connecting region are taken. However the area S does not contain area of cross line which is shown in Fig. 1, Considering these lines area, we use an area Sˆ which is 1.16 times size of area S. Using these parameters of connecting region, a degree of circularity of connecting region e is calculated by e=

4π Sˆ L2

The degree of circularity takes the value of 0 ≤ e ≤ 1, and perfect circle has 1. Then we set a threshold and detect the connection region with a bigger the degree of circularity than the threshold (shown in Fig. 2(d)). In this paper set the threshold 0.6 in order to allow some rotation of the mark. 3.1.2. Recognition of the cross mark Here we detect the cross mark on the search region which is the circle region as mentioned. The search line which is the square region is prepared, and in Fig. 3, the search line is described as a dashed line. Detection of cross mark uses the cross candidate points which are set of a black pixel on the search line. This paper assumes that the cross implements the following conditions. (i)There are four cross candidate points on the search line. (ii)There are two pairs if the angle which cross candidate point and search center make. (iii)There are four cross candidate points that the black pixel continues to the search center. If the cross is detected by above conditions, the mark position on the image is taken as a center of search region (uk , vk ).

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iT

4—. sIcTJ TIUB

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(b)

Figure 3. (a)Method of cross detection (b)Detect the cross mark

3.2. Mark position measurement This section explains about the position measurement of the mark. Fig. 4 shows the position relation between observation device and mark and deﬁnes coordinates. A device coordinate is showed as OR − XR YR ZR , a camera coordinate is described as OC − XC YC ZC and a laser coordinate is expressed as Ol − Xl Yl Zl . The device coordinate exists in center of the observation device and a world coordinate corresponds with initial condition of the device coordinate, and position measurement is conducted based on this coordinate. Additionally the camera coordinate and the laser coordinate change posture, depending on the rotation of the device coordinate.

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a

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B

Figure 4. Position relation between observation device and mark

That follow describe about the position measurement of the mark. This paper supposes that the mark faces the front to the observation device. Following information is given form the observation device. A rotation angle of each axis of the observation device φenc , θenc is taken by encoders. A distance from the observation device to the mark l is obtained from the laser range ﬁnder. Furthermore the CCD camera gives the position of the mark on the image (uk , vk ) which were above mentioned. First a position of camera center which is C in Fig. 4 is calculated, considering the relation between the camera and the laser. Equation (1) and (2) express the distance between OR and C, and posture angle φcam .

l =

a 2 2

+ (l + b)

2

φcam = φenc − arctan

(1)

a

(2)

l

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Then, position of the camera center C is given by the following equation using information of distance and angle given by equation (1) and (2). ⎡

⎤ ⎡ ⎤ xc 0 ⎣ yc ⎦ = Rφ Rθ ⎣ 0 ⎦ zc l ⎡

⎤ 0 sin φcam ⎦ 1 0 0 cos φcam

⎡

⎤ 0 − sin θenc ⎦ cos θenc

cos φcam 0 Rφ = ⎣ − sin φcam

1 0 Rθ = ⎣ 0 cos θenc 0 sin θenc

(3)

Then mark position B is given by following equations. xk = xc + s · u · sin φenc yk = yc + s · v zk = zc − s · u · cos φenc

(4)

where s means width of each pixel in actual space. zoom is the zoom value of the zoom lens, and l is the depth information of laser range ﬁnder. Then we calculate s as follow. s=

l xCCD · XSIZE f1 · zoom

(5)

where xCCD is width of CCD (mm), f1 means the focal length in case zoom value is 1, and XSIZE is width of image (pixel). And we set these parameters, xCCD = 3.6, f1 = 4.1, XSIZE = 320, respectively. By the way, the mark recognition needs to keep the mark size on the image constant in the situation that distance between camera and mark changes. Therefore an optimal zoom value is given following equation as transformation of equation (5).

zoom =

xCCD l · ximg f1

where ximg means width of image (mm) and given as follow. ximg = XSIZE ·

MSIZE Mpix

where MSIZE means width of the mark (mm) and Mpix is width of mark on image (pixel). And this paper MSIZE = 300 and Mpix .

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4. TRACKING CONTROL This section explains a control system. The control system means the posture control in order to let the mark puts on the center of the image. In this paper, the control system uses the image information as a control input. Therefore, using mark position on the image uk and vk , error angle φimg and θimg are given by following equation. s · u k φimg = arctan l s · v k θimg = arctan l We construct the control system in order to revise the error. However, the measurement system which we developed needs calculation time for the whole processing. This processing includes the depth measurement of laser range ﬁnder, the image capturing and the image processing. Therefore, because of the calculation time, a time delay occurs to the tracking control. Then, we introduce the extended Kalman ﬁlter. Using the extended Kalman ﬁlter, we estimate the angle, angular velocity and angular acceleration xˆk = θˆk φˆk θˆ˙k φˆ˙k θˆ¨k φˆ¨k . Then using these estimated values, we improve the tracking performance. We construct PID control system and calculate control values by following equations. dφe φcmd = kP φe + kI φe dt + kD + φm dt (6) dθe + θm θcmd = kP θe + kI θe dt + kD dt φe and θe are error values. And these values are calculated as follow. φe = φimg − φd θe = θimg − θd φd and θd are desired values and this paper set desired values 0, in order to capture the mark on the image center. In addition φm and θm in equation (6) mean estimated variation of the mark based on the extended Kalman ﬁlter which is calculated by following equations. 1 ¨ 2 φm = φˆ˙k · ∆T + φˆ k · ∆T 2 1ˆ ˆ θm = θ˙k · ∆T + θ¨k · ∆T 2 2

(7)

where ∆T means the sampling time, and this paper sets it 80ms. This sampling time includes the image capturing and the image processing. In addition, let kP , kI and kD mean feedback gains. These gains are set experimentally, then, we set these parameters, kP = 1.0, kI = 0.01 and kD = 0.5. Fig. 5 shows a block-diagram of control system.

5. EXPERIMENTS This section shows results of experiments and veriﬁes the availability of the observation device. First in order to verify a recognition performance, we conduct an experiment of recognition. Next to verify the tracking performance of the observation device, we conduct a experiment of tracking control. Finally we measure the working radius of the crane, and verify the availability of the observation device.

5.1. Structure of experimental device Fig. 6 shows the observation device which we developed in our research (shown in Fig. 6). In addition, the observation device is controlled by a control computer which has a CPU (Pentium4:3.2 GHz), a memory (1GB). Moreover, its OS is Windows XP.

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Figure 5. Block diagram of control system

Figure 6. The observation device

5.2. Experiment of recognition First we verify the recognition performance of the observation device. In this experiment, the distance between the observation device and the mark changes in 10m to 50m. Changing the zoom value, the observation device recognizes the mark. An experimental result is shown in Fig. 8.

(a)

(b)

Figure 7. (a)Capture image of 50m distance (b)Capture image of 10m distance

From the experimental result, the observation device realizes the stable recognition of the mark. Fig. 7 shows the camera images when the mark exists in 50m and 10m. From Fig. 7, we checked that the zoom lens had chosen the right zoom value, since the size on image was keeping constant even if depth distance changed. In addition, Fig. 8 expresses the change of zoom value and the mark size on the image. In this experiment, we control the zoom lens to keep the mark size at 80 pixels. However it is diﬃcult because the zoom value can choose only an integer. From Fig. 8, it keeps the mark size among from 70 pixels to 80 pixels. Though, when the zoom value is 20 times, the mark size on the image becomes small rapidly. The reason is the change of the digital zoom, however, this paper does not consider about this problem.

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mooS euIv

sic

Figure 8. Change of zoom value and mark size depend on depth distance

5.3. Experiment of tracking control This experiment veriﬁes the tracking performance of the observation device for the moving mark. Fig. 9 shows an arrangement of this experiment. The mark which is attached to an overhead crane is arranged in 5m from the observation device. The mark is moved by operating of the overhead crane. Further, the mark movement is a pendulum movement. This experiment veriﬁes the tracking control using the mark position which is measured by the observation device and posture of the device which given by encoder. The illumination of the environment is 270lx. Fig. 9 expresses the results of tracking the cross mark. As the experimental result, the observation device can track each mark. From the experimental result, the camera position conforms to the mark position. Therefore, the observation device can track the moving mark without time delay. 000r

A1

or

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r

or

A

or

8r

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errñT [a]

(a)

(b)

Figure 9. (a)Arrangement of device in tracking experiment (b)Result of experiment for cross mark

5.4. Experiment of position measurement This experiment veriﬁes the measurement accuracy of the observation device. In this experiment, two marks are arranged in 20m of the front of the observation device as shown in Fig. 10. Then, one mark is a static mark and other mark is a dynamic mark. The observation device measures a distance between these marks. In addition, using a total station DTM-505C (NICON), we measure the distance. The total station is measuring device on the market and this device can measure the distance with accuracy. Then, we compare these measurement results which are taken by each device. In this experiment, we suppose that the mark does not move during measurement. We conduct two kinds of experiments as follow. (a) The moving mark is moved to transverse direction, namely, when the posture of the observation device changes. (b) The moving mark moves in the depth

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3cesqA rnsIJr

'-S

(p)

IocsT8cqcffJ

qeAlce

Figure 10. Arrangement of device in static measurement experiment Table 1. Measurement result

Result of (a) Distance [m] Error [mm] 2 -12.79 4 0.67 10 -17.58 20 15.17 30 -17.21 50 -2.41

Result of (b) Distance [m] Error [mm] 15 -6.76 30 -19.13 40 -8.62 50 0.22 60 -8.91 80 -28.73

direction, in other words the posture of the observation device does not change during measurement. Here, the environment of this experiment is conducted in outdoor and illumination is 15000lx. Table 1 shows measurement results of (a) and (b). In the table, a distance is the distance between two marks, and an error is the diﬀerence of results of the observation device and the total station. From the error is less than 30mm, measurement of the observation device is high accuracy.

5.5. Measurement of working radius In this experiment, the observation device measures the working radius of the crane. As shown in Fig. 11, the crane, the observation device and total station are arranged in outdoor. Recall that the working radius is the distance between the rotation center of the crane and the crane hook. In this experiment, we want to measure more than 50m working radius, however, the crane which we use has only 20m working radius. Then, we measure the mark which is attached to a cart in stead of the crane hook as shown in Fig. 11. In this paper, we call the cart the crane hook. For the measurement of the working radius, we use the observation device and the total station. Using the observation device, it is diﬃcult to measure the actual position of the rotation center. Then, we attach three marks to the crane, and measure the position of rotation center using position of three marks. As for the total station, the position of the rotation center is measured directly without using three marks. This experiment veriﬁes the measurement accuracy like section 5.2 using total station. In this experiment, working radius are 20m, 30m, 40m, 50m and the result of measurement is shown in Table 2. From the experimental result, since the error is within 2cm, we can say that the observation device enables high accuracy measurement.

6. CONCLUSION The objective of this paper was to measure the working radius of the crane automatically. Then, we developed the observation device with CCD camera and laser range ﬁnder. In addition, we proposed the methods of recognition, position measurement of the mark and tracking control system. As for the recognition, we used a

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Total station

11 Working radius

Crane hook

Marks

Crane Total station

Cart with mark (Crane hook)

Rotation center

Observation device

Observation device

Figure 11. Arrangement of device in experiment Table 2. Result of measurement

Working radius [m] 20 30 40 50

Error [mm] -19 -14 -16 -16

special marks which are called the cross mark. As for the tracking control, we constructed PID control with the extended Kalman ﬁlter to realize control system without time delay. Then, by some experiments, we veriﬁed availability of the observation device for the measurement of working radius of the crane. As for the recognition, we realized stable recognition in controlling zoom lens and keeping the mark size on the image constant for the changing depth distance. Then the observation device can track to moving mark without time delay. Moreover, as for the measurement using the crane, the measurement result of working radius using the observation device is very accurate and the error is less than ±2cm. Therefore the observation device which is developed is available for the measurement of working radius of crane.

REFERENCES 1. S. Kaneko, K. Horiuchi and T. Honda, “Estimation of Three Dimensional Motion Based on Multiple Distributed Kalman Filters,” Transactions on the Institute of Electronics, Information and Communication Enginners J79-D-II-5, pp. 840-850, 1996. (in Japanese) 2. S. Murakami, “Image Processing Technology,” Tokyo Denki University Press, 1996. (in Japanese) 3. M. Shibata and T. Honma, “A Control Technique for 3D Object Tracking on Active Stereo Vision Robot,” IEEJ Transactions on Electronics, Information and Systems 125-3, pp. 536-537, 2005. (in Japanese) 4. K. Saruta, H. Fujimoto and Y. Hori, “Visual Servoing System with Feature Prediction using Motion Observer,” IEEJ Transactions on Industry Applications 122-5, pp. 516-521, 2002. (in Japanese) 5. T. Shiozaki and T. Murakami, “3D Position Detection of a Moving Object in Active Stereo Vision System with Multi-DOF Motion,” IEEJ Transactions on Industry Applications 125-6, pp. 561-567, 2005. (in Japanese) 6. K. Sabe, M. Fukuchi, J. S. Gutmannand, T. Ohashi, K. Kawamoto and T. Yoshigahara, “Obstacle Avoidance and Path Planning for Humanoid Robots using Stereo Vision,” Proceedings on International Conference on Robotics and Automation, 2004.

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Catheter Kinematics and Control to Enhance Cardiac Ablation Yusof Ganjia , Farrokh Janabi-Sharifib a Department

of Electrical & Computer Engineering, University of Waterloo, 200 University Ave. West, Waterloo, ON, Canada N2L 3G1;

b Department

of Mechanical & Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, ON, Canada M5B 2K3 ABSTRACT

Catheter ablation is the preferred minimally invasive treatment for cardiac arrhythmias. Limited maneuverability of currently available catheters undermines the success of this treatment and subjects operations to prolonged repeated attempts to pace suspicious zones and ablate the arrhythmogenic substrates under ionizing radiation of ﬂuoroscopy. To compensate for such ineﬃciencies, a control system that can replace operators hand during the procedure is desired. This system should be able to direct catheter tip toward the ablation site and maintain its contact with the substrate during ablation, accelerating the process and enhancing its precision. To realize such a system, the ﬁrst step is to kinematically model the catheter and to devise a control strategy to embed the kinematics of the catheter. This paper proposes a simpliﬁed approach to model and control a general singlesegment active catheter as a continuum robot. In this approach, the ﬂexible catheter is modeled as a rigid manipulator having coupled joints. Utilizing the structural coupling of the catheter, joint-variables are reduced to actuatable parameters thus lifting some of the mathematical diﬃculties in formulation of a control strategy for redundant manipulators. The modeling is validated through experiments with a typical steerable ablation catheter equipped with an electromagnetic tracker in vitro. Keywords: Catheter, cardiac ablation, kinematics, modeling, control

1. INTRODUCTION Arrhythmias are erratic heartbeats caused by irregularities in the heart conduction systems. An estimated 2.3 million people in the United States1 suﬀer from atrial ﬁbrillation, a common form of arrhythmia. Cardiac catheterization is the minimally invasive approach in treatment of such abnormalities. Radio frequency (RF) ablation is the standard method through which the arrhythmogenic substrate is heated to create a hyperthermic lesion, thus disabling its beating function. As a result, the re-entry circuit is disconnected or the source of irregular beats is made inactive, and the heart regains its normal beating rhythm. Catheters are the tools to perform electrophysiological mapping of the heart to ﬁnd the type of arrhythmia and its substrate, and to conduct ablation in order to cure or palliate the abnormality. Catheters are either passive, i.e. they are preformed tubes whose shape is not controllable by the operator, or active, i.e. the proximal end can be ﬂexed or extended in at most two directions similar to a hand ﬁnger taking the shape of a ’J’ letter. In both cases, the ﬂexibility of the catheter limits the control of the operator over its proximal tip position as the operator can manipulate the catheter using its handle at distal end, outside the body. The handle typically houses a knob though which the proximal end can be deﬂected. When the catheter is threaded into the heart, it is subject to changes in pressure, volume and ﬂow dynamics in intracardiac cavities. These dynamics hinder the ﬂexible catheter from moving toward the intended position as desired. This means catheter steerability is very restricted. Mechanical deﬁciencies limit the navigability of the catheters which, in turn, subject catheter-based Further author information: (Send correspondence to Yusof Ganji) Yusof Ganji: E-mail: [email protected], Telephone: 1 519-888-4567, ext. 37266 Farrokh J. Shariﬁ: E-mail: fshariﬁ@ryerson.ca, Telephone: 1 416-979-5000, ext. 7097

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740U, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.686434

Proc. of SPIE Vol. 6374 63740U-1

procedures to repeated attempts to reach the target site before it is ﬁnally approached and then if contact with the target cannot be maintained long enough for pacing or ablation, closing in on the target is started over. As a result, successful ablation of hard-to-reach substrates is undermined. Cardiac contractions, respiration and patient movements during the operation impede precise targeting of the substrate. In addition, guidance of the catheter by hand has limited agility due to the natural delay in hand-eye coordination and fatigue in prolonged operations. The issues in catheter steering has motivated the design of actuated catheters,2–4 magnetic catheter navigation5 and robotic catheter control system.6 If a system can replace cardiologist’s hand in maneuvering the catheter with more agility, no fatigue and more precision, catheter ablation will be more successful and less costly. The ﬁrst step to control the catheter position is to model the catheter and to identify a control method for the modeled catheter. In this paper, a typical commercially-available active catheter is modelled as a special robotic manipulator. The paper is organized as follows. Section 2 reviews the existing methods in catheter modeling. In section 3 the proposed model is described. Section 4 explains the experiments performed to verify the model. The paper is concluded by section 5.

2. RELATED WORK Catheter is expected to be modeled as a ﬂexible mechanism that pushing, pulling and twisting actions on its distal end is translated into movements of the proximal end. Most of the literature on catheter modeling is focused on catheter simulation inside vascular structures. This simulation is mostly utilized in catheter navigation training. One approach models the catheter as a multibody system composed of a set of rigid links connected with joints.7 Angular springs ﬁtted on the joints connecting consecutive links approximate length-wise bending of the catheter. Twisting exerted on the distal end also aﬀects all the links. Another multibody approach8 tries to ﬁnd the most plausible conﬁguration of segments given the mechanical and physical constraints. To obtain a realistic simulation, the multi-body dynamics of the model is needed be known along with model interactions with its surrounding environment. In addition, the ﬂexibility constraint of the catheter requires several small links to be embedded in the model. Another approach constructs a virtual catheter using ﬁnite elements based on linear elasticity theory.9 This FEM∗ -based method requires small displacements in catheter movements to remain valid. A hybrid approach have also been recorded.10 In this method, catheter is a multibody of ﬂexible links. Multibody dynamics analysis yields the displacements and FEM characterizes deformations. Non-linear FEM is a requirement for such approaches to account for non-linearities in catheter deformations. Recently, physics-based models for catheter and guidewire simulation have been proposed.11, 12 In this model, catheter is composed of connected ﬂexible beam elements. The model simulates non-linear behaviour of the catheter in real-time and models bending and twisting of the catheter as well. Spline-based deformable models have also been used in similar simulations for one dimensional objects. For instance, surgical threads are modeled as dynamic splines utilizing lagrangian formulations to account for continuous mass distribution along the thread.13 Such a method can be used in catheter modeling if bending and twisting is incorporated in the model. All the preceding methods are used for simulation purposes where the surrounding vascular structure is known priorly enabling the model to adjust to its environment. However, in real world, the constraining intravascular/intracardiac anatomy is not exactly known. This means the catheter model should approximate the catheter conﬁguration with almost no information of the constraints. A few published studies have addressed catheter modeling for the purpose of control. These models, however, are mostly for prototype active catheter with in-situ actuators. For instance, the bending of a multi-segment actuated catheter is modeled as a function of its microrobot segments’ deﬂections.3 A model of a conventional catheter deployed in catheterization laboratories was not found in the literature. We present an approach to model the catheter as a continuum robotic manipulator based on the method developed by Walker.14, 15 ∗

Finite Element Method

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C a tiacter

cg ZI, X4!

2(5

c

0 (a)

(b)

Figure 1. Catheter and its model. (a) Deﬂectable section of the catheter, (b) Catheter model with assigned D-H coordinate frames.

3. KINEMATIC MODEL OF THE CATHETER We hypothesize that the catheter can be modeled as a robotic manipulator. According to Robinson and Davies16 classiﬁcation, continuum robots do not contain distinct joints and rigid links. Instead, they bend along their length continuously similar to elephant’s trunk and squid’s tentacles, their biological counterparts. Catheter can be called a continuum robot by this deﬁnition. In fact, it is a planar extrinsic continuum robot; it is extrinsic as the actuation mechanism transfers motion to the tip from its distal end, external to the body; and it is planar as the catheter is deﬂected in a single plane of bending. With this hypothesis, we formulate the kinematic model of the catheter and then verify the formulation through measurement experiments. The proposed catheter modeling is based on the kinematics approach for continuum robots, originally developed by Walker.14, 15 Catheter is modeled as a single-segment continuum robot having constant curvature along its length with no torsion† . The catheter tip can be modelled in 3D space as seen in ﬁgure 1. In this ﬁgure the assigned Denavit-Hartenberg (D-H) coordinate frames are depicted. When there is no torsion (catheter bends in a single plane) and the curvature is constant (the bent catheter is like an arc), movement along the planar catheter curve can be described in three steps: rotation by an angle θ, translation by a displacement of ||d||, and rotation by the angle θ again.14 These steps inspire us to replace rotations with two revolute joints and the translation by one prismatic joint. Hence, the ﬂexible catheter can be modelled by rigid components. This simpliﬁed model is applied to the spatial case adding two more revolute joints as shown in ﬁgure 1(b). In this ﬁgure, the preceding angle θ is denoted by θ3 . The catheter, is composed of a bending tip and a long body as seen in ﬁgure 1(a). Since the catheter body is constrained by the lumen of the vasculature on its way to the heart, it can be modelled as a rigid prismatic joint. This assumption is valid since pushing/pulling on the distal shaft is linearly translated to the tip. As long as the motion rate of the body (d1 ) and not actual position of the model base is of concern, kinematic calculations are valid. Now, using Denavit-Hartenberg (D-H) convention, the kinematics of the catheter can be constructed (see ﬁgure 1(b)). D-H parameters are presented in table 1. Curvature constancy and the coupling †

Curvature and torsion are deﬁned in classical diﬀerential geometry.

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link 1 2 3 4 5 6

a 0 0 0 0 0 0

α 0 π/2 π/2 π/2 π/2 π/2

d d∗1 0 0 d∗4 0 0

θ 0 π − θ2∗ π/2 + θ3∗ 0 θ5∗ θ6∗

Table 1. D-H table. Joint variables are denoted with asterisks.

in the parameters yields θ5 = 3π/2 − θ3 and θ6 = θ2 . Finally based on table 1 the transformation matrix of the catheter tip position and orientation from its distal end pose is computed. Matrix (1) is the simpliﬁed forward kinematics transformation matrix computed with D-H parameters in table 1. In this matrix, c stands for cos and s denotes sin function. ⎡

2

(cθ2 ) c2θ3 − (sθ2 )

2

⎢ ⎢ − (1 + c2θ ) sθ cθ 3 2 2 ⎢ ⎢ ⎢ −cθ2 s2θ3 ⎣ 0

−cθ2 s2θ3

(1 + c2θ3 ) sθ2 cθ2

sθ2 s2θ3

− (sθ2 ) c2θ3 + (cθ2 )

−c2θ3

−sθ2 s2θ3

0

0

2

−cθ2 cθ3 d4

2

⎤

⎥ ⎥ ⎥ ⎥ d4 sθ3 + d1 ⎥ ⎦ sθ2 cθ3 d4

(1)

1

3.1. A Note on Control In order to control and plan catheter tip path, the relationship between joint-space parameters and actuation mechanism is required to be known. In the forward kinematics, four parameters of d1 , θ2 , θ3 , and d4 are present. d1 and θ2 are directly actuatable. θ3 is also actuated by the knob on the catheter handle and the angle θ3 as a function of knob rotation can be found experimentally or analytically. However, d4 is not directly actuated and is coupled with θ3 . As shown by Hannan et. al.14 the relationship between d4 and θ3 can be easily formulated. Assuming the length of bending segment of the catheter to be constant L, we have d4 =

L sin(θ3 ). θ3

(2)

Equation 2 holds as long the catheter is curved and not straight which means θ3 = 0. Thus, having three actuators there are three parameters to control. A note on the forward kinematic formulations is necessary. The bending section of the catheter is not directly connected to the ablative tip. Instead a short section, housing several electrodes comprises the ﬁnal end of the catheter along with the ablative tip (see ﬁgure 1(a)). This ﬁnal section is not as ﬂexible as the bending part and cannot be deﬂected. In formulations presented here this section is assumed to be of length zero. In catheter navigation, the main concern is position of the catheter tip. Having the formulated kinematics, inverse kinematic position control can be achieved. Position of the catheter can be tracked using an electromagnetic tracker mounted on the catheter as used in available navigation systems.17 Having the position feedback of the catheter tip and position Jacobian derived from forward kinematics the control loop can be devised.

4. EXPERIMENTAL VALIDATION 4.1. Setup To validate kinematic formulations that calculate position of catheter tip, a ﬁxture was built on which the catheter is mounted. The catheter handle is housed in the ﬁxture so that push/pull/twist on the handle could be measured. The rotation of the knob is also measured using a jig with built-in protractor connected to the knob. The catheter is a standard-curve SteeroCath-T (BostonScientiﬁc, Natik, MA) ablation catheter. The catheter

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Parameter Position accuracy Orientation accuracy Sensor dimensions (diameter × length) Maximum number of sensors Maximum update rate Measurement volume

Value 0.9 mm 0.8◦ 1.8 × 9 mm 4 (6DOF) or 8 (5DOF) 45 Hz (up to 6 sensors) or 20 Hz (up to 8 sensors) 500 × 500 × 500 mm3

Table 2. Electromagnetic tracking system speciﬁcations.

H (a)

(b)

Figure 2. Experiment setup. (a) measurement ﬁxture (b) catheter tip with an Aurora sensor in front of EM ﬁeld generator.

body is threaded in a PVC ﬂexible tubing to mimic the vasculature. The tubing was ﬁxed on a V-shaped support which keeps the tubing straight. The deﬂectable section of the catheter was left unsupported out of the tubing. To track the position of the desired points on the deﬂectable section of the catheter, Aurora system (NDI, Waterloo, Canada) was used. Aurora is an electromagnetic tracking system that enables touchless position and orientation measurement of an object placed in the volume covered by its (electromagnetic) ﬁeld generator. Sensor coils are mounted on the object of interest for tracking. The speciﬁcations of the system are summarized in table 2. The measurement ﬁxture and the catheter tip equipped with an Aurora tracker are shown in ﬁgure 2. In the experiments, one sensor was mounted at the tip of the deﬂecting section of the catheter, and provided the position of the tip. The other sensor was ﬁxed at the other end of the deﬂecting section where joints 2 and 3 intersect in the model (ﬁgure 1(b)). With this sensor conﬁguration, parameters θ2 and θ3 was measured and their relationship with twisting of the catheter handle and rotation of the knob was investigated respectively.

4.2. Experiments and Results Assuming that the eﬀects of push/pull on the catheter handle, twisting the handle and rotating the knob to bend the distal end section are decoupled motions, meaning their contribution to the pose of the catheter tip is independent of each other, the experiments were conducted. This assumption is evident in the catheter modeling formulations as well (see forward kinematics transformation matrix (1)). According to (1) position vector of the catheter tip is P =

−cθ2 cθ3 d4

sθ2 cθ3 d4

d4 sθ3 + d1

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.

(3)

To validate this vector formula, the catheter was translated or rotated for each degree of freedom and the compliance of the position readings with the calculated position vector was studied. In order to unveil the possible hysteresis in catheter motion, steering in any direction was followed by steering in the reverse direction. Figure 3 illustrates the measured readings when catheter is pushed/pulled or deﬂected. From (3), it is expected that translation of catheter tip linearly translates catheter tip in Z direction, (d1 ). Figure 3(a) veriﬁes this relationship. X and Y elements of the measured position vector exhibit small changes that can be attributed to Aurora system’s resolution and precision of position readings as well as the eﬀects of catheter and sensor weight. Z element of the position vector changes linearly as expected during the course of backward and forward translation. To verify the validity of vector (3) in terms of θ3 , i.e. when catheter tip is bent, catheter was placed so that its planar deﬂection lies in X − Z plane while weight vector of the catheter is along Y axis. Figure 3(b) and (c) show the measured and expected position vector elements. The eﬀect of hysteresis in backward and forward motion is apparent in the measured data. The X and Z proﬁles follow the expected curve but the dynamic eﬀect of weight is not negligible in Y measurements and induces a large error compared to X and Z measurements. Table 3 presents the error values associated with kinematic calculations. 0.5

50

0

0.4

45

0.3

40

0.2

35

0.1

30

−0.5

−1.5

Y (mm)

X (mm)

−1

−2 −2.5 −3 −3.5 −4

Z (mm)

0.5

0

20

−0.2

15

−0.3

10

−0.4 0

10

20 30 Handle Displacement (mm)

40

−0.5

50

25

−0.1

5 0

10

20 30 Handle Displacement (mm)

40

0

50

0

10

20 30 Handle Displacement (mm)

40

50

(a) 55

5

50 40

50 0

30

40 35 30

Measured Z (mm)

Measured Y (mm)

Measured X (mm)

45

−5

−10

25

10 0 −10 −20

−15 20 15 −60

20

−30

−40

−20

0 20 Deflection Angle (deg)

40

60

−20 −60

80

−40

−20

0 20 Deflection Angle (deg)

40

60

−40 −60

80

−40

−20

0 20 Deflection Angle (deg)

40

60

80

−40

−20

0 20 Deflection Angle (deg)

40

60

80

(b) 55

5

40

50

30 0

40 35 30

Calculated Z (mm)

20 Calculated Y (mm)

Calculated X (mm)

45

−5

−10

25

10 0 −10 −20

−15 20 15 −60

−30

−40

−20

0 20 Deflection Angle (deg)

40

60

80

−20 −60

−40

−20

0 20 Deflection Angle (deg)

40

60

80

−40 −60

(c) Figure 3. Calculated and measured position proﬁles, (a) measured position during translation along d1 (push/pull), (b) measured position while deﬂecting the catheter tip, (c) expected position proﬁle (as a result of knob rotation).

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Parameter d1 θ3

X -1.44±0.98 mm 0.29±4.38 mm

Y -0.15±0.19 mm 4.84±4.52 mm

Z 0.59±0.51 mm -1.78 mm±4.9 mm

Table 3. Error values in position calculations (mean±standard deviation)

Tip Twist Angle (deg)

150

100

50

0

−50

0

50

100

150 200 250 Handle Twist Angle (deg)

300

350

Figure 4. Catheter tip rotation angle (θ2 )

To study the eﬀect of catheter twist, the rotation angle was measured directly. Figure 4 illustrates the measured rotation of catheter tip in response to handle rotation. Change of rotation direction induces hysteresis again as can be seen in the ﬁgure. In addition, ﬁgure 4 reveals that twisting of the handle does not create the same rotation at the tip. It is noted that though the rotations are not equal, their relationship is linear with a correlation coeﬃcient of 0.9861 at conﬁdence level of 95%. The results presented above indicate that the rigid model of the ﬂexible catheter approximates the catheter with a bounded error especially in the absence of external forces and dynamics. The aim of this study is to achieve a model to be utilized in catheter position controller design, and the proposed simpliﬁed model is the ﬁrst step to this end. Evidently, the controller should compensate for any unmodeled non-linearities.

5. CONCLUSION Dexterity of the current state-of-the-art catheters is very limited. In order to enhance the steering of the catheter in procedures like ablation, a control system that can direct the catheter and react to disturbances faster than human operator is desired. In an attempt to achieve such a system, a rigid model for a deﬂectable catheter is proposed and the kinematic relations of the model are derived. The validity of the predicted catheter tip position is tested through experiments. Based on this model, position control will become feasible. Realizing such a control system is the future work of the authors.

ACKNOWLEDGMENTS The authors wish to thank Devin Ostrom, Ryerson University, for his eﬀorts in the design and preparation of the measurement ﬁxture.

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REFERENCES 1. A. Go, E. Hylek, K. Phillips, Y. Chang, L. Henault, J. Selby, and D. Singer, “Prevalence of Diagnosed Atrial Fibrillation in Adults. National Implications for Rhythm Management and Stroke Prevention: the Anticoagulation and Risk Factors In Atrial Fibrillation (ATRIA) Study,” May 2001. 2. K. Ikuta, H. Ichikawa, K. Suzuki, and D. Yajima, “Multi-degree of freedom hydraulic pressure driven safety active catheter,” in Robotics and Automation (ICRA 2006). Proceedings of the 2006 IEEE International Conference on, pp. 4161–4166, May 2006. 3. Y. Bailly and Y. Amirat, “Modeling and control of a hybrid continuum active catheter for aortic aneurysm treatment,” in Robotics and Automation (ICRA 2005). Proceedings of the 2005 IEEE International Conference on, pp. 924–929, April 2005. 4. Y. Haga, Y. Muyari, T. Mineta, T. Matsunaga, H. Akahori, and M. Esashi, “Small diameter hydraulic active bending catheter using laser processed super elastic alloy and silicone rubber tube,” in Microtechnology in Medicine and Biology, 2005. 3rd IEEE/EMBS Special Topic Conference on, pp. 245–248, 2005. 5. C. Pappone, G. Vicedomini, F. Manguso, F. Gugliotta, P. Mazzone, S. Gulletta, N. Sora, S. Sala, A. Marzi, G. A. amd Laura Livolsi, A. Santagostino, and V. Santinelli, “Robotic Magnetic Navigation for Atrial Fibrillation Ablation,” Journal of the American College of Cardiology 47, pp. 1390–1400, April 2006. 6. W. Saliba, J. Cummings, S. Oh, Y. Zhang, T. Mazgalev, R. Schweikert, J. Burkhardt, and A. Natale, “Novel Robotic Catheter Remote Control System: Feasibility and Safety of Transseptal Puncture and Endocardial Catheter Navigation,” J Cardiovasc Electrophysiol 17, pp. 1–4, 2006. 7. S. Cotin, S. Dawson, D. Meglan, D. Shaﬀer, M. Ferrell, R. Bardsley, F. Morgan, T. Nagano, J. Nikom, P. Sherman, et al., “ICTS, an interventional cardiology training system.,” Stud Health Technol Inform 70, pp. 59–65, 2000. 8. M. Kukuk and B. Geiger, “A real-time deformable model for ﬂexible instruments inserted into tubular structures,” in Medical Image Computing and Computer-Assisted Intervention - MICCAI 2002: 5th International Conference Proceedings, pp. 331 – 338, (Tokyo, Japan), September 2002. 9. W. L. Nowinski and C.-K. Chui, “Simulation of interventional neuroradiology procedures,” MIAR , p. 87, 2001. 10. Y. Wang, C. Chui, H. Lim, Y. Cai, and K. Mak, “Real-time interactive simulator for percutaneous coronary revascularization procedures,” Computer Aided Surgery 3(5), pp. 211–227, 1998. 11. S. Cotin, C. Duriez, J. Lenoir, P. F. Neumann, and S. Dawson, “New approaches to catheter navigation for interventional radiology simulation.,” in MICCAI (2), J. S. Duncan and G. Gerig, eds., Lecture Notes in Computer Science 3750, pp. 534–542, Springer, 2005. 12. J. Lenoir, S. Cotin, C. Duriez, and P. Neumann, “Interactive physically-based simulation of catheter and guidewire.,” Computers & Graphics 30(3), pp. 416–422, 2006. 13. J. Lenoir, P. Meseure, L. Grisoni, and C. Chaillou, “Surgical thread simulation,” in Modelling and Simulation for Computer-aided Medecine and Surgery (MS4CMS), pp. 102–107, November 2002. 14. M. W. Hannan and I. D. Walker, “Kinematics and the implementation of an elephant’s trunk manipulator and other continuum style robots,” Journal of Robotic Systems 20, pp. 45–63, February 2003. 15. B. A. Jones and I. D. Walker, “Kinematics for multisection continuum robots,” IEEE Transactions on Robotics 22, pp. 43–55, February 2006. 16. G. Robinson and J. Davies, “Continuum robots-a state of the art,” Robotics and Automation, 1999. Proceedings. 1999 IEEE International Conference on 4, pp. 2849–2854, 1999. 17. S. A. Ben-Haim, “Catheter navigation in modern electrophysiology,” Journal of Cardiovascular Electrophysiology 11, pp. 1193–1195, November 2000.

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An Investigation of Phenomenal Parasitics and Robust Control of Parallel-Plate Electrostatic Micro Actuators Guchuan Zhua , Jean-Franc¸ois Chianettab , Mehran Hosseinib , and Yves-Alain Peterb a Department of Electrical Engineering, Ecole ´ Polytechnique de Montr´eal, C.P. 6079, Succursale centre-ville, Montreal, QC, Canada H3C 3A7 b Engineering Physics Department, Ecole ´ Polytechnique de Montr´eal, C.P. 6079, Succursale centre-ville, Montreal, QC, Canada H3C 3A7 ABSTRACT This paper extends the modeling of the effect of fringing field, proposed in our recent work,1 to more generic devices: electrostatic parallel-plate actuators with deformations. Though these devices can be model as two parallel capacitors with a variable factor depending on the displacement,2 it is difficult to determine the analytical expression of such a function. It is shown that, like the effect of fringing field, the modeling error of the effective actuator due to deformations can be compensated by introducing a variable serial capacitor. When a suitable robust control is used, the full knowledge of the introduced serial capacitor is not required, but merely its boundaries of variation. Based on this model, a robust control scheme is constructed using the theory of input-to-state stability (ISS) and backstepping state feedback design. This method allows loosening the stringent requirements on modeling accuracy without compromising the performance. The stability and the performance of the system using this control scheme are demonstrated through both stability analysis and numerical simulation. Keywords: Phenomenal parasitics; modeling of electrostatic MEMS; FEM based simulation; input-to-state stability; robust nonlinear control.

1. INTRODUCTION In the most popular model of electrostatic parallel-plate actuators, the moveable plate is supposed to be a rigid body without deformation and only the main electrical field (perpendicular to both electrodes) is considered. The capacitance of such structures is computed by A , (1) C= G(t) where A is the area of electrodes, G the air gap, and the permittivity in the gap. This model is subject to modeling errors due to, e.g., deformations, fringing field effect, and parasitics related to the layout. Fabrication deviations and environmental fluctuations may also introduce parameter variations, affecting the reliability of the model. The performance of the controller obtained from the simplified model might be compromised for applications where the precise positioning is required, e.g. adaptive optics.3 To assure a high performance, one might want to use more accurate model. However, this might result in more complicated mathematical model and, consequently, make the control system difficult to implement and unreliable. For examples, modeling the fringing field and deformations leads in general to distributed parameter systems described by partial differential equations. The control of such systems requires distributed sensing and actuation, which is very hard to implement for microsystems. We have proposed, in our recent work,1 to model the effect of fringing field by a serial capacitor. Combined with an appropriate robust control, the full knowledge of the introduced serial capacitor is not required, but only its boundaries of variation, which can be obtained by simulations using off-the-shelf commercial software tools, e.g. ANSYSTM , COMSOLTM , and CoventorWareTM , or by experimental measurements. This ideal considerably simplified the complexity of the model without compromising the performance of the control system. In this work, we will extend this method to Further author information: (Send correspondence to G. Zhu or Y.-A. Peter) G. Zhu: E-mail: [email protected] Y.-A. Peter: E-mail: [email protected] Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740V, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.692301

Proc. of SPIE Vol. 6374 63740V-1

deformed structure and will shown that in the presence of deformation, the modeling error can also be compensated by introducing a suitable serial capacitor. The robust control scheme used in this work is based on the theory of input-to-state stabilization (ISS) and backstepping state feedback design. The nominal model used in control law design is the simplified parallel-plate actuator, but the controller is made robust against parasitics and parametric uncertainties. The stability and the performance of the system using this control scheme are demonstrated through both stability analysis and numerical simulation. The rest of the paper is organized as follows. Section 2 models the capacitance of 1DOF parallel-plate electrostatic actuator in the presence of deformation. Section 3 is devoted to the construction of control law. The simulation results are reported in Section 4 and Section 5 contains some concluding remarks.

2. MODELING OF PARALLEL-PLATE ELECTROSTATIC MICRO ACTUATORS IN THE PRESENCE OF PHENOMENAL PARASITICS 2.1. Modeling of Ideal Devices Denote by m the weight of the moveable plate, by k the elastic constant of the suspension beams, and by b the damping coefficient of the structure. The equation of motion of the actuator is then given by ¨ + bG(t) ˙ mG(t) + k(G(t) − G0 ) = F (t),

(2)

where G0 is the zero voltage gap and F (t) the force due to electrical field. Let Q(t) be the charge on the device and Va (t) the actuation voltage. One can deduced from the capacitance (1) the electrostatic force of ideal parallel-plate actuator which reads F (t) =

AV 2 Q2 (t) Va2 ∂C =− 2a =− . 2 ∂G 2G (t) 2A

(3)

Note that the electrostatic force is always attractive regardless of the polarization of the control signal. Assuming the system started operating from an initially uncharged state at t = 0, then the charge on the electrodes at the time t is: t

Q(t) = 0

Is (τ )dτ,

(4)

or equivalently ˙ Q(t) = Is (t),

(5)

where Is (t) is the source current through the loop resistor R. By a simple application of Kirchhoff’s Voltage Law we obtain:4 1 Q(t)G(t) ˙ Q(t) = Vs (t) − , (6) R A where Vs (t) is the source voltage, which is the actual control variable.

2.2. Capacitance Model of Deformed Devices When deformation happens, the displacement is no longer uninform: the center portion is largest whereas the portions near the step-up supports hardly move at all. The deformed device can be modeled as the sum of two onedimensional (1-D) capacitances: a variable capacitor, representing the effective actuator, in parallel with another one whose equivalent surface is parameterized by the air gap, as shown in Fig. 1. The total capacitance of such devices can be expressed as:2 C = Ca + Cp ∝

γ 1−γ + , G G0

(7)

where Ca is the capacitance of the actuator, Cp is the the capacitance of the parallel capacitor, and γ is a proper function that increases as the gap closes. To illustrate the effect of deformation, we have simulated a micro structure using finite element methods (FEM) based MEMS CAD software package CoventorwareTM . The electrodes are square of 206×206 µm2 and the moveable plate is

Proc. of SPIE Vol. 6374 63740V-2

+0 KI

,

=

Figure 1. Schematic representation of the deformed structure and its equivalent circuit.

—— O.M

,I.?3, •j t.•á

111.1

Figure 2. FEM based simulation of a deformed micro-structure.

sustained by four beams clamped at the corners. The thickness of the moveable plate is 1.5088µm and the initial gap is 5µm. The deformation and the distribution of charge density at a position of deflection is shown in Fig. 2. The capacitance of the device obtained from CoventorWareTM simulation and the one calculated from the rigid body approximation (1) are given in Table 1. It can be seen that for small deflections, the deformation is not significant and the capacitance of the simulated device is higher than the one calculated from the rigid body approximation (about 17% higher at the zero voltage position). This is due to the unmodeled phenomena, e.g., the effect of fringing field. For large deflections, the deformation becomes important. In this case, the capacitance calculated from (1) is overestimated. For a deflection of 4.8431 µm, the modeling error can be as high as 47%. Note that the effect of fringing field decreases as the gap closes. Therefore, the modeling error for large deflections is mainly due to the deformation. Obviously, it is very difficult to determining the function γ in (7), because it changes with the structure, the geometry, and the material of the actuator. To overcome this difficulty, we adopted the method developed in our recent work1 by modeling the device as an ideal rigid body, called also the nominal structure, combined with an appropriate variable serial capacitor. The capacitance of the nominal structure, Ca , follows the ideal model (1), but uses an effective area Aef f to compensate the modeling errors at the zero voltage position. Since the deformation has effect of decreasing the capacitance and the effect of fringing field is maximum at the initial gap, the nominal structure gives overestimated capacitance for any non zero deflection. The introduced serial capacitor has the effect of reducing the total capacitance and, hence, it will eliminate the modeling error. The value of the introduced serial capacitor is a function of the gap and can be expressed as 1 1 1 = − . Csp Creal Ca

(8)

Obviously, since Creal is unknown, one can not determine Csp . However, as mentioned earlier, for an appropriate robust control scheme, the full knowledge of the relationship between serial capacitance and deflection is not required, but only its variation boundaries.

Proc. of SPIE Vol. 6374 63740V-3

Table 1. Capacitances for different deflections.

Deflection (µm) 0 0.6459 1.1798 1.9488 2.4944 3.1086 3.5897 4.1133 4.5522 4.7492 4.8431

Capacitance (pF) FEM Simulation Rigid Body Approximation 0.0909 0.0751 0.1004 0.0863 0.1103 0.0983 0.1292 0.1231 0.1485 0.1499 0.1811 0.1986 0.2220 0.2663 0.3049 0.4236 0.4973 0.8386 1.0253 1.4972 1.6286 2.3934

4 FEM based simulation 3.5

rigid structure approximation nominal rigid structure

Capacitance (pF)

3

equivelant serial capacitor

2.5 2 1.5 1 0.5 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Normalized Deflection

Figure 3. Capacitance of the simulated device, the rigid structure approximation, the nominal structure, and the introduced serial capacitor.

Figure 3 shows the capacitance of the simulated device, the rigid body approximation, and the nominal structure. The introduced serial capacitor is computed from (8) using the capacitances of the simulated device and the nominal structure. The value of the nominal capacitor at the initial gap is equal to 0.0909 pF (the same as the real capacitor at this position). Except for the initial separation gap, there is a difference between the value of nominal capacitor and the real one. The role of the serial capacitor is to compensate this difference. As shown in Fig. 3, this serial capacitance is infinite at the initial gap and has a minimum that is about 0.7126 pF for this structure. Since the smaller the introduced serial capacitance, the bigger the influence of modeling errors, we can use this value to determine the boundary of the introduced serial capacitor in the model. As the introduced serial capacitor and the parallel capacitor due to the deformation are essentially unknown, following the terminology of Ref. 2, we can call them phenomenal parasitics. Obviously, the effect of fringing field can also be considered as serial parasitics.1 A generic capacitance model of the deformed parallel-plate is given in Fig. 1, in which Cpp is composed of different unmodeled parallel capacitors due to, e.g., the deformation and the layout.

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2.3. Dynamics of the Actuator in the Presence of Parasitics When taking into account for parasitics, the dynamic equation of the electrical subsystem is given by1 G˙ G0 1 G ˙ Vs − Qa (t) = + ρs + Rρp Qa , G A A G0 R 1 + ρp ρs + ρp G0 where ρp =

(9)

Cpp C0 , ρs = , C0 Csp

with C0 = Aef f /G0 , the capacitance of the nominal structure at the initial gap G0 . In our modeling, ρp and ρs represent the influence of parasitics. When their value is set to zero, the dynamics of the electrical subsystem will be reduced to the one for ideal devices given in (6). It can be seen from (9) that the parallel parasitic capacitance will not change the static behavior of the device. However, the dynamics of the electrical subsystem will be affected: the bigger the parallel parasitic capacitance, the slower the dynamics of the driving circuit. Consequently, the performance of the system will be degraded if the parallel parasitic capacitance is not taken into account in the design of the control system. The serial parasitic capacitance will affect both the static and the dynamic behavior of the system. It is straightforward to show that the serial parasitic capacitance will change the position of pull-in. Note that since the nominal plan is an ideal rigid body, the mechanical subsystem still follows (2) with electrostatic force given in (3). Therefore the parasitics affect only the dynamics of the electrical subsystem. To make the system analysis and control design easier, we transform (2) and (9) into normalized coordinates by changing the time scale, τ = ω0 t, and performing a normalization as follows:5 x=1−

G Qa Vs Is , q= , u= , i= , r = ω0 C0 R, G0 Qpi Vpi Vpi ω0 C0

where Vpi = 8kG20 /27C0 is the nominal pull-in voltage, Qpi = 32 C0 Vpi the nominal pull-in charge, ω0 = k/m the undamped natural frequency, and ζ = b/2mω0 the damping ratio. We then have dq 1 2 dx = u − (1 − x)q − ρs q + rρp q . (10) dτ r (1 + ρp (1 − x) + ρp ρs ) 3 dτ Let x1 = x, x2 = v, and x3 = q 2 . System (2)-(10) can then be written in the normalized coordinates as dx1 =x2 dτ dx2 1 = − 2ζx2 − x1 + x3 dτ 3 √ 4 x3 dx3 =β u − 2(1 − x1 )x3 − 2ρs x3 + 2rρp x2 x3 dτ 3

(11a) (11b) (11c)

where

1 r (1 + ρp (1 − x) + ρp ρs ) is a function of deflection. System (11) is defined on the state space X = (x1 , x2 , x3 ) ⊂ R3 | x1 ≤ 1, x3 ≥ 0 . β=

(12)

Note that the considered actuator exhibits switching behavior. First of all, when the moveable plate hits the fixed one (x1 = 1), the dynamics of the mechanical subsystem collapse.6 In addition, q = 0 (x3 = 0) is a singular point at which System (11) is not linearly controllable (see, e.g., Ref. 6). However, it is easy to see that the system is symmetric except for the sign of the charge. For simplicity, we ignore the contact dynamics and consider only the branch defined by (11c). Consequently, the stability property obtained through the proposed control will hold locally. Since in what follows we deal only with normalized quantities, we can use t to denote the time and omit the qualifier “normalized.”

Proc. of SPIE Vol. 6374 63740V-5

3. ROBUST CONTROL DESIGN 3.1. Preliminaries of input-to-state stability The concept of input-to-state stability is introduced by Sontag7 and ISS-based design is a popular tool in the field of system control. We present here only the notations required in the development of the control law. The interested reader is referred to, for example, Ref. 8, 9 for a formal presentation. The following comparison functions are required for presenting the method of input-to-state stabilization. A function α : [0, a) → [0, ∞) is said to belong to class-K if it is continuous, strictly increasing, and α(0) = 0. If a = ∞ and α is unbounded, the function is said to belong to K∞ . A function β : [0, a) × [0, ∞) → [0, ∞) is said to belong to KL if it is nondecreasing in its first argument, nonincreasing in its second argument, and lims→0+ β(s, t) = limt→∞ β(s, t) = 0. The system x˙ = f (x, u)

(13)

is said to be input-to-state stable if for any x(0) and for any input u(·) continues and bounded on [0, ∞) the solution exists for all t ≥ 0 and satisfies |x(t)| ≤ β(x(0), t) + γ

sup u(|τ |) , ∀t ≥ 0,

0≤τ ≤t

(14)

where β(s, t) ∈ KL and γ(s) ∈ K. System (13) is ISS if and only if there exists a smooth positive define radially unbounded function V and class K∞ functions α1 and α2 such that the time derivative of V along the solutions of (13) verifies ∂V V˙ = f (x, u) ≤ −α1 (|x|) + α2 (|u|). ∂x

(15)

The function V satisfying the above inequality is called ISS-Lyapunov function. Note that the method of ISS provides a convenient framework for robust system control, which amounts to finding a control with which the closed-loop system is stable with respect to the disturbances, considered now as the inputs to the system.

3.2. Control synthesis In this work, we consider both the parasitics and parametric uncertainties, such as the variations of damping coefficient and loop resistance. We make then the following assumptions on the uncertainties in System (11). A SSUMPTION 1. The parasitic capacitances are bounded by known constants: 0 ≤ ρp ≤ ρ¯p , 0 ≤ ρs ≤ ρ¯s .

(16)

A SSUMPTION 2. The damping ratio is positive and bounded and can be written as: ζ = ζ0 + ∆ζ,

(17)

where ζ0 is positive-valued representing the nominal damping ratio and ∆ζ the modeling error. A SSUMPTION 3. The upper and lower bounds of the resistance in the loop, r, are known: 0 < r ≤ r ≤ r.

(18)

Since x1 ≤ 1, β in (12) may be bounded as follows: 0 < β ≤ β ≤ β,

(19)

where β = 1/r. Note that since the electrostatic force is always attractive, the control allowing the moveable plate to move as far as possible beyond the initial gap is the one that can remove the charge from the device in an arbitrary small

Proc. of SPIE Vol. 6374 63740V-6

time interval. However there is no equilibrium beyond the zero voltage gap and the mechanical subsystem (11-a)-(11-b) globally exponentially converges to the origin with zero input (x3 = 0).10 This implies that x1 should not be smaller than −1. Therefore, in a normal operational condition, β should be lower bounded by 1

. r 1 + ρp (2 + ρs )

(20)

|β − β0 | ≤ β − β ∆β.

(21)

β= Furthermore, the variation of β is denoted by

where β0 is the nominal value of β. In this work, we will consider the tracking problem with y = x1 as the output. Following a classical approach, we choose a sufficiently smooth reference trajectory yr for x1 as a function of time and then make this trajectory attractive. A recursive procedure, called also backstepping design (see, e.g., Ref. 9 for a detailed presentation of this technique), is used in the design of the control law, which consists of, for System (11), the following three steps. Step 1. Consider the control of the subsystem (11a) with x2 as a virtual input. Let z1 = x1 − yr be the position tracking error and select a Lyapunov-like function 1 V1 = z12 . 2 The time derivative of V1 along the solutions of (11.a) is V˙ 1 = z1 (x2 − y˙ r ). The desired input (also called stabilizing function) can be chosen as: x2d = y˙ r − k1 z1 , k1 > 0.

(22)

Step 2. Consider now the subsystem (11a)-(11b) with x3 as a virtual input. Define z2 = x2 − x2d and augment V1 to yield: 1 V2 = V1 + z22 . 2 Letting z3 = x3 − x3d , the time derivative of V2 along the solutions of the corresponding subsystem is given by V˙ 2 = − k1 z12 + z2 (z1 + x˙ 2 − x˙ 2d ) 1 = − k1 z12 + z2 z1 − 2(ζ0 + ∆ζ)x2 − x1 + (z3 + x3d ) − x˙ 2d . 3 In order to counteract the uncertainty ∆ζ, a nonlinear damping term should be added to the stabilizing function. The desired input in this case is of the following form:

(23) x3d = 3 2ζ0 x2 + x1 + x˙ 2d − z1 − κ2 ζ0 x22 z2 − k2 z2 , where k2 > 0 and κ2 is the gain of the nonlinear damping term, the lower bound of which will be given latter on. Step 3. Finally the Lyapunov function candidate for System (11) is chosen to be 1 1 1 1 V3 = V2 + z32 = z12 + z22 + z32 2 2 2 2 whose time derivative along the solutions of System (11) is given by z 2 − 3(ab1 + b2 ) + 6∆ζb1 x2 V˙ 3 = − k1 z12 − k2 z22 − 2∆ζx2 z2 − κ2 ζ0 x22 z22 + z3 3 √ 4 x3 u − 2x3 (1 − x1 ) + 2rρp x2 x3 − 2ρs x3 +β 3

Proc. of SPIE Vol. 6374 63740V-7

(24)

where 1 a = − 2ζ0 x2 − x1 + x3 , 3

b1 =2ζ0 − k1 − k2 − κ2 ζ0 2x2 z2 + x22 ,

b2 =yr(3) + k1 y¨r + y˙ r + κ2 ζ0 x22 + k2 x˙ 2d . Let U =

4√ 3 x3 u.

The proposed backstepping controller is given by:

3 z2 1 1 z 2 2 1 ab1 + b2 − − k3 z3 − κ31 ab1 + b2 − z3 − κ32 ζ0 b21 x22 z3 β 9 β β 9 β 1 1 − κ33 x22 x23 z3 − κ34 x23 z3 β β

U =2x3 (1 − x1 ) +

(25)

with k3 > 0, where κ31 , κ32 , κ33 , and κ34 are the gains of the nonlinear damping terms. T HEOREM 3.1. For System (11) with the uncertainties satisfying Assumptions 1-3 and yr being sufficiently smooth, the backstepping controller (25) with κ2 >

1 1 1 , κ31 > 1, κ32 > , κ33 > 1, κ34 > 2 , 2ζ0 ζ0 r

(26)

renders the closed-loop error dynamics locally ISS with respect to the uniformly bounded inputs ∆β, ρp , ρs , and ∆ζ. Furthermore, the ultimate bound for the tracking error z1 can be rendered arbitrarily small by picking the feedback gains k1 , k2 , and k3 large enough. The proof the the above theorem is given in Appendix A. Note that the actual control u is singular when x3 = 0. This is due to the uncontrollability of System (11) at the zero voltage position. However this situation happens only at this point. It is easy to see that System (11) is stabilizing at this position with an input u = 0. By defining an open ball Bε = {X| X < ε} ⊂ X of radius ε centered at the origin, where X = (x1 , x2 , x3 )T and · the usual Euclidean norm, a more practical control law can be expressed as ⎧ ⎨ √3 U, for X ∈ / Bε u = 4 x3 (27) ⎩ 0, for X ∈ Bε where U is given by (25).

3.3. Reference Trajectory Design In general, reference trajectories can be chosen to be any sufficiently smooth function t → y(t), connecting the initial point at time ti to a desired point at time tf , such that the initial and final conditions are verified. The reference trajectory used in our control schemes is a polynomial of the following form: yr (t) = y(ti ) + (y(tf ) − y(ti ))τ 5 (t)

4

ai τ i (t),

(28)

i=0

where τ (t) = (t − ti )/(tf − ti ). For a set-point control, the coefficients in (28) can be determined by imposing the initial and final conditions ˙ f ) = y¨(ti ) = y¨(tf ) = y (3) (ti ) = y (3) (tf ) = 0, y(t ˙ i ) = y(t which yield a0 = 126, a1 = −420, a2 = 540, a3 = −315, and a4 = 70. The polynomial in (28) is one of the most used reference trajectories in flatness based control. A more general formulation can be found in Ref. 11.

Proc. of SPIE Vol. 6374 63740V-8

(b)

0.5

Normalized Deflection

Normalized Deflection

(a)

0.4 0.3 ρ = 0.1276 s

0.2

ρs = 1.0

0.1 0 0

ρs = 2.0 5

10

0.5 0.4 0.3 ρp = 1.0

0.2

ρp = 3.0

0.1

ρ = 5.0 p

0 0

15

5

10

15

Normalized Time

Normalized Time

Figure 4. Influence of parasitics: (a) variation of serial parasitics ρs ; (b) variation of parallel parasitics ρp . (b)

0.5

Normalized Deflection

Normalized Deflection

(a)

0.4 0.3 0.2 ζ = 0.2 ζ = 5.0

0.1 0 0

5

10

15

0.5 0.4 0.3 0.2 r = 0.5 r = 2.0

0.1 0 0

5

10

15

Normalized Time

Normalized Time

Figure 5. Robustness against parametric uncertainties: (a) variation of damping coefficient ζ; (b) variation of resistance in the loop r.

4. SIMULATION STUDY In our simulation study, the parameters of the nominal plant are ζ0 = 1, r0 = 1, ρp = 0, and ρs = 0. The actuator is supposed to be driven by a bipolar voltage source. The boundaries of parasitics and parametric uncertainties are fixed to be ρs = 2, ρp = 5, r = 2, and r = 0.5. We have then β = 0.0238. Note that a small bias voltage is applied to the device in order to avoid the singularity at the origin. Firstly we consider only the influence of the parasitics. Based on the simulation in Section 2.2 we have for the device considered ρsmax = 0.1276. Therefore ρs >> ρsmax and the tested system should support more important modeling errors. It can be seen from Fig. 4 that in the simulated range of variation of the parasitics, the system performs nearly identically.

Normalized Deflection

The second test is concerned with the uncertainties in the damping coefficient ζ and the resistance in the loop r. It is shown (see Fig. 5) that the system still performs very well even for very important parameter variations.

1 0.8 0.6 0.4 0.2 0 0

5

10 Normalized Time

Figure 6. Simulation results of set-point control.

Proc. of SPIE Vol. 6374 63740V-9

15

In the last test, we simulated the system for set-point control. The parameters for the simulated system are chosen as ρs = 0.1276, ρp = 1.0, ζ = 0.5, and r = 1.5. It can be seen from Fig. 6 that the performance of the system is quite uniform for different deflections. Note that the performance of the controller presented in this work is quite similar to the one obtained by cascade ISS synthesis proposed in our previous work.1

5. CONCLUSIONS This paper considered the effect of deformation of the moveable plate of parallel-plate electrostatic micro-actuators and extended the idea of introducing a variable serial capacitor to compensate modeling errors due to deformation. Combined with an appropriate robust control scheme, the exact analytical expression of the serial capacitance is not required, but merely its boundary represented by the ratio of its minimal value and the equivalent nominal capacitance at the initial position. CoventorWareTM has been used to estimate the variation range of the introduced serial capacitor for a microstructure. A state feedback robust control scheme using the technique of ISS and backstepping design is constructed and the closed-loop stability of the system is demonstrated. Numerical simulations show that the proposed control system has satisfactory performance and robustness vis-`a-vis parasitics and parametric uncertainties. It has been shown that presenting different type of modeling errors by parasitics, using numerical simulation or experimental measurements to determine the variation boundaries of parasitics, and then employing robust control techniques will considerably simplify the modeling of micro-devices. Obviously, this idea can be applied to micro-devices with more complex structure for which building accurate model is a very challenging task.

APPENDIX A. PROOF OF THEOREM 3.1 Substituting the input in (24) by the backstepping controller (25) and taking into account the bounds (16), (18), and (19) yields β z2 β 2 2 2 2 ˙ ab1 + b2 − V3 = − k1 z1 − k2 z2 − 2∆ζx2 z2 − 2κ2 ζ0 x2 z2 + z3 − k3 z3 + 3 −1 β β 9 z 2 2 β β β z3 + 6∆ζx2 b1 − κ32 ζ0 b21 x22 z3 + 2βρp rx2 x3 − κ33 x22 x23 z3 − κ31 ab1 + b2 − β 9 β β β −2βρs x3 − κ34 x23 z3 β β−β β z2 β z2 2 2 ab1 + b2 − = − k1 z12 − k2 z22 − k3 z32 − 2∆ζx2 z2 − 2κ2 ζ0 x22 z22 + 3 z3 − κ31 ab1 + b2 − z3 β β 9 β 9 β β β + 6∆ζx2 b1 z3 − κ32 ζ0 b21 x22 z32 + 2βρp rx2 x3 z3 − κ33 x22 x23 z32 − 2βρs x3 z3 − κ34 x23 z32 . (29) β β β Applying Young’s inequality and noting that β ≥ β and βr ≤

1 , 1 + ρp (2 + ρs )

the last expression can be bounded as follows β β z 2 2 2 V˙ 3 ≤ − k1 z12 − k2 z22 − k3 z32 − (2κ2 ζ0 − 1) x22 z22 − κ31 − 1 ab1 + b2 − z3 − κ32 ζ0 − 1 b21 x22 z32 β 9 β 2 2 ρp + ρs β β 1 9 − κ33 − 1 x22 x23 z32 − κ34 − 2 x23 z32 + 10∆ζ 2 + + ∆β 2 . (30) 2 β β r (1 + ρp (2 + ρs )) 4 If (26) is satisfied, then V˙ 3 ≤ −α(z) + 10∆ζ 2 +

ρ2p + ρ2s 9 + ∆β 2 (1 + ρp (2 + ρs ))2 4

Proc. of SPIE Vol. 6374 63740V-10

(31)

where

α(z) = −k1 z12 − k2 z22 − k3 z32

is obviously a class K∞ function. Noting that (ρ2p + ρ2s )/(1 + ρp (2 + ρs ))2 is uniformly bounded, the closed-loop error dynamics are thus ISS with ∆ζ, ρp , ρs , and ∆β as the inputs.

REFERENCES 1. M. Hosseini, G. Zhu, and Y.-A. Peter, “A new formulation of fringing capacitance and its application to the control of parallel-plate electrostatic micro actuators,” in 2006 DTIP of MEMS & MOEMS, pp. 211–216, (Stresa, Italy), 26-28 April 2006. 2. E. Chan and R. Dutton, “Electrostatic micromechanical actuator with extended range of travel,” 9, pp. 321–328, Spet. 2000. 3. N. Doble and D. Williams, “The application of MEMS technology for adaptive optics in vision science,” IEEE J. Select. Topics Quantum Electron. 10, pp. 629–635, May/June 2004. 4. S. Senturia, Microsystem Design, Kluwer Academic Publishers, Norwell, MA, 2002. 5. J. Pont-Nin, A. Rodr´ıguez, and L. Casta˜ner, “Voltage and pull-in time in current drive of electrostatic actuators,” 11(3), pp. 196–205, 2002. 6. D. H. S. Maithripala, J. M. Berg, and W. P. Dayawansa, “Control of an electrostatic MEMS using static and dynamic output feedback,” ASME Journal of Dynamic Systems, Measurement and Control 127, pp. 443–450, 2005. 7. E. Sontag, “Smooth stabilization implies coprime factorization,” 34, pp. 435–443, 1989. 8. E. Sontag, “The ISS philosophy as a unifying framework for stability-like behavior,” in Nonlinear Control in the Year 2000 (Volume 2), A. Isidori, F. Lamnabhi-Lagarrigue, and W. Respondek, eds., Lecture Notes in Control and Information Sciences, pp. 443–468, Springer-Verlag, Berlin, 2000. 9. M. Krsti´c, I. Kanellakopoulos, and P. Kokotovi´c, Nonlinear and Adaptative Control Design, John Wiley & Sons Ltd, New York, 1995. 10. D. Maithripala, J. Berg, and W. Dayawansa, “Nonlinear dynamic output feedback stabilization of electostatically actuated MEMS,” in Proc. of the 42nd IEEE Conference on Decision and Control, pp. 61–66, (Maui, Hawaii), December 2003. 11. J. L´evine, Analyse et Commande des Systmes Non Linaires, [Online] Available: http://cas.ensmp.fr/%7Elevine/Enseignement /CoursENPC.pdf, 2004.

Proc. of SPIE Vol. 6374 63740V-11

Hybrid Neural Networks and Genetic Algorithms for identification of complex Bragg Gratings Ali Rostamia, Arash Yazdanpanah-Goharrizia, Amin Yazdanpanah-Goharrizib and F. Janabi-Sharific a) Photonics and Nanocrystals Research Lab. (PNRL), Faculty of Electrical Engineering, University of Tabriz, Tabriz 51664, Iran Tel/Fax: +98 411 3393724 E-mail: [email protected] b) Department of electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran c) Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada M5B 2K3

ABSTRACT In this paper a novel method for investigation of inverse scattering in optical complex mediums is proposed. The proposed method is based on Radial Basis Function Neural Networks (RBFNN) and Genetic Algorithms (GAs). Medium discrimination is performed by RBFNN and corresponding medium parameters identification is done using GAs. In the proposed method for simplicity the apodized, chirped and simultaneously apodized and chirped types of mediums are considered as RBFNN library. The proposed method tries to open a new insight to inverse scattering in optical devices and systems identification. The simulated results closely follow full numerical simulations to illustrate the ability of the proposed algorithm. Key words- Hybridization, RBFNN, Complex Bragg Gratings, Inverse Scattering, Identification.

1. INTRODUCTION The problem of synthesizing or reconstructing of non-uniform Fiber Bragg Gratings (FBG) from the corresponding reflection coefficient is important in device design for high-speed optical fiber communication (e.g., selection of wavelength multiplexed channels), compensation of the link dispersion and optical computing. For these devices and systems, design strategy needs some standard design rules and values. For obtaining these values and rules, the design ideas should be examined in practice. On the other hand, one needs to check the theoretical idea with practical measurements. In optical domain, for example, device design with optical complex Bragg Gratings need to measure manufactured structure. For this purpose, a model for medium should be assumed and optimized with numerical methods. For example, in reconstruction of optical mediums based on the measured reflection coefficient intelligence methods are used to obtain optimum medium parameters. These structures have some interesting applications such as information gathering, measurement of strain or temperature, etc. [1-5]. Several experimental techniques have been demonstrated to fabricate non-uniform gratings, permitting an accurate control of both the local grating pitch and the apodization profile along the structure [6, 7]. These techniques give substantial flexibility to the grating design process. For all of these applications, inverse scattering techniques [8] are needed, offering a great variety of possibilities for the design of gratings. For weak gratings, the synthesis problem of fiber gratings reduces to an inverse Fourier transform of the reflection coefficient. This is known as the first-order Born approximation, and applies only to gratings for which the reflectivity is small. Several modifications on the method have been applied and have improved its performance at high reflectivity [9, 10]. Fourier transform technique has been extended by Winick and Roman

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740W, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.684880

Proc. of SPIE Vol. 6374 63740W-1

[4], yielding a better approximation, enabling the design of practical fiber grating filters. However, this synthesis procedure is approximate in nature and consequently, not reliable for the design of very complex filters. An exact solution of this inverse scattering problem was found by Song and Shin [8] who solved the coupled Gel’fand–Levitan–Marchenko (GLM) integral equations that appear in quantum mechanics. Their method is exact, but is restricted to reflection coefficients that can be expressed as a rational function. However, the need to approximate the desired spectral response by rational functions is difficult and also can result in inaccuracies. To overcome this limitation, an iterative solution of the GLM system was proposed by Peral to synthesize arbitrary spectral responses [2, 11]. Some fiber grating designs calculated with this method have already been fabricated, proving the usefulness of the method [12]. The iterative solution of the GLM equations [13] has some weaknesses. However, the solution is approximate due to the finite number of iterations computed, which translates into considering only a limited number of reflections within the medium. This is particularly noticeable for strong gratings with discontinuities in the coupling function. Also, when specifying ideal filter responses, it is desirable to have a weighting mechanism, which makes it easier to weight the different requirements. The iterative GLM method does not support such a mechanism in a satisfactory way. Another group of exact inverse scattering algorithms, as known as differential or direct methods [14–17], developed by geophysicists like Robinson and Goupillaud [14, 15], exploit fully the physical properties and structure of the layered media in which the waves propagates. The methods are based again on causality arguments and identify the medium recursively layer by layer. For this reason, they are sometimes called layerpeeling or dynamic de-convolution algorithms. Recently, several heuristic approaches have been developed for the solution of the inverse problem with the goal of designing gratings as filters for telecommunication applications. Skaar, Risvik and Cormier et al developed genetic algorithms (GAs) to obtain physical parameters of the Bragg gratings from the measured reflected intensity spectrum [18,19]. Skaar and Risvik encoded the grating coupling coefficient using a real number formulation and used a Runge–Kutta algorithm to calculate the spectral response of the grating [18]. Cormier et al reduced the spectral response calculation time using the transfer-matrix (T-matrix) formulation [19]. This formulation is based on approximating the grating coupling coefficients as a piecewise constant function along the grating. Cormier et al characterized the Bragg grating in terms of three parameters: the length, period and amplitude of the index of refraction modulation [19]. While this method is excellent for the design of Bragg gratings as filters, the parameterization of Cormier et al does not allow for a period variation along the grating (e.g., due to a non-constant applied strain). In these presented works, the type of medium was well known and only extraction of medium parameters was a problem. But, there is a basic question that if there is a problem without information about medium type, how one can proceed. Here, we try to present a novel method to incorporate this problem. For this purpose combination of RBFNN and GAs is examined. In our method there are a large classes of medium types predefined to RBFNN. The RBFNN has access to these mediums through the learning process. Now, if there is an unknown (belongs to one of predefined medium types) reflection coefficient, which is applied to this RBFNN, the trained RBFNN would recognize medium type. Now, the input vector is passed to special GA block corresponding to determined medium type. Then, the corresponding GA starts to determine the parameters of the recognized medium. After this process the real and extracted medium are compared with each other where our results show excellent agreement. The presented method provides excellent method for practical cases with a large library. The organization of the paper is as follows. In section 2, mathematical formulation of the problem is presented. In this section coupled mode and the Riccati equations are presented. RBF neural network and genetic algorithms are reviewed in section 3. In section 4 identification algorithm are presented. Simulation results and discussion are discussed in section 5. Finally the paper ends with a conclusion.

Proc. of SPIE Vol. 6374 63740W-2

2. MATHEMATICAL FORMULATION In this section the coupled mode theory (CMT) leading to the Riccati equation and the transfer matrix method (TMM) for calculation of the reflection coefficient of the complex Bragg Gratings are reviewed. For these structures, the index of refraction is given as follows [20]. ⎛ 2π ⎞ n( z ) = n0 + ∆ndc + A( z ) ∆nac cos ⎜ z + Φ (z )⎟ , Λ ⎝ ⎠

(1)

where n0 , ∆n dc , ∆n ac , A(z ) , Λ , Φ (z ) and z are the refractive index of core, average refractive index of core, ac index of refraction, Apodization function, fixed period of Grating, arbitrary spatially varying phase, and the light propagation axis along the medium ( 0 ≤ z ≤ L , where L is the grating length) respectively. For these structures after some mathematical manipulation of the Maxwell’s equations the coupled wave equations can be obtained [21-23]. Using these coupled wave equations, the Riccati equation for managing of the reflection coefficient can be obtained as follows.

(

) (

)

dρ ( z , ω ) = ik ( z ) 1 + ρ 2 ( z, ω ) + i 2ω − Φ ' ( z ) ρ ( z, ω ) , dz

(2)

where ρ ( z, ω ), k ( z ) and ω are the reflection coefficient at given position ( z ) and frequency ( ω ), the coupling coefficient and the detuning frequency respectively. Now, the following relations can be used for the mentioned above constants. ⎛ π ⎞ ∆nac ⎟⎟ A( z ) = k 0 A( z ) , k ( z ) = ⎜⎜ ⎝ λD ⎠

(3)

where λ D = 2neff Λ is the Bragg wavelength. In this relation neff is effective index of refraction.

ω=

2π

λ

neff −

π Λ

.

(4)

The Range-Kutta numerical method can be applied on Eq. (2) and using the following boundary condition the reflection coefficient for the proposed structures can be obtained.

ρ ( L, ω ) = 0 .

(5)

For obtaining the reflection coefficient of a fiber Bragg grating, we use the transfer matrix method as follows. The transfer matrix method can be used to solve non-uniform gratings. This method is effective in the analysis of the almost-periodic grating. A non-uniform fiber Bragg grating can be divided into many uniform sections th

along the fiber. The incident light wave propagated through each uniform section ( i layer) can be described by a transfer matrix Fi . For the structure of the fiber Bragg grating, the matrix Fi can be written as follows [22]. ) σ ⎡ γ cosh( z ) i sinh(γ B ∆n( z ) ∆ − B ⎢ γB ⎢ Fi = ⎢ k ⎢i γ sinh(γ B ∆z ) ⎣ B

Proc. of SPIE Vol. 6374 63740W-3

⎤ sinh(γ B ∆z )⎥ γB ⎥ , (6) ) σ ⎥ cosh(γ B ∆z ) + i sinh(γ B ∆n( z ) ⎥ γB ⎦ −i

k

where γ B is denoted as )

γ B = k2 −σ 2 .

(7)

The whole grating can be represented in matrix form as

⎡ R ( L)⎤ ⎢ S ( L) ⎥ = FM .FM −1 . ⎣ ⎦

.

.. Fi .

.

.

⎡ R ( 0) ⎤ ⎥, ⎣ S ( 0) ⎦

.. F1 .⎢

.

(8)

where L is the length of the medium. The amplitude of the reflection coefficient can be written as

ρ=

S ( 0) . R ( 0)

(9)

3. RBF NEURAL NETWORKS AND GENETIC ALGORITHM In this section a short overview to RBFNN is presented. The RBFNN for pattern classification and functional approximation have been used. The proposed network has single hidden layer, which main classification algorithm is done here [24]. Neurons in hidden layer have radial transfer function. Also, neurons in output layer have linear, usually, transfer function. Fig. 1 shows typical RBFNN.

Input Layer

hidden Layer

Output Layer ZI

Output

/3 Fig. 1. Schematics of RBFNN.

The following definitions for description of Fig. 1 chould be made.

[ x1 ,..., xl1 ]T : Input vector l1 : Dimension of the input vector

Proc. of SPIE Vol. 6374 63740W-4

l2 : Number of neurons in hidden layer

vm : Prototype vector corresponding to the m th hidden cell ( [v1m ,..., vl1m ]T ). V: matrix of prototype vectors ( [v1 ,..., vl 2 ] ) ym : Output of m th hidden cell l3 : Dimension of the output vector u j : Weight vector of the j th output cell ( [u1 j ,..., ul 2 j ]T )

U : Weight matrix of output layer ( [u1 ,..., ul 3 ] ) z j : Actual output of the j th output cell Since in this paper we need to identify medium profiles then we consider pattern recognition aspect of RBFNN. In this treatment the input space should be classified to subclasses and a prototype vector to each class is assigned. For these classified space the membership function ( f m (x ) ) of input vector for each subclass is determined by a function of its distance from the prototype vector ( f m ( x ) = f ( x − vm ) ). The suitable choice for the function f m (x ) is the Gaussian function. For each subclass, one can consider some neurons to incorporate feasibility in learning process. After obtaining the membership values of input vector in the subclasses the results should be combined to obtain the membership degrees in every class. The two-layered feedforward neural network of RBF type is illustrated in Fig. 1. The neurons in the hidden layer of network have a Gaussian activation function and their input–output relationship is given as follows.

y m = f m ( x ) = exp(−

x − vm 2 2σ m

2

),

(6)

where σ m is the Gauss width parameter. th

The operation field region of the m neuron is part of input space, where f m (x ) is high. The neurons in the output layer could be sigmoid, linear, or pseudo-linear, i.e. linear with some squashing property, such that the output could be calculated using one of the following equations:

⎧ 1 , Sigmoid, ⎪ −s ⎪1 + e j ⎪⎪ s j 1 z j = ⎨ , Linear, with squashing function, l2 ⎪ l2 ⎪ sj 1 ⎪ , Pseudo − linear, with squashing function, ⎪⎩ ∑ y m ∑ ym

where s j =

l2

∑ ym umj

m =1

(7)

j = 1,..., l3 .

In the most of literature, the neurons with linear, pseudo-linear or sigmoidal activation functions have been considered for the output layer.

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Now, training algorithm for this network is presented as follows. Training algorithms- Here, we present the back propagation (BP) based algorithm for training of the RBFNN. Before starting the training, a cost function should be defined and then minimized through the training process by gradient calculations and weight-updating corresponding to the appropriate parameters. Total sum-squared error (TSSE) is the most popular cost function. For implementing this method, the error gradients versus the ∂E ∂E ∂E parameters ( , , ) should be calculated layer by layer, starting from the output layer and 2 ∂umj ∂vim ∂σ m

proceeding backwards. In the following updated weight parameters are calculated for the next step. umj (n + 1) = umj ( n ) − α1

∂E , ∂umj

(8)

vim ( n + 1) = vim ( n ) − α 2

∂E , ∂vim

(9)

σ 2 m ( n + 1) = σ 2 m ( n ) − α 3

∂E ∂σ 2 m

,

(10)

where, α1 ,α 2 ,α 3 are learning rate factors in the range [0, 1]. The algorithm for all training inputs should be repeated in epochs. In our case, two-dimensional input vectors for all three considered mediums including bandwidth and central wavelength (wavelength at maximum reflection) for training are used. For example, in our experiments, the RBF neural network has been trained with the respected input data and a TSSE of 0.000804086 after 312 epochs has been obtained. After this the algorithm works such that an 3 × 1 output vector is made to illustrate the result of classification. Genetic Algorithm- A GA is designed to efficiently search in a large and poorly understood search space, where expert knowledge is limited. The basic principles of GAs are well described in [25, 26]. GAs form search algorithms based on the process of biological evolution [27]. In GAs the mechanics of natural selection and genetics are emulated artificially. The search for a global optimum in an optimization problem is conducted by moving from an old population of individuals to a new population using genetics-like operators. Each individual (chromosome) represents a candidate to the optimization solution where a population is an array of individuals. An individual is modeled as a fixed length string of symbols. An evaluation function, called fitness function, assigns a fitness value to each individual within the population. This fitness value is a measure for the quality of an individual. The fitness function presents an objective function in optimization. The basic optimization procedure involves nothing more than processing highly fit individuals in order to produce better individuals as the search progresses. Three basic operators used in a conventional GA, to create the next generation from the current population, are Selection, Crossover and Mutation. Here, the GAs operators are described as follows. Selection- Selection operator selects the individuals, called parents that contribute to the population at the next generation. It is clear that the more fit individual from the old population have more chance to be selected to the next generation. On the other hand, selection options specify how the genetic algorithms choose parents for the next generation. We choose this function stochastically uniform. Crossover- Crossover operator combines two parents to form children for the next generation or this option specifies how the genetic algorithm combines two individuals, or parents, to form a crossover child for the next generation. Crossover function specifies the function that performs the crossover. We used the single point function for crossover. Mutation- Mutation operator applies random changes to individual parents to form children. This option specifies how the genetic algorithm makes small random changes in the individuals in the population to create

Proc. of SPIE Vol. 6374 63740W-6

mutation children. Mutation provides genetic diversity and enables the genetic algorithm to search a broader space. We choose the Gaussian function as the mutation operator.

4. PROPOSED IDENTIFICATION ALGORITHM In this section whole algorithm for classification of medium type and identification of medium parameters are presented. The algorithm is illustrated in Fig. 2. The measured reflection coefficient is input of the algorithm. After entering the measured reflection coefficient, the type of medium is determined by RBFNN. After determining the types of medium with RBFNN then the algorithm chooses a suitable GA block that corresponds to the specified medium type. In this step the GA starts to iterate for obtaining the specified medium type parameters.

Fig. 2. Identification Algorithm based on RBFNN and Gas.

For the GAs the initial population for individuals and fitness function are considered as follows. The initial population for each block of GAs depends on the necessary unknown parameters of the medium according to physical model for the complex Bragg gratings. Therefore we consider a N p × M matrix as follows.

U = [u1

u2

.

.

.

um ] N p × M ,

(11)

where N p and M denote the number of population for each variable and the number of variables respectively. The choice of the fitness function is fundamental in order that a correct and efficient search of the solution is carried out by the algorithm. In our problem, the fitness is a function that measures the distance between the theoretical and the experimental reflection coefficient, bandwidth, and the maximum reflection. In this paper the fitness function is proposed as follows: ns

E = ∑ ρ exp (λ j ) − ρ Cal. (λ j ) + BWexp (λ ) − BWcal . (λ ) + ρ exp (λ ) − ρ cal . (λ ) ,

(12)

j

where ρ exp . , ρ Cal. , BWexp . , BWCal. λ j and n s are the experimental reflection coefficient, calculated reflection coefficient, the experimental bandwidth, calculated bandwidth, sampled wavelengths of the reflection coefficient and the number of samples respectively.

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5. SIMULATION RESULTS AND DISCUSSION For illustration of the method three types of medium including Gaussian Apodization, Linear Chirping and simultaneous Apodization-Chirping are considered. For these three cases medium classification by RBFNN and parameters identification by GAs are carried out. For uniform FBG the following values are considered. 1. The length of grating ( L ) = 10 mm, 2. The period of grating ( Λ ) = 0.5356 µm , 3. The effective refractive index ( n eff ) = 1.447. For all of histogram figures (best current individual versus number of variables), the parameters are normalized. 1. Gaussian Apodization- In this case the Gaussian profile for apodization is considered and the coupling coefficient ( k (z ) ) is defined as follows.

k ( z) =

⎡ π ⎛ z − 0.5L ⎞⎤ ∆n ( z ) exp ⎢− 20⎜ ⎟⎥ . λ B ac ⎝ α ⎠⎦ ⎣

(13)

For this Apodization, the amplitude of the index modulation ( ∆nac ( z ) ) and the Gaussian parameter ( α ) are important and affect the FBG characteristics strongly. The simulated results for this case are presented in Figs. (3-5). Fig. 3 shows the fitness value and best individuals ( α and ∆nac ( z ) ) for this case. Approximately, after 100 iterations optimum condition is reached. The reflection coefficients for real (full numerical simulation) and reconstructed ones are illustrated in Fig. 4. The presented method extracts medium reflection coefficient completely compatible with real case. Finally the coupling coefficient for this case is illustrated in Fig. 5 demonstrating excellent compatibility.

Best: 0.0028087 Mean: 0.0095998

Fitness value

15 Best fitness Mean fitness 10

5

Current best individual

0

10

20

30

40

50

60

70

80

90

100

Generation Current Best Individual 10

5

0

1

2

Number of variables (2) Fig. 3. The evaluated fitness function and the normalized calculated parameters.

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1 Real profile Reconstracted profile

0.9

Reflection coefficient

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.549

1.5495

1.55

1.5505

1.551

1.5515

Weavelenght(micrometre) Fig. 4. The Reflection Coefficient for real parameters (solid line) and reconstructed ones (dotted line). −3

4

x 10

Real profile Reconstracted profile

Coupling coefficient k(z)

3.5 3 2.5 2 1.5 1 0.5 0

0

2000

4000

6000

8000

10000

Position(micrometre) Fig. 5. The coupling coefficient for real parameters (solid line) and reconstructed ones (dotted line).

For this case the initial population for individuals considered as

U = [ ∆nac ( z ) α ]20× 2

(14)

The measured reflection coefficient for Gaussian apodization corresponds to the full numerical simulation with α = 0.8 × L , ∆nac ( z ) = 9 × 10 −4 , and the reconstructed medium parameters using our proposed approach with α = 0.798987 × L and ∆nac ( z ) = 9.00234 × 10 −4 . As it is shown the reconstructed values closely follow input measured values. 2. Linear Chirping- In this case linear chirped is considered. According to linear chirp function the following relation is defined.

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z 1 dΦ =F 2, 2 dz L

(15)

where F is the chirp parameter, defined as follows: L2 dλ D L2 F = 2 Φ ( z ) = −4πneff 2 λ D dz z

(16)

dλ D is the rate of the chirp in the complex Bragg grating. For this case the amplitude of the index dz dλ modulation ( ∆nac (z ) ) and the rate of the chirp ( D ) are important and affect the FBG characteristics dz strongly. The simulated results for this case are presented in Figs. 6-8. Fig. 6 shows the fitness value and best dλ D individuals ( ∆nac (z ) and ) for this case. Approximately after 50 iterations optimum condition is reached. dz The reflection coefficient for real (full numerical simulation) and reconstructed ones is illustrated in Fig. 7. Presented method extracts medium reflection coefficient closely matching the real case. Finally the chirp function for this case is illustrated in Fig. 8, demonstrating close agreement.

where

Best: 0.034431 Mean: 0.26121

Fitness value

40 Best fitness Mean fitness

30 20 10

Current best individual

0

5

10

15

20

25

30

35

40

45

50

Generation Current Best Individual 6 4 2 0

1

2

Number of variables (2) Fig. 6. The evaluated fitness function and the normalized calculated parameters

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1 Real profile Reconstracted profile

0.9

Reflection coefficient

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.548 1.549

1.55

1.551 1.552 1.553 1.554 1.555 1.556 1.557

Weavelenght(micrometre) Fig. 7. The reflection coefficient for real parameters (solid line) and reconstructed ones (dotted line) 5

0

x 10

Real profile Reconstracted profile

−2

Chirp function

−4 −6 −8 −10 −12 −14 −16

0

2000

4000

6000

8000

10000

Position(micrometre)

Fig. 8. The chirp function for real parameters (solid line) and reconstructed ones (dotted line)

For this case, the initial population for individuals considered as U = [ ∆n ( z )

dλ D ]20× 2 . dz

(17)

The measured reflection coefficient for linear chirped function corresponds to the full numerical simulation dλ D with = 2 × 10 − 7 , ∆n( z ) = 5 × 10 − 4 , and the reconstructed medium parameters using our proposed dz

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dλ D = 2.00001 × 10 − 7 and ∆n( z ) = 5.00581 × 10 −4 . As it is shown, the reconstructed dz values closely follow input measured values.

approach with

3. Simultaneous Apodization-Chirping- In this case, we consider simultaneously the Gaussian apodization and linear chirp functions. For this case, the amplitude of the index modulation ( ∆nac (z ) ), the Gaussian dλ D ) are important and affect the FBG characteristics strongly. The dz simulated results for this case are presented in Figs. 9-11. Fig. 9 shows the fitness value and best individuals dλ D ( ∆nac (z ) , α and ) for this case. Approximately after 100 iterations optimum condition is reached. The dz reflection coefficients for real (full numerical simulation) and reconstructed ones are illustrated in Fig. 10. Presented method extracts medium reflection coefficient with values completely compatible with real case. Finally the coupling coefficient and chirp functions for this case are illustrated in Fig. 11, demonstrating excellent match.

parameter ( α ), and the rate of the chirp (

Best: 0.038761 Mean: 0.10928

Fitness value

15 Best fitness Mean fitness 10 5

Current best individual

0

10

20

30

40

50

60

70

80

90

100

Generation Current Best Individual 6 4 2 0

1

2

3

Number of variables (3) Fig. 9. The evaluated fitness function and the normalized calculated parameters.

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0.9 Real profile Reconstracted profile

0.8

Reflection coefficient

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.551 1.5515 1.552 1.5525 1.553 1.5535 1.554 1.5545 1.555 1.5555

Weavelenght(micrometre)

Coupling coefficient k(z)

Fig. 10. The reflection coefficient for real parameters (solid line) and reconstructed ones (dotted line).

−3

3

x 10

Real profile Reconstracted profile 2

1

0

0

2000

4000

6000

8000

10000

8000

10000

Position(micrometre)

Chirp function

0

−100

−200

−300

0

2000

4000

6000

Position(micrometre) Fig. 11. The coupling coefficient and chirp function for real parameters (solid line) and reconstructed ones (dotted line).

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For this case the initial population for individuals considered as U = [ ∆n ( z )

dλ D α ]20×3 dz

(18)

The measured reflection coefficients for simultaneous Gaussian apodization and linear chirped function correspond to the full numerical simulation for simulated parameters with dλ D = 3 × 10 − 7 , ∆n( z ) = 6 × 10 − 4 ,α = 0.5 × L , and the reconstructed medium parameters using the dz dλ D proposed approach are = 3.00158 × 10 − 7 , α = 0.501529 × L and ∆n ( z ) = 5.97715 × 10 −4 , dz respectively. As it is shown the reconstructed values follow closely input measured values. The proposed method was examined with several other examples and the results illustrated graphically. Presented results illustrated that the developed method could be of high interest for inverse problem solving.

6. CONCLUSION In this paper a novel method including combination of RBF neural network and Genetic Algorithm for classification and identification of complex Bragg Gratings has been developed. In this work large classes of predefined medium types can be defined and applied to RBF neural network that would enable widely-spread medium type classification after learning process. After classification by RBFNN, the GAs can identify medium parameters precisely. The presented method for identification of complex Bragg Gratings demonstrated excellent performance providing precise agreement with full numerical simulations.

REFERENCES

1. M. Matsuhara, K. O. Hill, and A. Watanabe, “Optical-waveguide filters: Synthesis,” J. Opt. Soc. Am, 65, 2. 3. 4. 5. 6. 7. 8.

804-809,(1975). E. peral, J. Capmany, and J, Marti, “Iterative solution to the Gel'Fand-Levitan-Marchenko coupled equations and applications to synthesis of fiber gratings,” IEEE J. Quantum Electron. 32, 2078-2084 (1996). R. Feced, M. N. Zzervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of non uniform fiber Bragg gratings,” IEEE J. Quantum Electron., 35, 1105-1115 (1999). K. A. Winick and J. E. Roman, “Design of corruGAsted waveguide filters by Fourier Transform techniques,” IEEE J. Quaantom Electron., 26, 1918-1929 (1990). P. Roberts and G. Town, “Design ofmicrowave filters by inverse scattering,” IEEE Trans. Microwave Theory and Techniques, 43, 739-743 (1995). W. H. Loh, M. J. Cole, M. N. Zervas, S. Barcelos, and R. I. Laming,“Complex grating structures with uniform phase masks based on the moving fiber-scanning technique,” Opt. Lett., 20(20), 2051–2053 (1995). A. Asseh, H. Storoy, B. E. Sahlgren, S. Sandgren, and R. A. H. Stubbe, “A writing technique for long fiber Bragg gratings with complex reflectivity profiles,” J. Lightwave Technol., 15, 1419–1423 (1997). G. H. Song and S. Y. Shin, "Design of corrugated waveguide filters by the Gel "Fand-Levitan-Marchenko inverse-Scattering method," J. Opt. Soc. Am. A., 2, 1905-1985.

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9. J. A. Dobrowolski and D. Lowe, “Optical thin film synthesis program based on the use of Fourier transforms,” Appl. Opt., 17(19), 3039–3050 (1978).

10. B. G. Bovard, “Fourier transform technique applied to quarterwave optical coatings,” Appl. Opt., 27 (15),

3062–3063 (1988). 11. E. Peral, J. Capmany, and J. Marti, “Design of fiber grating dispersion compensators using a novel iterative solution to the Gel’fan-Levitan- Marchenko coupled equations,” Electron. Lett., 32(10), 918–919 (1996). 12. J. Skaar, B. Sahlgren, P. Y. Fonjallaz, H. Storoy, and R. Stubbe, “Highreflectivity fiber-optic bandpass filter designed by use of the iterative solution to the Gel’fan-Levitan-Marchenko equations,” Opt. Lett., 23(12), 933–935 (1998). 13. P. V. Frangos, D. J. Frantzeskakis, and C. N. Capsalis, “Pulse propaGAstion in a nonlinear optical fiber of parabolic index profile by direct numerical solution of the Gel’fan-Levitan integral equations,” Proc. Inst. Elect. Eng., pt. J, 140,(2), 141–149 (1993). 14. A. M. Bruckstein, B. C. Levy, and T. Kailath, “Differential methods in inverse scattering,” SIAM J. Appl. Math., 45(2), 312–335 (1995). 15. A. M. Bruckstein and T. Kailath, “Inverse scattering for discrete transmission-line models,” SIAM Rev., 29,(3), 359–389 (1987). 16. K. P. Bube and R. Burridge, “The one-dimensional inverse problem of reflection seismology,” SIAM Rev., 25(4), 497–559 (1983). 17. K. P. Bube, “Convergence of difference methods for one-dimensional inverse problems,” IEEE Trans. Geosci. Remote Sensing, 22, 674–682 (1984). 18. J. Skaar and K. Risvik, “A genetic algorithm for the inverse problem in synthesis of fiber gratings,” J. Lightwave Technol.16, 1928–1932 (1998). 19. G. Cormier, R. Boudreau and S. Theriault, “Real-coded genetic algorithm for Bragg grating parameter synthesis,” J. Opt. Soc. Am. B, 18, 1771–1776 (2001). 20. A. Othonos and K. Kalli, “Fiber Bragg Gratings: fundamentals and applications in telecommunications and Sensing”, (Aetech House), 1999. 21. A. W. Snyder and J. D. Love, “Optical waveguide theory”, (Chapman and Hall, London), 542, (1983). 22. T. Erdogan, “Fibre grating spectra”, Journal of Lightwave Technology, 15(8), 1277-1294 (1997). 23. L. R. Chen, S. D. Benjamin, P. W. E. Smith, and J. E. Sipe, “Ultrashort pulse reflection from fiber gratings: a numerical investigation”, Journal of Lightwave Technology, 15(8), 1503-1512 (1997). 24. M. T. Vakil-Baghmisheh and N. Pavesic, "Training RBF networks with selective backpropagation," Journal of Neurocomputing, 62, 39- 64 (2004). 25. J. H. Holland, Adaptation in Natural and Artificial Systems, MIT, Cambridge, MA, 2nd Edn., 1992. 26. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, 1989. 27. W. M. Spears, K. A. D. E. Jong, T. Baeck, and P. Bradzil “An overview of evolutionary computation,” Proceedings of European Conference on Machine Learning, Springer-Verlag, Berlin, 1993, 667, p. 442459.

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Identification of complex Bragg Gratings based on optical transfer function estimation using Genetic Algorithm A. Rostamia, A. Yazdanpanah-Goharrizia, A. Yazdanpanah-Goharrizib and F. Janabi-Sharific a) Photonics and Nanocrystals Research Lab. (PNRL), Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz 51664, Iran Tel/Fax: +98 411 3393724 E-mail: [email protected] b) Department of Electrical Engineering, K. N. Toosi University of Technology

c) Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada M5B 2K3

ABSTRACT In this paper an optical transfer function for description of the operation of complex fiber Bragg Gratings similar to electrical ones is presented ( H ( jω ) ). For this purpose and reconstruction of the transfer function, the Genetic Algorithm (GA) is used to find optimum number of poles and zeros from the measured reflection coefficient. After building the transfer function according to the developed algorithm in this paper, the reflection coefficient for this approximated system is obtained (simulated) and compared with measured values. The results obtained from the approximated transfer function in these cases are so close to real measured data. So, the presented method introduces an interesting approach for identification of the complex Bragg Gratings in frequency domain. Some of optical characteristics (both frequency domain and time domain parameters) of these systems can be extracted from the approximated transfer function easily. Keywords: Fiber Bragg Grating, Genetic Algorithm, Optical Transfer Function, Optical System Identification

1. INTRODUCTION Optical device and system design based on complex fiber Bragg Gratings is interesting for high-speed optical communication and computing, particularly within Optomechatronic systems. Complex fiber Bragg Gratings are very interesting but complex for synthesis in practice [1-5]. Investigation of the effect of the parameters of designed system and input waveform on output characteristics is extremely important in optomechatronic systems engineering and design optimization. Also, in optical engineering this subject is very necessary for device and system design and reliable tuning purposes. For this aim, introducing optical system transfer function illustrating all system parameters effects on output behavior in frequency domain is interesting for control and system analysis purposes, such as traditional methods in control system engineering tools. In this paper, a novel method for evaluating a transfer function for Fiber Bragg Gratings is examined. For this purpose a model for medium should be assumed and then optimized using numerical methods [6, 7]. As an example, in reconstruction of optical medium types based on the measured reflection coefficient, intelligence methods are used to obtain optimum medium parameters [8]. An analytical proposal for system input-output characteristic is also interesting from system identification point of view. In this case optical transfer function can provide excellent tool and successful inverse problem algorithms can be applied. In this paper, we try to present an efficient method to extract optimum transfer function for the mentioned structures. In this field there are some interesting reported works for managing inverse problem as follows. A nontrivial inverse problem consists in the derivation of such a modulation (Bragg Grating) from the knowledge of spectrum reflected (or transmitted) by grating. One of the simplest approaches to the solution of the inverse problem is Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740X, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.684881

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based on the existence of a Fourier-transform relation between the spectral response and the grating coupling coefficient [9]. This relation is however exact only for weak gratings and its extension to high reflectivity has an approximate validity. An exact solution of the inverse problem can be obtained at least in principle by the coupled integral equations derived in scattering theory by Gelfand, Levitan and Marchenko (GLM) [10]. These equations, unfortunately, can easily be solved by numerical methods only when the reflection coefficient can be written as a rational function [11, 12]. This limitation was overcome by a method based on an iterative solution of GLM equations with the expense of increased mathematical complexity [10]. A recently proposed and efficient method for grating reconstruction is the layer peeling algorithm that provides a path integral solution to the inverse problem by use of causality arguments and by taking into account all the multiple reflections inside the grating [13]. The above-mentioned methods consider both the amplitude and the phase of the spectral response to recover the grating properties. In contrast, an integral relation was derived between the reflected intensity spectrum alone and the index modulation phase for a given modulation amplitude. In some experiments, this integral relation enabled determination of the non-uniform strain acting along the grating from the knowledge of the reflected intensity spectrum. Another related approach considers only the phase spectrum of the complex reflection coefficient. A measurement of this quantity makes it possible to derive the relative delays among the spectral components of the signal reflected from the strained grating and hence the applied strain. Both methods present some limitations. Here, we present an efficient method based on GAs [14] to find optimum number of poles and zeros for reconstruction of medium profile. Our method is as follows. Based on Least Square (LS) technique in system control engineering, we approximate the reflection coefficient in frequency domain in terms of some poles and zeros (optimum number of poles and zeros). Then a suitable transfer function in frequency domain can be considered for the reflected light from complex optical Grating systems. Also, our presented method is for complete and full scale range of the reflection coefficient. Finally we compare the presented method with complete numerical solution and we show that there is excellent agreement. The organization of the paper is as follows. In section 2, brief mathematical principle of Fiber Bragg Gratings is reviewed. Optical transfer function optimization using GAs is discussed in section 3. Simulation results is presented and discussed in section 4. Finally the paper ends with a conclusion.

2. FIBER BRAGG GRATINGS In this section, the Riccati equation for the reflection coefficient of the complex Bragg Gratings is reviewed. For these structures the index of refraction is given as follows [1]. ⎛ 2π ⎞ n( z ) = n0 + ∆ndc + A( z ) ∆nac cos ⎜ z + Φ (z )⎟ , ⎝ Λ ⎠

(1)

where n0 , ∆ndc , ∆nac , A(z ) , Λ , Φ (z ) and z are the refractive index of core, average refractive index of core, ac index of refraction, Apodization function, fixed period of Grating, arbitrary spatially varying phase, and the light propagation axis along the medium ( 0 ≤ z ≤ L , where L is the grating length) respectively. For these structures after some mathematical manipulation of the Maxwell’s equations, the coupled wave equations can be obtained [2-4]. Using these coupled wave equations, the Riccati equation for managing the reflection coefficient can be obtained as follows.

(

) (

)

dρ ( z, ω ) = ik ( z ) 1 + ρ 2 ( z, ω ) + i 2ω − Φ ' ( z ) ρ ( z , ω ) , dz

(2)

where ρ ( z , ω ), k ( z ) and ω are the reflection coefficient at given position ( z ) and frequency ( ω ), the coupling coefficient and the detuning frequency respectively. Now, the following relations can be used for the above-mentioned constants. ⎛ π ⎞ k ( z ) = ⎜⎜ ∆nac ⎟⎟ A( z ) = k 0 A( z ) , (3) λ ⎝ B ⎠

Proc. of SPIE Vol. 6374 63740X-2

where λ B = 2neff Λ is the Bragg wavelength and neff is effective index of refraction, related to the frequency by the following equation.

ω=

2π

λ

neff −

π Λ

.

(4)

The Range-Kutta numerical method can be applied to Eq. (2) and using the following boundary condition the reflection coefficient for the proposed structures can be obtained.

ρ ( L, ω ) = 0 .

(5)

3. OPTICAL TRANSFER FUNCTION OPTIMIZATION In this section, we explain the complex curve fitting algorithm and find a continuous-time transfer function that corresponds to a given complex reflection coefficient. This algorithm can be used to convert the magnitude and phase information from given reflection coefficient to transfer function and returns the real numerator and denominator coefficients in vectors b and a of the transfer function. H ( s) =

b s + b2 s −1 + . . .bn +1s − n B( s) , = 1 A( s ) a1s + a 2 s −1 + . . .a m +1s − m

(6)

where s = jω is the Laplace domain variable. Here, we arrange the sampled frequency in a vector ω and the corresponding reflection coefficient in ρ (0, ω ) . Scalars n and m specify the desired orders of the numerator and denominator polynomials, respectively. The proposed algorithm is used to incorporate the conjugate ρ (0, ω ) at −ω to ensure the proper frequency domain symmetry for a real medium. Now, the proposed algorithm is explained in detail as follows. For the above purpose, a weighted least square type error (Eq. (7)) is used to identify the best model from the data as follows. The vectors b and a (of Eq. (6)) can be found by minimizing the error function defined in Eq. (7) and creating a system of linear equations and solving them numerically [5]. ⎛ p 2⎞ e = min⎜ ∑ wt K ρ (0, ω ) A(ω K ) − B(ω K ) ⎟ . ⎜ ⎟ ⎝ K =1 ⎠

(7)

where A(ω K ) , B(ω K ) , p and wt K are the Fourier transforms of the polynomials a and b at the frequency ω (K ) , the number of frequency points (the length of ρ (0, ω ) and ω ), and a vector of weighting factors respectively. The proposed algorithm in this work uses the nonlinear least squares Gauss-Newton method for iterative search [6] with the output of the first algorithm as the initial estimation. ⎛ p B (ω K ) e = min⎜⎜ ∑ wt K ρ (0, K ) − A(ω K ) ⎜ K =1 ⎝

2⎞

⎟ ⎟⎟ ⎠

(8)

It is important to note that for the above strategy, we guess the initial values for m and n and evaluate the estimated transfer function H ( j ω ) at s = jω . Then, the absolute value of H ( jω ) is compared with the absolute value of the

Proc. of SPIE Vol. 6374 63740X-3

reflection coefficient ( ρ (0, ω ) ), which is calculated by solving the Riccati equation. If these two spectrums ( ρ (0, ω ) and H ( j ω ) ) don’t match each other with an acceptable error, other values for m and n are guessed and the above steps are repeated. The effectiveness of the proposed methodology strongly depends on the values of m and n . Thus, for obtaining better performance the optimal values for m and n are calculated in this paper by using GAs. Here, our objective is to minimize system cost function f that measures the distance between the real reflection coefficient ρ (0, ω ) and the estimated one H ( jω ) . The simplest choice is a fitness function defined as ns

2

f = ∑ ρ (0, ωi ) − H ( jωi ) ,

(9)

i =1

where ωi are the sampled frequencies of the reflection coefficient whose total number is ns . Note that several alternatives exist for the definition of a fitness function [8], including the possibility that the contributions from different spectral regions could be weighted. In this case we want to obtain the optimal values for the degrees of numerator and denominator polynomials. Therefore, an individual is an unknown quantity ( {ni }{ , mi }, i = 1, . . .,V , where V is the possible solution for each individual in the initial population). In each generation the population size is kept as 50. The Roulette wheel is used as selection operator. For the population size of V the probability of selection of each fitness value f i (i.e., Pi ) is

i th individual with

f Pi = V i (i = 1,2,....,V ) . ∑ fm

(10)

m =1

Our crossover function is uniform crossover. In uniform crossover each bit of children are randomly picked from the parents with the crossover probability. Mutation operator is set uniform, so that a random real value makes a random change in a bit of the unknowns m, n . In each generation the cost function for minimization is checked. The GA process repeats until the specified maximum number of generations is reached. Explained algorithm is illustrated in Fig. 1.

n.m Trail value for

n, m

From initial population

ρ (0, ω )

Complex curve fitting algorithm For estimation of frequency response

H(ω) f = min

∑

H ( jω ) − ρ ( 0, ω )

2

New trail value for the unknown parameters (m, n) organized by Selection, Crossover and Mutation

Fig. 1. Schematic diagram of frequency domain identification using complex curve fitting and Genetic Algorithm.

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In the next section the simulated results using the developed algorithm is illustrated. The accuracy and efficiency of the proposed method for identification of non-uniform fiber Bragg gratings (FBGs) in frequency domain such as apodized and chirped FBGs are shown and discussed.

4. SIMULATION RESULTS AND DISCUSSION In this section, using the above methodology frequency response of Apodization and chirped FBGs in frequency domain (poles and zeros) is estimated. In general case, the Riccati equation (Eq. (2)) has to be evaluated numerically. To make the numerical result more broadly applicable, it is convenient to introduce the normalized quantities such as z / L, δL, kL

and Φ ' L scaling to medium length. For the case study, we consider three Apodization functions and only one kind of chirp function as follows. 1. 2. 3. 4.

Gaussian apodization function Raised-cosine apodization function Quadratic apodization function Linear chirp function

3π . 4 1. Gaussian Apodization function- In this case the Gaussian Apodization profile is assumed as follows.

For all of our simulations the value of k 0 L is assumed to be

⎡ ⎛ z − 0.5L ⎞ 2 ⎤ A( z ) = exp ⎢ − a ⎜ ⎟ ⎥, L ⎠ ⎥ ⎢⎣ ⎝ ⎦

(11)

where a = 15 is the Gauss width parameter. For this Apodization function and given constant the real and estimated reflection coefficients are shown in Fig. 2. n=16,m=29,Gaussian 0.9 Real Estimation

0.8

Reflection coefficient

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

2

4

6

8

10

Normalized Frequency

Fig. 2. The real and estimated reflection coefficients vs. normalized frequency.

The estimated poles and zeros are illustrated in Table 1.

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Table 1: Estimated Poles and Zeros Gaussian Apodization 249.862 , 0.639 ± 54.175i, 14.227 ± 46.645i, 4.819 ± 48.153i, 16.748 ± 19.363i , -12.534533841755 , 9.744, 8.689 , -2.515, 1.679, -0. 03096 ± 0. 268

Zeros(16)

-6.335, 10

Poles(29)

−9

× (-721.20376, -28.93100 ± 635.553i, -106.60728 ± 620.60261i, -0.0243 ± 536.453i, -94.76511 ± 48.330347i, -39.824 ± 472.98i, -92.19 ± 396.265i, -90.876 ± 318.829i, -86.302 ± 248.115i, -81.684 ± 179.776i, -72.911 ± 112.648i, -57.754 ± 54.115i, -39.138 , -26.841 , -0.2955 ± 2.6653i, -16.161 )

2. Raised-cosine Apodization function- For this case the following Apodization function is adopted.

⎛ ⎛ z − 0.5L ⎞ ⎞ A( z ) = 0.5⎜⎜1 + cos⎜ π ( ) ⎟ ⎟⎟ , L ⎝ ⎠⎠ ⎝

(12)

For this Apodization function the real and estimated reflection coefficients are illustrated in Fig. 3. n=25,m=46,Raise−cosine 1 Real Estimated

0.9

Reflection coefficient

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

2

4

6

8

10

Normalized Frequency

Fig. 3. The real and estimated reflection coefficients versus normalized frequency. The estimated poles and zeros are illustrated in Table 2. Table 2: Estimated Poles and Zeros Rise-cosine Apodization

Zeros(25)

-146.742 , -66.309, 54.422 ± 39.364i, -43.529 ± 24.751i, -0.096 ± 62.083i -12.431 ± 50.774i, -0.0474 ± 59.065i, -0.422 ± 54.4742i, 32.71899 ± 20.819i 41.632,-0.0923 ± 43.227i,-0.0891 ± 26.902i, 10.0689, -5.0009,1.856, .35659

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-144.668 , -85.143 ± 78.126i, -31.264 ± 83.102i, -2.6597 ± 74.272i, -4.015 ± 70.944i, -0.0026 ± 59.177i, -7.376 ± 59.372i, -0.411 ± 54.48697i, -20.559 ± 56.2946i, -32.835 ± 49.0497i, -10.726 ± 51.770039i, -42.844 ± 35.808i, -44.9298 ± 27.390i, -49.096 ± 19.0146i, -49.870 ± 10.628i, -50.323 ± 3.506i, -13.071 ± 45.6424i, -13.854 ± 38.879i, -31.270 ± 23.334i, -20.3229 ± 24.1896i, -7.889 ± 22.976i, -18.787, -10.903, -4.966, -1.84998, -0.35148 ,

Poles(46)

3. Quadratic Apodization function- For the third case, the quadratic Apodization is considered. For simulation purpose, the Apodization parameter T = 6 is assumed. T z − 0.5L 2 ⎞ ⎛ +T( A( z ) = ⎜1 − ) ⎟, 12 L ⎝ ⎠

(13)

For this type of apodization, the real and estimated reflection coefficients are illustrated in Fig. 4.

n=29,m=29,Quadratic 1.4 Real Estimated

Reflection coefficient

1.2

1

0.8

0.6

0.4

0.2

0

0

2

4

6

8

10

Normalized Frequency

Fig. 4. The real and estimated reflection coefficients vs. normalized frequency. The estimated poles and zeros are illustrated in Table 3.

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Table 3: Estimated Poles and Zeros Quadratic Apodization

Zeros(2 9)

Poles(2 9)

-57.741 ± 60.200i, -71.612, 2.286 ± 81.673i, -55.269 ± 15.354i, 53.919 ± 20.522i, 53.306, 23.753 ± 50.147i, -0.185 ± 60.917i, 0.252 ± 59.922i, -0.882 ± 54.058i, -2.649 ± 46.764i, 0.107 ± 40.787i, 0.117 ± 19.1098i, 15.756 , -10.1178, 4.214 , -2.0466898, 0.329,

-78.207, -11.0297 ± 77.991i , -33.72099 ± 62.438i , -55.822 ± 13.709i , -0.0366 ± 60.149i,-8.695 ± 59.761i,-23.867 ± 49.793i ,-37.4587 ± 29.6597i -0.8639 ± 54.054i, -2.649 ± 46.763i, -6.195 ± 39.864i, -3.3486 ± 18.664i, -29.0615, -18.503, -8.5158 , -5.20644 , -1.603 , -0.390 ,

4. Linear chirp function- For final simulation, the chirping case is considered. For this situation, the following linear chirp function is adopted. Φ ' ( z) =

2 F (z − 0.5L ) L2

,

(14)

where the chirp parameter (F ) is assumed to be π . For this given chip function, the real and estimated reflection coefficients are illustrated in Fig. 5. n=12,m=21,Linear chirp 1.4 Real Estimated

Reflection coefficient

1.2

1

0.8

0.6

0.4

0.2

0

0

2

4

6

8

10

Normalized Frequency

Fig. 5. The real and estimated reflection coefficient Vs. normalized frequency.

The estimated poles and zeros are illustrated in Table 4.

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Table 4: Estimated Poles and Zeros Linear chirp Zeros(1 2) Poles(2 1)

5.568 ± 67.213i, 1.0278 ± 61.693i, 1.482 ± 42.582i, 2.439 ± 24.298i, 9.147 , 0.848 , 0.356 ± 0.442i, -59456.559,-1093.824,-10.402 ± 77.098i,-0.384 ± 63.328i, -16.972 ± 49.850i -7.694 ± 51.435i,-9.8297 ± 40.097i, -19.0889 ± 27.0676i, -5.6734 ± 22.624i -17.7278, -10.34798 , -0.8977 , -0.3167 ± 0.4768i,

In this section our proposed method for obtaining optimal number of poles and zeros has been investigated. We have shown that the optimum transfer function closely estimates the real reflection coefficient. Therefore, the proposed method can be an excellent method to implement and illustrate the optical systems in frequency domain.

5. CONCLUSION In this paper, GAs has been used to estimate an optimal transfer function to describe operation of complex fiber Bragg Gratings. For illustrating the ability of our method, useful examples have been considered. The simulated results have illustrated excellent agreementcompatibility between estimated and real functions. The presented results facilitate application of control system analysis to optical systems, covering both linear and especially nonlinear cases.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

T. Erdogan, “Fibre Grating spectra,” Journal of Lightwave Technology, 15(8), 1277-1294 (1997). Y. Sun, C. Yun, J. Lin, Y. Qian, B. Bai, Y. Yang and W. Qiu, “Study on the Apodized Function of chirped fibre grating for dispersion compensation,” Journal of Optoelectronics Laser, 10(3), 228-231 (1999). M. LeBlanc. S. Y. Huang, M. M. Ohn. R. M. Measures, A. Guemes, and A. Othonos, "Distributed strain measurement based on a fiber Bragg grating and its reflection spectrum analysis," Opt. Lett. 21, 1405-1407 (1996). H. Kogelnik, “Filter response of Non-uniform almost-periodic structures,” Bell Sys. Tech. J., 55, 109–126. J. Azana and L. R. Chen, “Synthesis of temporal optical waveforms by Fiber Bragg Gratings: a new approach based on space-to-frequency-to-time mapping,” J. Opt. Soc. Am. B, 19(11), Nov. 2002. J. E. Dennis, and R. B. Schnabel, “Numerical methods for unconstrained optimization and nonlinear equations,” Prentice-Hall, 1983. E. C. Levi, "Complex-Curve Fitting," IRE Trans. on Automatic Control, AC-4, 37-44 (1959). R. L. Haupt and S. Ellen Haupt, Practical Genetic Algorithms, John Wiley & Sons, 2004. H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Sys. Tech. J., 55, 109–126 (1976), D. L. Jaggard and Y. Kim, “Accurate one-dimensional inverse scattering using a nonlinear renormalization technique,” J. Opt. Soc. Am., 2(11), 1922-1930 (1985). E. Peral, J. Capmany and J. Marti, “Iterative Solution to the Gelfand-Levitan-Marchenko Coupled equations and application to synthesis of fiber gratings,” IEEE J. Quantum Electronics, 37, 165-173 (2001). G. H. Song and S. Y. Shin, “Design of corrugated waveguide filters by the Gelfand-Levitan-Marchenko inverse scattering method,” J. Opt. Soc. Am. A, 2, 1905-1915 (1995). J. E. Roman, and K. A. Winick, “Waveguide Grating filters for dispersion compensation and pulse compensation,” IEEE J. Quantum Electronics, 32, 2078-2084, 1996.

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14. J. Skaar, L. Wang and T. Erdogan, “On the Synthesis of fiber gratings by layer peeling,” IEEE J. Quantum Electronics, 37, 165-173 (2001). 15. J. Skaar and K. Magne Risvik, “A Genetic Algorithm for the inverse problem in synthesis of Fiber Gratings,” J. Lightwave Technology, 16(10), (1998).

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Physical parameters identification of non-uniform fiber Bragg gratings using interpolation method A. Rostamia, A. Yazdanpanaha and F. Janabi-Sharifib a) Photonics and Nanocrystals Research Lab. (PNRL), Faculty of Electrical Engineering, University of Tabriz, Tabriz 51664, Iran Tel/Fax: +98 411 3393724 E-mail: [email protected] b) Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada M5B 2K3 E-mail: [email protected]

ABSTRACT The Interpolation method for identification of the Apodized and Chirped Fiber Bragg Gratings is used. For this purpose, the Riccati equation for obtaining the reflection coefficient is used and numerically solved. Then for various system parameters, the maximum reflection peaks, bandwidth of the reflection coefficient and the central frequency are determined. Then using interpolation technique, three analytical equations can be extracted for the above-mentioned quantities. Therefore using the obtained reflection coefficient there is a map from the reflection coefficient in frequency domain to real space (index of refraction space). Hence, for the measured reflection coefficient, one can determine the index of refraction profile including Apodized and Chirped functions. The proposed method is effective and can easily determine the index of refraction profile. Key words- Inverse Scattering, Interpolation method, Apodized and Chirped Fiber Bragg Grating

1. INTRODUCTION High speed optical fiber communication systems depend critically on the design of complex filters to perform various functions such as selection of wavelength multiplexed channels or compensation of the link dispersion. The technology of ultraviolet photo-induced fiber gratings has reached now the necessary maturity to implement these filters [1]. Several experiments have been demonstrated to fabricate nonuniform gratings, permitting an accurate control of both the local grating pith and the apodization profile along the structure [2, 3]. For design of these complex filters there are some interesting methods including: 1. Approximate Fourier Transform method [4-7]; 2. Exact Solution of the problem expressed in terms of integral equations [8-13]; and 3. Exact inverse scattering algorithms called differential or direct methods [14-17]. Since the design of optical complex systems is necessary for optical applications, identification of complex optical integrated systems and devices is very important for optimum optical integrated system design. In practice estimation of the implemented structure is critical for scaling of the output signal and relating the measured quantity to the physical parameters. There are some published works in this domain. But, all of the Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740Y, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.684886

Proc. of SPIE Vol. 6374 63740Y-1

presented methods are based on complex electro-optical setup [18-20]. However, arranging these complex setups need more careful tuning for precise measurement. Here, we present a novel algorithm based on interpolation technique to identify the system parameters of the complex Bragg gratings. In this method, we extract three distinguishable quantities such as maximum reflection peak, bandwidth of the reflection coefficient and the central frequency, which are interesting and easy to measure in practice. The proposed method can be easily implemented in all-optical domain. Therefore, the presented method will offer highspeed for reconstruction of the medium profile. The organization of the paper is as follows. In section II, the mathematical modeling of the complex Bragg Gratings is presented. Also, the Riccati equation is derived. In section III, interpolation relation and simulation result of the proposed method are illustrated. Finally the paper ends with a conclusion.

2. MATHEMATICAL MODELING OF COMPLEX BRAGG GRATINGS A fiber Bragg grating is a periodic perturbation structure of the refractive index in a waveguide. The Apodized and chirped index of refraction for the fiber Bragg gratings can be written as follows [21].

n( z) = n0 + ∆ndc +

A( z)∆nac i[( 2πΛN ) z +Φ( z )] (e + c.c.) , 2

(1)

where n0 , ∆ndc , ∆n ac , Φ (z ) , N , Λ and A(z ) are constant index of refraction, the average refractive index of the core, the modulated ac refractive index, an arbitrary spatially varying phase, an integer that signifies its harmonic order, the period of the perturbation, and the Apodization function respectively.

z Fig. 1. Refractive index change of the fiber Bragg grating.

Based on Helmholtz equation, the following electric field distribution can be considered for the Grating mentioned above as [21]

Et =

1 i (ω t − β µ z ) i (ω t + β µ z ) ( Aµ ξ µt e + B µ ξ µt e + cc ) 2

(2)

, Aµ , Bµ and β µ are the radial transverse field distribution of the µ

th

guided mode, the

amplitude of direct and indirect propagating modes and the propagation constant of µ Also the propagation constant can be defined as follows.

th

mode respectively.

Where ξ

µt

βµ =

2π

λ

n0 cos θ =

2π

λ

neff ,

Proc. of SPIE Vol. 6374 63740Y-2

(3)

where n0 , λ , and θ are the refractive index of the core, input wavelength and beam angle respectively. The appeared electric field amplitudes in Eq. (2) can be related together by the standard coupled-wave equations [22, 23] as follows.

∂Bµ ∂z ∂Aµ ∂z

= iK dc Bµ + iK ac Aµ e −i ( ∆βz −Φ ( z ))

= −iK dc Aµ − iK ac∗ Bµ ei ( ∆βz −Φ ( z )) ,

(4)

where the phase mismatch ∆β , as known as detuning, is given by Eq. (5), 2π 4π 2π 1 1 ∆β = 2 β − = n eff − = 4πn eff ( − ), λ λ λD Λ Λ

(5)

where λ D = 2neff Λ is the Bragg wavelength. The coupling dc coefficient can be calculated as follows.

K dc =

2π∆n ac

λ

.

(6)

Also the ac coupling constant K ac is given as follows:

K ac =

π ∆ n ac . λ

(7)

Now based on introducing the following variables [24], a new form of the coupled wave equations can be derived that is easy for extraction of physical quantities. i −( )[∆βz −Φ ( z ) ]

R = Aµ e

S = Bµ

2

i ( )[∆βz −Φ ( z ) ] e2 .

(8)

By substitution Eq. (8) into Eq. (4) the following set of coupled wave equation can be obtained.

1 dΦ ( z ) dR )]R = −iK ac∗ A( z ) S , + i[ K dc + (∆β − dz 2 dz dS 1 dΦ ( z ) − i[ K dc + (∆β − ]S = iK ac A( z ) R. 2 dz dz

(9)

Here, for simplicity we assume that both the ac coupling coefficient K ac A(z ) and the grating phase

Φ ( z ) are slowly varying functions of z , indicating the non-uniformity in the grating parameters. We assume that the structure has a length L and extends from z = 0 to z = L . The boundary conditions for our scattering problem are:

R ( 0 ) = 1, S ( L ) = 0 . Then a local reflection coefficient ρ ( z ) is defined as

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(10)

ρ (z) =

S R

(11)

So, based on the above-mentioned definition and using coupled mode equations the following differential equation can be obtained that is Riccati equation. 4π 2π π .∆ n dρ dΦ ) A ( z )( 1 + ρ 2 ) + i ( )ρ = i( − n effnew − λ Λ dz λ dz

(12)

where n effnew = ∆ n dc + n eff .The boundary condition for this equation according to boundary conditions presented in Eq. (10) can be presented as ρ ( L ) = 0 . Based on exact or numerical solutions of the Riccati equation, the reflection coefficient and energy reflection can be extracted.

3. RESULTS AND DISCUSSION In this section the presented relations in section 2 is applied for two practical interesting cases. These cases are linear chirped Bragg Grating and Gaussian Apodization. Hence, we first consider the linear chirped Bragg Gratings. a) Linear Chirped Bragg Gratings- In this case linear chirped is considered. According to basic information about chirp concept the following relations can be used [25]. 1 dΦ z (13) = F 2 dz ( FWHM ) 2 where F is chirp parameter and defined as [26] F =

where FWHM and

( FWHM z2

)2

Φ ( z ) = − 4 π n eff

( FWHM

λ

2 D

)2 dλD dz

(14)

dλD are full-width-at-half-maximum of the Grating profile and rate of change of the dz

design wavelength with the position in the grating, respectively. Now based on the presented simulation results, three analytical relations based on interpolation technique are presented for three main parameters that were presented in introduction (the maximum reflection coefficient, bandwidth, and the central frequency) as follows. In this case, we consider four different values of modulated index of refraction, i.e., 0.0002, 0.0004, 0.0006 and 0.0009.

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0.8 0.7 0.6

reflectivity

0.5

(a)

(b)

0.4 0.3 0.2 0.1 0 1.54

1.545

1.55 1.555 Weavelenght(micrometre)

1.56

1.565

Fig. 2. The reflection coefficient vs. incident wavelength for chirped Bragg grating dλ ∆n ac = 0.0004 , and (a) dλ D = −2.5 ; (b) D = 2.5 . dz dz

1

(a)

0.9 0.8

(b)

reflectivity

0.7 0.6

(c)

0.5 0.4

(d)

0.3 0.2 0.1 0 1.52

1.525

1.53

1.535 1.54 1.545 Weavelenght(micrometre)

1.55

1.555

Fig. 3. The reflection coefficient vs. wavelength for chirped Bragg grating

dλ D dλ D dλ D ∆nac = 0.0006 , (a) = −1, (b) = −2, (c) = −4, dz

dz d λ D (d) = −6. dz

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dz

1

(d)

0.9 0.8

(c)

reflectivity

0.7

(b)

0.6 0.5 0.4 0.3

(a)

0.2 0.1 0 1.544

1.546

1.548

1.55 1.552 1.554 Weavelenght(micrometre)

1.556

1.558

Fig. 4. The reflection coefficient vs. wavelength for chirped Bragg grating

dλ D = −2.5 (nm/cm), ∆n ac = (a) 0.0002; (b) 0.0004; dz (c) 0.0006; (d) 0.0009.

1.1 1

maximum reflectivity

0.9 0.8

0.0009 0.0006 0 0006

0.0004

0.7 0.6 0.5

0.0002

0.4 0.3 0.2 0.1 −5

−4.5

−4 −3.5 −3 −2.5 −2 chirp variable(nonometre/centimetre)

Fig. 5. The maximum reflection vs.

−1.5

−1 −7

x 10

dλD with different modulated refractive index as parameter dz ∆n ac varies

Fig. (4) shows our simulations for four different modulated Index of refractions. In the following figures the lines show simulated results and circles show corresponding interpolated versions.

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dλ D 3 dλ dλ ) + 9.97 × 1012 ( D ) 2 + 4.57 × 10 7 ( D ) dz dz dz dλ 11 dλ D 3 11 dλ D 2 = −1.30099 × 10 ( ) − 1.1345 × 10 ( ) + 1.47 × e 6 ( D ) dz dz dz d d d λ λ λ = −2.84 × 1018 ( D ) 3 − 3.2 × 1012 ( D ) 2 − 4.8 × 10 5 ( D ) dz dz dz d λ d λ dλ = 3.336969 × 1018 ( D ) 3 − 4.692 × 1011 ( D ) 2 − 3.3 × 10 5 ( D ) dz dz dz

1) ρ max = 7.92 × 1018 ( 2) ρ max 3) ρ max 4) ρ max

(15)

After interpolation of the maximum reflection coefficient, we consider the case for bandwidth. Using simulated results the following interpolated relations can be obtained for different modulated refractive indices of 0.0002, 0.0004, 0.0006 and 0.0009 for following cases 1 to 4 respectively. dλ D ) − 1.6 × 10 − 4 dz dλ 2)∆ω = 1.88 × 10 4 ( D ) + 1.6 × 10 − 4 dz 4 dλ D 3)∆ω = 1.85 × 10 ( ) + 5.3 × 10 − 4 dz dλ 4)∆ω = 1.85 × 10 4 ( D ) + 1.01 × 10 −3 dz

1)∆ω = 1.92 × 10 4 (

(16)

Here based on the interpolated relations the following figure show good agreement between complete simulations and our interpolations. As a final interpolation, we consider central frequency of the reflection coefficient. Our simulations show that in this case for different modulated refractive index really the central frequency approximately is unique and we can consider only one interpolated relation for the case. So, the following relation shows the central frequency in terms of system parameters. dλ dλ ⎡ ⎤ λ0 = ⎢4.4643 × 10 8 ( D ) 2 + 9.85 × 10 3 ( D )1 + 1.55⎥ . dz dz ⎣ ⎦

(17)

Using the interpolated relation, Fig. 7 shows complete simulation (two curves) and interpolated case (curve with circles) that follow each other closely. Using the interpolated relations for basic three factors, now in the following we consider two maps between the bandwidth and maximum reflection coefficient versus modulated refractive index that are shown in Figs. (7 and 8). Using these figures one can obtain the modulated refractive index in terms of the measured bandwidth and the maximum reflection coefficient. Now, we first present the interpolated relation as follows. (18) ∆ω = −2.525252 × 10 5 (∆nac ) 3 + 5.9 × 10 2 (∆nac ) 2 + 9.9 × 10 −1 (∆n ac )1 + 4.59 × 10 −3 Fig. (7) Shows the simulation results and interpolated curves (F=200) and illustrate close compatibility between them.

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−3

x 10

10

0.0006

9

Bandwidth(micrometre)

8

0.0009

7 6

0.0002

5

0.0004

4 3 2 1

1

1.5

2

2.5 3 3.5 Chirp variable(nm/cm)

4

4.5

5 −7

x 10

Fig. 6. The 3dB bandwidth vs. dλ D with different modulated refractive index ∆n ac values. dz

central wavelenght(micrometre)

1.557

1.556

0.0002

1.555

0.0004 1.554

1.553

1.552

0.5

1

1.5

2 2.5 3 3.5 chirp variable(nm/cm)

4

4.5

5 −7

x 10

Fig. 7. The central wavelength vs. dλ D with different modulated refractive index ∆nac values.

dz

Proc. of SPIE Vol. 6374 63740Y-8

−3

6

x 10

5.5

200

Bandwidth(micrometre)

5 4.5

150

4 3.5

100

3 2.5 2

2

3

4

5 6 modulation index

7

8

9 −4

x 10

Fig. 8. The bandwidth vs. the modulated refractive index for different F values.

Now, the maximum reflection coefficient can be considered. The following relations show the interpolated relations for the maximum reflection coefficient versus modulated refractive index for different chirp parameters 100, 150 and 200 respectively. 1) ρ max = 3.896 × 10 9 (∆nac ) 3 − 8.37 × 10 6 (∆nac ) 2 + 5.89 × 10 3 (∆n ac )1 − 3.58 × 10 −1 (19) 2) ρ max = 1.787 × 10 9 (∆n ac ) 3 − 4.95 × 10 6 (∆n ac ) 2 + 4.4469 × 10 3 (∆nac )1 − 2.97 × 10 −1 3) ρ max = 1.829 × 10 9 ( ∆n ac ) 3 − 2.212 × 10 7 (∆n ac ) 2 + 3.193 × 10 4 (∆n ac )1 − 2.28 The following figure shows simulated and interpolated (blue curves) cases and illustrates good compatibility in different values of the chirp parameter.

maximum reflectivity

1.4

1.2

100

1

150

0.8

0.6

200

0.4

0.2

0

1

2

3

4 5 6 7 refractive index modulation

8

9

10 −4

x 10

Fig. 9. The maximum reflection coefficient vs. the modulated refractive index for different values of the chirp parameter F.using both simulation and interpolation methods.

b) Gaussian Apodization- In this case we consider the Gaussian Apodization as follows.

Proc. of SPIE Vol. 6374 63740Y-9

L ⎤ ⎡ (z − )2 ⎥ ⎢ , 2 A ( z ) = exp ⎢ − a ⎥ , z ∈ [0 , L ] L ⎢ ⎥ ⎣ ⎦

(20)

where a is Gauss width parameter [27]. Using the simulated results the following relation can give a suitable interpolated relation for the maximum relation versus Gauss parameter.

ρ max = −5.49 × 10 −7 (a) 3 + 1.142 × 10 −6 (a) 2 − 2.07 × 10 −6 (a) + 0.9999996 .

(21)

Fig. (9) shows the simulated result and interpolated case. Interpolated curve is shown with blue curve that is compatible with real case that is illustrated with red curve. These curves are hardly distinguishable. 1

1

maxreflectance

1

1

1

0.9999

0.9999

0

0.5

1

1.5

2 2.5 3 Gauss width parameter

3.5

4

4.5

5

Fig. 10. The maximum reflection coefficient vs. the Gauss width parameter

∆nac = 0.0004 . 4. CONCLUSION In this paper a novel method based on interpolation technique for identification of complex Bragg Gratings has been developed. Here, three main factors, which are critical, interesting and easy for measurement have been considered for interpolation. Our proposed analytical relations are greatly compatible with complete numerical simulations. Also, our proposed method provides a map from frequency domain to position to identify medium optical characteristics. The proposed method is easy for practical engineering and can be extended for more complex cases. REFERENCES 1. 2.

G. Meltz, W. W. Morey, and W. H. Glen, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Opt. Lett., vol. 14, no. 15, pp. 823–825, Aug. 1989. W. H. Loh, M. J. Cole, M. N. Zervas, S. Barcelos, and R. I. Laming, “Complex grating structures with uniform phase masks based on the moving fiber-scanning technique,” Opt. Lett., vol. 20, no. 20, pp. 2051–2053, Oct. 1995.

Proc. of SPIE Vol. 6374 63740Y-10

3.

A. Asseh, H. Storoy, B. E. Sahlgren, S. Sandgren, and R. A. H. Stubbe, “A writing technique for long fiber Bragg gratings with complex reflectivity profiles,” J. Lightwave Technol., vol. 15, pp. 1419–1423, Aug. 1997. 4. K. I. Hopcraft and P. R. Smith, “An introduction to electromagnetic inverse scattering.” Dordrecht, The Netherlands: Kluwer, 1992. 5. J. A. Dobrowolski and D. Lowe, “Optical thin film synthesis program based on the use of Fourier transforms,” Appl. Opt., vol. 17, no. 19, pp. 3039–3050, Oct. 1978. 6. B. G. Bovard, “Fourier transform technique applied to quarterwave optical coatings,” Appl. Opt., vol. 27, no. 15, pp. 3062–3063, Aug. 1988. 7. K. A. Winick and J. E. Roman, “Design of corrugated waveguide filters by Fourier-transform techniques,” IEEE J. Quantum Electron., vol. 26, pp. 1918–1929, Nov. 1990. 8. I. M. Gel’fand and B. M. Levitan, “On a determination of a differential equation from its spectral function,” Amer. Math. Soc. Trasl., Ser. 2, vol. 1, pp. 253–304, 1955. 9. G. L. Lamb, Jr, “Elements of soliton theory.” New York: Wiley, 1980. 10. A. M. Bruckstein, B. C. Levy, and T. Kailath, “Differential methods in inverse scattering,” SIAM J. Appl. Math., vol. 45, no. 2, pp. 312–335. Apr. 1995. 11. P. V. Frangos and D. L. Jaggard, “A numerical solution to the Zakharov- Shabat inverse scattering problem,” IEEE Trans. Antennas Propagat., vol. 39, pp. 74–79, Jan. 1991. 12. B. Gopinath and M. M. Sondhi, “Inversion of the telegraph equation and the synthesis of nonuniform lines,” Proc. IEEE, vol. 59, pp. 383–392, Mar. 1971. 13. P. V. Frangos and D. L. Jaggard, “The reconstruction of stratified dielectric profiles using succesive approximations,” IEEE Trans. Antennas Propagat., vol. 35, pp. 1267–1272, Nov. 1987. 14. I. Kay, “The inverse scattering problem when the reflection coefficient is a rational function,” Commun. in Pure Appl. Math., vol. 13, pp. 371–393, 1960. 15. G. H. Song and S. Y. Shin, “Design of corrugated waveguide filters by the Gel’fan-Levitan-Marenko inversescattering method,” J. Opt. Soc. Amer. A, vol. 2, no. 11, pp. 1905–1915, Nov. 1985. 16. J. E. Roman and K. A. Winick, “Waveguide grating filters for dispersion compensation and pulse compression,” IEEE J. Quantum Electron., vol. 29, pp. 975–982, Mar. 1993. 17. E. Peral, J. Capmany, and J. Marti, “Design of fiber grating dispersion compensators using a novel iterative solution to the Gel’fan-Levitan- Marchenko coupled equations,” Electron. Lett., vol. 32, no. 10, pp. 918–919, May 1996. 18. “Iterative solution to the Gel’fan-Levitan-Marchenko coupled equations and application to synthesis of fiber gratings,” IEEE J. Quantum Electron., vol. 32, pp. 2078–2084, Dec. 1996. 19. J. Skaar, B. Sahlgren, P. Y. Fonjallaz, H. Storoy, and R. Stubbe, “Highreflectivity fiber-optic bandpass filter designed by use of the iterative solution to the Gel’fan-Levitan-Marchenko equations,” Opt. Lett., vol. 23, no. 12, pp. 933–935, June 1998. 20. P. V. Frangos, D. J. Frantzeskakis, and C. N. Capsalis, “Pulse propagation in a nonlinear optical fiber of parabolic index profile by direct numerical solution of the Gel’fan-Levitan integral equations,” Proc. Inst. Elect. Eng., pt. J, vol. 140, no. 2, pp. 141–149, Apr. 1993. 21. R. Kashayap, Fiber Bragg Gratings, Academic, Londan, 1999. 22. A.Yariv, “Coupled-mode Theory for guided-wave optics,” IEEE J.Quantum Electron ., QE-9 (September 1973) , pp.919-913. 23. H. Kogelnik, “Theory of Dielectric waveguides,” in Integrated optics , ed . T . Tamir , Heidelberg : Springer , 1975 . 24. E. Kreyszig, Advanced Engineering Mathematics , 5 th Ed. , p .345, Wiley , New York, 1992. 25. T. Erdogan, “Fiber grating spectra,”, Journal of Lightwave Technology , vol. 15, no.8, 1997, pp. 1277-1294. 26. H.Kogelnik , “Filter response on nonuniform almost-periodic structures.” Bell system Technical Journal, vol.55, no.1, 1976, pp. 109-126. V. Tzolov, D. Feng, S. Tanev, and Z.Jakubczyk, “Modeling tools for integrated and fiber optical devices,” Proc. Integrated Optics Devices ΙΙΙ , Photonics West 99, San Jose, CA,1999, pp. 23-29.

Proc. of SPIE Vol. 6374 63740Y-11

Circuit modeling of Multiple Quantum Well Lasers optimized by carrier tunneling A. Rostamia, H. Rasoolib and F. Janabi-Sharific a) Photonics and Nanocrystals Research Lab. (PNRL), Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz 51664, Iran Tel/Fax: +98 411 3393724 E-mail: [email protected] b) Department of Electrical Engineering, Islamic Azad University of Tabriz, Tabriz, Iran c) Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada M5B 2K3

ABSTRACT In this paper, the effect of carrier tunneling between wells on multiple-quantum well (MQW) laser characteristics is investigated. Based on the rate equations developed for 3-levels (carrier transport between 3-D, 2-D and quasi 2-D states) including carrier tunneling effect, a circuit model is proposed. According to simulation results with change of tunneling time three interesting regions of operation are obtained. The operation of the proposed laser doesn’t change for tunneling time larger than a threshold value (0.1 nsec). For the tunneling time smaller than another threshold value (0.01 nsec) the operation of the laser strongly degraded. For the tunneling time between the two thresholds values the operation of the laser can be optimized, which in this paper it is done for obtaining low turn-on delay time, leading to suitable operation from simultaneous filling of the wells, high output intensity and large bandwidth points of view. Keywords- Multiple Quantum Well Laser, Carrier Tunneling, Spice Circuit Modeling

1. INTRODUCTION Nowadays high speed optical communication and computing are basic demands in industry and biology. For this purpose, high speed laser diodes, broadband optical fibers and high speed photo-detectors are necessary. Recently it is illustrated that Multiple Quantum Well Lasers (MQWL) has inherent properties such as lower threshold current and low temperature dependency, high differential gain and higher bandwidth. Also, it is demonstrated that MQWL has faster dynamics [1]. These effective properties are excellent to introduce MQWL for high speed optical communication and computing. For analysis of the quantum well lasers first one level rate equation was presented [2]. In this model the interaction between quantum wells confined states and photon population has been considered. This method had some problems for description of dynamic response such as low frequency roll off degradation [3]. So, for description of this problem, two levels model was presented [3]. In this model transportation of carriers across optical confinement layer (OCL) was considered and it was shown that the origin of the problem is related to this phenomenon. This model had good ideas about transportation of carriers across OCL but it couldn’t illustrate clearly quantum coupling between OCL (3-D) states and confined (2-D) states in well [4]. The capturing and escaping between 3-D and 2-D states is so important for exact modeling of high speed

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740Z, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.683990

Proc. of SPIE Vol. 6374 63740Z-1

laser diodes. For introducing suitable model to incorporate this phenomenon, the three levels rate equations proposed by [5]. For building of this model the gateway states has been added to two levels rate equations [6]. For MQWL there is another interesting phenomenon related to transportation of carriers across the barriers. For handling of this phenomenon, there are two basic events including thermionic emission and carrier tunneling [7]. For solving of the obtained equations in each of mentioned above models the transmission line method (TLM) [8], full numerical self consistent methods based on finite difference (FD) and finite element (FE) and circuit models have presented [6]. From simulation point of view the circuit modeling is interesting especially there is a little problem about convergence compared other methods. Also, this type of simulation can help to total system evaluation. In this direction the circuit model for single quantum well lasers using three levels rate equations was presented by B. P. C. Tsou et al [6]. Also, for MQWL the circuit modeling based on three levels rate equations was presented by G. Rossi et al [9]. For integrated laser diodes such as MQWL the tunneling effect between wells is possible. In this paper, we try to incorporate the tunneling effect to these circuit models and investigate it properties. We like study the tunneling effect on output intensity, turn on delay time, transient behavior, inhomogeneous wells filling up and bandwidth of the MQWL. In this study the tunneling time based on optimum laser operation will be adopted. So, in our treatment generally different tunneling time for each well should be considered. The organization of this paper is as follows: In section II the mathematical modeling based on three levels including the tunneling effect is considered. The circuit model is presented in section III. In section IV simulation results and discussion will be presented. Finally the paper ends with a conclusion.

2. MATHEMATICAL MODELING In this section the operation of MQWL based on the 3-levels rate equation is explained as follows [7]. Fig. 1 shows carrier transportation processes and light emission in MQWL. According to the 3-levels rate equations fundamental there are four sets of equations for carriers including left and right OCLs , the quasi 2-D states (gateway) and confined states (wells) and one equation for photon density variation. In this analysis the ambipolar model is used [7]. I Dout

thff]$!©=©

da-ajff]si© th©,]li©rn SCH

tlu bt

1qui-2D]

çui-2D] 1qui-2D]

L_° L_° cT HIT LIT J/ — J/

Clathhng I OCL L_&to&

Lan.r

QW3

cui-2D)

cui2D1

______

______

OCL

LIT LIT _)Stthd

Cladding

QW4

P-side

N-side

Fig. 1. Schematics of Multiple Quantum Wells Laser.

The following sets of equations are presented to describe the operation of MQWL [9]. In these equations the tunneling effect is inserted in Eq. (8) considering carrier flow due to this phenomenon. (1) RS ,B,W = AS ,B,W nS ,B,W + BS , B,W nS2,B,W + CS , B,W nS3,B,W

Proc. of SPIE Vol. 6374 63740Z-2

I inj dn S1 I = − R S1 − D , qV S 1 dt qV S1

(2)

VS 1nS 1 − VW nB1 , τD

(3)

dn S 2 I D ( N QW ) − I DOut n V nW ( N QW ) = − RS 2 − [ S 2 − W ], dt qV S 2 τ C VS 2 τ e

(4)

ID =

VS 2 nS 2 , τD I −I n n = D ( j ) D ( j +1) − RB − [ B ( j ) − W ( j ) ] , τC τe qVW I Dout =

dnB ( j ) dt

I D( j ) = dnW ( j ) dt

=[

n B( j )

τC

−

VW nB ( j ) − VW nB ( j −1)

nW ( j )

τe

τB

G[nW ( j ) ] 1+ ∈ s

G[nW ( j ) ] = G0 [1 + ln

(6)

,

(7)

] − RW ( j ) −ν g G[nW ( j ) , S ]S +

G[nW ( j ) , s ] =

(5)

nW ( j −1)

τ Tun ( j −1)

−

nW ( j )

τ Tun ( j )

,

nW ( j ) N0

(8) (9)

],

τ−p1 = [α + ln( Rm−1 ) / LC ] / vg , K dS K s = ∑ Γ ( j ) vg G[nW ( j ) , s ]s + ∑ Γ ( j )β( j ) RSp [nW ( j ) ] − , τ dt j =1 j =1 p

R=

,

τC 2 = R0 + R1 J inj , τe

(10)

(11) (12)

(13)

where A, B, C, n Sj , nW ( j ) , n B ( j ) , RSj , RWj , RBj ,VSj ,VWj , I inj , I D , I D , I D ( j ) , G , G0 , N 0 ,τ p , LC , , τ D ,τ C ,τ e ,τ B ,τ Tun ( j ) , ε Out

Γ, β , R, S , α , Rm , vg , Rsp and N QW are the recombination coefficients, the carrier density of left (j=1) and right (j=2) OCL, carrier density in quantum wells, carrier density in quasi 2-D states, recombination rates for left and right OCLs, recombination rates for wells, recombination rates for quasi 2-D states, the volume of OCLs, the volume of Wells, injected current from p-side (left) OCL, drift-diffusion current from left OCL to the first quasi states, outgoing current from right OCL, drift-diffusion current between two adjacent quasi states, optical Gain for each Well, parameter extracted from characterization of real device, parameter extracted from characterization of real device, photon life time in the cavity, cavity length, effective space transport time [7], carrier capture time, carrier escape time, diffusion time across the barriers, the tunneling time, gain suppression factor, optical confinement factor, spontaneous emission factor, the ratio of capture to

Proc. of SPIE Vol. 6374 63740Z-3

escape times, photon density, internal loss, mirror reflection coefficient, group velocity, spontaneous emission rate and the total number of quantum wells respectively. In these sets of equations Eqs. (2), (4), (6), (8), and (12) are the carrier rate equations for left and right OCLs, the carrier rate equations for quasi 2-D states, carrier rate equations for the wells and the photon density equation respectively. Also, in these equations we let the density of carriers in each well change with the tunneling effect between wells. For this purpose, there is a possibility to change the density of carriers inside each well with incoming rate of carriers from left and outgoing to the right well. In this calculation, the tunneling time from left and to the right can be different. Also, in this paper the tunneling effect is assumed completely stochastic and Eq. (8) can show this effect.

3. CIRCUIT MODELING For solution of these coupled equations mentioned above in section II, we try to present circuit model that can be solved by SPICE simulation software. For this purpose, the following sets of equations that are based on the rate equations can be arranged.

VS 1

d (qnS 1 ) = I inj − I Sric1 − I D , dt I Sric1 = qVS1 RS 1 , vS 1 = qnS 1

(14)

,

CS 1 = vS 1 dv CS 1 S 1 = I inj − I Sric1 − I D , dt CB

CW ( j ) =

dvB ( j ) dt

dvW ( j ) dt

= [ I D ( j ) − I D ( j +1) ] − I Bric( j ) − [ I C ( j ) − I e ( j ) ] ,

= [ I C ( j ) − I e ( j ) ] − I Wric( j ) − I stm ( j ) + I tun ( j −1) − I tun ( j ) ,

(15) (16) (17)

I Bric,W = qV B ,W RB ,W ,

v B ,W = qn B ,W , C B ,W = VB ,W , I Tun ( j −1) = qVW ( j −1)

nW ( j −1)

I Tun ( j ) = qVW ( j ) CW ( j ) =

dvW ( j ) dt

I c = qVB

,

τ Tun ( j −1) nW ( j )

τ Tun ( j )

,

(18) (19)

= [ I C ( j ) − I e ( j ) ] − IWric( j ) − I stm ( j ) ,

(20)

nB Rn , I e = qVW W , τC τC

(21)

Proc. of SPIE Vol. 6374 63740Z-4

C fm

dv fm dt

=

N QW

∑Γ j =1

NQW

I

( j ) stm ( j )

+ ∑ Γ ( j ) I sp ( j ) − j =1

v fm R fm

,

I stm ( j ) = qVW vg G[nW ( j ) , s ]s ,

(22) (23)

I sp ( j ) = qVW β( j ) Rsp [nW ( j ) ] ,

(24)

hv , qVW qV = W , hv

R fm = τ p C fm

S

I

So, based on electrical passive component relations and circuit principles such as KCL and KVL, the following figure shows the circuit model for describing the laser operation. For example Eq. (16) shows a capacitor, which variation of the current of this element is controlled by some current sources connected to the node.

Fig. 2. Circuit model for MQWL including Tunneling effect (CPL and CPR are constants depending on device geometry and parameters).

Also, Eq. (15)-(17) and Eq. (22) show the circuit model for left OCL, quasi 2-D states, confined states (Wells) and photon density respectively. The tunneling effect on circuit modeling is introducing two current incoming and outgoing sources for each well, which is shown in Eq. (17).

Proc. of SPIE Vol. 6374 63740Z-5

4. SIMULATION RESULTS AND DISCUSSION In this section for simplicity the circuit modeling is done for 5 wells of InGaAsP laser diode. This laser is tuned for 1.55µm to apply to optical communication. Also, the active layer of the laser diode includes two OCLs

In0.13 Ga 0.87 As 0.45 P0.55 ( 1000A 0 ) with density of impurity at level 5 × 1017 cm −3 , 5 wells

In0.27 Ga 0.73 As 0.75 P0.25 ( 90A 0 ) and 4 barriers In0.13 Ga 0.87 As 0.45 P0.55 ( 96A 0 ).The simulation parameters are given in Table 1. In this section the circuit model presented in section 3 is simulated using SPICE software. The static, transient and frequency response are illustrated. It is shown that using optimal tunneling time for each well (generally different from together) some of interesting quantities such as the output intensity, bandwidth and turn-on delay time are improved. Therefore, the tunneling effect can be engineered to introduce better operation for MQWL in high speed optical communication. Table 1. Simulation parameters. Name Symbol Number of well NQW Spontaneous emission factor Β Optical confinement factor Г (mean value for one well) Trap aided recombination coefficient A Radiative recombination coefficient B Auger recombination coefficient C Ambipolar Diffusivity Da Barrier width LB Well width LW Active region width W Gain coefficient G0 Gain carrier weighting coefficient N0 Gain suppression factor ε Capture time τc Capture to escape time ratio eq(2-13) R0 Capture to escape time ratio eq(2-13) R1 Internal losses α Facet reflectivity Rm Parasitic capacitance Cp Parasitic series resistence Rp

Value 5 0.0001 0.0235 ~108 s-1 ~10-11 s-1cm3 ~10-28 s-1cm6 ~1s-1 cm2 9.6 nm 9 nm 2.3 µm 980 cm-1 2.5*1018 cm-3 5*10-17 1 ps 0.01 30*10-12 (cm2/A)2 30 cm-1 0.32 7 pF 3.5 Ω

In Fig. 3 the carrier distribution without tunneling in wells is illustrated. As it can be seen the population is decreased from first to fifth wells. On the other hand the population for left hand side well is highest and for right hand side is lowest between all wells (nonuniform population distribution). Hence, population is inhomogeneous and the output intensity is low.

Proc. of SPIE Vol. 6374 63740Z-6

Lc Inmi T loCi

B

Ohhoi tunneling eIc1e)

B

ci B

4

co uJ

3 =

0 2 C)

U U

IU

2U

3U

4U

BU

BU

7U

8U

9U

IUU

Current [mA]

Fig. 3. Nonuniform distribution of carriers in Wells (without Tunneling).

Fig. 4 shows the case for nonzero tunneling effect. As it can be seen the population is more uniform than previous case. This is related to the tunneling possibility between wells that make another way for carrier transportation between wells. Therefore the population in all wells near together.

Lc Inmi T loCi

B

sfth tunneling eIc1e)

B

ci B

4

co uJ

3 =

0 2 C)

U U

IU

2U

3U

4U

BU

BU

7U

8U

9U

IUU

Current [mA]

Fig. 4. Distribution of carriers in Wells (with Tunneling) ( τ Tun −1 = τ Tun − 2 = 0.2 n sec,τ Tun −3 = 0.3 n sec,τ Tun − 4 = 0.5 n sec ).

Output power in terms of bias current for both cases is illustrated in Fig. 5. In this simulation for given parameters the output power for nonzero tunneling case is more than zero tunneling case. This can be related to uniform population distribution in wells that is related to tunneling effect.

Proc. of SPIE Vol. 6374 63740Z-7

T20 [oC]

Lc200 [nm] 10

9-

——

8- _______________ — — —without tunneling effects

/ -:'

withtunneling effects

7

--

__ —

,_ —

8-

-

8

0-4-

-

-

3-

/

-

///, -7/

ft

-

20

30

:7 U

ID

-

-

;.

40

;.

80

80

70

80

90

lOU

Current [mA]

Fig. 5. Output Optical Power Vs. current of the LD ( τ Tun −1 = τ Tun − 2 = 0.2 n sec,τ Tun −3 = 0.3 n sec,τ Tun − 4 = 0.5 n sec ).

Now the transient behavior for current pulse including 2 × I th amplitude and 3 nsec pulse width is investigated for both cases. Fig. 6 and Fig. 7 are for without and with tunneling effect respectively. One can conclude that the transient behavior for nonzero tunneling times is more uniform than zero tunneling case from amplitude point of view and has low turn-on delay time. Especially from rise-time point of view, the situation is better for nonzero tunneling case. In this case, wells approximately fill up simultaneously. Also fall-time for this case is approximately close to previous one.

Lc Inmi T loCi

3.6

wfthoi tunneling eIc1e

3

V1 2.6

6

co

1.6

C)

0.6

U U

1000 2000 3000 4000 6000 6000 7000 8000 9000 10000 Time [ps]

Fig. 6. Carrier Density Transient behavior (without Tunneling).

Proc. of SPIE Vol. 6374 63740Z-8

Lc Inmi T loCi

2.6

wfth tunneling eIc1e

2

ci 6 co

1.6

=

0 C)

0.6

U

1000 2000 3000 4000 6000 6000 7000 8000 9000 10000

U

Time [ps]

Fig. 7. Carrier Density Transient behavior (with Tunneling).

Now the transient behavior of the output power is illustrated for both cases in Fig. 8. For considering the tunneling case, there are advantages such as lowering the turn-on delay time near to 55 Psec, increasing the amplitude of output power, decreasing the relaxation-time and decreasing the fall-time. These improvements in the transient characteristic are related to the tunneling process, which make faster transport of carriers between wells. Therefore, the tunneling possibility and selection of suitable tunneling time constant for each well can improve efficiency of the MQWL. Lc.Thnm

--

ThZ ccl

Ir2Ith

———without tunneling effects

with tunneling effects

U

US

IS

26

3

Time Ens]

Fig. 8. Transient Behavior of the LD.

Finally our simulation is concentrated on the frequency response of the laser diode. In this case with considering tunneling effect the bandwidth is increased more than 2 GHz. This is clearly related to faster dynamics made by the tunneling effect.

Proc. of SPIE Vol. 6374 63740Z-9

Lc200 ]nm]

T20 [oC]

ID

IUU288IUi8i82, Frequency ]GHz]

Fig. 9. Relative intensity vs. frequency.

In this section our simulations including the tunneling effect have been considered. It has shown that with considering the tunneling process, the output intensity is increased that is related to the effect of tunneling on static characteristic (uniform population distribution in wells) of the laser diode. Also, the modulation bandwidth (large and small signals point of views) of the laser is increased. This is related to faster dynamics of carrier transport due to the tunneling effect.

5. CONCLUSION In this paper the effect of tunneling process between wells in MQWL has been investigated. It has been shown that in presence of tunneling, the output intensity and modulation bandwidth can be improved. The circuit model including tunneling effect has been proposed. Our simulations have shown that there is a band for the tunneling time ( 0.01 n sec < τ Tun < 0.1 n sec ) for obtaining better characteristics for MQWL. Our proposal for improving the laser diode performance will be more visible as the number of wells increases.

REFERENCES 1. 2. 3. 4. 5. 6.

Y. Suematsu and A. R. Adams, Handbook of Semiconductor Laser and Photonic Integrated Circuits, London, U.K.: Chapman & Hall, 1994, pp. 1–22. L. V. T. Nguyen, A. J. Lowery, P. C. R. Gurney, and D. Novak, “A time-domain model for high-speed quantumwell lasers including carrier transport effects,” IEEE J. Select. Topics Quantum Electron., vol. 1, pp. 494–504, 1995. R. Nagarajan, T. Fukushima, M. Ishikawa, J. E. Bowers, and R. S . Geels, “Transport limits in high-speed quantumwell lasers: experiment and theory,” IEEE Photonics Technology Letters, vol. 4, no. 2, Feb. 1992. D. McDonald and R. F. O’Dowd, “Comparison of two- and three-level rate equations in the modeling of quantumwell lasers,” IEEE J. Of Quantum Electronics. vol. 31, no. 11, Nov. 1995. J. A. Brum and G. Bastard, “Resonant carrier capture by semiconductor quantum wells,” Phys. Rev. B, vol. 33, pp. 1420-1423, Jan. 1986. B. P. C. Tsou and D. L. Pulfrey, “A versatile SPICE model for quantum-well lasers,” IEEE J. Of Quantum Electronics, vol. 33, no. 2, Feb. 1997.

Proc. of SPIE Vol. 6374 63740Z-10

7.

A. D. Vandermeer and D. T. Cassidy, “A rate equation model of asymmetric multiple quantum-well lasers,” IEEE J. Quantum Electronics, vol. 41, no. 7, July 2005. 8. R. Nagarajan, M. Ishikawa, T. Fukushima, R. S. Geels, and J. E. Bowers, “High speed quantum-well lasers and carrier transport effects,” IEEE J. Quantum Electron., vol. 28, pp. 1990–2007, 1992. 9. L. V. T. Nguyen, A. J. Lowery, P. C. R. Gurney, and D. Novak, “A time-domain model for high-speed quantumwell lasers including carrier transport effects,” IEEE J. Select. Topics Quantum Electron., vol. 1, pp.494–504, 1995. 10. G. Rossi, R. Paoletti, and M. Meliga, “SPICE simulation for analysis and design of fast 1.55 m MQW laser Diodes,”IEEE, J. Of Lightwave Technology, vol. 16, no. 8, Aug. 1998.

Proc. of SPIE Vol. 6374 63740Z-11

A Micro Optical Electromechanical System (MOEMS) for high precision displacement sensor design using ring resonator array A. Rostamia,b, A. Ghanbarib and F. Janabi-Sharific a) Photonics and Nanocrystals Research Lab. (PNRL), Faculty of Electrical Engineering, University of Tabriz, Tabriz 51664, Iran Tel/Fax: +98 411 3393724 E-mail: [email protected] b) Center of Excellence of Mechatronics, University of Tabriz, Tabriz, Tabriz 51664, Iran c) Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada M5B 2K3

ABSTRACT An efficient method for high precision displacement measurement based on micro scale ring resonator and MOEMS is presented. The proposed structure can be used as discrete and integrated sensor in engineering applications. Photo-elastic effect is used to convert the physical displacement to the index of refraction variation in the ring resonator array. Analytical relation for description of system transfer function is derived. Single and multiple ring resonators are examined for increase of the system sensitivity. It is shown that an array of multiple ring resonators (array) is better than single ring case. Effects of optical and geometrical parameters of the proposed structure on sensitivity are studied. Keywords- MOEMS, High Precision Displacement Sensor, Ring Resonator, Photo-elastic Effect.

1. INTRODUCTION In recent years, fiber optical sensors and optical micro-mechatronic systems have moved out of the laboratory and assumed a significant role in sensing, measurement, and control of Optomechatronic systems. These optical techniques are important to a broad range of applications, including biomedicine, environmental sensing, mechanical and industrial measurement and art preservation. Optical techniques have been used for sensors and especially high-precision sensors design [1]. Among all integrated optical elements optical ring resonators are interesting elements for integrated applications from sensors to signal conditioners [2-5]. In this paper, displacement sensor design based on ring resonators is examined. In this paper a micro optical electromechanical system (MOEMS) for high-precision displacement measurement is presented. The proposed method has many advantages over other proposed methods. First, an integrated sensor doesn’t require any alignment while it can be used for wide applications. Second, integrated sensors are suitable due to their compactness, simplicity and potential for mass production. It should also be mentioned that integrated sensors such as piezo-resistive sensors have less sensitivity than external sensors such as optical levers. Using an integrated optical sensor, we expect to achieve sensitivity as high as that of external sensors. Integrated optical devices can be inexpensive and they can be used in harsh environments such as ultra-high vacuum (UHV) systems and electromagnetically active environments. Recently there have been several studies on integrated optic pressure sensors, biosensors, temperature sensors and strain sensors. These sensors consist of an integrated optical device, such as MachZehnder interferometer, a directional coupler and a ring resonator, with transmission characteristics changes due to external effects. In this paper an interesting displacement sensor based on array of ring resonators is investigated. Coupled mode theory for extracting input-output transfer function is used. It is shown that applied displacement introduces stress on the implemented ring resonators and then the changed index of refraction will change the output intensity and frequency response. Based on the output profile and related important characteristics high precision displacement can be measured. For the proposed structure sensitivity in the range of (10−4 − 10−5 ) Ao can be obtained.

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 637410, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.684717

Proc. of SPIE Vol. 6374 637410-1

2. MATHEMATICAL MODELING High-precision micro optical electromechanical displacement sensor is illustrated in Fig. 1. As it is shown N ring resonators coupled together are implemented on the cantilever surface and all coupled to main optical waveguide. External force applies vertical displacement to cantilever that introduces stress in the surface. If material of the ring resonators implemented on the cantilever has high photo-elastic coefficient, thus displacement through applied force will change the index of refraction of the ring resonators. Variation in the index of refraction causes variations in the output intensity and after calibration one can treat inversely and determine displacement based on the output intensity. Now, based on the proposed structure, we will try to evaluate relation between displacement and variation of the index of refraction in the following lines.

Fig. 1: Schematic of the proposed Displacement Sensor (MOEMS high-precision Displacement Sensor). For the proposed structure maximum stress on the surface of the base of the cantilever as a function of tip displacement, z, can be written as

σ max =

3Et z, 2 L2

(1)

where E, t and L are the Young’s Modulus of the cantilever material, thickness and the length of the cantilever respectively. Due to the photo-elastic effect, the index of refraction changes ( neff ) due to the applied stress is as follows.

neff = n0 + ∑ C iσ i ,

(2)

i

where C i and

σ i are the stress optic constants of the ring resonator waveguide and the local stress respectively. Usually

the longitudinal stress in the proposed structure is much larger than transverse stress, and hence it can be neglected. Also, for GaAs longitudinal and transverse stress optic coefficients are 1.7 × 10 −11 Pa −1 and 1 × 10 −11 Pa −1 respectively. Therefore, the index of refraction variation can be approximated as follows.

∆n max = C l σ l ≅ where

3C l Et z, 2L 2

(3)

σ l = σ max and C l are longitudinal stress and stress optics constant respectively.

Here, because of small ring radius, we assume that the applied stress is uniform on the ring resonator. However, in general applied stress would not be uniform for large ring dimensions. In those cases finite element and difference methods can be used for determining stress distribution numerically.

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In this paper we assume that stress distribution is uniform and the following analytical relations can be used for extraction of output intensity. Fig. 2 shows the coupling of some ring resonators with a main optical single mode waveguide. Using coupled mode theory the following relations manage the field near to the coupling regions.

E1 K1 E2

Fig. 2. Detail information about the proposed displacement sensor from coupling point of view

E 2 = 1 − γ 1 [ 1 − k 1 E 1 + j k 1 E 4 ],

(4)

E 3 = 1 − γ 1 [ 1 − k 1 E 4 + j k 1 E 1 ],

(5)

α

E4 = E6 e

− πr 2

α

E5 = E3 e

− πr 2

e − jKπr ,

(6)

e − jKπr ,

(7)

E 6 = 1 − γ 2 [ 1 − k 2 E 5 + j k 2 E 7 ],

(8)

E 8 = 1 − γ 2 [ 1 − k 2 E 7 + j k 2 E 5 ],

(9)

α

− πr 2

e − jKπr ,

(10)

− πr 2 e − jKπr .

(11)

E 7 = E9 e

α

E10 = E8 e

where K 1 , K 2 , γ 1 , γ 2 , α , r , E i and K are the coupling coefficient of first coupler, the coupling coefficient for the second coupler, the coupler loss of first and second couplers, optical loss in ring resonator, radius of the rings, Electric fields in different points, and the propagating wave vectors respectively. These relations should be extended to include N coupled ring resonators. In the following transfer function for the proposed structure can be concluded for different numbers of ring resonators. For single ring resonator, the following relation shows transfer function of the system.

E2 = 1− γ1 [ E1

1 − K 1 − 1 − γ 1e

α

− 2π r 2

1 − (1 − γ 1 )(1 − K 1 )e

e − jK 2π r

α

− 2π r 2

e

],

(12)

− jK 2π r

Also, for double ring resonators coupled together the following relation can be extracted for the transfer function of the system.

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E2 = 1 − γ1 [ 1 − K 1 − E1

K 1 (1 − γ 1 )(1 − γ 2 )[ 1 − K 2 − 1 − γ 2 e 1 − (1 − γ 2 )(1 − K 2 )e

α

− 2π r 2

α

− 2π r 2

e − jK 2π r ]e

α

− 2π r 2

e − jK 2π r

e − jK 2π r − (1 − γ 1 )(1 − K 1 )(1 − γ 2 )(1 − K 2 ) + (1 − γ 2 ) (1 − K 1 )(1 − γ 1 )e

α

− 2π r 2

]

,

(13)

e − jK 2π r

This method can be generalized for N ring resonators coupled together. In the next section, we simulate the extracted relations and illustrate the operation of the proposed sensor.

3. SIMULATION RESULTS AND DISCUSSION In this section based on derived relations for single and doubles ring resonators operation of the optical displacement sensor is demonstrated. For this purpose some simulations are presented and discussed. Transmission coefficient for single ring resonator with and without displacement is illustrated in Fig. 3. As it is illustrated the displacement affects the intensity and frequency response of output, so they can be used for displacement sensing. It is observed that the small coupling coefficient introduces very narrowband and high variation in the amplitude of the output and is excellent for sensor operation. High output signal is a good point for high sensitivity.

0.9

08 07 0.6 0.5 0.4 0.3 0.2 0.1

1.54

1.545

1.55

1.555

\Vavelengtli

1.56

1.565

x

Io

Fig. 3. Transmission coefficient for single ring resonator Vs. Wavelength for without (blue) and with (red) displacement

In the following double ring resonators is examined as displacement sensor. Also, the transmission coefficient for this structure is simulated and illustrated in Fig. 4. We observed that in double ring resonators the sensitivity of the system is increased near to two times. This subject is hold both in amplitude and wavelength shifting. So, it is interesting to see that with increase of the number of rings the sensitivity of the proposed structure is increased. Also, in double ring resonators case there are two transmission forbidden bands occurred around 1.55 um that the single ring case is designed for this wavelength. In this sensor the coupling factor has critical effect on sensitivity, so tuning of this parameter is important.

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0.9 0.8 0.7 0. 6

0. 5 0. 4

0.3 0. 0.

1.53

1.54

1.55

1.56

1.57

1.58

I0

a ci en gti I

Fig. 4. Transmission coefficient for double ring resonator Vs. Wavelength for without (blue) and with (red) displacement

The effect of coupler loss on the transmission coefficient of single and double ring resonators based optical displacement sensor is illustrated in Fig. 5. It is observed that effect of the coupler loss on double ring resonators is so critical compared single ring case.

0.9 0.8 0.7

0.6 0.5 0.4 0.3

Coupler Loss=O.1

Coupler Loss=O.O1 0.2 0.1

1.52

1.53

1.54

1.55

1.56

\Vaveleugtli

1.57

1.58

x I0

Fig. 5. Transmission coefficient for single and double ring resonator Vs. Wavelength including the effect of the coupler loss (blue and red related to double and black related to single ring resonator)

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In double ring case the amplitude is decreased considerable and it is broadened. In the following figure effect of different coupling coefficient on transmission coefficient is investigated and illustrated. It is observed that the first coupling coefficient is critical in operation of the sensor. So, it is constructive to hold the first coupling coefficient in small values. Change of the first coupling coefficient introduces small wavelength shift but considerable decreasing in amplitude. Changes of the second coupling coefficient don’t change the amplitude and only shift the wavelength.

0.9 0.8 0.7 0. 6

0. 5

04 0.3 0.2

1.54

1.545

1.55

1.555

1.56

a ci en gti I

1.565

.57

x I0

Fig. 6. Transmission coefficient for single and double ring resonator Vs. Wavelength including the effect of the different coupling coefficients

As a final simulated result, we considered effect of different coupling coefficient and applied displacement. These are against together. So, it should be considered in sensitivity calculation that these are opposite together.

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(0

P

co

P P

05

P

P P A

Traiinioii Coefficient

P

P Fig. 7. Transmission coefficient for single and double ring resonator Vs. Wavelength including the effect of the different coupling coefficients as well as displacement

4. CONCLUSIONS In this paper a novel optical displacement sensor based on ring resonator implemented on cantilever has been investigated. Transfer function of the proposed sensor was derived analytically. Effect of all parameters on output intensity and frequency response can be analyzed and some of them were considered. We observed that the sensitivity of the proposed sensor with increase of the number of rings is increased. So, the proposed sensor structure is enough flexible for tuning of the sensitivity and one can make trade off between complexity and sensitivity.

REFERENCES 1. W. Suh, O. Solgaard and S. Fan, “Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs,” Journal of Applied Physics Letters, 98, 033102, 2005. 2. A. Rostami and G. Rostami, “Full optical analog to digital converter based on kerr–like nonlinear ring resonator,” Optics Communications, 228 (2003) 39–48. 3. G. Rostami and A. Rostami, “All Optical Integrated Coding System for Optical Analog to Digital (A/D) Converter,” J. Laser Phys. Lett. Vol. 1, No. 8, 1-5 (2004). 4. A. Rostami and G. Rostami, “Integrated Delay Line Using Cross Phase Modulation,” Proc. of IST2003, Isfahan Iran, August 16-18, 2003. 5. A. Rostami and G. Rostami, “All-Optical Implementation of Tunable Lowpass, Highpass and Bandpass Optical Filters Using Ring Resonator,” IEEE Journal of Lightwave Technology, Vol. 23, No. 1, Jan. 2005.

Proc. of SPIE Vol. 6374 637410-7

Tunable dispersion management using thermo optical effect in ring resonator G. Rostamia, b, A. Rostamia and F. Janabi-Sharific a) Photonics and Nanocrystals Research Lab. (PNRL), Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz 51664, Iran Tel/Fax: +98 411 3393724 E-mail: [email protected] b) Optical Communication Group, Communication Technology Institute, Iran Telecommunication Research Center (ITRC), Tehran, Iran c) Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada M5B 2K3

Abstract In optical and optomechatronics applications including hybrid and integrated cases, there are some inherent phenomena such as dispersion, loss and many others that must be critically removed for performance improvement. Among the others, one of the most quantities is dispersion. Dispersion is important in most optical applications such as optical communications including all accessories and optical sensors. Optical pulse broadening and chirping are main disadvantages of dispersion effect. Dispersion cancellation in these applications is crucial. Dispersion compensators are widely spread with many methods for realization of that. In this paper a novel dispersion compensator and management system based on thermo optical effect is introduced. Thermo optical effect and the index of refraction changes due to temperature in ring resonator are used to manipulate dispersion quantity. Thermal source is generated in this case with application of electrical potential on metallic layer coated on ring resonator. Introduced idea is realized using ring resonators and results are presented.

Keywords: All-pass Optical Circuits, Optical Delay Lines, Tunable Dispersion, Optical Filters, Thermo Optic Effect, Ring-Resonator, Tunable Delay Lines

1. INTRODUCTION Dispersion compensators provide an optical block for signal processing in communication and have been considered in several different contexts in Optomechatronic systems. In optical time division multiplexed (OTDM) communication systems and dense wavelength division multiplexing (DWDM), dispersion compensation is required for synchronization purposes and large distance transmission [1]. Also in full optical analog-to-digital (A/D) converter based on nonlinear ring resonator and optical coding system for synchronization between most significant bit (MSB) and least significant bit (LSB) bits delay lines are necessary that can be implemented by this block [2, 3]. For example, in OTDM demultiplexers, optical (A/D) converter, optical coding system, optical logic gates, and local control signals need to be overlapped in time with incoming data signals. Another example that highlighted request for optical tunable delay and dispersion is optical buffering [1]. For any of these applications, it is advantageous to develop a programmable optical delay and dispersion system, where true time delay and dispersion quantities can be varied continuously over large ranges [4, 5].

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 637411, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.693244

Proc. of SPIE Vol. 6374 637411-1

In the area of radio frequency (RF) photonics, broadband phased arrays require true time delay. Phased arrays can create very directional beams, which can be steered by changing the relative phase fed to the different array elements. If these phases are frequency dependent, then different spectral components of broadband transmission will point in different directions, causing degradation of the signal. This phenomenon (known as beam squinting) can be avoided if delays rather than phases are adjusted [6]. In this case, the RF signal is on optical carrier and the delay line is an optical one. In nonlinear optical systems, employing an enhanced delay is also desirable since it increases the effective nonlinear interaction length or interaction time. For example, it has been shown that the effective nonlinearity is enhanced in periodic structures when the propagation is near the stop band, where the group velocity can become very small [7]. In nonlinear cavities, the effective nonlinear length is enhanced due to the large number of roundtrips in the cavity [8, 9]. Single-mode optical fiber is an attractive delay medium for processing microwave frequency signals due to its extremely low loss (0.1 dΒ / µs ) and large available time-bandwidth product. Recent progress in the efficient trapping of light from single-mode fibers has made it possible to construct recirculation and nonrecirculating (tapped) delay-line structures that can perform a variety of important signal processing functions. These functions include coded sequence generation, convolution, correlation, matrix-vector multiplication, and frequency filtering [10]. Also, there are some interesting methods for delay line design based on Integrated Resonance-Enhanced [11], optical filters [12] and cross-phase modulation [13]. However, the presented techniques are so hard for integration and tunability. Most of the presented ideas introduce significant complexity for implementation. For example, in most of the proposed ideas, Fiber Bragg Gratings or optical filters made from Gratings were used that introduces reflection signals. The reflected signals are hard from optical system implementation point of views in practice and forces some additional blocks for compensation. Therefore, a proposal for optical dispersion compensators including large and tunable properties is excellent for integrated optical system designers. The proposed idea uses ring resonator element that has been studied extremely [2, 3, 13-19]. For this purpose, in this paper, we discuss tunable dispersion management using thermo optic phenomenon in integrated and wave optics. With application of electrical signal to metal plate, because of power dissipation, it starts to warm up and increases temperature of the metal and sub optical layers. Therefore, the index of refraction of optical waveguide changes due to applied variable temperature. With change of the refractive index, the group delay can be varied and, hence, tunable group delay and dispersion are introduced. Organization of this paper is as follows. In section 2, we will introduce the mathematical modeling of ring-resonator and its role in the optical dispersions. Simulation results of the proposed system are illustrated in section 3. Finally, the paper ends with a short conclusion.

2. THEORETICAL ANALYSIS OF THE PROPOSED DISPERTION ELEMENT In this section, mathematical background for investigation of the input-output transfer function as well as the effect of control signal is presented. The introduced and applied control signal is electrical that leads to variable temperature that causes variable refractive index and ring resonator length. Special implementation of the method based on ring resonator is illustrated in Fig. (1-a). Finally for more visual conception 3-D and cross sectional view of the idea is demonstrated in Fig. (1-b). Now, after introducing our proposed architecture, the coupled mode theory and Transfer Matrix Method (TMM) developed for ring resonators are used, and based on these methods, an analytical formalism for derivation of interesting quantities are proposed.

Proc. of SPIE Vol. 6374 637411-2

A

a

IiI

a

2

N

N

EDED - ED Ii!

2!

C1

(II

(b)

4 Metal Layer EulTer Layer Optwal Waveguide

layer

(c) Fig. 1. Schematic of the proposed integrated dispersion compensator. (a) Array of ring resonator as a tunable all-optical dispersion; and (b) 3-D and cross sectional illustration of delay line.

Therefore, according o the explained analytical methods and using light propagation in linear medium and matrix formulation, the following relations can be used for the proposed structure. For simplicity, first we present the mathematical relations to manage single ring resonators as well as two main waveguides coupled to the ring. b1 = (1 − γ 1 ) [ 1 − K1 a1 + j K1 a1′ ], a ′ = (1 − γ ) [ 1 − K a + j K b ], 1

1

1 1

1 1

where b1, γ 1, K1, a1 and a1′ are the outgoing and propagating electric field to the right hand side from upper coupler, the dissipation coefficient of the upper coupler, the coupling coefficient, the electric field inside ring near to the upper coupler from left hand and the electric field inside ring near to the upper coupler from right hand sides respectively. Also, one can write

Proc. of SPIE Vol. 6374 637411-3

c1 = (1 − γ 2 ) [ 1 − K 2 d1 + j K 2 a2 ], a2′ = (1 − γ 2 ) [ 1 − K 2 a2 + j K 2 d1 ],

where c1, γ 2 , K 2 , a2 and a2′ are outgoing electric field to the left hand side from the bottom coupler, the dissipation coefficient of the bottom coupler, the coupling coefficient, the electric field inside ring near to the bottom coupler from right hand and the electric field inside ring near to the upper coupler from left hand sides respectively. Also, the following equations are given for inside ring electric fields components. α

L

α

L

− L − jK n 2, a2 = a1′e 4 e − L − jK n 2, a1 = a2′e 4 e

where α i and K n =

2π

λ

n are the ring attenuation coefficient and propagating wave vector inside ring respectively.

Eqs. (1, 2) based on above mentioned basic relations are presented to demonstrate light propagation through the couplers between ring and two main optical waveguides. α

b1 =

(1 − γ 1 )(1 − K1 ) − (1 − γ 1 ) (1 − γ 2 )(1 − K 2 ) e

− L 2 e − jK n L

α

1 − (1 − γ 1 )(1 − K1 )(1 − γ 2 )(1 − K 2 (1 − γ 1 )(1 − γ 2 ) K1K 2

− L ) e 2 e − jK n L

K α − L −j nL 4 e e 2

α

1 − (1 − γ 1 )(1 − K1 )(1 − γ 2 )(1 − K 2

− L ) e 2 e − jK n L

a1 −

(1)

d1,

α

(1 − γ 1 )(1 − K1 ) − (1 − γ 1 ) (1 − γ 2 )(1 − K 2 ) e

c1 =

α

1 − (1 − γ 1 )(1 − K1 )(1 − γ 2 )(1 − K 2 (1 − γ 1 )(1 − γ 2 ) K1K 2

−

2π

λ

− L ) e 2 e − jK n L

K α − L −j nL 4 e e 2

α

1 − (1 − γ 1 )(1 − K1 )(1 − γ 2 )(1 − K 2

where γ i , K i , L, α i and K n =

− L 2 e − jK n L

− L ) e 2 e − jK n L

d1 −

(2)

a1,

n are loss in the couplers, the coupling coefficient, ring length, the attenuation

coefficient of the ring and the traveling wave vector (n is the refractive index inside ring) respectively. For simplification of the relations and matrix formulation the following definitions can be made. b TTransmission1 = 1 , a1 d1 = 0

(3)

c R1 = 1 . a1 d1 = 0

(4)

Proc. of SPIE Vol. 6374 637411-4

where TTransmission1 and R1 are transmission and reflection coefficients respectively. Now based on definitions presented above and using matrix formalism, the following relation is presented for transport matrix for the light propagation through the proposed structure.

⎡a1 ⎤ 1 ⎢c ⎥ = ⎣ 1 ⎦ TTransmission1

− R1

⎡1 ⎢ ⎢⎣ R1

2 Transmission1

T

⎤ ⎡b1 ⎤ , ⎥ − R ⎥⎦ ⎣⎢d 1 ⎦⎥ 2 1

(5) Now for generalization of the presented relation, the distance between first and second rings should be incorporated in the calculations. α

Λ

b1 = e 2 e jK n Λ a2 ,

(6)

α

d1

− Λ = e 2 e − jK n Λ c

2,

where Λ is distance between rings. As in a conventional grating, for constructive interference of the reflected waves from each ring to occur within the pass-band, we require that the periodic spacing Λ to be equal to an odd multiple of a quarter wavelengths Λ = ( 2 M + 1)

where nW and

λ0

λ0 4nW

, ( M = 0,1,...) ,

(7)

are the optical waveguide refractive index and central wavelength respectively. Transfer Matrix

formulation of an array of N ring resonators can be derived as follows. ⎡bN ⎤ ⎡a1 ⎤ N ⎢c ⎥ = ∏ (TDi TPi ) ⎢d ⎥, ⎣ 1 ⎦ m =1 ⎣ N⎦

(8)

where TDi =

1 TTransmissioni

TTransmissioni = Ri =

⎡1 ⎢ ⎢⎣ Ri

− Ri ⎤ ⎥, Ti2 − Ri2 ⎥⎦

bi , ai d i = 0

ci , ai d i = 0

⎡ αΛ ⎢ e 2 e jK n Λ 0 TPi = ⎢ α ⎢ − Λ ⎢⎣ 0 e 2 e − jK n Λ

(9) ⎤ ⎥ ⎥. ⎥ ⎥⎦

After some simplification applied on Eq. (8), the matrix formulation of the light propagation through array of ring resonators can be explained in terms of a 2 × 2 matrix as follows.

Proc. of SPIE Vol. 6374 637411-5

⎡bN ⎤ ⎡a1 ⎤ ⎢ c ⎥ = H ⎢ d ⎥, ⎣ 1⎦ ⎣ N⎦

⎛ h11 H = ⎜⎜ ⎝ h21

h12 ⎞ ⎟, h22 ⎟⎠

(10) System intensity transfer functions including the transmission and reflection coefficients can be obtained as follows. TTransmission = R=

bN , a1 d N = 0

c1 , a1 d N = 0

(11) In the following, effect of temperature on transfer function quantities is investigated. For this purpose the following definition are done. Therefore, there is a linear relation between temperature and controlling signal. L = L0 +

∂L (T − T0 ), ∂T T0

(12)

∂n n = n0 + (T − T0 ), ∂T T0

Using electrical equivalent circuit of metal plate on buffer layer, generated temperature is function of applied voltage and circuit parameters that is illustrated in the following. Tem. = f (VControl (t )),

(13)

Therefore, the following relation is calculated that is an important part of the derived relations incorporating temperature effect on transfer function. Θ = K n L = [ K n0 L0 + ( K n0

2π ∂n 2π ∂n ∂L ∂L + L0 )(T − T0 ) + ( )( )( )(T − T0 ) 2 ], λ ∂T λ ∂T ∂T ∂T

(14)

As an especial case, we consider in the following single stage two port ring resonator. Using developed transfer matrix formalism, the transmission ( TTransmission ), reflection ( R ) coefficients, phase difference ( Φ Transmission , Φ R ) and the group ( τ DT ,τ DR ) delay are derived analytically as follows. −

TTransmission =

α

−

L

α

L

(1 − γ 1 )(1 − K1 ) − (1 − γ 1 ) (1 − γ 2 )(1 − K 2 ) e 2 cos(Θ) + j (1 − γ 1 ) (1 − γ 2 )(1 − K 2 ) e 2 sin( Θ) , −

α

−

L

α

L

1 − (1 − γ 1 )(1 − K1 )(1 − γ 2 )(1 − K 2 ) e 2 cos(Θ) + j (1 − γ 1 )(1 − K1 )(1 − γ 2 )(1 − K 2 ) e 2 sin(Θ)

R=

− (1 − γ 1 )(1 − γ 2 ) K1K 2 e 1 − (1 − γ 1 )(1 − K1 )(1 − γ 2 )(1 − K 2 ) e

−

α 2

L

−

α 4

L

Θ Θ (cos( ) − j sin( )) 2 2

cos(Θ) + j (1 − γ 1 )(1 − K1 )(1 − γ 2 )(1 − K 2 ) e

Proc. of SPIE Vol. 6374 637411-6

, −

α 2

L

sin( Θ)

(16)

(15)

(1 − γ 1 ) (1 − γ 2 )(1 − K 2 ) e

Φ Transmission = tan −1[

−

α 2

L

sin(Θ)

(1 − γ 1 )(1 − K1 ) − (1 − γ 1 ) (1 − γ 2 )(1 − K 2 ) e tan −1[

(1 − γ 1 )(1 − γ 2 )(1 − K1 )(1 − K 2 ) e

−

1 − (1 − γ 1 )(1 − γ 2 )(1 − K1 )(1 − K 2 ) e

Θ Φ R = π − − tan −1[ 2

α 2 −

L

α 2

sin(Θ) L

α 2

]− L

cos(Θ)

(17)

],

cos(Θ)

(1 − γ 1 )(1 − γ 2 )(1 − K1 )(1 − K 2 ) e

−

α

1 − (1 − γ 1 )(1 − γ 2 )(1 − K1 )(1 − K 2 ) e

τ DT = −

−

2 −

L

α 2

sin(Θ) L

],

(18)

cos(Θ)

∂Φ Transmission , ∂ω ∂Φ τ DR = − R . ∂ω

(19)

(20)

For calculation of these quantities, the following relations are defined. P1 = (1 − γ 1 ) (1 − γ 2 )(1 − K 2 ) e

−

α 2

L

,

P2 = (1 − γ 1 )(1 − K1 ) , P3 = (1 − γ 1 )(1 − γ 2 )(1 − K1 )(1 − K 2 ) e

(21) −

α 2

L

,

So, using Eq. (15) and Eq. (16), we can write Φ Transmission = tan −1[

P1 sin(Θ) P sin(Θ) ] − tan −1[ 3 ], P2 − P1 cos(Θ) 1 − P3 cos(Θ)

P sin(Θ) Θ Φ R = π − − tan −1[ 3 ]. 2 1 − P3 cos(Θ)

(22)

The following final relations for group delay of the reflection and transmission coefficients can be obtained using Eq. (22). ∂Φ ∂Θ τ DT = − T ⋅ , ∂Θ ∂ω (23) ∂Φ R ∂Θ τ DR = − , ⋅ ∂Θ ∂ω where Φ T , Φ R and Θ are defined as follows. ⎡ P 2 − P1P2 cos Θ ⎤ ∂Φ Transmission P32 − P3 cos Θ ⎥ = −⎢ 2 1 2 + , ⎢ P + P2 − 2 P1 cos Θ 1 + P32 − 2 P3 cos Θ ⎥ ∂Θ ⎣ 1 ⎦ ∂Φ R − 1 ⎡ 1 − P3 cos Θ ⎤ = ⎢ ⎥, ∂Θ 2 ⎢⎣ 1 + P32 − 2 P3 cos Θ ⎦⎥

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(24)

∂Θ 1 ∂L ∂n ∂n ∂L = ( )[n0 L0 + ( n0 + L0 )(T − T0 ) + ( )( )(T − T0 ) 2 ]. ∂ω c ∂T ∂T ∂T ∂T

(25)

Based on the proposed relations for delay times, dispersion quantities can be obtained easily ( D = ∂τ ). In the ∂ω following sections simulation results of the introduced system of equations are discussed. Also, based on the proposed relations other interesting quantities such as dispersion relations and group velocity can be extracted that can be used for special applications. In the next section, based on the obtained relations numerical evaluations are presented and discussed.

3. SIMULATION RESULTS In this section, the proposed device with single and two stages is investigated from the control of delay time perspective. First general behavior of the proposed structure and it dependency to the structural parameters is considered. Figs. (2-5) show the transmission and reflection coefficients versus wavelength for the different coupling and loss coefficients. With decrease of the coupling and loss coefficients, the obtained filter will be sharp with small bandwidth. This is acceptable, because with increase of the coupling coefficient, most part of incident power couples to the ring and with change of the incident wavelength there is small sensitivity for the variation of the output power. For simulation, we considered GaAs as basic material for implementation of the proposed ring resonators and optical waveguides. For GaAs and InP the index of refraction and the temperature ( T ) coefficients are given in Table 1. For other materials also the parameters can be used from handbooks. Table 1. Simulation parameters of GaAs and InP. n ∂n ∂T

Matter

3 .6 3 .4

GaAs InP

2.17 × 10 −4 / 0 C

∂L ∂T 6 × 10 −6 / 0 C

2.19 × 10 −4 / 0 C

4.56 × 10 −6 / 0 C

1

k1=k2=0.01 k1=k2=0.05 k1=k2=0.2 k1=k2=0.5

0.9

Transmission Coefficient

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.55

1.555

1.56

1.565

1.57

1.575

1.58

λ

1.585

1.59 -6

x 10

Fig. 2. Transmission (absolute value) coefficient vs. wavelength (single Ring) ( 1 − K1 = K 2 = 0.01, 2 − K1 = K 2 = 0.05, 3 − K1 = K 2 = 0.2,4 − K1 = K 2 = 0.5 ).

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Also, the effects of the dissipation in the couplers on the transmission and reflection coefficients are illustrated in Fig. (3, 5). With increase of the dissipation coefficient, as it is described for the coupling coefficient, the designed filter is broadened. 1

γ1=γ2=0 γ1=γ2=0.05 γ1=γ2=0.2 γ1=γ2=0.5

0.9

Transmission Coefficient

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.55

1.555

1.56

1.565

1.57

1.575

1.58

1.585

λ

1.59 -6

x 10

Fig. 3. Transmission (absolute value) coefficient vs. wavelength (single Ring). (Effect of the attenuation coefficient of the coupler) (1 − γ 1 = γ 2 = 0 , 2 − γ 1 = γ 2 = 0.05, 3 − γ 1 = γ 2 = 0.2, 4 − γ 1 = γ 2 = 0.5) 1 k1=k2=0.01 k1=k2=0.05 k1=k2=0.2 k1=k2=0.5

0.9

Reflection Coefficient

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.55

1.552

1.554

1.556

1.558

1.56

λ

1.562

1.564 -6

x 10

Fig. 4. Reflection (absolute value) coefficient vs. wavelength (single Ring) ( 1 − K1 = K 2 = 0.01, 2 − K1 = K 2 = 0.05, 3 − K1 = K 2 = 0.2,4 − K1 = K 2 = 0.5 )

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1

γ1=γ2=0 γ1=γ2=0.05 γ1=γ2=0.1 γ1=γ2=0.3

Reflection Coefficient

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.55

1.552

1.554

1.556

1.558

1.56

λ

1.562

1.564 -6

x 10

Fig. 5. Reflected (absolute value) coefficient vs. wavelength with attenuation coefficient of the coupler (for single Ring) (1 − γ 1 = γ 2 = 0 , 2 − γ 1 = γ 2 = 0.05, 3 − γ 1 = γ 2 = 0.1, 4 − γ 1 = γ 2 = 0.2) .

The variation of the phase difference for the transmission coefficient is demonstrated in Fig. 6. The phase variation is changed suddenly near to the resonance wavelength with decrease of the coupling coefficient. Because in small coupling coefficient, small part of incident light is coupled to the ring, outgoing light is governed by the incident light not by combination of incident light and light coupled from ring to the upper waveguide. Hence, the phase of the outgoing light is nearly uniform. But in resonance wavelength because of sudden coupling of the incident light to the ring, the output light phase changes suddenly. The following graphs show that the phase difference can be controlled with the coupling parameter and coupler dissipation. 3.5

Transmitted Phase

3

k1=k2=0.01 k1=k2=0.05 k1=k2=0.1 k1=k2=0.3

2.5

2

1.5

1

0.5

0 1.551 1.5512 1.5514 1.5516 1.5518 1.552 1.5522 1.5524 1.5526 1.5528 1.553

λ

-6

x 10

Fig. 6. Phase difference of transmitted light vs. wavelength with coupling parameter (for single Ring) (1 − K1 = K 2 = 0.01, 2 − K1 = K 2 = 0.05, 3 − K1 = K 2 = 0.1, 4 − K1 = K 2 = 0.3) .

Also, the group delay time of the designed device is illustrated in Fig. 7. It shows that the group delay time can be controlled with the coupling parameter and coupling dissipation coefficient, but control of the coupling parameter is hard from practical point of view. Also if the coupler dissipation parameter can be controlled, a tunable optical delay line is achieved.

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-10

x 10

k1=k2=0 k1=k2=0.05 k1=k2=0.03 k1=k2=0.1

3.5 3

Group Delay

2.5 2 1.5 1 0.5 0 1.5513

1.5514

1.5515

1.5516

1.5517

λ

1.5518 -6

x 10

Fig. 7. Delay time of transmission coefficient vs. wavelength with coupling parameter (for single Ring) (1 − K1 = K 2 = 0.01, 2 − K1 = K 2 = 0.03, 3 − K1 = K 2 = 0.05, 4 − K1 = K 2 = 0.1)

Also, the group velocity of the designed device is illustrated in the Fig. 8. It shows that the group velocity can be controlled with the coupling parameter and the coupler dissipation coefficient. 13

4

x 10

k1=k2=0.01 k1=k2=0.03 k1=k2=0.05 k1=k2=0.1

3.5

Group Velocity

3 2.5 2 1.5 1 0.5 0 1.551 1.5512 1.5514 1.5516 1.5518 1.552 1.5522 1.5524 1.5526 1.5528 1.553

λ

-6

x 10

Fig. 8. Normalized group velocity of transmission coefficient vs. wavelength with coupling parameter (for single Ring) (1 − K1 = K 2 = 0.01, 2 − K1 = K 2 = 0.03, 3 − K1 = K 2 = 0.05, 4 − K1 = K 2 = 0.1) .

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13

4

Group Velocity

3.5 3

x 10

γ1=γ2=0 γ1=γ2=0.01 γ1=γ2=0.02 γ1=γ2=0.03

2.5 2 1.5 1 0.5 0 1.551 1.5512 1.5514 1.5516 1.5518 1.552 1.5522 1.5524 1.5526 1.5528 1.553

λ

-6

x 10

Fig. 9. Normalized group velocity of transmission coefficient vs. wavelength with attenuation coefficient of the coupler (for single Ring) (1 − γ 1 = γ 2 = 0 , 2 − γ 1 = γ 2 = 0.01, 3 − γ 1 = γ 2 = 0.02, 4 − γ 1 = γ 2 = 0.03) .

Also, the dispersion factor of the designed device is illustrated in Figs. (10, 11). The results show that dispersion factor can be controlled with the coupling coefficient and the coupler dissipation coefficient. High level variation of the dispersion factor is obtained by small coupling and dissipation parameters. Also, the coupling and dissipation coefficients have same effect on the dispersion factor. Near to the resonance wavelength, anomalous dispersion is observed. k1=k2=0.01 k1=k2=0.015 k1=k2=0.02 k1=k2=0.025

20 15

Dispersion Factor

10 5 0 -5 -10 -15 -20 1.5515

1.5515

1.5516

1.5516

1.5517

λ

1.5517 -6

x 10

Fig. 10. Dispersion of transmission coefficient vs. wavelength with coupling parameter (for single Ring) (1 − K1 = K 2 = 0.01, 2 − K1 = K 2 = 0.015, 3 − K1 = K 2 = 0.02, 4 − K1 = K 2 = 0.025) .

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γ1=γ2=0 γ1=γ2=0.01 γ1=γ2=0.015 γ1=γ2=0.02

20

Dispersion Factor

15 10 5 0 -5 -10 -15 -20 1.5515

1.5515

1.5516

1.5516

1.5517

1.5517

λ

1.5518 -6

x 10

Fig. 11. Dispersion of transmission coefficient vs. wavelength with attenuation coefficient of the coupler (for single Ring) (1 − γ 1 = γ 2 = 0 , 2 − γ 1 = γ 2 = 0.01, 3 − γ 1 = γ 2 = 0.015, 4 − γ 1 = γ 2 = 0.02)

With control of the electrical signal on the bottom layer, temperature in optical waveguide is tuned. The effect of temperature on transfer function in frequency domain is illustrated in Fig. 12. With increase of temperature, the transfer function is shifted to higher wavelengths. Hence, this characteristic of the proposed structure can be used for implementation of tunable delay time. -10

x 10

dT=0 dT=0.3 dT=0.5 dT=1

3.5

Group Delay

3 2.5 2 1.5 1 0.5 0 1.5514 1.5515 1.5515 1.5516 1.5516 1.5517 1.5517 1.5518 1.5518 1.5519

λ

-6

x 10

Fig. 12. Delay time of transmission coefficient vs. wavelength with controlling signal that changes temperature parameter (for single Ring) 1 − ∆T = 0 0C , 2 − ∆T = 0.3 0C , 3 − ∆T = 0.5 0C , 4 − ∆T = 1 0C .

Also, in the following figure, normalized group velocity is illustrated and the effect of control signal on this curve is demonstrated. Tunable dispersion factor due to temperature variation is illustrated in Figs. (13, 14). It is shown that with increase of the applied control signal, generated temperature dispersion curve is shifted to the higher wavelengths.

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dT=0 dT=0.1 dT=0.2 dT=0.3

20 15

Dispersion Factor

10 5 0 -5 -10 -15 -20 -25 1.5514

1.5515

1.5515

1.5516

1.5516

1.5517

1.5517

λ

1.5518

1.5518 -6

x 10

Fig. 13. Dispersion of transmission coefficient vs. wavelength with controlling signal that changes temperature parameter (for single Ring) 1 − ∆T = 0 0C , 2 − ∆T = 0.1 0C , 3 − ∆T = 0.2 0C , 4 − ∆T = 0.30C . dT=0 dT=0.1 dT=0.5 dT=1

20 15

Dispersion Factor

10 5 0 -5 -10 -15 -20 -25 1.5515 1.55151.5516 1.55161.55171.5517 1.55181.5518 1.55191.5519

λ

-6

x 10

Fig. 14. Dispersion of transmission coefficient vs. wavelength with controlling signal that changes temperature parameter (for single Ring) 1 − ∆T = 0 0C , 2 − ∆T = 0.1 0C , 3 − ∆T = 0.5 0C , 4 − ∆T = 10C .

Finally the effect of temperature on delay time for two ring resonators is illustrated in Fig. 15. It is shown that with increase of the number of ring resonators, wavelength shift raises and finally the sensitivity of the proposed structure is increased. On the other hand with low value of the control signal, tuning in a wide range can be readily done.

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-9

x 10

dT=0 dT=0.1 dT=0.3 dT=0.5

Delay Time for Two Ring Resonators

7 6 5 4 3 2 1

0 1.5512 1.5513 1.5514 1.5515 1.5516 1.5517 1.5518 1.5519 1.552 1.5521

λ

-6

x 10

Fig. 15. Delay time of transmission coefficient vs. wavelength with controlling signal that changes temperature parameter (for two cascode Ring) 1 − ∆T = 0 0C , 2 − ∆T = 0.1 0C , 3 − ∆T = 0.3 0C , 4 − ∆T = 0.5 0C .

4. CONCLUSION The realization of a ring-resonator fiber-optical delay line filter for synchronization of optical signal processing systems and dispersion compensation has been presented. The group delay and dispersion value of the device can be easily controlled by applying control signal to top layer of the proposed device. The easy integration in a transmission system is a benefit that is not obtained by planar or bulk-optic components. In further investigations, the capability of the device has to be proven in system experiments. The sensitivity of the proposed structure can be increased using a large number of ring resonators.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.

R. Ramaswami and K. N. Sivarajan,Optical Networks: A Practical Perspective, San Francisco, CA: Morgan Kaufmann, 1998. A. Rostami and G. Rostami, “Full optical analog to digital converter based on kerr–like nonlinear ring resonator,” Optics Communications 228, 39–48.(2003). G. Rostami and A. Rostami, “All optical integrated coding system for optical analog to digital (A/D) converter,” J. Laser Phys. Lett. , 1(8), 1-5 (2004). K. Deng, K. Kang, I. Glask, P. Prucnal, “A 1024-channel fast tunable delay line for ultrafast all-optical TDM networks, “ IEEE Photon. Technol. Lett., 9, 1496-1499 (1997). K. Jinguji, N. Takato, Y. Hida, T. Kitoh, and M. Kawachi, “Two-port optical wavelength circuit composed of cascaded Mach-Zehnder Interferometers with point-symmetrical configurations,” IEEE J. Lightwave Technol. 10, 14.Oct.1996, 2301-2310 (1996). I. Frigyes and A. J. Seeds, “Optically generated true-time delay in phased-array antennas,” IEEE Trans. Microwave Theory Tech., 43, 2378 (1995). B. J. Eggleton, C. M. deSterke, and R. E. Slusher, “Bragg solutons in the nonlinear Schrodinger limit: Experiment and theory,” J. Opt. Soc. Am.B—Opt. Phys., 16, 587 (1999). J. E. Heebner and R. W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett., 24, 847 (1999).

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R. E. Slusher, S. Spalter, B. J. Eggleton, and S. Pereira, “Bragg-grating enhanced polarization instabilities,” Opt. Lett., 25, 749 (2000). 10. K .P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman and H. J. Shaw, “Optical fiber delay-line signal processing” IEEE Transaction on Microwave Theory and Technologies, MMT-33(3), (1985). 11. M. S. Rasras, Ch. K. Madsen, M. A. Cappuzzo, E. Chen, L. T. Gomez, E. J. Laskowski, A. Griffin, A. Wong-Foy, A. Gasparyan, A. Kasper, J. L. Grange, and S. S. Patel, “Integrated resonance-enhanced variable optical delay lines,” IEEE Photonics Technology Lett., 17(4), (2005). 12. G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, “Optical delay lines based on optical filters,” IEEE J. Quantum Electronics, 37(4), (2001). 13. A. Rostami and G. Rostami, “Integrated delay line using cross phase modulation,” Proc. of IST2003, Isfahan Iran, (2003). 14. A. Rostami and G. Rostami, “All-optical implementation of tunable lowpass, highpass and bandpass optical filters using ring resonator,” IEEE Journal of Lightwave Technology, 23(1). 15. A. Rostami and G. Rostami, “Optical transmission properties of light propagation through Fibonacci-class ringresonators,” Eur. Phys. J. B 47, 137-143 (2005). 16. G. Rostami and A. Rostami, “A novel structure for optical filters using special ensembles of ring-resonators,”, IL Nouvo Cimento B, 2005. 17. G. Rostami and A. Rostami, “Stability performance analysis of the optical engineering systems designed by single pole and zero blocks,” Proc. of IEEE (ICCC2004) Beijing, China, Sep.2004. 18. G. Rostami and A. Rostami, ““A new tructure for optical integrated digital filters using ring resonators,” Proc. of IEEE (APCC2004), Beijing, China.G. Rostami and A. Rostami, “All-optical pole and zero blocks for implementation of optical engineering systems,” Proc. of IEEE (APCC2004), Beijing, China. 9.

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