Microwave Radiometer Systems Design and Analysis Second Edition
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Microwave Radiometer Systems Design and Analysis Second Edition
Niels Skou David Le Vine
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Library of Congress Cataloging-in-Publication Data Skou, Niels, 1947– Microwave radiometer systems: design and analysis/Niels Skou, David Le Vine.—2nd ed. p. cm.— (Artech House Remote Sensing library) Includes bibliographical references and index. ISBN 1-58053-974-2 (alk. paper) 1. Radiometers—Design and construction. 2. Microwave detectors. I. Le Vine, D. M. II. Title. III. Artech House remote sensing library. TK7876.S5767 2006 621.381’3—dc22 2005057085
British Library Cataloguing in Publication Data Skou, Neils, 1947– Microwave radiometer systems: design and analysis.—2nd ed.—(Artech House remote sensing library) 1. Radiometers—Design and construction 2. Microwave detectors I. Title II. Le Vine, David 621.3’813
ISBN 1-58053-974-2 Cover design by Igor Valdman
© 2006 ARTECH HOUSE, INC. 685 Canton Street Norwood, MA 02062 All rights reserved. Printed and bound in the United States of America. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. All terms mentioned in this book that are known to be trademarks or service marks have been appropriately capitalized. Artech House cannot attest to the accuracy of this information. Use of a term in this book should not be regarded as affecting the validity of any trademark or service mark. International Standard Book Number: 1-58053-974-2 Library of Congress Catalog Card Number: 2005057085 10 9 8 7 6 5 4 3 2 1
Contents Preface
xi
1
Introduction References
1 2
2
Summary
3
3
The Radiometer Receiver: Sensitivity and Accuracy
7
3.1
What Is a Radiometer Receiver?
7
3.2
The Sensitivity of the Radiometer
7
3.3
Absolute Accuracy and Stability References
9 11
4
Radiometer Principles
13
4.1
The Total Power Radiometer (TPR)
13
4.2
The Dicke Radiometer (DR)
14
4.3
The Noise-Injection Radiometer (NIR)
16
4.4
The Correlation Radiometer (CORRAD)
18
4.5
Hybrid Radiometer
20
v
vi
Microwave Radiometer Systems: Design and Analysis
4.6
Other Radiometer Types
21
References
22
5
Radiometer Receivers on a Block Diagram Level
25
5.1 5.1.1
Receiver Principles Direct or Superheterodyne
25 25
5.1.2
DSB or SSB with or without RF Preamplifier
26
5.2 5.2.1
Dicke Radiometer Microwave Part
27 27
5.2.2 5.2.3 5.2.4
The Noise Figure and the Sensitivity of the Radiometer The IF Circuitry and the Detector The Extreme Signal Levels
29 30 32
5.2.5 5.2.6 5.2.7
The LF Circuitry The Analog-to-Digital Converter On the Sampling in the Radiometer: Aliasing
33 34 37
5.3
The Noise-Injection Radiometer
38
5.4
The Total Power Radiometer
40
5.4.1
DSB Receiver without RF Preamplifier
40
5.4.2
SSB Receiver with RF Preamplifier
42
5.5
Stability Considerations
43
References
44
6
The DTU Noise-Injection Radiometers Example References
47 53
7
Polarimetric Radiometers
55
7.1
Polarimetry and Stokes Parameters
55
7.2
Radiometric Signatures of the Ocean
57
7.3 7.3.1 7.3.2
Four Configurations Polarization Combining Radiometers Correlation Radiometers
57 57 60
7.4
Sensitivities
62
7.5
Discussion of Configurations
64
Contents
7.6
vii
The DTU Polarimetric System
64
References
68
8
Synthetic Aperture Radiometer Principles
69
8.1
Introduction
69
8.2
Practical Considerations
72
8.2.1 8.2.2 8.2.3
RF Processing Basic Equation Image Processing
72 73 74
8.2.4
Sensitivity
75
8.3
Example References
76 78
Selected Bibliography
79
9
Calibration and Linearity
81
9.1
Why Calibrate?
81
9.2
Calibration Sources
82
9.3
Example: Calibration of a 5-GHz Radiometer
86
9.4
Linearity Measured by Simple Means
87
9.4.1 9.4.2 9.4.3
Background Simple Three-Point Calibration Linearity Checked by Slope Measurements
88 89 92
9.4.4
Measurements
93
9.5
Calibration of Polarimetric Radiometers References
96 98
10
Sensitivity and Stability: Experiments with Basic Radiometer Receivers
99
10.1
Background
99
10.2
The Radiometers Used in the Experiments
100
10.3
The Experimental Setup
101
10.4
5-GHz Sensitivity Measurements
102
viii
Microwave Radiometer Systems: Design and Analysis
10.5
Stability Measurements
103
10.5.1 10.5.2
Discussion of the 5-GHz DR Results The 5-GHz DR with Correction Algorithm
103 105
10.5.3
The 17-GHz NIR Results
109
10.5.4 10.5.5
Discussion of the TPR Results Back-End Stability
111 113
10.6
Conclusions References
114 115
11
Radiometer Antennas and Real Aperture Imaging Considerations
117
11.1
Beam Efficiency and Losses
117
11.2
Antenna Types
119
11.3
Imaging Considerations
121
11.4
The Dwell Time Per Footprint Versus the Sampling Time in the Radiometer
125
11.5
Receiver Considerations for Imagers References
130 131
12
Relationships Between Swath Width, Footprint, Integration Time, Sensitivity, Frequency, and Other Parameters for Satellite-Borne, Real Aperture Imaging Systems
133
12.1
Mechanical Scan
134
12.2
Push-Broom Systems
139
12.3
Summary and Discussion
140
12.4
Examples
143
12.4.1 12.4.2 12.4.3
General-Purpose Multifrequency Mission Coastal Salinity Sensor Realistic Salinity Sensor
143 143 144
13
First Example of a Spaceborne Imager: A General-Purpose Mechanical Scanner
147
Background
147
13.1
Contents
ix
13.2
System Considerations
149
13.2.1 13.2.2
General Geometric and Radiometric Characteristics Instrument Options
149 152
13.2.3
Baseline Instrument Specifications
156
13.2.4
Instrument Layout and Receiver Type
156
13.3
Receiver Design
157
13.3.1 13.3.2 13.3.3
The Direct Receivers (10.65–36.5 GHz) The 89-GHz DSB Receivers Integrated Receivers: Weight and Power
157 158 159
13.3.4 13.3.5
Performance of the Receivers Critical Design Features
160 161
13.4
Antenna Design
163
13.5 13.5.1 13.5.2
Calibration and Linearity Prelaunch Radiometric Calibration On-Board Calibration
165 165 166
13.6 13.6.1 13.6.2
System Issues System Weight and Power Data Rate
167 167 168
13.7
Summary References
169 170
14
Second Example of a Spaceborne Imager: A Sea Salinity/Soil Moisture Push-Broom Radiometer System 171
14.1
Background
171
14.2
The Brightness Temperature of the Sea
172
14.3
The Brightness Temperature of Moist Soil
175
14.4 14.4.1 14.4.2
User Requirements for Geophysical and Spatial Resolution Salinity Measurements Soil Moisture Measurements
177 177 177
14.5 14.5.1 14.5.2
A 1.4-GHz Push-Broom Radiometer System Sensitivity Considerations The 1.4-GHz Noise-Injection Radiometer Receiver
177 177 178
x
Microwave Radiometer Systems: Design and Analysis
14.5.3
Antenna Considerations
181
14.5.4
Layout of the System
181
14.6
Calibration
184
14.7 14.7.1 14.7.2
A Disturbing Factor: The Faraday Rotation The Faraday Rotation Correction Based on Knowing the Rotation Angle
186 186 187
14.7.3 14.7.4 14.7.5
Correction Based on the Polarization Ratio Consequences for Instrument Design Circumventing the Problem by Using the First Stokes Parameter
189 191 191
14.8 14.8.1 14.8.2
Other Disturbing Factors: Space and Atmosphere Space Radiation Atmospheric Effects
192 192 193
14.9
Summary References
193 194
15
Examples of Synthetic Aperture Radiometers
197
15.1
Introduction
197
15.2
Implementation of Synthesis
198
15.3
Airborne Example: ESTAR
200
15.3.1 15.3.2 15.3.3
Hardware Image Reconstruction Calibration
200 204 205
15.3.4 15.3.5
Discussion Example of Imagery
207 208
15.4
Spaceborne Examples
211
15.4.1 15.4.2
HYDROSTAR SMOS References
211 214 217
Acronyms
219
Index
221
Preface Two important microwave remote sensors are the radar and the radiometer. There have been a number of books written on various aspects of radar, but there have been only a few written on microwave radiometers, especially on subjects of how to design and build radiometer systems. This book, which is the second edition of a book originally published in 1989, attempts to fill this void. The background for this book is many years of work with radiometer systems including design and manufacture of airborne imaging radiometer systems, laboratory as well as airborne field experiments with the systems, and design of future spaceborne imagers. This book would not have been possible without the support and encouragement of several colleagues. Søren Nørvang Madsen, who is working with synthetic aperture radar systems, and, before him, Finn Søndergaard have both contributed much to the work with radiometer systems through many fruitful discussions and via joint airborne experiments. Much support was received from Professor P. Gudmandsen, especially in the initial phases. The value of fruitful interaction with Ph.D. students like Brian Laursen and Sten Søbjærg also cannot be overestimated. Finally, the partnership with Calvin Swift and several of his students in the development of the synthetic aperture radiometer, ESTAR, provided invaluable learning that helped make this book possible.
xi
1 Introduction This book is the second edition of the book originally published in 1989. The reason for updating the book is twofold: Certain issues are outdated, and new developments and concepts have emerged. Of course, all the basic principles and concepts are still valid, and parts of the chapters are largely unchanged from the first edition. However, when it comes to practical examples, like for example, the design of a spaceborne radiometer system, significant technology developments must be taken into account: A spaceborne radiometer will hardly still be assembled using individual waveguide components, but it will be implemented using Monolithic Microwave Integrated Circuit (MMIC) technology in order to save significantly on weight and bulk. A completely new concept has also received considerable attention lately, namely, the polarimetric radiometer measuring the full Stokes vector. A new chapter, Chapter 7, is dedicated to this important new technique. Most importantly, the synthetic aperture—also called interferometric—radiometer has been developed for Earth remote sensing. This is indeed a very interesting and important new technique that does a lot towards solving the problem associated with high-resolution imaging, especially at low microwave frequencies requiring large antenna apertures. This book describes many years of work with microwave radiometers and radiometer systems. It concentrates very much on practical experiences and how to do it, not on the theoretical backgrounds. It is assumed that the reader is familiar with the basics of radiometry—to a level comparable with that given in [1]. Actually, this book may be seen as a continuation of [1], which ends where
1
2
Microwave Radiometer Systems: Design and Analysis
much of the fun (and much of the trouble!) starts: namely, when the realization of the ideas and theories is commenced. This book deals with radiometers used for sensing the surface of the Earth. Radiometers are also used for sensing the atmosphere and used within radio astronomy. There are, however, adequate differences, especially from a practical point of view, to warrant a dedicated treatment for each application. Earth sensing receivers are typically characterized by relatively high brightness temperatures (100–300K), short integration times, and relatively large bandwidths. Radio astronomy receivers are often faced with very low brightness temperatures and narrow bandwidths (spectral measurements) but large integration times (although there are also wideband examples like the observation of the cosmic background). Atmospheric sensors may face a mixture of the above: high temperatures but narrow bandwidths (spectroscopy) and long integration times (although there are short integration time examples like spaceborne limb sounding). Radiometer receivers for radio astronomy are dealt with in [2], for example. The practical background for the book can be described in a few keynotes: • Design and manufacture of airborne, multifrequency, imaging radiom-
eter systems including polarimetric systems, imaging antennas, and synthetic aperture systems; • Calibration exercises including linearity and stability assessments using the radiometers of the airborne system; • Several airborne experiments with the systems measuring sea ice around Greenland; oil pollution, wind vectors, and salinity in European and U.S. waters; soil moisture in Europe and United States; • Design and evaluation of spaceborne radiometer systems for specific purposes, based on the practical experience with the airborne systems.
References [1]
Ulaby, F. T., R. K. Moore, and A. K. Fung, Microwave Remote Sensing, Vol. 1, Dedham, MA: Artech House, 1981.
[2]
Evans, G., and C. W. McLeish, RF Radiometer Handbook, Dedham, MA: Artech House, 1977.
2 Summary Overall the book can be divided into two main parts: one part consisting of Chapters 3 through 12 describing the fundamentals of how to make a radiometer system and leading up to another part consisting of Chapters 13 through 15 describing how to arrive at a system design from certain specifications, whether it is purely technical or whether it takes geophysical realities into account. Chapter 3, “The Radiometer Receiver: Sensitivity and Accuracy,” explains what a radiometer is, namely, a sensitive, calibrated microwave receiver. Radiometric sensitivity is defined and explained. The basic sensitivity formula is described. Absolute accuracy is explained and some of the problems associated with it are stressed. Chapter 4, “Radiometer Principles,” describes the four major classical radiometer principles: total power, Dicke, noise-injection, and correlation radiometers. Their sensitivities are derived from the basic sensitivity formula. It is also discussed how modern technology enables circuit implementations that softens the distinction between total power and Dicke radiometers (the hybrid radiometer). Additional radiometer principles are only briefly mentioned (for the sake of completeness), as they are not normally used for Earth sensing. Chapter 5, “Radiometer Receivers on a Block Diagram Level,” is an important engineering chapter. We discuss whether to use direct or superheterodyne receivers and how to combine double-sideband or single-sideband mixer operation (in the latter) with a possible microwave preamplifier. After that, a Dicke radiometer is worked through in detail on a block diagram level. Some specifications are fixed (frequency, bandwidth, and so forth) so that signal levels, gains, and signal-to-noise ratios can be discussed realistically. Signals are sketched and discussed throughout the receiver. The sampling process (and
3
4
Microwave Radiometer Systems: Design and Analysis
possible aliasing) associated with the analog-to-digital conversion is discussed. The Dicke radiometer is enhanced to a noise-injection radiometer. This in turn re- quires new gains, new signal levels, and the stability of the feedback loop is as- sessed. The total power radiometer is worked through stressing its special features and problems: dc stability, offset, tunnel diode detector, and so forth. The opportunity to discuss the differences between a double-sideband receiver without preamplifier and a single-sideband receiver with preamplifier is taken here: The total power radiometer is implemented both ways. Finally, some general comments about stability and the AC coupling in Dicke type switching radiometers are made. The DTU (Technical University of Denmark) noise-injection radiometer system is briefly reviewed in Chapter 6, “The DTU Noise-Injection Radiometers Example,” partly to facilitate a discussion of important features in practical radiometer design (temperature-stabilized RF enclosure and digital thermometer) and partly to introduce the radiometers that are used in the investigations of Chapters 9 and 10. The radiometers discussed so far are traditionally used to measure the vertically and horizontally polarized brightness temperatures by connecting them to properly polarized antenna ports. Chapter 7, “Polarimetric Radiometers,” describes the extension associated with the measurement of the full set of Stokes parameters. There are two fundamentally different ways of implementing the polarimetric radiometer system: polarization combining or correlation radiometer systems. Also, within each fundamental category there are significant tradeoffs. This chapter discusses the different implementation possibilities. Paramount issues are potential instrument stability and sensitivity as well as the tradeoff between increased microwave hardware complexity and fast digital correlator circuitry. Another important issue is the isolation between channels. Finally, an airborne, imaging polarimetric radiometer system, used for ocean wind direction sensing, is described and discussed. Chapter 8: “Synthetic Aperture Radiometer Principles” marks a significant change in instrument design philosophy. The chapter introduces the basic concept of aperture synthesis and provides a motivation for why one would choose to use it for remote sensing. The basic equations and the RF circuitry necessary for coherent processing are presented in simplified form. The approximations and parameters (sensitivity, resolution, and fringe washing) needed to design a sensor system using this concept are presented. Chapter 8 concludes with an example for an idealized system (uniform sampling on a Cartesian grid) to illustrate the principles and performance that can be expected. Chapter 9, “Receiver Calibration and Linearity,” explains the purpose of calibration and how to do it. Calibration facilities are presented and, as an example, a calibration curve for a 5-GHz noise-injection radiometer is shown. Linearity is often taken for granted due to the low signal levels in radiometers, but for
Summary
5
modern radiometers with tough calibration requirements, it may have to be checked. Simple setups to do this are presented. Chapter 10, “Sensitivity and Stability: Experiments with Basic Radiometer Receivers,” is a substantive chapter, trying to answer the question that many must have posed: Is the noise-injection radiometer (NIR) really superior to the Dicke radiometer concerning stability, which in turn is superior to the total power radiometer concerning the same issue—given real-life instruments with possibly imperfect components and thermal conditions? Using the already-described radiometers (properly modified for the purpose), extensive measurements of the stability against thermal variations inside the instruments have been carried out regarding the Dicke, the NIR, and the total power mode. The thermal variations were designed to resemble those that may be encountered in a satellite orbiting the Earth. The answer to the question is: Yes, the NIR is superior, but both the Dicke and the total power radiometers are well behaved; the variations in their outputs can be explained and modeled; hence, simple correction algorithms can be applied. Finally, the radiometer sensitivity formulas for the three modes are confirmed by measurements of sensitivities. The antenna is an important part of a radiometer system, warranting a brief description in Chapter 11, “Radiometer Antennas and Real Aperture Imaging Considerations.” Antenna types, loss, and beam efficiency are key words. Imaging antenna systems are discussed: the line scanner, the conical scanner, and the push-broom system. The dwell time per footprint is defined and the proper sampling of the antenna signal is discussed. We find that for realistic antenna patterns a sampling time of 0.7 times the dwell time per footprint ensures aliasing-free sampling. Finally, we discuss how the different radiometer modes each have their role to play in the different imagers: the total power radiometer in scanners and the Dicke type switching radiometers (especially the NIR) in push-broom systems. Chapter 12 deals with the relationships between swath width, footprint, integration time, sensitivity, frequency, and so forth for satellite-borne, real aperture imaging systems, and it describes the differences between scanning systems and push-broom systems: Small footprints and tough requirements to sensitivity favor the push-broom solution. Two examples illustrate this. Chapter 13, “First Example of a Spaceborne Imager: General-Purpose Mechanical Scanner,” deals with a system much like SSM/I—using a 1-m aperture and better receivers—and it is included to enlighten the special aspects of a mechanical scanner. The design is based on technical specifications (not specifications to geophysical measurements). A tradeoff is carried out between the number of antenna beams (hence receivers) per frequency (at the highest frequencies) and sensitivity potential plus antenna scan rate. Rough designs of the receivers are carried out, resulting in weight and power budgets. A few aspects of
6
Microwave Radiometer Systems: Design and Analysis
the antenna design are covered, and calibration, prelaunch as well as in-orbit checks, is discussed. Chapter 14, “Second Example of a Spaceborne Imager: A Sea Salinity/Soil Moisture Push-Broom System,” shows how we arrive at the design of a system beginning with specific geophysical measurement requirements. From a model for the brightness temperature of the sea, we determine frequencies and polarizations to be measured. From a study of relevant literature, we find that soil moisture measurements are well supported using the same channels. Based on this and user requirements for ground resolution and geophysical parameter resolution, system considerations are carried out. A suitable 1.4-GHz noise-injection radiometer is designed, weight and power budgets are made, some considerations are given for the highly specialized push-broom antenna, and a layout of the total system is sketched. Calibration checks, once in orbit, are necessary for even the best radiometer design, and aspects of this are considered with special emphasis on the problems associated with push-broom systems. A dedicated push-broom calibration scheme, in which a relative intercalibration of all channels (entirely done in the data analysis process) is carried out together with absolute calibration of one channel (using conventional sky horn and hot load technique), is described. Disturbing factors like Faraday rotation, space radiation, and atmospheric effects are considered with special emphasis on the Faraday rotation. Finally, Chapter 15, “Examples of Synthetic Aperture Radiometers,” begins with a description of the trades that are involved in designing a synthetic aperture radiometer for Earth remote sensing. Then a description is given of three synthetic aperture radiometers. The first is a real (i.e., existing) aircraft sensor called, ESTAR. This is a well-known instrument that was critical in demonstrating the viability of this technology for remote sensing. The hardware is described (with a picture) as well as the techniques employed for image reconstruction and calibration. An image from a soil moisture experiment is also presented. The second example is a sensor called HYDROSTAR that has been proposed for remote sensing from space. Design parameters are given together with expected performance. This instrument is similar in principle to the aircraft instrument, and therefore, it is easy for the reader to imagine how it will perform. Finally, the MIRAS/SMOS system, a spaceborne system with aperture synthesis in two dimensions, is briefly described.
3 The Radiometer Receiver: Sensitivity and Accuracy 3.1 What Is a Radiometer Receiver? The objective of a radiometer is to measure power. However, in many microwave applications, such as remote sensing of the Earth’s surface, it is common practice to express power in terms of an equivalent temperature. This may be the temperature of a blackbody that would radiate the same power, called the brightness temperature, TB, or the temperature of a resistor (termination) that has the same output power as that of the receiving antenna, called the antenna temperature, TA. At microwave frequencies the Rayleigh-Jeans law is applied to express power in terms of temperature. Now, consider an idealized antenna pointed towards an object of interest with equivalent brightness temperature, TB (see Figure 3.1). The output power of the antenna is expressed in terms of its antenna temperature, TA. The goal of the measurement is usually to relate the antenna temperature to the brightness temperature of the object. The task of the microwave radiometer is to measure this antenna temperature with sufficient resolution and accuracy that this connection can be made. In this sense, the radiometer is simply a calibrated microwave receiver.
3.2 The Sensitivity of the Radiometer The next step in the description of the microwave radiometer is illustrated in Figure 3.2.
7
8
Microwave Radiometer Systems: Design and Analysis Antenna P = power to be measured
Object TB
Figure 3.1 The measurement situation. TA
P = k·B·G·TA
B, G Radiometer
Figure 3.2 Idealized radiometer.
The radiometer selects a certain portion of the available output power from the antenna, that is, a certain bandwidth B around a given center frequency. This power is amplified (G) and presented, in a suitable fashion, to some output medium, here illustrated by a simple power meter. The meter measures: P = k ⋅ B ⋅G ⋅T A ( watts)
(3.1)
where k is Boltzmann’s constant: 1.38 × 10−23 J/K. Figure 3.2 shows a highly idealized radiometer. In real life the radiometer will generate noise, and this noise will add to the input signal (Figure 3.3). As the antenna signal is also a noise signal and the two signals are independent, they will add and cannot be separated later. The meter now measures: P = k ⋅ B ⋅G ⋅ (T A + T N
)
(watts)
(3.2)
To illustrate the sensitivity problem associated with all radiometer measurements, let us consider a case, where an antenna temperature of 200K is needed with 1-K resolution. A possible value for TN is 800K. So we are faced with the problem of finding a 1-K signal on top of a total signal of 1,000K; or, to put it differently, we want to see the difference between 1,000K and 1,001K. Note: It must continuously be remembered that the signals we discuss here are noise signals having a well-defined mean but with a random fluctuation about TA B, G TN
Figure 3.3 “Real” radiometer.
Radiometer
P = k·B·G·(TA + TN)
The Radiometer Receiver: Sensitivity and Accuracy
9
the mean. In the ideal case the fluctuations can be reduced by averaging (integration). The resulting sensitivity (standard deviation of the output signal) is: ∆T =
T A +T N
(3.3)
B ⋅τ
This is the basic radiometer sensitivity formula, in which TA is the input temperature to the radiometer, TN is its noise temperature, B is its bandwidth, and τ is its integration time (how the integration is carried out will be shown later). The sensitivity formula is quite difficult to arrive at, and it shall not be derived here. For more information on the derivation of this result, see [1, 2]. A typical example using figures already quoted shall be given. Consider a radiometer having a noise temperature of 800K, a bandwidth of 100 MHz, and an integration time of 10 ms. An antenna signal of 200K can then be measured with a resolution of: ∆T =
200 + 800
10 8 ⋅10 −2 ∆T = 1K
K
3.3 Absolute Accuracy and Stability Apart from sensitivity, stability and absolute accuracy are problems to consider. Let us take a closer look at the equation linking input and output quantities: P = k ⋅ B ⋅G ⋅ (T A + T N
)
(3.4)
If k, B, G, and TN are really constants, we have no stability problems: A given TA results in a certain P · k is, of course, a constant, and B is relatively stable and need not worry us too much. The bandwidth of the radiometer is determined by a filter, that is, a passive component, and if this is designed and built with care, we can assume a stable bandwidth. What about gain and noise temperature? Both represent specifications for active components like amplifiers or mixers, and both are dependent on, for example, supply voltage and physical temperature. Let us again consider the previous example with TA = 200K and TN = 800K. The resolution was found to be 1K, and it would be reasonable to aim at an absolute accuracy also of 1K. This means determining 1K on 1,000K, and both G and TN must be known and stable to within less than 1 per thousand, which corresponds to 0.004 dB, and it is not difficult to see the problem in
10
Microwave Radiometer Systems: Design and Analysis
keeping the gain of a 100-dB amplifier (a typical value in a radiometer) stable to better than 0.004 dB! However, there are ways around these problems, as will be described in the following, starting with Chapter 4. If k, B, G, and TN are not only constants but also known constants, we additionally have no absolute accuracy problems: a given TA results in a given P that can be calculated. Such knowledge of the constants are rarely available, leading to the necessity for calibration (see Chapter 9). This illustrates the fundamental difference between stability and accuracy: Stability is a highly appreciated virtue of an instrument, but a stable instrument need not be accurate. The steps towards accuracy includes the calibration process. In the following we will describe a slightly different aspect of absolute accuracy, which stresses the care that must be exercised when designing or working with radiometers. Consider losses in a signal path—it could be the waveguide connecting the antenna with the radiometer input or a passive component in the radiometer front end (see Figure 3.4). The symbol ᐉ denotes the fractional loss (or the absorption coefficient) and To is the physical temperature. T1 is the input temperature and the output temperature is: T 2 = T 1 (1 − ᐉ ) + ᐉ ⋅T o
(3.5)
The difference between output and input is: T D = T 2 − T 1 = ᐉ (T o − T 1 )
(3.6)
If T1 is 100K and To is 300K, a loss as small as 0.01 dB (ᐉ = 0.0023) results in a difference, TD, of 0.5K. Bearing in mind that the losses of a real signal path are much greater than 0.01 dB, the physical temperature of the path must be measured and used for correction of the measured brightness temperature. The corresponding losses must be known to an accuracy of better than 0.01 dB and must remain stable within the same limits. Consider a mismatch, for example, at the input of a radiometer, with a reflection coefficient ρ (Figure 3.5): T 2 = T 1 (1 − ρ) + T RAD ⋅ ρ
T1
ᐉ T0
Figure 3.4 Lossy signal path.
T2
(3.7)
The Radiometer Receiver: Sensitivity and Accuracy T1
T2 ρ
11
Radiometer
Figure 3.5 Mismatch at input.
T D = T 2 − T 1 = ρ(T RAD − T 1 )
(3.8)
where TRAD is the microwave temperature as seen from the point of reflection into the radiometer. TRAD is typically 300K and if T1 again is assumed to be 100K, a reflection coefficient of −26 dB will give an error (TD) of 0.5K. Care must be exercised to obtain reflection coefficients better than −26 dB.
References [1]
Ulaby, F. T., R. K. Moore, and A. K. Fung, Microwave Remote Sensing, Vol. 1, Dedham, MA: Artech House, 1981.
[2]
Tiuri, M. E., “Radio Astronomy Receivers,” IEEE Trans. on Antennas and Propagation, Vol. 12, No. 7, 1964, pp. 930–938.
4 Radiometer Principles The extremely simplified block diagram of a radiometer, as displayed in Figure 3.3, will in this chapter be somewhat elaborated as a first step towards a full block diagram to be discussed in later sections. Some of the principles used to avoid degradation of accuracy due to gain and noise temperature instabilities will be worked through.
4.1 The Total Power Radiometer (TPR) In principle we are still talking about the same radiometer as discussed in Chapter 3, but the block diagram has been expanded in Figure 4.1, to explain better the function of the radiometer. The gain in the radiometer has been symbolized by an amplifier with a gain G, and the frequency selectivity has been symbolized by a filter with a bandwidth B (centered around some given frequency). The microwave power has to be detected to find some measure of its mean. Two straightforward detector types can be made, using microwave semiconductor diodes: the linear detector and the square-law detector. In the present case, it is very attractive to use the square-law detector. Then the output voltage will be proportional to the input power and hence the input temperature. Finally, we indicate where the integration takes place: The signal from the detector is smoothed by the integrator to reduce fluctuations in the output, and the longer the integration time, the more smoothing there is. The output can be expressed as: V OUT = c ⋅ (T A + T N ) ⋅G
13
(4.1)
14
Microwave Radiometer Systems: Design and Analysis τ
2
B
G
TA
x
~~ ~
VOUT
TN
Figure 4.1 Total power radiometer.
where c is a constant. VOUT is totally dependent on TN and G. These can, for some applications, not be regarded as stable enough to satisfy reasonable requirements for accuracy. In other cases, however, the total power radiometer is very useful, namely, where frequent calibration, for example, once every few seconds, is possible. The sensitivity of the total power radiometer shall for completeness be repeated here: ∆T =
T A +T N
(4.2)
B ⋅τ
4.2 The Dicke Radiometer (DR) In 1946 R. H. Dicke found a way of alleviating the stability problems in radiometers [1]. By using the radiometer not to measure directly the antenna temperature, but rather the difference between this and some known reference temperature, the sensitivity of the measurement to gain and noise temperature instabilities are greatly reduced (see Figure 4.2). The input of the radiometer is rapidly switched between the antenna temperature and the reference temperature. The switch frequency FS is typically 1,000 Hz. The output of the square-law detector is multiplied by +1 or −1, depending on the position of the Dicke switch, before integration. The input to the integrator is then FS TA
G
TR
Figure 4.2 Dicke radiometer.
TN
B
~ ~ ~
τ
2
x
±1
VOUT
Radiometer Principles
15
V 1 = c ⋅ (T A + T N ) ⋅G in one half-period of FS, and V 2 = −c ⋅ (T R + T N ) ⋅G in the second half-period. Provided that the switch frequency FS is so rapid that TA, TN, and G can be regarded as constants over the period, and that the period is much shorter than the integration time, the output of the radiometer is found as: V OUT = V 1 + V 2 = c ⋅ (T A + T N ) ⋅G − c ⋅ (T R + T N ) ⋅G V OUT = c ⋅ (T A − T R ) ⋅G
(4.3)
It is seen that TN has been eliminated, while G is still present, although with less weight. Now G multiplies the difference between TA and TR, where TR is reasonably chosen to be in the same range as TA, while in the total power case, G multiplied the sum of TA and the rather large TN. The Dicke principle has proven to be very useful, and Dicke radiometers have been used extensively over the years. A price has to be paid, however, for the better immunity to instabilities. Since only half of the measurement time is spent on the antenna signal (the other half is spent on the reference temperature), the sensitivity is poorer than for the total power radiometer. The output of the Dicke radiometer can be regarded as the difference between the outputs of two identical total power radiometers: TPR1 measuring the antenna signal and TPR2 measuring the reference signal. Each radiometer uses an integration time of τ/2. The standard deviation of the output from TPR1 is [using (4.2)]: ∆T 1 =
T A +T N B ⋅τ 2
and for TPR2: ∆T 2 =
T R +T N B ⋅τ 2
As the output signals are statistically independent, the standard deviation of the difference signal is:
16
Microwave Radiometer Systems: Design and Analysis
∆T =
[( ∆T
) 2 + ( ∆T 2 ) 2 ]
12
1
(T A + T N ) 2 (T R + T N ) 2 ∆T = + B ⋅τ 2 B ⋅τ 2 ∆T
(2(T =
A
+T N
) 2 + 2(T R B ⋅τ
+T N
12
(4.4)
)2 )
12
TR is, as mentioned earlier, selected as close to TA as possible, and TR is often replaced by TA in (4.4), which then reduces to: ∆T = 2 ⋅
T A +T N B ⋅τ
(4.5)
It is seen that the sensitivity of the Dicke radiometer is degraded by a factor of 2 compared with the total power radiometer. Alternatively, we can replace TA by TR in (4.4), and we find: ∆T = 2 ⋅
T R +T N B ⋅τ
(4.6)
which will be the conservative version of the sensitivity formula for Dicke radiometers since usually TR > TA. The truth lies between (4.5) and (4.6) but this is normally ignored in real life, and either formula can be used.
4.3 The Noise-Injection Radiometer (NIR) The noise-injection radiometer represents the final step towards stability; that is, the output is independent of gain and noise temperature fluctuations [2, 3]. From (4.3) it is seen that the output from a Dicke radiometer is zero (independent of G and TN) if the reference temperature and the antenna temperature are equal. The noise-injection radiometer is a specialization of a Dicke radiometer in which this condition is continuously fulfilled by a servo loop. In almost any case encountered in Earth remote sensing, the antenna temperature is below about 300K (emissivities between 0 and 1 are multiplied by the physical temperature). The reference temperature in a Dicke radiometer is conveniently equal to the physical temperature in the microwave front end, that is, 300–320K. In Figure 4.3 we show how the output TI of a variable noise generator is added to the antenna signal TA, so that the resultant input (TA ′ ) to the
Radiometer Principles
TA
17
TA’ = TA + TI Dicke radiometer
TA’
VOUT ≈ 0 Loop gain
TI
Figure 4.3 Noise-injection radiometer.
Dicke radiometer is equal to the reference temperature (TR), and a zero output results from it. A servo loop adjusts TI to maintain the zero output condition, or rather the near zero output condition: The loop gain can be made large but not infinite. From (4.3) we have: V OUT = c ⋅ (T A ′ − T R ) ⋅G = 0 and as T A ′ =T A +T I we find: T A =T R −T I TR is a known constant, and knowledge of TI is required to find TA. The accuracies of the Dicke radiometer part of the NIR and of the loop gain are, given large loop gain, completely insignificant for the accuracy with which we determine TA. This is solely dependent on the accuracy of TI. Accurate and stable noise sources with variable output can be made, and they are used for “injecting” the required signal TI into the input line, so that TI and TA are added. The sensitivity of the noise-injection radiometer is easily found using (4.5): ∆T = 2 ⋅
T A ′ +T N B ⋅τ
But asT A ′ is equal to TR, we find: ∆T = 2 ⋅
T R +T N B ⋅τ
(4.7)
18
Microwave Radiometer Systems: Design and Analysis
The sensitivity of the noise-injection radiometer is very close to that of the Dicke radiometer; see (4.5) and (4.6) and the associated discussion. The noise-injection radiometer includes a feature worthy of further elaboration. The front-end circuitry in a radiometer is illustrated in Figure 4.4. If these components are surrounded by a temperature stabilized box kept at the physical temperature equal to TR, the radiometric reference can be a microwave termination. An isolator is added after the filter to obtain well-defined output conditions. For the noise-injection radiometer the situation is then as shown in Figure 4.5. The input signal can be substituted by a termination on the switch inside the enclosure. The enclosure thus contains only passive components, all of temperature TR, and the output signal is: POUT = k ⋅T R ⋅ B independent of details about the circuitry, and in particular independent of losses and reflections in the embedded Dicke radiometer. Of course, the accuracy of the radiometer is still dependent upon the accuracy with which the injected noise is known (i.e., upon the quality of the noise source and other components in the noise injection circuitry).
4.4 The Correlation Radiometer (CORRAD) The correlation radiometer is a multichannel system that finds use in the case where two brightness temperatures are measured as well as the correlation between them. This is the case in the polarimetric radiometer (see Chapter 7), Filter
Switch
TA
TR
Figure 4.4 Radiometer front end.
TA’ = TR
Switch TR
Figure 4.5 NIR front end.
Filter
Isolator
Tphys = TR
Radiometer Principles
19
where the vertical and the horizontal brightness temperatures are measured together with their correlation, thus finding the so-called Stokes parameters. This is also the case in interferometric radiometers like the synthetic aperture radiometer (see Chapter 8), where the outputs of two different antennas pointing in the same direction in space are measured. The correlation radiometer is shown in Figure 4.6. Two identical receivers, which here are total power radiometers, are connected to the two output ports of the antenna system. The outputs of the receivers are detected the usual way to yield the normal brightness temperatures. The signals of the receivers are also (before detection) fed into the complex correlator providing the real and the imaginary parts of the cross correlation between the two input signals from the antenna system. For the two normally detected outputs, we, of course, find the usual sensitivity of a total power radiometer as shown in (4.2)—let us call it ∆TTPR (assuming identical receiver performance). The correlator outputs have a sensitivity that can be found by considering the analogy to the radio astronomer’s interferometer with correlation receiver [4]: If the interferometer observes a small source in the boresight direction, and it is assumed that the two radiometer channels collect equal but independent background noise, the sensitivity is expressed as ∆T = ∆TTPR / 2 (the two receivers are identical with a sensitivity ∆TTPR). It is thus assumed that the two input signals are only weakly correlated and can be modeled as sums of large “background” signals (uncorrelated channel to channel) and a small correlated signal. This is the case for the applications to be considered later in this book. Concerning stability, the situation is much like that for the total power radiometer, and proper attention to frequent calibration schemes must be exercised. Note, however, that the correlator outputs are relatively more stable than the total power outputs: Since the internally generated noise in the two receivers G
TA1
B
~~ ~
2
x
τ VOUT1
TN1 real
Complex corr. G
TA2
TN2
Figure 4.6 Correlation radiometer.
B
~~ ~
x
2
imag τ VOUT2
20
Microwave Radiometer Systems: Design and Analysis
is uncorrelated, these noise signals do not contribute to the correlator outputs. There will be more about stability in Chapter 7.
4.5 Hybrid Radiometer The radiometers as described hitherto in this chapter are the classical receiver types, and their implementation are indicated in the classical way using for example analog integration after detection, and analog subtraction of antenna and reference signals (in the Dicke radiometer). Indeed, many radiometers are still implemented this way. However, with the advent of analog-to-digital converters and digital processing, other implementation forms are possible and often used. This is illustrated in Figure 4.7. As soon as possible following detection, the signal is analog-to-digital converted—only a low-pass filter is indicated to condition the signal bandwidth to the sampling frequency of the converter. The signal from the converter is led to some kind of digital processor, typically a PC or a field programmable gate array (FPGA), where suitable data handling takes place. This can typically be digital integration to the required integration time τ, as well as subtraction of the antenna signal and the reference signal. Since these processes are under computer control, flexibility becomes a keyword, and the distinction between total power and Dicke radiometer vanishes to some extent. If the processor operates the input switch rapidly and regularly, we can regard it as a Dicke case, while if the measurement situation is such that the antenna signal can be measured (with interruptions when the switch points to the reference signal) without loss of data, then we have a total power case with frequent calibration. There will be much more about this in Chapter 13. A classical Dicke radiometer spends half of its time measuring the well-known reference temperature and thus only half of its time doing its real job, namely, measuring the unknown antenna temperature. Thus, over the years researchers have considered a better duty cycle for the antenna measurements (in turn potentially leading to improved sensitivity). See, for example, [5]. However, having an analog subtraction of the signals, the 50% duty cycle is
G
TA
B
~~ ~ TR
TN
Figure 4.7 Hybrid radiometer.
x2
LPF
~~
A/D
Processor
OUT
Radiometer Principles
21
instrumental to having simple and stable circuitry, but with the subtraction done digitally, this is no longer a limitation, and optimized duty cycles can be found on a case-by-case basis. A word of warning: The naïve notion that spending more time on the unknown antenna signal will lead to improved sensitivity is not necessarily true! When more time is spent on the antenna, less time is left for the reference and this in turn leads to an increased standard deviation for that measurement. Thus, the final standard deviation after subtraction might not decrease. This can actually be seen from the calculations in Section 4.2, but it can also be seen that for specific cases with specific values of TA, TN, and TR, an optimization of the duty cycle and the sensitivity can be made. This will in general not be far from the classical values! However, there are possible improvement schemes: Since the reference temperature and the receiver noise temperature are assumed to be relatively stable while the antenna temperature may change rapidly, averaging over several reference temperature measurements will reduce the standard deviation of this measurement and thus allow a non-50% duty cycle to be employed. Initial instrument fluctuations and averaging times must, of course, be considered carefully. See a further discussion in [6]. In the present book only the classical radiometers will be discussed. The reason is that this way all the difficult design issues are briefly covered. The circuitry for the hybrid radiometer is slightly simpler, so when the design of a classical radiometer is familiar to the reader, the design of a hybrid radiometer is straightforward.
4.6 Other Radiometer Types The radiometer types already discussed are those that are widely used for sensing the properties of the Earth and are the ones that will be considered further in the following chapters. However, other types have been suggested and they may find use for special purposes. The two-reference radiometer [7] alleviates the problem with possible gain instabilities still present in the basic Dicke radiometer. Two different reference temperatures are alternatively selected and an extra synchronous detector will give an output enabling determination of the gain and hence a correction of the radiometer output. Also, the basic total power radiometer scheme can be modified to eliminate gain stability problems. In the noise-adding radiometer [8–10], a train of noise pulses is added to the antenna input signal. The ratio of the receiver detected output during the noise “on” period to that during the noise “off” period is a measure of the gain. The added noise does, however, contribute to
22
Microwave Radiometer Systems: Design and Analysis
the system noise temperature, and the full potential of the total power radiometer sensitivity cannot be exploited. A variation of the noise injection radiometer suitable for correlation radiometers should also be mentioned. This was developed at the University of Massachusetts for use in the ESTAR radiometer (see Chapter 15). In this case, noise is injected as described earlier (see Figure 4.3), but instead of using a Dicke radiometer, the switch at the front end (see Figure 4.5) is replaced by a hybrid. The hybrid accepts two inputs (T A ′ = TA + TI) and the signal from the reference load (TR). The two outputs from the hybrid are the sum and difference: T A ′ ± TR. (The signals are labeled here as if they were power, but at this point, before detection, they are voltages.) The two signals (voltages) out of the hybrid then become the input to a correlation radiometer such as that shown in Figure 4.6 but using only the path through the complex correlator. It is not difficult to show that if the receiver noise in the two paths is independent, then the magnitude of the output of the correlation receiver is VOUT = c·(TA + TI – TR)·G1·G2 where G1 and G2 are the gains of the two paths in the correlation radiometer. Finally, the noise injection loop adjusts TI so that VOUT = 0. The special feature of this radiometer is that it does not require a Dicke switch and achieves the stability of a noise injection radiometer. As in an NIR, the stability depends on control of the reference load and noise source but is independent of receiver gain. Even further radiometer types are possible—like the Graham receiver [11] or different kinds of special correlation receivers [12–15]—but they only find use within radio astronomy and thus clearly fall outside the scope of this book.
References [1]
Dicke, R.H., “The Measurement of Thermal Radiation at Microwave Frequencies,” Rev. Sci. Instr., Vol. 17, 1946, pp. 268–279.
[2]
Goggins, W. B., “A Microwave Feedback Radiometer,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 3, No. 1, 1967.
[3]
Hardy, W. N., K. W. Gray, and A. W. Love, “An S-Band Radiometer Design with High Absolute Precision,” IEEE Trans. on Microwave Theory and Techniques, Vol. 22, No. 4, 1974, pp. 382–390.
[4]
Kraus, J. D., Radio Astronomy, 2nd ed., Powell, OH: Cygnus-Quasar, 1986.
[5]
Bremer, J. C., “Improvement of Scanning Radiometer Performance by Digital Reference Averaging,” IEEE Trans. on Instrumentation and Measurement, Vol. 28, No. 1, 1979, pp. 46–54.
[6]
Tanner, A. B., W. J. Wilson, and F. A. Pellerano, “Development of a High-Stability L-Band Radiometer for Ocean Salinity Measurements,” Proc. of IGARSS’03, 2003, pp. 1238–1240.
Radiometer Principles
23
[7] Hack, J. P., “A Very Sensitive Airborne Microwave Radiometer Using Two Reference Temperatures,” IEEE Trans. on Microwave Theory and Techniques, Vol. 16, No. 9, 1968, pp. 629–636. [8] Ohm, E. A., and W. W. Snell, “A Radiometer for a Space Communication Receiver,” Bell System Technical Journal, Vol. 42, 1963, pp. 2047–2080. [9] Batalaan, P. E., R. M. Goldstein, and C. T. Stelzried, “Improved Noise-Adding Radiometer for Microwave Receivers,” NASA Tech. Brief. 73-10345, JPL, 1974. [10] Yerbury, M. J., “A Gain-Stabilizing Detector for Use in Radio Astronomy,” Rev. Sci. Instr., Vol. 46, No. 2, 1975, pp. 169-179. [11] Graham, M. H., “Radiometer Circuits,” Proc. IRE, Vol. 46, 1958. [12] Goldstein, S. J., “A Comparison of Two Radiometer Circuits,” Proc. IRE, Vol. 43, 1955. [13] Fujimoto, K., “On the Correlation Radiometer Technique,” IEEE Trans. on Microwave Theory and Techniques, Vol. 12, No. 3, 1954, pp. 203–212. [14] Clapp, R. E. and J. C. Maxwell, “Complex-Correlation Radiometer,” IEEE Trans. on Antennas and Propagation, Vol. 15, No. 2, 1967, pp. 286–291. [15] Aitken, G. J. M., “A New Correlation Radiometer,” IEEE Trans. on Antennas and Propagation, Vol. 16, No. 2, 1968, pp. 224–227.
5 Radiometer Receivers on a Block Diagram Level The block diagram of a 17-GHz radiometer will be covered in some detail in order to discuss the different aspects of designing a radiometer. The chapter will first concentrate on the design of an instrument operating in the Dicke mode, followed by comments to the necessary additions and special considerations regarding the NIR mode. Finally, a total power instrument will be discussed. In order to enable the calculation and discussion of gains, signal levels, and so forth throughout the instrument, some major specifications will be given in Table 5.1. Before proceeding to the specific examples, a few subjects of general nature are covered.
5.1 Receiver Principles 5.1.1
Direct or Superheterodyne
The radiometer is merely a very sensitive microwave receiver and, like any receiver, it employs front-end circuitry, which has two prime tasks: input frequency band selection, and amplifying the incoming signal to a proper level for the detector and subsequent low-frequency circuitry. This amplification may have to be very large, typically 50–80 dB for microwave radiometers. It can be obtained by two entirely different schemes, either by direct use of amplifiers at the input frequency (the direct receiver) or by use of a mixer, local oscillator, and IF frequency amplifiers (the superheterodyne receiver). In the direct receiver, all amplification takes place at the input frequency, and all selectivity is determined by filters in the same RF range. In the superheterodyne receiver most of the 25
26
Microwave Radiometer Systems: Design and Analysis
Table 5.1 Receiver Specifications Frequency
17 GHz
IF bandwidth
500 MHz
Noise figure
5 dB
Integration time
5 ms
Input range
0–313K
amplification takes place at the much lower IF, and selectivity is determined by a combination of filters at RF and IF levels. Regarding amplification, it has long been a desirable feature of the superheterodyne receiver that most (or all) of the gain could be at IF level, due to either unavailability of proper microwave amplifiers or very bulky and costly microwave amplifiers—at least until at few years ago. Now microwave FET amplifiers with excellent noise figures are available, covering the frequencies well beyond 40 GHz. Hence, the possibility of using direct receivers cannot be excluded based on RF amplifier considerations. Regarding selectivity, the direct receiver may run into problems. All selectivity is determined by the microwave filter meaning that many sections may be required. Such a filter is lossy and bulky—the loss may deteriorate the noise figure of the radiometer while bulky components should be avoided in some applications like spaceborne instruments. The superheterodyne receiver includes a modest microwave filter for out-of-band suppression of strong signals, and the final selectivity is achieved by the IF filter. The microwave filter needs to only have a few sections (not excessively lossy or bulky) and at the IF level, filters of high order are small and easy to implement. Moreover, loss is of little concern. Many microwave radiometers, and indeed most millimeter wave radiometers (amplifiers not readily available), are made as superheterodyne receivers, and so too are most of the designs covered in this book. It should be noted that having understood the design of a superheterodyne receiver, a direct design will be regarded as a simpler effort, generally following the same guidelines. There will be more about direct receivers in Section 13.3.1. 5.1.2
DSB or SSB with or without RF Preamplifier
Having selected the superheterodyne principle, the designer still has a fundamental choice to make: double sideband (DSB) or single sideband (SSB) operation. Again, this depends on whether a RF preamplifier is used. In the receiver without RF preamplifier, the receiver noise figure is largely determined by the mixer in combination with the first IF amplifier. Hence, such a receiver should use the DSB operation principle as the mixer-first IF amplifier
Radiometer Receivers on a Block Diagram Level
27
has a DSB noise temperature that is 3 dB lower than the SSB noise temperature. This can generally be exploited in radiometry as both input sidebands contain information (the brightness input signal to the radiometer is wideband noise). The radiometer has an input bandwidth twice the IF bandwidth, the local oscillator frequency is equal to the center frequency of the input band, and the IF frequency is “DC” (IF band from DC up to B, the radiometer bandwidth). It should be stated at this stage that the radiometer bandwidth B in the sensitivity formula is the predetection bandwidth, that is, the IF bandwidth, and not the total RF bandwidth, which is 2B in DSB receivers. The benefit of the larger input band has been used already in the DSB-SSB noise figure advantage and cannot be exploited again in the sensitivity formula. Turning to the receiver with RF preamplifier the situation is very different. Here the receiver noise figure is largely determined by the preamplifier and going from the SSB to the DSB mixer operation only results in a larger input bandwidth to the radiometer with no gain in sensitivity. This may not matter in some situations, but should generally be avoided, as it results in larger susceptibility to interference from other sources. Spaceborne radiometers especially should use SSB operation and preamplification. The high gain antenna covers large areas on the ground, and in the low end of the microwave spectrum many active services are potential hazards to radiometric operations. Hence, the radiometer input bandwidth should be as low as possible while still fulfilling sensitivity requirements. In general, the SSB operation with a preamplifier should be used whenever possible/feasible, that is, at moderate frequencies, while the DSB option, having no RF amplification, is used whenever such amplifiers are unavailable or deemed too expensive. This chapter will cover both possibilities: The Dicke type switching radiometers use DSB operation and no RF amplifier, while the total power radiometer will be designed likewise, as well as with an amplifier and a SSB operation.
5.2 Dicke Radiometer The block diagram for the Dicke radiometer is shown in Figure 5.1. The radiometer receiver is a superheterodyne receiver: The input signal is not directly amplified and detected, but rather converted to an intermediate frequency, where the amplification takes place before detection. 5.2.1
Microwave Part
At the relatively high frequency of 17 GHz, the best performance is obtained by using waveguide technology. Here it is assumed that individual, off-the-shelf
28
Microwave Radiometer Systems: Design and Analysis
7.7mVpp 1.1 µW 7 mV/µW 500 MHz 50 dB IF AF 10 MHz 30 dB 2.4 Vpp
313 K 17.5 GHz TA
↔ 0K
~ ~ ~ 16.5 GHz
G = 25 dB
~ ~~
IF Mix - preamp
313 K
~
17.0 GHz
0.5 VDC/1 Vpp 9.5 V
10 V=100% ∆/Σ
±1
1.2 V 5 msec
DC 18 dB
DATA CK = 205 kHz
FS = 2225 Hz
Figure 5.1 Dicke radiometer, TA = 0K.
microwave components are joined together using waveguide sections. This is the fast and straightforward method generally used by research institutions and commercial companies. Today, however, there is an alternative: the Monolithic Microwave Integrated Circuits (MMIC) technology. The big advantage is much reduced bulk and weight; the drawback is the high cost of units from a few specialized vendors. This directly points at the use of MMICs in space applications (see further discussions in Chapter 13), while ground and airborne instruments are still implemented as shown in the following. The first component to be encountered is the Dicke switch. This is a latching ferrite circulator, which is a circulator, where the magnetic field, and hence the signal direction, can be reversed by electronic means. A typical switching time is 1 µs and 0.3 dB is a typical loss in a high quality latching circulator. A trigger frequency (FS) for the Dicke switch around 1 kHz is often reported in the literature concerning radiometer designs. Here a frequency of roughly 2 kHz is chosen and a few arguments for this choice are presented. It is quite clear that the integration time of the radiometer has to be much greater than 1/FS to ensure a correct subtraction G ·TR – G · TA on the integrator. With the integration time being 5 ms, FS has to be at least 2 kHz if “much” is assumed equal to 10. Furthermore, the 1-µs switch time of the latching circulator requires an upper limit to FS. The finite switch time represents an uncertainty in the duty cycle of the Dicke switch, and exactly 50% is a precondition for all calculations concerning Dicke radiometers. A 2.5-kHz switch frequency yields an uncertainty in duty cycle of:
Radiometer Receivers on a Block Diagram Level
29
2 ⋅1 µs 0.4 ms = 5 parts per thousand which is not unreasonable, as would be a much greater value . The Dicke principle involves great sensitivity to noise around the switch frequency, and multiples of the power line frequencies, 50 Hz or 400 Hz, should be avoided when deciding upon the exact FS. A fair choice is 2,225 Hz. The reference temperature TR is generated by a well-matched microwave termination at the physical temperature TR (a microwave termination absorbs all incident energy; hence it has an emissivity of 1). The microwave front end, and with it the reference termination, is enclosed in a temperature stabilized box to enhance stability. A reasonable operating temperature for the electronic components is 40°C and thus the reference temperature is 273 + 40 = 313K. The microwave filter is included to prevent strong signals outside the input band of the radiometer from saturating the mixer (the proper bandwidth limitation is carried out at IF level). Hence it is designed for low loss (0.2 dB) and adequate bandwidth (0.1 dB limits at 16.5 GHz and 17.5 GHz). A five-section Chebyschev filter is a good candidate. An isolator is situated between the filter and the mixer. For proper operation, the filter requires well-matched output conditions, which a mixer cannot provide. The isolator may have a loss of 0.3 dB. Because a microwave preamplifier is not included, the mixer is very important for the performance of the radiometer. The best conversion loss figures can be obtained if double sideband operation is possible, as it is in radiometers. The IF band is 0–500 MHz and the two input sidebands (16.5–17.0 GHz and 17.0–17.5 GHz) are added when DSB operation is used. High quality DSB mixers are often integrated with the first section of the IF amplifier (and named a mixer-preamplifier), so that the manufacturer can optimize the interface between the two, for best noise figure and conversion loss. A good quality mixer-preamplifier exhibits a 4 dB noise figure and a total RF to IF gain of 25 dB. A 17-GHz local oscillator is needed. No special requirements to frequency stability are present in this broadband application, and a standard dielectric resonator oscillator (DRO) is adequate. 5.2.2
The Noise Figure and the Sensitivity of the Radiometer
The noise figure of the radiometer can now be calculated in Table 5.2 as the noise figure of the mixer-preamplifier added to the losses of the components preceding this. This noise figure is equivalent to a noise temperature of (5.0 dB ~ 3.2): T N = 290(NF − 1) = 290(3.2 − 1) = 640K
30
Microwave Radiometer Systems: Design and Analysis
Table 5.2 Radiometer Noise Figure NF Mixer-preamplifier
4.0 dB
Isolator
0.3 dB
Filter
0.2 dB
Latching circulator
0.3 dB
Waveguide
0.2 dB
Total
5.0 dB
The sensitivity of the radiometer is calculated using (4.6). TR is 313K. B is the bandwidth before detection, which is 500 MHz. For 5-ms integration time, we thus find: ∆T = 2 ⋅
313 + 640 0.5 ⋅10 9 ⋅10 −3
K
. K ∆T = 12 5.2.3
The IF Circuitry and the Detector
The IF filter finally determines the bandwidth of the radiometer. Here the required steep cutoff is easy to implement, and losses are no problem after the large gain in the mixer-preamplifier. The IF band does not extend all the way down to DC. For practical reasons a 10-MHz highpass section is included in the filter, and the IF band is 10–500 MHz. Further amplification takes place in the final IF amplifier stage, and the signal is ready for detection. Schottky barrier diodes make good detectors and may yield a sensitivity of 7 mV/µW. They are quadratic for input levels up to some −20 dBm (where they become linear detectors). The decision of which signal level to put on the square-law detector includes a compromise. A low level ensures good square-law behavior but results in a very small output signal, which may cause noise problems in the following amplifier. A level of −25 dBm is chosen. Then it is possible to calculate the necessary gain of the IF amplifier. The input power level is calculated from: P = k ⋅ (T A + T N ) ⋅ B RF where BRF is the total input bandwidth (1 GHz). Hence
Radiometer Receivers on a Block Diagram Level
31
P = 138 . ⋅10 −23 ⋅ (313 + 640 ) ⋅10 9 W P = 132 . ⋅10 −8 mW P = −79dBm The total RF + IF amplification is found to be −25 dBm − (−79 dBm) = 54 dB. The microwave components have a loss of 1 dB, and the mixer-preamplifier has a RF to IF gain of 25 dB. Hence, the IF amplifier must have a gain of 54 + 1 − 25 = 30 dB. The detector dramatically changes the character of the signal. Figure 5.2(a) shows the signal before detection. It is a high-frequency signal with two levels corresponding to the two different positions of the Dicke switch. The detector reveals only the envelope of the signal as shown in Figure 5.2(b). The levels still correspond to the input levels (TR + TN and TA + TN). If, however, the output of the detector is AC-coupled, the signal now only contains information about the difference between TR and TA, which is exactly what we want [see Figure 5.2(c)]. This square wave signal of frequency FS has to be amplified by the subsequent, so-called AF (audio frequency), amplifier. To preserve the signal waveform, a frequency range of approximately 0.1 · FS − 10 · FS or 200 Hz–20 kHz is required (hence the name AF amplifier). Before proceeding with the AF amplifier, it is necessary to calculate the extreme signal levels in the radiometer. ←TR + TN ←TA + TN a) Before detection:
0
←TR + TN ←TA + TN b) After detection:
0
c) After AC coupling:
0 Peak amplitude ~ TR − TA
Figure 5.2 Waveforms around the detector: (a) before detection, (b) after detection, and (c) after AC coupling.
32
5.2.4
Microwave Radiometer Systems: Design and Analysis
The Extreme Signal Levels
The maximum dynamic signal arises when the antenna signal is 0K, which is the situation shown in Figure 5.1. The difference in levels is ∆Tmax = 313K [see Figure 5.2(a)], and this corresponds to: ∆P max = 138 . ⋅10 −23 ⋅ 313 ⋅10 9 W ∆P max = 0.43 ⋅10 −8 mW At the detector (54-dB total RF + IF gain), the signal is: ∆P max = 11µW . After the detector, at the input of the AF amplifier, the signal is: S max = 11 . µW ⋅ 7 mW µW S max = 7.7mV pp The minimum signal, which has to be handled without degradation by the radiometer circuitry, is reasonably assumed as equal to the sensitivity, 1K. This situation arises when the input signal is 312K (see Figure 5.3). After the detector, at the input of the AF amplifier, the minimum signal is: S min = 24 µVpp
24µVpp
1K 17.5 GHz TA
↔ 312 K
~ ~ ~ 16.5 GHz
G=25 dB
7 mV/µW
500 MHz
~~ ~ 10 MHz
IF Mix - preamp
IF 30 dB
50 dB AF
7.6mVpp
313 K
~
17.0 GHz
0.5 VDC/1 Vpp 30 mV
10 V=100% ∆/Σ
±1
3.8 mV 5 msec
DC 18 dB
DATA CK= 205 kHz
Figure 5.3 Dicke radiometer, TA = 312K.
FS = 2225 Hz
Radiometer Receivers on a Block Diagram Level 5.2.5
33
The LF Circuitry
The AF amplifier has, as already mentioned, a bandwidth of 200 Hz–20 kHz. It is, however, not this bandwidth that is used to calculate the equivalent input noise of the AF amplifier. Following the synchronous detector there is the analog integrator having a noise bandwidth of 100 Hz. Hence, the noise bandwidth before the synchronous detector (which can be regarded as a DSB mixer) is 200 Hz centered around the Dicke frequency FS. A good quality operational amplifier has an equivalent input noise of 10 −8 V Hz. This gives an input noise of: S N = 200 ⋅10 −8 VRMS . µVRMS S N = 014 Recalling that the minimum signal at this stage in the radiometer is Smin = 24 µVpp, a comfortable margin is seen to be present. A 50-dB gain in the AF amplifier results in the following minimum and maximum signals to be handled by the synchronous detector: S MIN = 24 µVpp ⋅ 316 = 7.6mVpp S MAX = 7.7mVpp ⋅ 316 = 2.4 Vpp The synchronous detector transforms the square wave signal from the AF amplifier into a DC signal (see Figure 5.4). This is done by multiplying the signal by +1 or −1 in synchronism with the switch frequency FS. The positive parts of the signal are left untouched, while the negative parts are reversed in polarity. Figure 5.5 shows how the circuitry can be realized. It is seen that a 1-Vpp signal is transformed into a 0.5-V DC signal. Hence the extreme signals after the synchronous detector are: S min = 3.8 mV DC S max = 12 . V DC
a) Before syn. det.:
b) After syn. det.:
0
0
Figure 5.4 Waveforms around the synchronous detector: (a) before and (b) after synchronous detection.
34
Microwave Radiometer Systems: Design and Analysis Op. amp. +
AC IN
DC OUT
−
Op. amp. + R
CMOS switch
− R
FS Inverter
Figure 5.5 Synchronous detector.
The analog integrator is just an RC lowpass filter, and the relationship between noise bandwidth b, equivalent integration time τ, component values, and cutoff frequency fo is given by the formula: b=
1 1 π = = ⋅f0 2 τ 4 RC 2
In the actual design the integration time is τ = 5 ms, giving a noise bandwidth of 100 Hz and a cutoff frequency of 63.7 Hz. The purpose of the DC amplifier is to condition the signal for the analog-to-digital (A/D) converter. This has a range of 0–10V, and the gain of the DC amplifier is chosen so that the maximum signal is amplified to just below 10V. A gain of 18 dB gives the following extreme signals on the A/D converter: S min = 30 mV S max = 9.5 V
5.2.6
The Analog-to-Digital Converter
The A/D converter is implemented as a so-called ∆/Σ converter. The ∆/Σ converter is in fact a voltage-to-pulse rate converter producing a pulse train in synchrony with a clock, the number of pulses per time unit being proportional to the input voltage. The converter tries to maintain a constant voltage on the capacitor C when the input voltage varies. To achieve this, a reference current is presented to
Radiometer Receivers on a Block Diagram Level
35
the capacitor for a certain percentage of time, K. Hence, K is proportional to VIN. See Figure 5.6. In this schematic diagram, A is an ideal operational amplifier, VIN is positive, VREF is negative, and the net voltage on C is zero. Then VOUT and Io are on average zero and I1 = I2. The input of the operational amplifier is a virtual ground, and −V IN R1 V I 2 = K ⋅ REF R2 I1 =
hence K = −V IN ⋅
R2 R 1 ⋅V REF
If K is synchronized to and gated with a clock frequency, two signals emerge from the converter: (1) pulses having variable duty cycle proportional to VIN, well suited for controlling the noise injection in a noise-injection radiometer (this feature is the cause for selecting the ∆/Σ converter in the presented design); and (2) a data pulse train consisting of a number of pulses ND equal to K multiplied by the number of clock pulses NC in any time interval. A more complete diagram showing the ∆/Σ converter is given in Figure 5.7. VREF
K I2 R2 R1
+ −
VIN I1
C I0
Figure 5.6 Explaining the ∆/Σ converter.
A
VOUT
36
Microwave Radiometer Systems: Design and Analysis
VREF
R2
+ −
VIN
Comparator − A
+
D
Q
K
CK
R1 C
DATA
CK
Figure 5.7 ∆/Σ converter.
The comparator decides when it is time to switch on the reference voltage, and the exact time of switching is synchronized to the clock pulses by the D flip-flop. A digital expression for the analog input is found directly by counting ND relative to NC (see Figure 5.8). When the clock counter is full—after 2N clock pulses—the data counter will contain an N-bit word representing the input voltage. This word is transferred to the data register, the data counter is reset, and a new conversion starts. The data word in the data register may be read when convenient. The magnitude of N is found by considering the resolution desired. The radiometer is designed for an input range of 0–313K and a sensitivity of 1.2K (τ = 5 ms). It is, of course, not acceptable for the digital resolution to degrade this resolution of the more difficult part of the radiometer. Ten bits will give a digital resolution of 1 in 1,024. Only 95% of the input range to the converter is used so that as a result the 313-K input range to the radiometer corresponds to a digital range of 1,024 · 0.95 = 973 counts. The converter resolution is thus 313/973 = 0.3K, which is adequate. The circuitry shown in Figure 5.8 is really a digital integrator of the integrate-and-dump type, and the integration time is equal to the conversion time. Having selected N, the conversion time is determined by the clock frequency. If a 5-ms conversion time is required, the clock frequency is found to be 1,024/5 ms = 205 kHz. A simple modification of the circuit in Figure 5.8 will result in a digital integrator with variable integration time: increasing both counters (and the output register) with extra bits results in the integration time being multiplied by powers of 2 (τ = 5, 10, 20, 40 ... ms). Externally selectable counter length is easily implemented.
Radiometer Receivers on a Block Diagram Level CK
37
N-bit counter Delay
DATA
N-bit counter
N-bit register
Reset
Load
Figure 5.8 Output counter.
If the digital integrator has a range as assumed here (5, 10, 20 ... ms), it may not be practical to allow the analog integrator to have an integration time of 5 ms: The two integrators will influence each other when the digital integrator is in the 5-ms position, resulting in a slightly increased effective integration time. Lowering the analog integration time to some 2 ms alleviates the problem, and the radiometer’s integration times are determined solely by the digital integrator. 5.2.7
On the Sampling in the Radiometer: Aliasing
As already mentioned, the digital circuitry is an integrator of the integrate-and-dump type. Hence a sampling of the input brightness signal is carried out, and the sampling interval is equal to the digital integration time. Due to the sampling, we need to discuss the response of the radiometer to time-varying input signals. The transfer function of the analog part of the radiometer is determined by the analog integrator, which is an RC lowpass filter with 63.7-Hz cutoff frequency. The function is shown as HRC in Figure 5.9. Assume that the digital integrator is in its 10-ms position and the corresponding sampling frequency fS is 100 Hz. The transfer function of the digital integrator (H I ) is of the (sinx)/x type with zeros at n · 1/(10 ms) = n · 100 Hz. The transfer function (HTOT ) of the entire radiometer is shown as the third curve in Figure 5.9. It is seen that the radiometer does not in itself provide adequate band limiting of the input signal to below fS /2 in order to avoid aliasing. We must ensure that the input signal is itself band-limited. When measuring in a stationary case (calibration, for example), this is, of course, no problem, but in considering an imaging radiometer, it is an important issue. The band-limiting is carried out by the antenna through its radiation pattern and the rate at which this sweeps across the scene to be sensed; or, to put it differently, there are certain relationships between the antenna footprint dwell time and the integration and sampling time of the radiometer to be taken into account. More about this subject is covered in Section 11.4.
38
Microwave Radiometer Systems: Design and Analysis 0
50
100
0
f(Hz)
HRC
−10
fs
HI HTOT
−20 −30 −40 H(f) dB
Figure 5.9 Transfer function of the radiometer.
5.3 The Noise-Injection Radiometer In Figure 5.10 we show the block diagram of a noise-injection radiometer, using the Dicke radiometer discussed in the previous sections as a basis. The Dicke radiometer has only been modified slightly: the gain in the LF section has been increased by 50 dB to account for the loop gain already defined in Section 4.3. In principle, we want the difference between the reference signal and the sum of
1K
312 K
17.5 GHz TA
↔ 0K
31200K
-20 dB
∼ ∼ ∼ 16.5 GHz
24µVpp
∼ ∼ ∼ 10 MHz
G=25 dB
7 mV/µW
500 MHz
IF Mix - preamp
IF 30 dB
0.24Vpp
313 K −3 dB
∼
17.0 GHz
0.5 VDC/1 Vpp 9.5 V
Noise Switch HI = ON
80 dB AF
95%
−2 dB
10 V=100% ∆/Σ
DC
±1
0.12 V 1.57 sec
∫
38 dB
−2.5 dB Noise Diode ENR = 28 dB
Figure 5.10 Noise-injection radiometer, TA = 0K.
DATA CK = 205 kHz
FS = 2225 Hz
Radiometer Receivers on a Block Diagram Level
39
the antenna signal plus the injected noise to be zero (the error signal in the servo loop is zero). This would, however, require infinite loop gain. Let us assume a maximum error signal of 1K—equal to the sensitivity of the radiometer. The maximum error signal occurs when the antenna signal is 0K, requiring maximum injected noise. Hence, the gain of the LF section has to be increased to give full output for a 1-K signal after the Dicke switch (and not for a 313-K signal as was the case in the Dicke radiometer); 313 corresponds to 50 dB and the AF amplifier gain has been increased by 30 dB, the DC amplifier gain by 20 dB. The loop gain (313 = 50 dB) requires that the integration time of the RC integrator be changed to 5 ms · 313 = 1.57 seconds to maintain the 63.7-Hz cutoff frequency of the radiometer. The noise is injected in the antenna line through a 20-dB directional coupler. Thus, the antenna signal is not attenuated to any measurable level. The signal for injection is generated by a semiconductor noise diode giving a high, well-specified noise signal. A typical excess noise ratio (ENR) is 28 dB, corresponding to 183,000K (ENR = 10 log (TN/290 − 1)). The output from the diode cannot be changed, and the variable signal for the injection is obtained by rapidly switching the noise signal on and off with a variable duty cycle: The zero duty cycle (i.e., the switch is maintained in its off position) corresponds to no injected signal, and the maximum duty cycle (in this design, 95%—the switch is on for 95% of the time) corresponds to a signal loss of 0.2 dB. The noise switch is a microwave PIN diode switch, which typically exhibits very short switching times and a loss in the on position of some 2 dB. The switch is directly controlled from the K output of the ∆/Σ converter. Two fixed attenuators are finally selected to give the correct signal levels: The generated noise is 183,000K, and the injected noise is 312K (in the TA = 0K situation of Figure 5.10). This is a ratio of 27.7 dB. Hence, 20 + ATT + 0.2 + 2 = 27.7 and ATT = 5.5 dB, here selected as a 3-dB attenuator and a 2.5-dB attenuator. The noise-injection radiometer is really a servo system and an analysis of the stability in the feedback loop is necessary. In the low end of the spectrum, the dominant frequency-dependent factor in the open loop transfer function results from the analog integrator—a simple RC lowpass filter. No stability problems will arise when closing the feedback loop because all circuit blocks of the radiometer—apart from the RC integrator, of course—have bandwidths far beyond 63.7 Hz, which is the point of 0-dB loop gain. The Dicke switch and synchronous detector complex may require some consideration. The switching frequency (2,225 Hz) is much higher than any frequency of interest in this analysis. The switching (apart from giving a
40
Microwave Radiometer Systems: Design and Analysis
contribution to the signal level from the reference temperature load, which is constant and therefore can be omitted), results in turning on and off the input signal—including injected signal—with a duty cycle of exactly 50%. This is equivalent to an attenuation by a factor of 2, which will clearly not disturb the stability of the closed loop. The sensitivity of the radiometer is 1.2K as was the case for the Dicke radiometer counterpart (see Section 5.2.2). Other quite detailed descriptions of the noise-injection radiometer can be found in [1, 2].
5.4 The Total Power Radiometer As already mentioned earlier, the total power radiometer will first be designed as a DSB receiver without microwave preamplifier just like the Dicke type switching radiometers covered so far. That way, the differences and similarities between the two classes of radiometers are best discussed. After that, the total power radiometer is designed with a microwave preamplifier and SSB mode of operation, and the differences from the earlier design discussed.
5.4.1
DSB Receiver Without RF Preamplifier
Figure 5.11 shows the block diagram of the radiometer operating in the total power mode. When comparing with the Dicke radiometer (Figure 5.1), great similarities are obvious but also some important differences may be noted. In the RF circuitry the only difference is the lack of the Dicke switch. However, the total power radiometer requires frequent calibration and the latching circulator is maintained, but now serves the purpose of a calibration switch (utilizing the former reference load as a calibration load). More substantial changes are found in the LF circuitry. As the signal is no longer modulated with the Dicke switching frequency the circuitry after the detector will have to be DC-coupled. Thus, Shottky barrier detectors are not very useful; rather, the tunnel diode detector should be employed due to its low-frequency stability being orders of magnitude better than that associated with Shottky diodes. Furthermore, the low video resistance of the tunnel diode facilitates low impedance levels at the first amplifier stage, which in turn resists drift problems. The price to pay is that the tunnel diode detector has lower sensitivity, typically 1 mV/µW, meaning that extra amplification is needed after the detector to regain the signal level. This is illustrated in the block diagram by adding a 17-dB DC amplifier. The tunnel diode detector plus the 17-dB amplifier directly replace the original Shottky detector from a signal level point of
Radiometer Receivers on a Block Diagram Level TN = 640K 313 K
953 K 17.5 GHz
TA 0K
∼ ∼ ∼ 16.5 GHz
↔ 313 K CAL LOAD
640 K
41
23.1mVDC
3.31µW G=25 dB
500 MHz
∼ ∼ ∼ 10 MHz
IF Mix - preamp
∼
IF
1 mV/µW 17 dB DC
30 dB 2.22µW
17.0 GHz
15.5mVDC OFFSET
9.7 V 10 V = 100% ∆/Σ
-15.4 mV
7.7mV 5 msec
DC 62 dB
∫ 0.1mV
0.13 V
Calibration
DATA CK= 205 kHz
Figure 5.11 DSB total power radiometer, TA = 0K and 313K.
view, and the remaining gain (62 dB) can be compared directly with that of the Dicke radiometer (50 dB + 18 dB − 6 dB in the synchronous detector = 62 dB). It is seen that due to the DC coupling, the AF amplifier and the synchronous detector have been omitted and all gain has been attributed to the DC amplifier. Because the 640-K noise temperature of the radiometer itself is now also constantly present as a signal in the LF section, an offset is required for compensation (otherwise, a very inefficient use of the A/D converter would result). The gains in the radiometer (although somewhat rearranged in the LF section, as already mentioned) are the same as in the Dicke radiometer and a change in input temperature of 1K will again result in a change of 25 µV at the output of the detector—the detector now being understood as the tunnel diode detector plus the 17-dB amplifier (see Section 5.2.4). The noise considerations brought forward in Section 5.2.5 are equally applicable here, but we additionally have to consider noise properties around this 17-dB amplifier. The 25 µV after the amplifier corresponds to 3.6 µV at its input, still comfortably large compared with the typical 0.14 µVRMS noise of a good quality operational amplifier. Due to the DC coupling, however, drift in the LF circuitry (including the offset) referred to the input must stay at the same low level. This is a stringent requirement, and careful circuit design, including thermal stabilization, and frequent calibration are needed. The sensitivity of the radiometer is calculated using (4.2) and the parameter values also used in Section 5.2.2 to assess the corresponding Dicke
42
Microwave Radiometer Systems: Design and Analysis
radiometer sensitivity. For TA we conservatively use the highest possible value of 313K, and we find: ∆T =
313 + 640
0.5 ⋅10 9 ⋅ 5 ⋅10 −3 ∆T = 0.6K 5.4.2
K
SSB Receiver with RF Preamplifier
In the final block diagram of this chapter (Figure 5.12), the opportunity is taken to show the differences when the radiometer is implemented with a microwave preamplifier. According to the discussion in Section 5.1.2, this also means single sideband operation. The obvious differences between the two implementations are the addition of the microwave preamplifier and an associated redistribution of gain between this and the IF amplifier. Also the filters have been changed substantially: The input bandwidth is now 500 MHz, like the IF bandwidth. The input band has here been selected to be 17.0–17.5 GHz, corresponding to the upper half of the original radiometers input band. The IF is no longer at DC but here is selected to be 100–600 MHz, and the local oscillator is at 16.9 GHz. An important function of the RF filter is now to cancel the lower sideband (16.3–16.8 GHz). Requirements to out-of-band suppression in this filter is TN = 168K
481 K
313 K
17.5 GHz
∼ RF ∼ ∼ 20 dB 17.0 GHz
TA
0K
313 K CAL LOAD
21.0mVDC 2.96mW 1 mV/µW 17 dB 600 MHz
G=25 dB
∼ ∼ ∼ 100 MHz
IF Mix - preamp
IF
DC
15 dB
7.3mVDC
1.03µW
168 K
∼
16.9 GHz
OFFSET 9.8 V
10 V=100% ∆/Σ
DC 57 dB 0.07 V
Calibration
DATA CK 205 kHz
Figure 5.12 SSB total power radiometer, TA = 0K and 313K.
13.8mV 5 msec
∫ 0.1mV
-7.2 mV
Radiometer Receivers on a Block Diagram Level
43
determined by the lower cutoff frequency of the IF filter. It is not attractive to make this cutoff frequency too low, as that will lead to a requirement for a very rapid cutoff in the RF filter, that is, a filter of high order (cost, loss, bulk). It is important that the RF filter is after the preamplifier in order to filter away the lower sideband noise from this amplifier. Also, this arrangement ensures the lowest possible noise figure as the filter loss will not contribute. It can be discussed whether a modest, low loss filter might be required in front of the preamplifier in order to suppress strong out-of-band interference that might otherwise overload the preamplifier. Experience shows that this is generally not necessary, but it might be in specific cases. The calculations of signal levels in the radiometer follow the same procedure as outlined previously. A typical good quality low noise amplifier exhibits a noise figure of 1.5 dB. Adding to this 0.3 dB for the latching circulator and 0.2 dB for miscellaneous waveguide losses, we find the noise figure of the radiometer to be 2.0 dB. This is equivalent to a noise temperature of 168K. The gain of amplifiers before the detector is then calculated so that the maximum input noise (168 + 313)K leads to −25 dBm on the detector. The gain after the detector and the offset is then determined so that reasonable use of the A/D converter range is ensured. All these gains and levels are indicated on Figure 5.12. The sensitivity of the radiometer is again calculated using (4.2) but the system parameter values are now changed due to the improved noise temperature as a result of incorporating a high quality preamplifier. For TA we again conservatively use the highest possible value of 313K, and we find: ∆T =
313 + 168
0.5 ⋅10 9 ⋅ 5 ⋅10 −3 ∆T = 0.3K
K
A good quality microwave preamplifier is an important improvement! Note that as the instrument noise temperature is improved, the choice of antenna temperature becomes increasingly important. If it is known that the radiometer in question will only measure a low antenna temperature, this should be used in the sensitivity formula in order to yield a more realistic sensitivity than the conservative value calculated above.
5.5 Stability Considerations Having become more familiar with radiometer circuitry, at this stage it is appropriate to discuss further the merits of each radiometer type to elaborate some of the subjects covered in Chapter 4. We stated that the stability of the Dicke
44
Microwave Radiometer Systems: Design and Analysis
radiometer depends only on gain stability (provided that the reference temperature is known). With reference to Figure 5.1, this is not the whole truth: after the synchronous detector, the circuitry is DC-coupled, and drift in the DC amplifier (and A/D converter) will result in offsets in the radiometer output that are independent of the changes associated with gain variations. This is not a big problem, however, as the signal levels are rather high and the gain is modest. Turning to the total power radiometer, we found in Chapter 4 that the stability depended on both the gain and noise temperature of the radiometer. With reference to Figure 5.11, we see that a drift in the DC coupled low-frequency part of the radiometer will have the same effect on the radiometer output as a drift in the noise temperature. Now the problem requires a little more design effort as the signal levels in the DC-coupled circuitry are small and the gain is comparatively high. From a radiometer designer’s point of view, the AC coupling in the Dicke type of switching radiometer is an interesting feature. Although the drift problems in the total power radiometer can be alleviated by careful design and different countermeasures (such as frequent calibration), stabilities as we find in even a rather simple Dicke design is difficult to achieve. This is not to say that adequate stability for a given purpose cannot be achieved, but it requires effort and perhaps complexity. Also it must be noted that accuracy requirements/stability/calibration schedule must be considered together: Even a relatively unstable radiometer may be useful for a certain application if calibration can be carried out very often. This is discussed in detail in [3]. Finally, it shall be stressed that good stability and the quality of temperature stabilization of radiometer components in practice are closely tied together. Although many tricks can alleviate effects of inadequate thermal control, the importance of the latter cannot be disregarded if one strives for the ultimate in radiometric stability. In [4] the design goal is not the usual 1K or a fraction of a Kelvin stability, but rather milliKelvins! This leads to a design where the thermal stability of the front end is measured in milliCentigrades. Of course, such control is often not possible, and ways to alleviate the resulting problems must be found, like frequent calibration or modeling; see, for example, Chapter 10.
References [1]
Hidy, G. M., et al., Development of a Satellite Microwave Radiometer to Sense the Surface Temperature of the World’s Oceans, NASA Report No. CR-1960, 1972.
[2]
Harrington, R. F., “The Development of a Stepped Frequency Radiometer and Its Applications to Remote Sensing of the Earth,” NASA Technical Memorandum No. 81837, Langley Research Center, 1980.
Radiometer Receivers on a Block Diagram Level
45
[3]
Racette, P. E., “Radiometer Design Analysis Based upon Measurement Uncertainty,” Ph.D. thesis, George Washington University, 2005.
[4]
Tanner, A. B., “Development of a High-Stability Water Vapor Radiometer,” Radio Science, Vol. 33, No. 2, 1998, pp. 449–462.
6 The DTU Noise-Injection Radiometers Example As an example of realization of the design considerations in Chapter 5, the noise-injection receivers employed in the first generation of the DTU airborne multifrequency radiometer system will be reviewed. A more detailed description can be found in [1, 2]. The system comprises three receivers at 5, 17, and 34 GHz. The major electrical characteristics are shown in Table 6.1. The design of the 17-GHz radiometer is very close to that given in Chapter 5 (NIR mode only). The two other radiometers are of equivalent design. The only major differences between the radiometers (apart from the frequencies, of course) is that the 34-GHz radiometer features two antenna inputs and an associated switch, while the 5-GHz radiometer has half the bandwidth of the others and employs a microwave preamplifier before the mixer to enhance performance. One of the basic assumptions in the noise-injection radiometer concept is the stabilization of the front-end microwave components to a temperature equal to the radiometric reference temperature. Hence, a temperature-stabilized enclosure is designed for these components. The directional coupler, Dicke switch, reference load, microwave filter, and the isolator have to go inside the enclosure but other components may well be included if advantageous. It is reasonable to keep the mixer-preamplifier (and possible RF amplifier) close to the other microwave components to minimize waveguide losses and to avoid an extra waveguide through the isolation of the temperature stabilized box.
47
48
Microwave Radiometer Systems: Design and Analysis
Table 6.1 DTU NIR Specifications Frequency
5 GHz
17 GHz
34 GHz
Bandwidth
250 MHz
500 MHz
500 MHz
Noise figure
4.5 dB
5 dB
5 dB
Sensitivity (τ = 8 ms)
1.15K
0.95K
0.95K
Sensitivity (τ = 64 ms)
0.41K
0.34K
0.34K
Integration times
4, 8, 16, 32, 64 ms
Input range
0–313K
The noise generating diode represents a special problem. The ENR of the diode has a typical temperature dependence of 0.01 dB/°C which on a 312-K level amounts to: 312 ⋅ 0.0023 = 0.72 K ° C Thus, temperature stabilization of the noise diode is obviously important, and the components in Table 6.2 will be mounted in the temperature-stabilized enclosure (see Figure 6.1). Note that the discussion about which components should go inside the thermally stabilized enclosure was specific for a noise injection radiometer. For total power and Dicke radiometers—being dependent on noise figures and gains
Table 6.2 Components in Enclosure The RF chain
Probe coupler Dicke switch Reference load Filter Isolator (RF amplifier—if included) Mixer-preamplifier Local oscillator
The noise injection branch Noise diode Attenuator Switch Attenuator
The DTU Noise-Injection Radiometers Example IF OUT
Heating wires
Noise generator
Mixer
49
Pre-amplifer
Isolator Local oscillator Filter
Switch
ATT
40°C Dicke switch ATT
Reference load
Probe coupler Silver coated pertinax Input Foam isolation Temperature sensor
Figure 6.1 Microwave components in temperature-stabilized enclosure.
that are again very dependent on physical temperature—the choice is clear: All microwave and IF components have to be carefully thermal stabilized. The components are mounted in an inner aluminum box having heating wires glued to the face-plates, and this box is mounted in a foam lined outer box. The heating wires are supplied from a power supply regulated from a thermistor
50
Microwave Radiometer Systems: Design and Analysis
at one of the faceplates. A temperature of 40°C is thus maintained. The microwave components are mounted without metallic contact to the box and all heat transfer takes place via the air, forced to circulate inside the enclosure by a fan. The system is quite slow in reaching temperature equilibrium, but a very uniform temperature distribution is ensured. To prevent heat flow in the input waveguide, it is made out of silvercoated Pertinax and it includes a Mylar window. However, temperature gradients inside the stabilized enclosure cannot be fully avoided in practice (some components are active and generate heat) and a thermometer monitoring the actual temperature of different components is incorporated. The data from this thermometer may then form the basis for later corrections of the measured radiometric temperatures. Small platinum sensors are glued onto eight components in the enclosure. The digital thermometer has a range of 38.0 to 46.0°C and a resolution of 32 counts/°C (the temperature is found as T = counts/32 + 38.0°C). The accuracy has proven to be better than two counts, that is, somewhat better than 0.1°C. The thermometer is wired as shown in Table 6.3. Table 6.4 shows the temperature distributions inside the radiometer front ends as measured by the digital thermometer. Two cases are shown: 1. The temperature without power to the microwave components, in which case a very uniform distribution is to be expected; 2. The temperature with the components powered. As may be seen from the table, the temperature distribution is indeed quite uniform in the case of no power. Note especially that the thermally isolating input waveguide is working satisfactorily (see sensor 00). With the microwave components powered, the temperature differences are 1.6°C maximum. Recalling also that the antenna noise temperature at this stage—after injection—is in the 40°C range (actually close to the temperature measured by the sensor at the reference load), the deviations from uniformity are supposed to be of no importance. Assuming a component having a loss of typically 0.2 dB and a physical temperature (To) 1°C off the noise signal passing through it, we have the following situation: T 2 = (1 − l )T 1 + l ⋅T o
T D = T 2 − T 1 = l(T o − T 1 ) T D = 0.047 ⋅1 = 0.047K , which is satisfactorily small
The DTU Noise-Injection Radiometers Example
51
Table 6.3 Guide to Sensor Numbers Sensor Number 34 GHz
17 GHz
5 GHz
00
Dicke switch
Probe coupler
Probe coupler
01
Mux switch
Reference load
Dicke switch
02
Reference load
Dicke switch
Reference load
03
Isolator
Microwave filter
Microwave filter
04
Mix-preamplifier
Isolator
Isolator
05
Diode switch (1)
Mix-preamplifier
Mix-preamplifier
06
Diode switch (2)
Diode switch
Diode switch
07
Noise generator
Noise generator
Noise generator
Table 6.4 Temperature Distributions in the Front Ends Sensor Number No power
Power
34 GHz 17 GHz 5 GHz 34 GHz 17 GHz 5 GHz 00
39.6
40.3
39.9
41.8
42.0
40.5
01
39.6
40.4
40.0
41.3
41.9
40.6
02
39.6
40.3
40.0
41.6
42.8
40.3
03
39.6
40.3
40.0
41.7
41.8
40.3
04
39.6
40.3
40.0
42.0
41.2
40.1
05
39.6
40.3
40.1
41.5
41.2
40.3
06
39.5
40.5
40.1
41.5
42.2
41.4
07
39.7
40.3
40.1
41.9
42.0
41.7
The temperature distributions shown in the table have proven to be very stable with time, and the absolute level marginally dependent on environment temperature. In addition to the eight channels for measuring the internal temperatures in the front end, the digital thermometer of each radiometer also has eight channels for measuring external temperatures. The range of these external sensors is –34°C to +30°C with a resolution of 4 counts/°C. The external channels are intended for measuring temperatures of lossy input devices like antenna feeds and waveguide runs, thus enabling later corrections of radiometric data.
52
Microwave Radiometer Systems: Design and Analysis
Figure 6.2 shows a photo of the 17-GHz radiometer telling more about the mechanical layout than words can. In the overview photo of the radiometer system (Figure 6.3), we see all three receivers plus two additional units necessary for the operation of the receivers: a digital processing unit and a power supply unit. The radiometer system is set up in the lab for a simple calibration as shall be described in Chapter 9. The digital processing unit collects the digital data from the three radiometers (transmitted in serial form by the ∆/Σ converters). It contains the counters of variable length (selectable integration time). The radiometer data is mixed with auxiliary data from the digital thermometer, and from an interface to the aircraft inertial navigational system (INS) before being formatted properly for a suitable recording system. The unit contains all controls for the radiometer system and displays for monitoring the receiver operation.
Figure 6.2 A view inside the temperature stabilized box of the 17-GHz radiometer. From left to right: probe coupler, latching circulator and reference load, filter, isolator, Gunn oscillator, and mixer-preamplifier. Following the semirigid line from the probe coupler, note the attenuator, diode switch, attenuator, and noise generator.
Figure 6.3 From right to left: the 5-GHz radiometer, the 17-GHz radiometer on top of the 34-GHz radiometer, and the digital processing unit on top of the power supply unit. The radiometers are via waveguides connected to calibration loads in a freezer for calibration purposes (see Chapter 9).
The DTU Noise-Injection Radiometers Example
53
The central power supply unit converts the primary power to preregulated voltages for the radiometers and the processing unit. Only linear power supplies are used. Switch mode power supplies should be avoided in radiometer designs due to possible interference.
References [1]
Skou, N., “Design of an Airborne Multifrequency Radiometer System,” Electromagnetics Institute, Tech. Univ. of Denmark, R 221, 1979.
[2]
Skou, N., “Airborne Multifrequency Radiometry of Sea Ice,” Electromagnetics Institute, Tech. Univ. of Denmark, LD 42, 1980.
7 Polarimetric Radiometers 7.1 Polarimetry and Stokes Parameters Generally, the radiation from an object is partly polarized, meaning that the brightness temperature at vertical polarization TV is different from the brightness temperature at horizontal polarization TH. A well-known example is the sea surface. To describe scenes with partial polarization, it is convenient to use the Stokes parameters. The Stokes vector is: E V2 + E H2 I Q 1 E V2 − E H2 I = = U z 2 ⋅ Re E V ⋅ E H* * V 2 ⋅ Im E V ⋅ E H
(7.1)
where z is the impedance of the medium in which the wave propagates. It is seen that I represents the total power, Q represents the difference of the vertical and horizontal power components, and U and V represent, respectively, the real and imaginary parts of the cross correlation of the electrical fields. Assuming that the Rayleigh-Jeans approximation is valid for signals in the microwave regime, the Stokes vector for the fields in (7.1) can be converted to an equivalent brightness temperature Stokes vector:
55
56
Microwave Radiometer Systems: Design and Analysis
TB =
λ2 ⋅I k
(7.2)
where λ is the wavelength and k is Boltzmann’s constant. The parameters ofT B λ2 are termed IB, QB, UB, and VB where I B = ⋅ I and so on. It can be shown that: k U B = T 45 ° − T −45 °
(7.3)
VB = T l − T r
where T45° and T−45° represent orthogonal measurements rotated 45° with respect to the reference directions for V and H polarizations, andT l and Tr refer to left-hand and right-hand circular polarized quantities. It is common in the radiometer literature to use the notations I, Q, U, V to mean the brightness Stokes parameters (rightfully termed IB and so on), so we can write: I T V + T H Q T V − T H λ2 TB = = = U T 45 ° − T −45 ° k ⋅ z V T l − T r
E V2 + E H2 2 2 EV − E H 2 ⋅ Re E ⋅ E * V H * E E ⋅ ⋅ 2 Im V H
(7.4)
and we shall adopt this notation here. This definition directly points to two fundamentally different ways of implementing the polarimetric radiometer system. In both cases the first and second Stokes parameters are measured conventionally using vertically and horizontally polarized (that is, normal linearly polarized) radiometer channels, followed by addition or subtraction of the measured brightness temperatures. The third Stokes parameter can be measured with a conventional two-channel radiometer connected to an orthogonally polarized antenna rotated 45° with respect to the V and H directions, and subtracting the measured brightness temperatures. The fourth Stokes parameter can be measured with the two-channel radiometer connected to a left-hand/right-hand circularly polarized antenna system. In the following sections we shall use the term polarization combining radiometer for this case, and we note that we are dealing with a fully incoherent case, as all Stokes parameters are found by addition or subtraction of brightness temperatures (i.e., detected power). Alternatively, returning to (7.4), we observe that all Stokes parameters are measured by a two-channel correlation radiometer (employing a complex correlator) connected to a conventional horizontally and vertically polarized
Polarimetric Radiometers
57
antenna system. We shall use the term correlation radiometer in the following sections, and we note that this is partly a coherent case, where we have to preserve phase and keep coherence between channels up to the correlator, in order to find the product between the vertical and horizontal electrical fields.
7.2 Radiometric Signatures of the Ocean As an example to illustrate typical signal levels, let us consider the ocean surface. The brightness temperature of the ocean depends on the wind speed and direction. At incidence angles around 50°, and in the frequency range Ku- and Ka-bands, the dependence is some 0.5K per meters per second wind at vertical polarization, and somewhat larger at horizontal polarization: 1–1.5K per meters per second; see, for example, [1]. This means that traditional radiometer measurements with an accuracy of 1K allows determination of the wind speed to better than 1 m/s (excluding other error sources), which can be regarded as quite satisfactory. However, the measurement of the Stokes parameters, in order to assess wind direction, places more stringent requirements on the accuracy of the radiometers. Typical variations in Q and U are 4–6K peak to peak and less regarding V (see [2–4]). This means that the measurement accuracy must be a fraction of a Kelvin, which is not easy for traditional radiometers.
7.3 Four Configurations 7.3.1
Polarization Combining Radiometers
The first configuration to be discussed is the full multiplex polarization combining radiometer outlined in Figure 7.1. The outputs from a normal horizontally and vertically polarized antenna are connected via a switchable microwave combination network to a single radiometer carrying out all necessary measurements in sequence. The switches can be PIN diode switches, which have good isolation properties. By combining the horizontal and vertical signals in a magic tee, providing the sum and difference signals, we obtain +45° and –45° linear polarizations (phase shifter, PS, set to 0°). With the phase shifter set to 90°, the combined signals from the magic tee become right-hand and left-hand circular polarizations. Table 7.1 gives an overview of switch positions versus measured brightness temperature component. Finally, a switch and reference load for Dicke operation or frequent calibration is shown in front of the receiver. The positive aspects of this radiometer system are: • With a suitable switching sequence we obtain a very satisfactory deter-
mination of the important second and third Stokes parameters even
58
Microwave Radiometer Systems: Design and Analysis
SWA
1
1 ver/hor
2
2
SWC 1 SWE
ver
Dicke/cal
PS 0/90° hor
SWB
RX
2
1 Σ
2
∆
−45 or ᐉ 1 SWD
REF
+/− 45 or r/ᐉ
2
+45 or r
OUT
Figure 7.1 Full multiplex polarization combining radiometer.
Table 7.1 Correspondence Between Positions of Switches in Figure 7.1 and Measured Brightness Temperature Component SWA SWB SWC SWD SWE PS
TV
1
d.c.
1
d.c.
1
d.c.
TH
d.c.
1
2
d.c.
1
d.c.
T45°
2
2
d.c.
2
2
0°
T−45°
2
2
d.c.
1
2
0°
Tr
2
2
d.c.
2
2
90°
Tl
2
2
d.c.
1
2
90°
(d.c. = don’t care)
without Dicke switching: they are found by subtracting the output values from one single receiver where the input is switched rapidly between two signals—quite analogous to the situation in a traditional Dicke radiometer, and gain and noise drifts/fluctuations are largely cancelled. • Only one radiometer receiver is required. Also note that, on a neutral note, with Dicke switching or frequent calibration we also get a good determination of the normal TH and TV signals. The negative aspects of this radiometer system are:
Polarimetric Radiometers
59
• The system sensitivity is hampered by substantial loss in the polariza-
tion combining network (may be alleviated by preamplifiers up front). • The potential sensitivity is very poor due to low duty cycle because all
measurements have to be multiplexed through a single receiver. Sensitivity may be regained with long integration time, precluding the use of this configuration in imaging systems where short integration time normally prevails. • The system requires complicated microwave combining and switching
hardware.
A system of this type has been used with great success by JPL for their airborne, profiling (nonimaging) measurements of ocean waves [2, 3]. The second configuration to be discussed is the parallel receiver polarization combining radiometer as shown in Figure 7.2. This is an alternative version of the system described above, where the same polarization combinations are produced, not sequentially by switching, but simultaneously using power dividers (and again magic tees and a 90° phase shift). Preamplifiers (with substantial gain) up front are a necessity in this configuration or the power divider scheme would strongly degrade the sensitivity. Six identical radiometers—these could be total power or Dicke—are required to measure the different polarization combinations. The positive aspect of this system is that parallel channels ensure optimum sensitivity (no duty cycle problems) appropriate for applications in imaging systems be it airborne or spaceborne.
3w div Σ
REF
∆
ver
RX 1
TV
RX 2
T−45
RX 3
T+45
RX 4
Tr
RX 5
Tᐉ
RX 6
TH
90°
hor REF
Σ
∆
3w div
Figure 7.2 Parallel receiver polarization combining radiometer.
60
Microwave Radiometer Systems: Design and Analysis
On a neutral note, Q, U, and V are found by subtraction of individual receiver’s outputs, leading to potential stability problems. The problem is partly alleviated by proper design where identical receivers track in temperature and supply voltages, and by Dicke switching or frequent calibration. In the present case Dicke switching may not be attractive due to the sensitivity penalty, whereas frequent calibration is readily possible while the scanning antenna looks away from the useful swath anyway (see Chapter 13). Also, frequent calibration ensures good determination of TV and TH. The negative aspect of this system is that the system requires six receivers and complex microwave hardware. 7.3.2
Correlation Radiometers
The first system to be described under this headline is the basic correlation radiometer shown in Figure 7.3 (based on Figure 4.6). Two identical total power receivers are connected to the horizontal and vertical outputs of the antenna system. The outputs of the receivers are detected the usual way to yield the normal horizontally and vertically polarized brightness temperatures. The outputs of the receivers are also (at IF level) fed into the complex correlator providing the U and V Stokes parameters after multiplying the real and the imaginary outputs by a factor 2 [see (7.4)]. The complex correlator consists of two sections each having a multiplier and an integrator. The real section operates directly on the outputs from the receivers, while the imaginary section multiplies the output from one receiver with the output from the other phase-shifted 90°. The correlator can be implemented in analog or digital technology. In the following, digital implementation is assumed due to better stability, and technology is no longer a problem for typical radiometer bandwidths around 500 MHz or less. See, for example, [5] for a brief description of such circuitry. The radiometers are generally implemented as superheterodyne receivers to enable the correlator to work REF TV
RX 1 ver LO hor
∼ RX 2
REF
Figure 7.3 Basic correlation radiometer.
Real complex Imag corr.
U/2 V/2 TH
Polarimetric Radiometers
61
at a suitable IF frequency. The correlation technique requires phase coherence between the two receivers. This is achieved by using one common local oscillator. The positive aspects of this configuration are: • Parallel channels ensure optimum sensitivity. • U and V are very well determined. This is associated with the way in
which the correlation radiometer works. The output of the digital correlator is the correlation coefficient ρ (typically around 0.01) which must be multiplied with the total system temperature TS (typically around 500K) to yield the true cross correlation between the two channels. The error in U can be expressed as δU = δρ · TS + ρ · δTS, where δρ is the error in the correlation coefficient, and δTS is the error in the knowledge of the system temperature. Due to the small values of ρ typical of measurements when observing natural scenes, the second term vanishes with any reasonable radiometric error, and the first term is very small, as a digital correlator can be made almost perfect. • The system requires only simple microwave circuitry.
On a neutral note, Q is found by subtraction of individual receiver’s outputs—see the earlier discussion concerning the parallel receiver polarization combining system. Also, frequent calibration ensures good determination of TV and TH. A negative aspect of this is that a fast digital correlator is needed. In the past, digital circuitry with clock frequencies around 1 GHz was bulky and power-consuming. However, with present-day technology, a three-level complex digital correlator can be implemented in a single chip consuming no more than 1W of power. A system of this type has been used with great success by DTU for airborne, imaging measurements of ocean waves [6]. The final system to be considered here is the switching correlation radiometer outlined in Figure 7.4. It is just a small enhancement of the basic correlation radiometer in which a crossover switching arrangement is added between the antenna and the receivers, and corresponding synchronous demodulators are added after the detectors. The crossover switches and synchronous demodulators operate simultaneously. A fast switching sequence as in a Dicke radiometer is assumed. Each of the two radiometers will now act as a Dicke type switching radiometer on the difference between vertical and horizontal polarization with the associated, well-known stability. The correlation processes are not influenced by the switching (the imaginary signal must be demodulated like the Q signals, which is easy in the digital circuitry, and not shown in the figure). A
62
Microwave Radiometer Systems: Design and Analysis REF ±1
RX 1
Q TV
ver LO hor
∼
U/2
Complex corr.
V/2 TH
RX 2
±1
Q
REF
Figure 7.4 Switching correlation radiometer.
potential problem is multiple reflections between the antenna, the switch matrix, and the first amplifier. Phase changes due to the switching action may lead to unwanted offsets. This must be further considered in an actual design and trade-off phase. The positive aspects of this configuration are: • Parallel channels ensure optimum sensitivity. • The important Stokes parameters Q, U, and V are all very well
determined. Some neutral notes are that frequent calibration ensures good determination of TV and TH, and the system requires slightly more complicated microwave circuitry than the basic correlation radiometer. A negative aspect of this system is that there are possibly problems with reflections within the microwave circuitry.
7.4 Sensitivities The sensitivity of the full multiplex polarization combining radiometer will not be discussed further here. It has already been mentioned that the potential sensitivity is poor, due to the fact that all measurements are multiplexed through a single receiver. Hence, this configuration is only useful where sensitivity is not an issue (nonimaging airborne or ground-based systems). Concerning the parallel receiver polarization combining radiometer, the sensitivity is assessed rather easily assuming identical receivers and identical
Polarimetric Radiometers
63
preamplifiers. Thus, the sensitivity of any radiometer channel (vertical, horizontal, +45°, ....) is that of a standard total power radiometer: ∆TTPR. Going to the Stokes parameters, this means that ∆I = ∆Q = ∆U = ∆V = 2 · ∆TTPR [∆I is the sensitivity (standard deviation) of the first Stokes parameter and so on], as they all are found by addition or subtraction of statistically independent signals with identical standard deviation ∆TTPR. For the basic correlation radiometer, we find as above ∆I = ∆Q = 2 · ∆TTPR assuming identical receiver performance. The correlator outputs have a sensitivity that (as already described in Section 4.4) can be found by considering the analogy to the radio astronomer’s interferometer with correlation receiver: If the interferometer observes a small source in the boresight direction, and it is assumed that the two radiometer channels collect equal but independent background noise, the sensitivity is expressed as ∆T = ∆T TPR / 2 (the two receivers are identical with a sensitivity ∆TTPR). In this case we also have a correlation receiver, but now one connected to the V and H ports of one antenna observing for example the sea surface. The V and H signals are only weakly correlated and can be modeled as sums of large “background” signals (uncorrelated channel to channel) and a small correlated signal. As before, we then find ∆T = ∆T TPR / 2, only assuming that the system temperatures in the two channels are equal, which is a fair assumption, although not fully correct, as the vertical and the horizontal brightness temperatures of the sea surface generally are somewhat different. However, the difference is relatively small and the addition of the receiver noise temperatures to find the system noise temperatures tends to further equalize the signals. Recalling the factor 2 in (7.4), we then find for the third and fourth Stokes parameters: ∆U = ∆V = 2 · ∆TTPR. We note that concerning sensitivity, there is no difference between the parallel receiver polarization combining radiometer and the basic correlation radiometer. They are both optimal in this respect. In the switching correlation radiometer each of the Q outputs will exhibit a sensitivity corresponding to that of a Dicke radiometer (i.e., 2 · ∆TTPR), assuming a radiometric performance of the receivers as before; but there are two of them, and they are statistically independent (when one channel measures the vertical brightness temperature, the other measures the horizontal and visa versa), so by combining them, we gain a factor of 2, and obtain a resulting sensitivity of ∆Q = 2 ⋅ ∆T TPR . As before, we find ∆U = ∆V = 2 ⋅ ∆T TPR as the correlation process is not influenced by the switching. Concerning sensitivity, this configuration is also optimal. The main advantage of this configuration is that we get the three important Stokes parameters Q, U, and V with “Dicke” stability yet without loss of sensitivity. However, in all fairness, it should be noted that the crossover switches have been assumed to be lossless. In real life a small sensitivity penalty will have to be sustained due to inevitable losses in these switches.
64
Microwave Radiometer Systems: Design and Analysis
7.5 Discussion of Configurations For basic airborne measurements of polarimetric signatures using circle flights with a staring (nonimaging) radiometer, the first configuration, the full multiplex polarization combining radiometer, is a strong candidate due to its relative simplicity and its very good determination of the important three Stokes parameters: Q, U, and V. For any imaging applications, as, for example, a future spaceborne mission to measure wind over the ocean, only the three other configurations are candidates due to severe requirements on sensitivity. The correlation technique seems to be a strong candidate, trading substantial microwave hardware for fast digital circuitry. With present technology, the required digital correlator is definitely feasible, and the development of digital technology is rapid, making it even more feasible in the near future. However, it should be noted that the present and future development of MMIC technology makes implementation of complex microwave hardware feasible. It must also be mentioned that the statement that the parallel receiver polarization combining radiometer and the correlation radiometer exhibit identical sensitivity is based on the assumption that they have identical bandwidths. If the bandwidth requirements are in excess of 1 GHz, which could be the case at Ka-band and above, it is felt that the digital correlator may be difficult to realize with present technology. Finally, it is noted that an ideal digital correlator with a sufficient number of bits has been assumed. If only a few bits (typically 1 or 2 bits for wideband applications) are used, some sensitivity degradation is observed [5]. The degradation can typically be 15%, as discussed later in Section 7.6, but it is dependent on the oversampling rate and the actual number of bits. The detailed trade-off between the parallel receiver polarization combining radiometer and the correlation radiometer requires technical studies including bandwidth, weight, volume, and power budgeting on a case-by-case basis. The choice between the basic correlation radiometer and the enhanced switching version is also not straightforward. No doubt, the switching system is superior in determining the Q parameter, but the question is, whether a modern, well-designed, paired set of receivers cannot do an adequate job. This requires further investigations of real hardware.
7.6 The DTU Polarimetric System As an example of polarimetric radiometer systems, aspects of the DTU ocean wind sensing system will be briefly described. The radiometers are of the basic correlation type as described earlier. This does not reflect a choice based on a detailed technical trade-off as described in the previous sections. Actually, the
Polarimetric Radiometers
65
radiometers were designed and built first, and these considerations were carried out afterwards—inspired by discussions with other researchers who were in favor of other implementation possibilities. The main reason for the following description of specific hardware is that—apart from the fact that real examples always further understanding—this gives an opportunity to touch on several aspects of proper radiometer design. The airborne, imaging, polarimetric DTU system features radiometers at Ku- and Ka-band. They are of identical design. The correlation radiometer employs two single sideband superheterodyne receivers (see Figure 7.5). The local oscillator frequency is 16 (or 34) GHz and the IF band is 75–475 MHz. The two total power receivers are connected to the vertical and the horizontal outputs of a dual polarized feed horn. Fast switches (latching circulators) are included for frequent calibration. It can be stressed that, in order for the correlation radiometer to work properly, the two receivers must be of the single sideband type. If DSB receivers were employed, the fourth Stokes parameter would always be zero since the
REF
∼ ∼ ∼
∼ ∼ ∼
∼ ∼ ∼ ver ϕ
A/D
TV
0° 0/180°
Σ ∆
hor
∫
IF
RF
~
Real 90°
LO
0°
0°
U/2
Complex digital corr. Imag V/2
∼ ∼ ∼ 90°
∼ ∼ ∼
RF REF
Figure 7.5 DTU correlation radiometer.
∼ ∼ ∼
IF
∫
A/D
TH
66
Microwave Radiometer Systems: Design and Analysis
contributions from the upper and the lower sidebands cancel due to the phase relationships in the system. The correlation technique requires phase coherence between the two receivers in order to measure the complex correlation between input signals. This is achieved by using one common local oscillator. The phase shifter between the local oscillator and the mixer in the horizontal channel is used to achieve phase balance in the two channels. It is adjusted to maximize the real part of the output signal (minimize the imaginary output) for equal, correlated input signals. These signals are generated by an external calibration system: A noise diode feeds a power divider, and the two identical signals are connected via identical attenuators and transmission lines to the inputs of the correlation radiometer. Experience has shown excellent phase stability and that the phase shifter only has to be checked and possibly adjusted when cables or components of the radiometer have been disconnected and reassembled. High isolation between the two channels is required. If a signal in one channel leaks to the other channel, this leaked signal and its source will correlate, and the output from the correlator will exhibit an offset, that is, a nonzero value even for completely uncorrelated inputs to the radiometer system. The local oscillator distribution circuitry is especially critical as it provides a direct path between the radiometer channels. A minimum isolation of 70 dB at RF as well as IF frequencies is obtained by a combination of isolators and waveguide filters. The isolators take care of RF frequencies, but cannot be expected to operate well at the much lower IF frequencies, while even the simplest waveguide filter effectively will cut off IF stray signals. When considering isolation issues, examine Figure 7.6 and recall that the detectors in a radiometer operate in the square law range. Assume identical receivers and system noise temperatures of 500K. Hence, the outputs T1 = T2 = 500K, while the correlator outputs are nominally zero, since the signals in the two receivers are assumed uncorrelated. At some point in receiver 1, where the leak to receiver 2 takes place, the 500-K output signal corresponds to a voltage g·V1
RX 1 V1 70 dB
x2
T1 = 500 K
Real Complex Imag corr.
V2 RX 2
g·V2
x2
+0.00032·g·V1
Figure 7.6 Leak signals in the correlation radiometer
T2 = 500 K
Polarimetric Radiometers
67
V1 and if the total gain between this point and the square law detector is g, we have: (g · V1)2 = 500K, and likewise in receiver 2. Assuming a leak of 70 dB (corresponding to 0.00032) between receivers, we have at the input of the detector and of the correlator in receiver 2 a signal 0.00032 · g · V1 and accordingly at the correlator output: g · V1 · 0.00032 · g · V1 = (g · V1)2 · 0.00032 = 500 · 0.00032 = 0.16 K . This signal may be in the real or in the imaginary channel dependent on phase details in the leak path. A similar signal arises via the leak from receiver 2 to receiver 1. The signals add according to phase details, and it is seen that the 70 dB of isolation will ensure a worst-case offset on the correlator output with a value of 0.3K (which seems reasonable, bearing in mind the small polarimetric signals that we intend to measure). This value is actually further reduced due to the fringe washing effect: The leak signal is not a monochromatic signal, but has in the present case a bandwidth of 400 MHz, and this, in combination with the leak signal electrical path length, causes decorrelation. Thus, we observe less than 0.1-K offset in practice. The network used to feed the analog detectors and the digital correlator consists of: (1) an in-phase two-way power divider used to divide the signal between the digital correlator and the analog detector circuit, and (2) a quadrature hybrid to make in-phase and 90° out-of-phase signals for the correlator. The analog detector is a tunnel diode detector, and this is followed by an integrator. The digital correlator consists of a multilayer printed circuit board with a three-level (2-bit) A/D conversion at the input and proper multipliers. The sampling rate is 1,540 MHz and an 8-ms averaging is carried out on the correlator outputs. The circuit board also holds circuitry for monitoring the quantization levels. This information is used for the normalization of the correlation values. Offsets on the output of the correlator are reduced significantly by phase-switching the local oscillator signal to one of the channels and properly demodulating after the correlator. This is implemented by switching the local oscillator at a 1-kHz rate between the sum and difference ports of a magic tee. The demodulation is done inside the digital correlator. The injection of uncorrelated noise in the two receivers from two independent loads is used to calibrate for the remaining offsets. The loads may be the same as those used for frequent calibration checks as well. The correlation radiometer concept requires a matched pair of receivers, and phase characteristics are especially important. The phase difference between receivers is described by a mean phase difference over the receiver frequency band, and an RMS term. The mean phase term cause a shift of U signal into the V channel and V into U. This is compensated for by the phase shifter in the local oscillator section. The RMS phase term causes some decorrelation between channels [5]. To find the correct correlation between measured signals in the radiometer system, a correction factor has to be applied. This correction factor is
68
Microwave Radiometer Systems: Design and Analysis
found by coupling known amounts of correlated noise from a common noise diode into the two radiometer inputs and checking the correlator outputs. The analog integration in the total power radiometers is 4 ms, and later a digital integration to 8 ms is carried out. The resulting radiometric sensitivity for the vertical (or horizontal) channel has been measured to 0.35K, which is very close to the theoretical value found using measured system noise temperatures and the normal sensitivity formula for a total power radiometer. The sensitivity of the correlation measurements (i.e., the third and fourth Stokes parameters) is then, following the discussion in Section 7.4, expected to be 0.35 · 2K. However, this figure must be further degraded by a factor of 1.15 due to the three-level digital correlator with a factor 1.6 oversampling rate [5]. Thus, the final sensitivity is expected to be 0.57K, which is in fair agreement with measured values of 0.59K (U ) and 0.52K (V ). The radiometer system just described is combined with a 1-m aperture scanning reflector antenna system, designed for operation from the open ramp of a C-130 Hercules transport aircraft. Several campaigns have been carried out over the ocean in order to investigate how well wind direction can be determined by an imaging, polarimetric system; see, for example, [6].
References [1]
Sasaki, Y., et al., “The Dependence of Sea-Surface Microwave Emission on Wind Speed, Frequency, Incidence Angle, and Polarization over the Frequency Range from 1–40 GHz,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 25, No. 2, 1987, pp. 138–146.
[2]
Yueh, S. H., et al., “Polarimetric Measurements of Sea Surface Brightness Temperatures Using an Aircraft K-Band Radiometer,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 33, No. 1, 1995, pp. 85–92.
[3]
Yueh, S. H., et al., “Polarimetric Brightness Temperatures of Sea Surfaces Measured with Aircraft K- and Ka-Band Radiometers,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 35, No. 5, 1997, pp. 1177–1187.
[4]
Skou, N., and B. Laursen, “Measurement of Ocean Wind Vector by an Airborne, Imaging, Polarimetric Radiometer,” Radio Science, Vol. 33, No. 3, 1998, pp. 669–675.
[5]
Thompson, A. R., J. M. Moran, and G. W. Swenson, Interferometry and Synthesis in Radio Astronomy, Malabar, FL: Krieger, 1991.
[6]
Laursen, B., and N. Skou, “Wind Direction over the Ocean Determined by an Airborne, Imaging, Polarimetric Radiometer System,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 39, No. 7, 2001, pp. 1547–1555.
8 Synthetic Aperture Radiometer Principles 8.1 Introduction In remote sensing, situations arise that require radiometric measurements with large antennas that must be scanned (moved) in order to form images. An example occurs in remote sensing of soil moisture where science requirements for spatial resolution lead to antenna systems so large that they may not be practical. Requirements already exist for antennas in excess of 10m in diameter for remote sensing from space [1]. Aperture synthesis is a technique for overcoming the limitation that a large antenna aperture places on passive microwave remote sensing from space. This is an interferometric technique in which pairs of small antennas are used together with signal processing to achieve the resolution of a single large aperture antenna. In this technique, the product of the signal from each pair of antennas is measured using a correlation radiometer (see Figure 8.1 and also the basic correlation radiometer in Chapter 7). The complex product (real and imaginary part) is recorded for pairs of antennas at many different spacings. The spacing is called a baseline and both the magnitude and orientation of the distance between the antennas is important. It can be shown that the output signal at each baseline produces a sample point of the Fourier transform of the scene at a “frequency” that depends on the distance between the antennas. Realizing this, the idea is to collect measurements at enough baselines to obtain a reasonable representation of the Fourier transform and then to form an image by inverting the transform. The latter is a relatively simple numerical integration of the sample data. The technique is similar to “Earth rotation synthesis” developed in radio astronomy [2].
69
70
Microwave Radiometer Systems: Design and Analysis
V(vx) T(x)
Figure 8.1 Basic viewing geometry for aperture synthesis: Two antennas separated by a distance, L, receive radiation from a scene with effective temperature T(x).
The critical feature for remote sensing applications is that the eventual spatial resolution does not depend on the antenna size but on how well the Fourier transform is sampled (number and choice of baselines). One can achieve high spatial resolution with sparse arrays of small antennas. Sparse arrays are possible because only one measurement is needed at each baseline. Small antennas can be used because the individual antennas do not determine resolution. In fact, small antennas can be an advantage by providing a wide field of view. Finally, mechanical scanning is not needed because an image of the entire field of view is obtained in software as part of the inverse transform. The concept is illustrated in Figure 8.1. Imagine two antennas Lm apart, receiving radiation from a scene with an effective surface temperature, T(x), that is to be measured. The voltages out of each antenna are multiplied together and averaged. Both phase and amplitude are measured, which is equivalent to recording the real and imaginary parts. In aperture synthesis applications, the output complex number is often called the visibility. Figure 8.2 is a block diagram showing how this measurement could be implemented in hardware (this is a portion of the basic correlation radiometer described in Chapter 7). As in a conventional receiver, the signals from the two antennas are mixed to a
H(f)
LO
∼ H(f)
∼ ∼
I
∼ ∼
Q
90°
Figure 8.2 Block diagram showing how the measurement needed for each antenna pair could be implemented in hardware.
Synthetic Aperture Radiometer Principles
71
convenient IF and then amplified and filtered. The process is represented in the figure by the effective transfer function, H(f). The IF outputs of each receiver are then multiplied together in-phase (no phase shift) and also after shifting one channel by 90° (quadrature). The products are averaged (equivalent to a lowpass filter). The output visibility is a complex number whose real part is the in-phase response (labeled “I” in the figure) and whose imaginary part is the output of the quadruature channel (labeled “Q”). When the radiation incident on the two antennas is incoherent (true for most natural scenes), the visibility is proportional to the Fourier transform of the temperature profile, T(x), evaluated at a “frequency” νx (for example, see [2, 3] for derivation of this result). The frequency, νx, is often referred to as a “spatial frequency”, and is given by: νx =L λ
(8.1)
where L is the distance between antennas and λ is the wavelength at which the measurement is made (i.e., corresponding to the center frequency of the receivers in Figure 8.2). Since νx depends on the antenna spacing, L, the point at which the Fourier transform is given by the output (visibility) can be changed simply by repeating the measurement with different L. In principle, one could make measurements at many different antenna baselines, L, and obtain a good representation of the transform. Then, the temperature profile itself, T(x), could be obtained by inverting the Fourier transform. The important point for aperture synthesis is that the resolution obtained in the image formed after Fourier transforming is determined by how well the transform has been sampled (i.e., by the number and spacing of the sample points, νx) and not by the size of the antennas used in the measurement. In principle, one could use very small antennas to obtain a wide field of view and by making many measurements closely spaced in spatial frequency space, one could obtain a map of T(x) with very high spatial resolution. Figure 8.3 illustrates how this technique might be applied for remote sensing from space. Imagine two antennas in orbit, one spiraling around the other and each looking at the same region on the surface. At intervals indicated by the dashes, the signals from the two antennas are multiplied together and averaged, producing a sample point in the (two-dimensional) Fourier transform of the scene. After the spiral is complete, the data are assembled and the sampled transform is inverted to produce an image of the scene. The individual antennas determine the field of view (oval on the surface in Figure 8.3). The resolution (boxes inside the oval) is determined by the longest baseline in the spiral. Hence, in principle, one could use small antennas to obtain a large field of view and a spiral with a large radius to obtain high spatial resolution.
72
Microwave Radiometer Systems: Design and Analysis
Figure 8.3 Illustration showing how aperture synthesis might be applied for remote sensing from space.
8.2 Practical Considerations 8.2.1
RF Processing
Figure 8.2 indicates the processing needed in aperture synthesis. The front end is a standard receiver in which the RF input is mixed to a convenient IF with appropriate gain and filtering. This must be done using a single side band mixer to preserve phase information and one common local oscillator (LO). If more than one LO is used, the LO signal at each front end must be “phase locked” to the same reference so as not to introduce phase errors. The net effect is represented in the diagram by the front-end filter, H(f ). The IF signals from each antenna-pair are then multiplied together twice: first directly (no phase shift) and then after shifting one arm by 90°. The products are then averaged (a lowpass filter). The principle is the same as discussed in Chapter 7 for the basic correlation radiometer (see, for example, Figure 7.5). The output from the in-phase channel (no phase shift) is the real part of the complex product of the output of the antennas and is proportional to A12 cos(ϕ1 − ϕ2). The output from the quadrature channel (90° phase shift) is the imaginary part of the product and proportional to A12 sin(ϕ1 − ϕ2) where A12 represents the magnitude of the product, and ϕ1 and ϕ2 are the individual phases. The complex number formed from these two parts is V(u,v) in (8.3).
Synthetic Aperture Radiometer Principles
73
The noise in the output of the correlator in Figure 8.2 is computed as in the case of a total power radiometer. However, in this case it is reasonable to assume that the noise in the two RF channels following each antenna (i.e., equivalent receiver noise) is independent. In this case, the receiver noise cancels when the product is averaged and one finds that the sensitivity of the measurement at each antenna pair is [4, 5]: ∆T = T sys
2B τ
(8.2)
where Tsys = TA + TN , B is the system (noise) bandwidth, and τ is the effective integration time represented by the lowpass filter. Equation (8.2) is similar to the result for a total power radiometer except for an improvement of a factor square root of 2. However, this is not the sensitivity of the image. It is the sensitivity of the RF electronics in a single measurement (a single point in the Fourier transform). To obtain the sensitivity of the image, one must include the pattern of the individual antennas and the image processing (Fourier transform). This is discussed in Section 8.2.4. 8.2.2
Basic Equation
Assuming a geometry such as shown in Figure 8.1, it is a relatively straightforward exercise in electromagnetic theory to compute the output of the two antennas when connected to a receiver such as shown in Figure 8.2 (for example, see [3]). Expressing the integration over the antenna field of view in a spherical coordinate system (θ, ϕ), one can write the correlator output in the form [6, 7]: V (u , v ) = C ∫ ∫T ( θ, ϕ)P ( θ, ϕ)e j 2 π[u sin
( θ ) cos ( ϕ ) +v sin ( θ ) sin ( ϕ ) ]
sin ( θ )dθdϕ (8.3)
In this expression, u,v are “spatial” frequencies that depend on the distance between the antennas: u = (x1 − x2)/λ and v = (y1 − y2)/λ where λ is wavelength and x1,2 and y1,2 are the coordinates of the two antennas in this pair. P(θ, ϕ) is the product of the voltage patterns of the individual antennas and T(θ, ϕ) is the effective temperature (physical temperature times emissivity) of the surface. The in-phase (I ) and quadrature (Q ) outputs of the correlator (Figure 8.2) are the real part and imaginary part of (8.3), respectively. Finally, C is a scale factor that depends on the details (shape and amplitude) of the effective passbands of the receivers, and the lowpass filters. Equation (8.3) is an approximation valid for most remote sensing applications from space. It assumes that the incident radiation is incoherent and that the antennas are identical and that the distance from the antenna array to the scene is large compared to the maximum baseline. (The latter is commonly
74
Microwave Radiometer Systems: Design and Analysis
referred to as the far-field approximation in electromagnetic theory. It neglects the curvature of the wave over the extent of the antenna array.) Another assumption inherent in (8.3) is that the effective bandwidth of the system can accommodate the time delay between signals arriving at pairs of antennas in the array. In general, there will be a time difference when comparing the signal arriving at the two antennas in a pair from a given point on the surface (e.g., the two ray paths shown in Figure 8.1 will be of different length). If the antennas are sufficiently far apart and the receiver impulse response is sufficiently short (very large bandwidth), it is possible for the response of receiver “a” due to the signal arriving at its antenna to decay before that signal arrives at receiver “b.” There will be a consequent decay in the correlation, which is called fringe washing after its counterpart in optics. One can obtain a rough idea of the limitations this imposes by approximating the impulse response of the receiver by the inverse of its bandwidth, B. Then, in order to have a nonzero signal, one obtains the limitation: L sin ( θ ) c < 1 B
(8.4)
where L is the distance between the antennas and θ is the angle between the line of sight to a point on the scene and the normal to the array. Problems associated with fringe washing arise when trying to employ large bandwidth to reduce noise (8.2). In this case it is possible for the right-hand side of (8.4) to be small and limit the maximum baseline (L) or the field of view (θ). For example, in the window at 1.413 GHz used for passive remote sensing of soil moisture and sea surface salinity, the available bandwidth is 27 MHz. This implies a maximum baseline on the order of 10m. One could employ a larger baseline by restricting the field of view (e.g., 15m if limited to 45°). The assumption made in (8.3) is that (8.4) is satisfied and there is no fringe washing (the fringe washing function is unity). Finally, differences among the antennas are not taken into account. Equation (8.3) assumes identical antenna patterns. Among the possible effects is electromagnetic coupling, which causes the pattern of an antenna to be changed by nearby antennas. This can be an issue especially for very short baselines [8]. Another possibility is thermodynamic coupling, in which case T(θ, ϕ) in (8.3) can be effected by the presence of the other elements in the array [9].
8.2.3
Image Processing
Equation (8.3) has the form of a Fourier transform. The resemblance of (8.3) to a Fourier transform can be made more obvious by rewriting it in terms of the direction cosines ξx = sin(θ)cos(ϕ) and ξy = sin(θ)sin(ϕ):
Synthetic Aperture Radiometer Principles
V (u , v ) =
∫ ∫ K (ξ
x
)
,ξy e
[
j 2 π uξ x + v ξ
y
75
]dξ dξ x y
(8.5a)
where the kernel K(ξx, ξy) is: K (ξ x , ξ y
) = CT ( ξ
x
)
, ξ y P (ξ x , ξ y
)
1 − ξ x2 − ξ y2
(8.5b)
and the integration is over all values inside the “unit circle” (i.e., ξ 2x + ξ 2y ≤ 1). In principle, the image is formed by inverting the transform to obtain the kernel K and then solving for the scene brightness temperature, T: T (ξ x , ξ y
[
)=
1 − ξ 2x − ξ 2y
(
CP ( ξ x ξ y
))]
∫ ∫V (u , v )e
[
− j 2 π uξ x + v ξ
y
]du dv
(8.6)
There are a number of practical considerations that impact one’s ability to obtain the inverse transform. First of all, in practice one will only have measurements of the visibility function V(u,v) over a limited range of values (e.g., the discrete points indicated by dashes in Figure 8.3 and only to some maximum radius). The implications of this type of limitation are well known in antenna theory (e.g., finite arrays of discrete elements) and in a more general form in “sampling” theory. The consequences include a limit on resolution (set by the maximum baseline) and the possibility of aliasing if the spacing between baselines is not small enough. A more serious problem that occurs in the practical application of this technique is that the antennas and even the receivers may not be identical. In this case, the kernel K in (8.5) is not the same for each baseline and the equation is no longer a Fourier transform. One approach for obtaining an image in this case is to replace the integral by its approximating sum. Then (8.5a) becomes a set of linear equations in which the sample values of the kernel, K, are unknown and the visibilities, V(u,v), are known (obtained from the measurements). This approach has been employed successfully in practical applications such as for remote sensing of soil moisture. It is discussed in Section 8.3 and again in more detail in Chapter 15.
8.2.4
Sensitivity
The trade one makes for employing aperture synthesis is a decrease in radiometric sensitivity. Each measurement employs a pair of antennas that are small compared to an antenna with the resolution of the final, synthesized array. Hence,
76
Microwave Radiometer Systems: Design and Analysis
other factors being equal, one would expect the signal-to-noise ratio of each measurement to be lower than would be obtained with a real aperture of the size that is being synthesized. This is the case; however, because the image is reconstructed using many baselines much of the penalty in signal-to-noise associated with using small antennas is recovered [5, 6]. In general, the noise in the image will depend on the processing. However, a reasonable approximation can be obtained by assuming an ideal discrete Fourier transform for the inversion. In this case, the RMS noise, ∆T, in the image can be written [5]:
[
∆T = T sys
]
2B τ Asyn
(NAe )
(8.7)
The term in brackets is the ideal response of a coherent correlation receiver (8.2) with system noise, Tsys, effective bandwidth, B, and integration time τ. The terms to the right of the brackets represent a factor that occurs during the image reconstruction. In this expression, Asyn is the effective antenna area corresponding to the synthesized beam (i.e., roughly the area covered by the spiral in Figure 8.3), Ae is the effective area of the actual individual antennas, and N is the square root of the number of independent baselines that were used in image reconstruction. In general, Asyn/(N Ae) > 1 and represents the penalty in noise performance paid for using aperture synthesis. Examples of the factor, Asyn/(N Ae), for several antenna configurations can be found in [5]. In general, one finds that the penalty grows with the amount of thinning.
8.3 Example To illustrate the procedure, consider a configuration in which the potential antenna positions are uniformly spaced on the principle axes of a Cartesian grid with center-to-center spacing dx and dy, respectively. That is, the individual an -tennas lie along the x- and y-axes with centers at x = p dx and y = q dy where p, q are integers. The baselines u,v possible with such an array can take on values (n ∆u, m ∆v) where ∆u = dx/λ and ∆v = dy /λ and n, m are integers. [See the definitions after (8.3).] Suppose that measurements are made so that the available baselines fill the space −N ≤ n ≤ N and −M ≤ m ≤ M. This could be done with pairs of antennas arranged along the arms of a cross “+” or a tee “T.” Assuming that the antennas and receivers are identical, (8.5) applies. However, this configuration provides only a limited set of discrete samples of V(u,v), one value for each available baseline. As mentioned earlier, an approach that is convenient in this case is to replace the integrals by their approximating sum. Doing this with (8.6a), one obtains:
Synthetic Aperture Radiometer Principles
K ′( ξ x , ξ y
)=∑ ∑ n
m
V (u , v )e
[
− j 2 π uξ x + v ξ
77
y
] ∆ u∆ v
(8.8)
where u = n dx /λ = n ∆u and v = m dy /λ = m ∆v and the sums are over all the n and m. The symbol, Σn is used to indicate that the sum is over all the values of n. Also, note the prime on K in (8.8). K ′ is the image generated from (8.8) as distinct from the unprimed K in (8.5) that is the actual value. It is possible to obtain a particularly useful form of (8.8) by substituting (8.5a) for V(u,v) and rearranging. Substituting (8.5a) and introducing “delta” functions δ(u − n∆u) to denote the sample values of V(u,v), one obtains [3]: K ′( ξ x , ξ y
) = F [V (u , v )] * D ( ξ −1
= K (ξ x , ξ y =
) * D (ξ
∫ ∫ K ( ξ, ξ ′)D ( ξ − ξ
x
x
,ξy
x
,ξy
)
(8.9a)
)
(8.9b)
)
(8.9c)
ξ ′ − ξ y dξdξ ′
where F −1 denotes an inverse Fourier transform and the asterisk * denotes a convolution. The significance of this rearrangement is that (8.9c) has the conventional form for the response of an antenna with gain D(ξx, ξy) when viewing a scene K(ξx, ξy) (for example, see [10, 11]). The function D in the expression above is the Fourier transform of a sum of delta functions: D (ξ x , ξ y
) = F [∑ ∑ −1
m
m
δ(u − n∆u )δ(v − m∆v )∆u∆v ]
(8.10)
The sum is over the all n and m: −N ≤ n ≤ N and −M ≤ m ≤ M. Equation (8.10) can be factored into separate sums and analytic expressions can be obtained by recognizing that the resulting sums over n and m are geometric progressions. One obtains: D (ξ x , ξ y
) = h ( ξ )g ( ξ ) x
= ∆u
y
sin [( 2N + 1)π∆uξ x ] sin [π∆uξ x ]
∆v
[
sin ( 2 M + 1)π∆vξ y
[
sin π∆vξ y
]
]
(8.11)
Note that the components h(ξx) and g(ξy) of D are the antenna array factors of a uniformly spaced, linear array with 2N + 1 elements. Hence, in this
78
Microwave Radiometer Systems: Design and Analysis
example the synthesis array behaves (mathematically) like a real aperture linear array of 2N + 1 elements. However, notice that measurement in the synthesis array is of power (e.g., brightness temperature) and that the functions h(ξx) and g(ξy) are, in antenna theory, the array factors for the electric field. Hence, if a real aperture linear array was used to make this measurement, the antenna pattern would be h(ξx)2. The power pattern of a real antenna has only positive side lobes; however, the sidelobes of the effective pattern in the synthesis array can be both positive and negative (see Chapter 15). On the other hand, there is a great amount of flexibility in designing a synthesis array and in choosing the image reconstruction algorithm. For example, weighting could be used in the sums above to control the sidelobes. The resolution of the synthesized pattern, D, is determined by the number of elements in the array and the spacing, d, and not the actual antennas themselves. Of course, the antenna pattern is part of the kernel K and it will be needed ultimately to retrieve a map of T. However, if small antennas are used with P ≈ 1 over the area of interest, then the antenna pattern itself is not a factor in determining the resolution of the synthesis array. Also, notice that in the limit that ∆u N → ∞, the function h(ξx) becomes a delta function [similarly for g(ξy)]. In this case, the measurement is perfect (K′ ≡ K). In the more general case, the image is a representation of K that is blurred because of the finite width of h and g. The width of these functions can be used as a figure of merit for the inversion. The distance between nulls is a convenient choice. In the case of h(ξx) these occur at ξx =1/ [(2N + 1)Du]. Using ∆u = dx/λ and ξx = x/R where R is the distance between the scene and the antenna array, one obtains the following expression for the resolution in x: ρ x = Rλ [d x ( 2N + 1)]
(8.12)
with similar results for the y-direction. (λ is the value at the center frequency of the measurement). Finally, notice that h(ξx) and g(ξy) are periodic functions. In order to avoid aliasing of the image, it is necessary to keep the effect of the grating lobes (peaks) out of the image plane (−1 < ξ < 1). This imposes a limit on the spacing between antennas and therefore on the minimum baseline. For example, restricting the image to the halfway point between peaks results in the restriction (−π/2 < π ∆u ξx < π/2) from which it follows that dx,y < λ/2.
References [1]
Le Vine, D. M., “A Multifrequency Microwave Radiometer of the Future,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 27, No. 2, March 1989, pp. 193–199.
Synthetic Aperture Radiometer Principles
79
[2] Thompson, A. R., J. M. Moran, and G. W. Swenson, Interferometry and Synthesis in Radio Astronomy, New York: Wiley, 1986. [3] Le Vine, D. M., and J. C. Good, “Aperture Synthesis for Microwave Radiometers in Space,” NASA Tech Memorandum 85033, 1983 (Avial. NTIS 83N-36539). [4] Tiuri, M. E., “Radio Astronomy Receivers,” IEEE Trans. Antennas and Propagation, Vol. AP-12, 1964, pp. 930–938. [5] Le Vine, D. M., “The Sensitivity of Synthetic Aperture Radiometers for Remote Sensing Applications from Space,” Radio Science, Vol. 25, No. 4, 1990, pp. 441–453. [6] Ruf, C. S., et al., “Interferometric Synthetic Aperture Radiometery for Remote Sensing of the Earth,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 26, No. 5, 1988, pp. 597–611. [7] Le Vine, D. M., et al., “ESTAR: A Synthetic Aperture Microwave Radiometer For Remote Sensing Applications,” IEEE Proc., Vol. 82, No. 12, December 1994, pp. 1787–1801. [8] Wiessman, D. E., and D.M. Le Vine, “The Role of Mutual Coupling in the Performance of Synthetic Aperture Radiometers,” Radio Science, Vol. 33, No. 3, 1998, pp. 767–779. [9] Corbella, I., et al., “The Visibility Function in Interferometric Aperture Synthesis Radiometry,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 42, No. 8, 2004, pp. 1667–1682. [10] Kraus, J. D., Radio Astronomy, New York: McGraw-Hill, Chapter 6, 1966. [11] Collin, R. E., and F.J. Zucker, Antenna Theory, Vol. 1, Chapter 4, New York: McGraw-Hill, 1969.
Selected Bibliography Bara, J., et al., “The Correlation of Visibility Noise and Its Impact on the Radiometric Resolution of an Aperture Synthesis Radiometer,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 38, No. 5, 2000, pp.2423–2426. Camps, A., et al., “RF Interference Analysis in Aperture Synthesis Interferometric Radiometers: Application to L-Band MIRAS Instrument,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 38, No. 2, 2000, pp. 942–950. Corbella, I., et al., “Analysis of Noise-Injection Networks for Interferometric-Radiometer Calibration,” IEEE Trans. on Microwave Theory and Techniques, Vol. 48, No. 4, 2000, pp. 545–552. Perley, R. A., F. R. Schwab, and A. H. Bridle, (eds.), “Synthesis Imaging in Radio Astronomy,” Astronomical Society of the Pacific Conference Series, Vol. 6, 1989. Rohlfs, K., and T. L. Wilson, Tools of Radio Astronomy, 3rd ed., New York: Springer, 2000.
9 Calibration and Linearity 9.1 Why Calibrate? The purpose of calibration is to establish the connection between the input brightness temperature and the output quantity (volts, watts, digital counts) of the radiometer. In principle, a full knowledge of all component specifications, waveguide losses, reflection coefficients, and physical temperatures would render calibration superfluous, as the behavior of the radiometer then could be perfectly predicted by modeling. In real life, however, such accurate predictions are very difficult, and modeling is best suited for prediction of relative dependencies such as: how the radiometer output will vary with the temperature of a certain amplifier. Thus basic absolute calibration becomes a vital and often time-consuming part of a radiometer development and maintenance. For Dicke radiometers we have from (4.3): VOUT = constant · (TA − TR), where TR is known. For noise-injection radiometers: TA = TR − TI, where TR is known andTI is proportional to some output quantity, usually digital counts. In both cases only one calibration point is needed, and the input-output relationship can be adequately described. It is then assumed that the radiometer in question is perfectly linear—an assumption that it would be nice to verify through calibration at several points. For total power radiometers we have from (4.1): VOUT = constant · (TA + TN ), where TN cannot be regarded as well known (i.e., to better than a fraction of a Kelvin). Hence, two calibration points are required, again assuming a linear calibration curve to be checked. In general, we need an accurate noise source with a variable output. The output range should ideally be 0–300K. 81
82
Microwave Radiometer Systems: Design and Analysis
9.2 Calibration Sources The most obvious solution is a cooled microwave load. As described earlier, a well-matched microwave load will generate a noise temperature equal to its physical temperature—and the physical temperature can be measured accurately. Figure 9.1 shows the simplest and cheapest possible setup. A microwave load is mounted in a freezer. A suitable liquid, continuously stirred by a motor-driven propeller, ensures a uniform temperature, which is measured by the thermometer. The temperature range of the simple setup is quite limited, but useful—especially for calibration and stability checks during a radiometer’s development. The microwave load can also be cooled by submerging it in a liquid with a low boiling point, that is, using cryogenic techniques. Figure 9.2 shows a low temperature calibrator with the load in liquid helium. It is evident from the figure that now the concept is far from being simple. Great care must be exercised to prevent heat flow and condensation of gasses in the waveguide. The temperature and the loss of the rather long waveguide must be carefully measured and used to correct the calibration temperature (see Section 3.3). This example is an extreme, going all the way to liquid helium temperatures. Usable loads cooled to liquid nitrogen temperatures around 77K are commercially available. Well-made cryogenic loads are far from being cheap. An alternative solution is a cooled target viewed by a suitable antenna connected to the radiometer (see Figure 9.3). A microwave absorber (normally used to cover the inside walls of radio-anechoic chambers) will emit a brightness temperature equal to its physical temperature To. Under ideal conditions, the antenna will sense nothing but the brightness temperature from the absorber and TA = TB = To. Figure 9.4 shows a practical layout of this concept. The radiometer is connected to an antenna horn through a short waveguide (very low losses!). The horn views a microwave absorber soaked with liquid nitrogen. The absorber and the liquid nitrogen are contained in an insulated metal bucket, and the excess opening of the bucket is covered by aluminum foil. In this way the antenna is only able to pick up energy from the absorber, which is cooled to 77K by the Radiometer
Input
Motor
Thermal block
Freezer
Figure 9.1 Simple calibration setup.
Themometer
Calibration and Linearity
83
Figure 9.2 Low temperature microwave noise standard. (From: [1]. © 1968 IEEE. Reprinted with permission.)
nitrogen. There is generally no problem with losses and heat flow in the antenna and the waveguide, liquid nitrogen is readily available, and the setup is cheap and simple. Overall this is a very useful radiometer calibrator. A slightly more refined version of this calibrator is discussed in [2]. TO TB
TA Radiometer Antenna
Microwave absorber Figure 9.3 Antenna target calibration.
84
Microwave Radiometer Systems: Design and Analysis
Radiometer
Antenna horn AL foil Foam insulation Microwave absorber Liquid nitrogen
Figure 9.4 Antenna target calibrator.
A very important parameter concerning a radiometer calibration target is its emissivity ε (or its reflection coefficient 1 − ε). If we assume that we are dealing with a liquid nitrogen cooled target at 77K and that the noise temperature being emitted from the radiometer out of the antenna towards the target is 300K, the radiometer under test will measure the following brightness temperature: T B = 77K ⋅ ε + 300K ⋅ (1 − ε) The error in the measurement can be expressed as: ∆ = T B − 77K ∆ = 233(1 − ε)K A return loss of 20 dB corresponds to an emissivity of 0.99, and to an error of: ∆ = 233 ⋅ 0.01K = 2K which normally is unacceptable. However, already as we pass the 30-dB reflection coefficient, the error drops below 0.2K, and we approach reasonable figures. Calibration targets are typically constructed using more or less standard microwave absorbing materials. Typical flat panel absorbers have a reflection
Calibration and Linearity
85
coefficient of 20 dB, so they can generally not be used. Typical pyramidal absorbers can exhibit a 35-dB return loss at L-band with a pyramid height of 30 cm. The 35 dB corresponds to an error of 0.07K. In general, the pyramidal height needs to approach twice the wavelength for such a performance. The liquid nitrogen (LN2) is soaked up into the pyramids, but it is advisable to let the level of LN2 be such that it is clearly visible between the pyramids. This is allowable since the reflection coefficient of LN2 is very small, and it ensures that even the tips of the absorbers are properly cooled. A more in-depth discussion of target reflectivity errors is found in [3]. Another solution to the calibrator problem is sky calibration. In fact, this is a derivation of the antenna target calibration just described in which the cooled target is “replaced” by the sky (see Figure 9.5). Again the radiometer is connected to a microwave horn antenna through a short waveguide. The antenna is pointed toward the cold sky. A large metal bucket ensures that nothing but the sky radiation is incident on the antenna. The brightness temperature of the sky, as viewed from the surface of the Earth through the atmosphere, is indicated in Figure 9.6. In the 1–10-GHz range the low temperature of the sky (∼6K) is rather undisturbed by the atmosphere. At higher frequencies, care must be exercised. At high altitudes (mountain tops) and in dry areas (deserts, arctic regions) problems with water vapor are minimized, but even in more normal areas, the concept is useful, especially on cold, clear winter days. (On satellites, there is no problem with the atmosphere, and a view of free space is often used for calibration checks on satellite-borne microwave radiometer systems.) The bucket technique has been brought to “perfection” on a mountain peak in New Mexico; see [4]. As already mentioned, in other areas of the world the concept can also be quite useful. This is illustrated in Figure 9.7, showing a bucket on the rooftop of a building at DTU. In the actual case the bucket was used to assess small antenna reflector losses by radiometric means [5]. TSKY
TSKY
Antenna
Radiometer
Figure 9.5 Sky calibration.
Metal bucket
86
Microwave Radiometer Systems: Design and Analysis TSKY (K)
1,000 Low humidity
90°
100
85°
10
60° θ = 0°
1 0.1
1
H20
10
02
100 F(GHz)
Figure 9.6 Sky radiometric temperature with zenith angle θ as a parameter.
Figure 9.7 Sky measurements using an aluminum lined bucket on a rooftop.
9.3 Example: Calibration of a 5-GHz Radiometer In Figure 9.8 we find a calibration curve for the DTU 5-GHz noise-injection radiometer carried out using the simple setup displayed in Figure 9.1. The usefulness of the method is clear: The linearity of the radiometer is confirmed (within a rather limited temperature range, though) and the slope of the curve is found to be 6.56 counts/°C. Zero counts correspond to 41.8°C.
Calibration and Linearity
87
°C 20
10
0
−10
−20
−30 100
200
300
400 Counts
Figure 9.8 Calibration curve, 5-GHz DTU radiometer.
Also the sky temperature was measured, using the setup of Figure 9.5. The radiometer output was 2,026 counts. Hence, the measured sky brightness temperature is found to be: TS = 41.8 + 273.2 − 2,026/6.56 = 6.2K, which is in good agreement with the expected sky temperature (see Figure 9.6). Normally the determination of the slope of the calibration curve is carried out the other way around, namely, using the sky temperature as a primary point. This gives a better estimate due to the large temperature difference between the sky and the reference load.
9.4 Linearity Measured by Simple Means Although a radiometer in principle need not be linear in order to carry out useful measurements provided it is properly calibrated throughout its range, linearity is a highly warranted virtue often strived for: A linear radiometer is much easier to calibrate in the first place. A radiometer launched into space must have
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Microwave Radiometer Systems: Design and Analysis
its calibration checked regularly, and this can in practice only be done if linearity prevails. Hence, linearity issues are important during a radiometer design phase, and a primary task to be carried out during calibration activities is a verification/check of radiometer linearity. This section describes two ways of measuring linearity of microwave radiometers only requiring relatively simple equipment. The calibration situation for a typical spaceborne radiometer is used as an example. 9.4.1
Background
This section deals with alternatives to the traditional way of calibrating radiometers. The traditional method is based on the principle of pointing the radiometer’s feed horn towards a target simulating a scene with variable temperature. Although conceptually simple, it is not technically simple. The target must exhibit excellent VSWR and be variable in temperature over a large range with extreme precision (in some cases ∼0.1K). Such a target is expensive, and moreover its operation is expensive as it requires a thermal vacuum environment. The on-board calibration in present spaceborne, scanning radiometer systems—like the well-known SSM/I, and as described in Chapter 13—is carried out in an almost ideal fashion: The feed horn cluster sequentially views the main offset parabolic reflector for the actual measurement of scene properties, the hot load for one calibration point, and the cold sky reflector for a second calibration point. The output of the hot load is known by careful measurements of the physical temperature of the absorbing elements, and by design taking into consideration the emissivity of the load and the VSWR of the load in conjunction with the noise temperature of the radiometers as seen through the feeds. The output from the main reflector is the antenna temperature modified by the main reflector loss. This loss can be quantified very accurately [5]. The output from the cold reflector is the sky temperature, which is known by design (feed/reflector radiation pattern, satellite geometry, orbit geometry), modified by the cold reflector loss. No VSWR problems are foreseen for the two reflector cases due to the offset geometry. Thus, as the losses and physical temperatures of the two reflectors are known with good accuracy, a perfect calibration takes place. This is in strong contrast to most earlier radiometer systems, where a switch matrix selects whether the antenna, the hot load, or the separate sky horn is connected to the radiometer receiver. This results in large problems with losses, switch isolations, and the fact that different signal paths when calibrating and when measuring the antenna temperature must be sustained. Ground calibration in this case becomes an intriguing exercise in determining all possible losses, isolations, and radiometer transfer function properties. In the first case, however, due to the “perfect” calibration scheme, the ground calibration exercise would be not necessary if the radiometers were known to be perfectly linear.
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89
Unfortunately, the radiometers cannot be assumed perfectly linear, so the main task of the ground calibration is to determine the transfer function of the radiometers with sufficient accuracy (plus the precise determination of the losses in the two reflectors, which is not the subject here).
9.4.2
Simple Three-Point Calibration
The purpose of this calibration procedure is to make a rough calibration of the radiometers and check their linearity with good accuracy yet using simple, low-cost, primary targets. The principle is illustrated in Figure 9.9. Two targets made of microwave absorber material in isolated metal buckets are used. Filling liquid nitrogen into a target provides a cold calibration temperature TC (∼77K) and leaving it without the liquid nitrogen provides the hot calibration temperature TH (= T0 ∼ 293K). Two identical antennas are connected with equal waveguides to a magic tee, the radiometer is connected to the sum port, and the difference port is terminated. The power from one antenna is split between the sum and difference ports. As the signals from the two antennas are uncorrelated, the sum port will provide to the radiometer the average value of the two antenna signals (in the ideal, lossless case and with an ideal, symmetrical magic tee). The noise signal from the termination is split equally between the two antennas.
Radiometer TM lM TM’
l1
l2
+
T1 T1’
k T0
TC or TH Figure 9.9 Setup for simple three-point calibration.
T2 T2’
TC or TH
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Microwave Radiometer Systems: Design and Analysis
The calibration procedure includes four cases: the hot case (HH) where both antennas view TH and the radiometer measures TH, the cold case (CC) where both antennas view TC and the radiometer measures TC, and two mixed cases (CH and HC) where one antenna views TC and the other views TH and the radiometer measures (TC + TH)/2 or (TH + TC)/2 that are equal in the ideal case. It is assumed that the transfer function of the radiometer looks like the “possible situation” shown in Figure 9.10. It is a very likely situation considering the way a radiometer is built. A dominating factor in the transfer function will be the square law detector. It is expected to be something between square law and linear, and “good” square law behavior is obtained for sufficiently low signal levels. A transfer function like the “impossible situation” shown in Figure 9.10 cannot be dealt with by the calibration method under discussion here. It is not a likely situation, and for many good reasons it must be avoided. Returning to the likely function of the figure and the procedure described earlier, it will be shown next that one can measure three points on the calibration curve with good accuracy even under nonideal conditions, that is, lossy components and nonperfect balance in the magic tee (k is not 0.5). The losses (l1, l2, and lM) are here represented by their transmission coefficients (i.e., 0.2-dB loss means −0.2-dB transmission and l = 0.95). By an inspection of Figure 9.9, the following set of equations can be established: T 1 ′ = T 1 ⋅ l 1 + (1 − l 1 ) ⋅T 0
(9.1)
T 2 ′ = T 2 ⋅ l 2 + (1 − l 2 ) ⋅T 0
(9.2)
Output (N) Possible situation
*
Impossible situation * 77 K Figure 9.10 Radiometer calibration curves.
Input (K) 293 K
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91
T M ′ = k ⋅T 1′+ (1 − k ) ⋅T 2 ′
(9.3)
T M = T M ′ ⋅ l M + (1 − l M ) ⋅T 0
(9.4)
By proper insertion, the following expression for the input to the radiometer is found: T M = k ⋅ l M ⋅ l 1 ⋅T 1 + k ⋅ l M ⋅ (1 − l 1 ) + (1 − k ) ⋅ l M ⋅ l 2 ⋅T 2 +
(1 − k ) ⋅ l M ⋅ (1 − l 2 ) ⋅T 0 + (1 − l M ) ⋅T 0
(9.5)
Let us assume the hot case: T1 = T2 = TH = T0, and by insertion and reduction we find: T M HH = T 0 which is not surprising! By letting T1 = T2 = TC in (9.5), we find an expression for the radiometer input in the cold case:T M CC . Likewise, T1 = TH = T0 and T2 = TC givesT M HC , while T1 = TC and T2 = TH = T0 givesT M CH . By proper insertion and reduction, it is straightforward to show that the average value T M av of T M HC and T M CH is equal to the mid-point value Tm ofT M HH andT M CC , that is:
(T
M HC
+ T M CH
)
2 = (T M HH + T M CC
)2
(9.6)
so with our radiometer under test we measure the extreme (hot and cold) cases—T M HH and T M CC —we calculate the mid-point value Tm, and we expect the radiometer to yield this value as an averageT M av of the two measurements of the mixed (hot/cold, cold/hot) cases. If not, the radiometer is nonlinear. A precondition for this to be able to work is that there is reasonable balance in the system, that is, k ≈ 0.5, which means that T M HC ∼T M CH , and that the radiometer has a “decent” nonlinear characteristic. A sensitivity analysis is warranted. Assume the magic tee imbalance to be ±0.1 dB corresponding to k = 0.51. Assume equal length waveguides so that l1 = l2 = lM = 0.95 (corresponding to a 0.2-dB loss). Let TH = T0 = 293K and TC = 77K. We can then calculate that T M HH = 293K, T M CC = 98.06K, and the mid-point value Tm = 195.53K. Likewise, we findT M HC = 197.48K andT M CH = 193.58K. The average value is T M av = 195.53K as we would have expected. It is seen that a realistic imbalance will result in a small difference in the TM values,
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Microwave Radiometer Systems: Design and Analysis
that is, we can average the results from a slightly nonlinear radiometer and thus get a measurement of the deviation from linearity midway between TC and TH. Further comments: l1, l2, and lM include the ohmic losses in the three ports of the magic tee. A lack of isolation between the difference port and the sum port will result in loss of some signal to the termination and generation of some signal in the sum port from the termination, that is, just like loss in the transmission line between the tee and the radiometer. Hence, this effect can be regarded as included in lM and, as the calculations show, has no effect in the present case. It shall be noted that the calibration method under discussion does not solve the problem of finding the transfer function below 77K, which could be a problem as the cold calibration point in space is only a few Kelvins.
9.4.3
Linearity Checked by Slope Measurements
Figure 9.11 shows another setup by which a roughly calibrated radiometer can be checked for linearity. An antenna horn points towards a simple liquid nitrogen target and a variable attenuator (Att2) with a low insertion loss and at an ambient temperature are able to produce any brightness temperature from ∼77K to ∼ 293K. The accurate value of the brightness temperature is not known, but can be assessed by the roughly calibrated radiometer. Through a directional coupler with a coupling value of 20 dB (in order not to attenuate the signal in the main arm unduly) a noise signal of variable amplitude is injected. The signal originates in a noise diode [typical excess noise ratio (ENR) larger than 20 dB] and is attenuated in a variable attenuator Att1. A PIN diode switch selects either this signal or the signal from a load at ambient for injection When the ambient load is on, the net result is that practically no extra noise is added to the signal from the antenna horn, while as the switch selects the signal from the noise diode a certain noise is added. The attenuators could be of the rotary vane type for low insertion loss and good stability. Figure 9.10 shows the transfer function for the radiometer under test. By the rough calibration, two points are established corresponding (as an example) to 77K and 293K. For simplicity the calibration constant (N/Ti) is assumed to be equal to 1. If the transfer function is linear (dashed curve), then the output change ∆N corresponding to a certain setting of Att1; hence, a certain input change ∆Ti will be the same for all settings of Att2 and hence all values of Ti. This is not the case if the transfer function is not linear. Let us assume a “nice” curve that deviates 0.1 from the linear curve midway between the two known calibration points (shown in Figure 9.10 strongly exaggerated as the “possible” curve). An input of 185K will result in an output of 185.1. If we select Att1 to give ∆Ti = 108K, we will observe a ∆N of 108.1 and 107.9 for two suitable settings of Att2.
Calibration and Linearity
93
Noise diode
Att1
Termination
Radiometer
Att2
20 dB Dir. coupler
LN2
Figure 9.11 Slope measurement setup.
This difference of 0.2 corresponding in the present example to 0.2K can be clearly detected. Hence, by this method we can readily detect deviations from a linear curve down to the 0.1-K level. Actually, we can measure the true deviation and assess the transfer function by proper selection of attenuator settings. It is noteworthy that, if the antenna horn is pointed towards the sky, the check can be extended almost down to the cold calibration point in space. 9.4.4
Measurements
9.4.4.1 Three-Point Method
A noise injection radiometer (NIR), a Dicke radiometer (DR), and a total power radiometer (TPR), all Ka-band, have been subjected to linearity checks as described in Section 9.4.2. In fact, the NIR and DR cases are not independent as we deal with one Dicke type switching radiometer able to operate in both modes. Figure 9.12 shows an example of the experiments with the NIR instrument. First, the hot case is measured to T M HH = 295.10K. Then follows, after filling one target with liquid nitrogen, a series of cold-hot/hot-cold
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Microwave Radiometer Systems: Design and Analysis
300
295.1
250
191.2
189.3
191.1
187.8
191.1
188.1
TM
200
150
100
50
1
2
3
4
5
6
7
87.8
88.0
88.7
8
9
10
77.3
11
Figure 9.12 Example of an NIR three-point experiment.
combinations by moving the targets around. We find T M HC = 188.43K and T M CH = 191.11K (averages over the three measurements of each). Hence,T M av = 189.77K. Filling the second target with nitrogen enables the three measurements of the cold case, and T M CC = 88.17K. Finally we show a case where a low-loss horn is connected directly to the radiometer input and pointed to the cold target to yield 77.27K as result. This, together with the hot case, provides the basic calibration of the radiometer. From the hot and cold cases are seen that the mid-point value is Tm = 191.64K, meaning that there is a deviation from linearity of 1.87K halfway between the hot-and-cold calibration point. As stated earlier, several experiments with different radiometer types were carried out, and representative examples are summarized in Table 9.1. It is seen that the NIR and the DR consistently reveals a nonlinear behavior, while the TPR is quite linear. The first hardware is from the 1970s based on a Schottky diode detector, while the TPR is a recent development with a high-quality tunnel diode detector. It is seen that the NIR and DR calibration curves bend upwards and not downwards as would be the case if the cause for nonlinearity were compression in low frequency circuitry or the fact that the detector law were somewhere between 2 and 1 (between square and linear law). However, Schottky detector diodes are known to be able to exhibit a transfer law exceeding square law (an exponent more than 2) in the transition region between square and linear under certain impedance conditions. This is probably the case here.
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95
Table 9.1 Summary of Experiments (Values in Kelvin)
TM HH
TM CC
TM av
Tm
Difference
NIR#a
295.1
88.2
189.8
191.6
1.9
NIR#b
299.2
91.2
193.2
195.2
2.0
DR#a
298.1
91.0
192.7
194.6
1.9
DR#b
294.1
89.9
190.1
192.0
1.9
TPR#a 294.3
91.0
192.8
192.7
−0.1
TPR#b 294.1
90.7
192.5
192.4
−0.1
9.4.4.2 Slope Method
Only the TPR has been examined by the slope method. The reason is that this radiometer already by design includes circuitry for injecting noise at the input for calibration purposes. Thus, only an attenuator between the radiometer and the antenna horn is needed to realize the setup of Figure 9.11 (with the limitation that only one value of injected noise is possible, as Att 1 is not present). Table 9.2 shows results from one experiment. By measuring liquid nitrogen and an internal calibration load, the radiometer is calibrated the usual way. The value of the injected noise is ∆Ti = 161.2K at low levels. The attenuator is set at different values with some (unknown) accuracy, but the cold point is measured by the now-calibrated radiometer. It is seen that at first (steps a through c) the injection of the noise results in the same change in radiometer output, indicating the linear behavior we expect from the three-point measurements. The measurement uncertainty is some 0.1K based on experience from repeated experiments. The last attenuator setting (d) reveals beginning compression, but note that the injected noise brings the total input to the radiometer up to 343.1K, which is beyond the design limit corresponding to natural Earth targets (one might say that this is a marginal design).
Table 9.2 Slope Measurements Att 2 a
0
b c d
Cold Point
TB
77K
161.2K
0.15 dB
92.9K
161.3K
0.3 dB
130.1K
161.1K
0.45 dB
182.4K
160.7K
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Microwave Radiometer Systems: Design and Analysis
In conclusion, it can be stated that the calibration methods described in this section are not able to deal with a full calibration of a nonlinear radiometer having arbitrary transfer characteristic. However, the methods are well suited for checking of linearity down to low levels and they may be used to assess the calibration curve for a radiometer that is slightly nonlinear in a neat fashion (second-order curve not deviating much from a linear curve). The three-point calibration method is the simplest seen from a hardware point of view. All that is needed is a magic tee, two horn antennas, two targets, and a few waveguide sections. On the other hand, it is probably the most demanding to handle. One measurement sequence as illustrated in Figure 9.12 takes about 20 minutes, and care must be exercised to ensure stability over that time span. The slope method requires more advanced hardware as a stable noise diode is required (if not already built into the radiometer). On the other hand, the experiments are easier and quicker to carry out, resulting in fewer potential error sources. Interesting work on nonlinearity is found in [6–8].
9.5 Calibration of Polarimetric Radiometers The calibration of polarimetric radiometers represents a special problem. The traditional vertically and horizontally polarized channels are calibrated following the procedures outlined earlier in this chapter, but the third and fourth Stokes parameters require other methods, and it is required to generate a pair of known signals with a known amount of correlation between them. Figure 9.13 illustrates a relatively simple yet very useful setup. As already mentioned, the two linearly polarized channels (normally the vertical and horizontal channels) are first calibrated as any other radiometer. The situation is easy to see referring to the basic correlation radiometer as illustrated Load In 1 Phase shifter
ϕ
Noise diode
Polarimetric radiometer
In 2 Load
Figure 9.13 Calibrating a polarimetric radiometer.
Calibration and Linearity
97
in Figure 7.3. Then the two inputs of the now partly calibrated radiometer system are connected to the input circuitry shown in Figure 9.13. The signal from the noise diode is divided equally to the two channels and injected via two couplers. The signals injected are adjusted to a reasonable level, 100K, for example, by proper coupling values and possibly additional attenuators not shown. The two signal paths from the diode to the injection points are of equal electrical length, but one path includes a variable phase changer. With the noise diode switched off, the loads produce well known uncorrelated signals to the inputs, and the third and fourth Stokes outputs should be zero. If they are not, adjustments within the radiometer system are carried out, or the biases are recorded for later correction purposes. Only small biases should be accepted. If large biases are found, further adjustment or even redesign within the system must be carried out. Switching on the noise diode produces an output from the correlator ideally only in the third Stokes channel (the phase changer is set to zero). If this is not the case, adjustments to the internal phasing/timing in the radiometer system are carried out. By means of the already calibrated first and second Stokes channels, the accurate amount of injected noise in each channel is determined. At this stage an accurate knowledge of the noise temperature of each channel is also required. The correlated and uncorrelated signals in each channel are now known, and by reading the output of the third Stokes channel, this can now be calibrated. By adjusting the external phase changer by 90°, the signal moves from the third to the fourth Stokes channel, and this is now calibrated. Actually, when building a practical polarimetric radiometer system—be it ground based, airborne, or spaceborne—it is highly recommended to include the relatively few microwave calibration components in the radiometer. This way calibration checks in the field or once spaceborne can be carried out. The situation is shown in Figure 9.14 where the basic correlation radiometer from Figure 7.3 has been augmented with the calibration components. The DTU REF RX 1 ver hor
Noise diode
∼
LO
TV Real Complex Imag corr.
RX 2 REF
Figure 9.14 Basic correlation radiometer with calibration circuitry.
U/2 V/2 TH
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Microwave Radiometer Systems: Design and Analysis
polarimetric system that was discussed in Section 7.6 are designed this way, but the components are not shown in Figure 7.5 for clarity at that stage. Although very useful, the calibration procedure described above has one deficiency: it does not represent the fundamental calibration method in which known signals (known by design) from a primary source/target are presented to the instrument in question—through its input connector/waveguide or through its antenna. A simple example of such a fundamental calibration was discussed in Section 9.2 for a single channel radiometer. It is, however, not a simple matter to conceive and design—let alone manufacture—primary targets being able to generate all four Stokes parameters with great accuracy. The reader is referred to [9, 10] for information about this subject.
References [1] Trembath, C. L., et al., “A Low-Temperature Microwave Noise Standard,” IEEE Trans. on Microwave Theory and Techniques, Vol. 16, No. 9, 1968, pp. 709–714. [2] Hardy, W. N., “Precision Temperature Reference for Microwave Radiometry,” IEEE Trans. on Microwave Theory and Techniques, Vol. 21, No. 3, 1973, pp. 149–150. [3] Randa, J., et al., “Errors Resulting from the Reflectivity of Calibration Targets,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 43, No. 1, 2005, pp. 50–58. [4] Carver, K. R., Antenna and Radome Loss Measurements for MFMR and PMIS, New Mexico State University, Report PA 00817, 1975. [5] Skou, N., “Measurement of Small Antenna Reflector Losses for Radiometer Calibration Budget,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 35, No. 4, 1997, pp. 967–971. [6] Walker, D. K., K. J. Coakley, and J. D. Splett, “Nonlinear Modeling of Tunnel Diode Detectors,” IGARSS’04 Proceedings, 2004, p. 4. [7] Harrison, R. G., and X. Le Polozec, “Nonsquarelaw Behavior of Diode Detectors Analyzed by Ritz-Galérkin Method,” IEEE Trans. on Microwave Theory and Techniques, Vol. 42, No. 5, 1994, pp. 840–845. [8] Reinhardt, V. S., et al., “Methods for Measuring the Power Linearity of Microwave Detectors for Radiometer Applications,” IEEE Trans. on Microwave Theory and Techniques, Vol. 43, No. 4, 1995, pp. 715–719. [9] Lahtinen, J., et al., “A Calibration Method for Fully Polarimetric Microwave Radiometers,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 41, No. 3, 2003, pp. 588–602. [10] Lahtinen, J., and M. Hallikainen, “Fabrication and Characterization of Large Free-Standing Polarizer Grids for Millimeter Waves,” Intl. Journal of Infrared and Millimeter Waves, Vol. 20, No. 1, 1999, pp. 3–20.
10 Sensitivity and Stability: Experiments with Basic Radiometer Receivers 10.1 Background The sensitivity of a microwave radiometer is generally expressed as ∆T = K ⋅
T A +T N B ⋅τ
where: TA = antenna temperature TN = receiver noise temperature B = predetection bandwidth τ = integration time The value of K is dependent on the radiometer type in question, and the value is generally 1 for total power radiometers and 2 for Dicke type switching radiometers. It is clear that the total power radiometers have much better sensitivity than the Dicke type of radiometers. However, regarding stability, total power radiometers are inferior to the other types. Stability is difficult to predict. For a spaceborne radiometer, certain constraints affect the choice of parameters and hence the sensitivity achievable: τ is limited by mission requirements to swath width and footprint size; B is limited due to fear of interference from external sources; and TN is limited by available technology. Hence, there is
99
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Microwave Radiometer Systems: Design and Analysis
great interest in the potentially better sensitivity of total power radiometers for certain applications, where sensitivity requirements are severe. The total power radiometer is simpler than the other types. It does not include the Dicke switch and the synchronous detector found in the Dicke type of receiver, and it certainly does not include the noise-injection circuitry found only in the noise-injection radiometer. Hence, a total power radiometer is smaller, lighter, and may consume less power than other radiometer types. However, this radiometer type can of course only find use for a given application if the accuracy and stability are adequate for that application. Accuracy is dependent on calibration, so the calibration scheme feasible for a given application must also be considered. However, the basic dark area is the initial stability of the total power receiver itself. Experiments with real radiometer hardware are required to enlighten the subject. Regarding the choice between Dicke and noise-injection radiometers, for applications where the total power radiometer fails to meet the requirements, a controversy between researchers seems to exist: Some favor Dicke; others favor noise-injection. In theory, the noise-injection mode of operation is superior to the Dicke mode, but is it true in real life? Again, experiments with real radiometer hardware may answer this question. The 5-GHz noise-injection radiometer discussed in Chapter 6 has been modified to operate in three different modes as: • DR: Dicke radiometer; • NIR: noise-injection radiometer; • TPR: total power radiometer.
Also, the 17- and 34-GHz radiometers were included in the experiments (NIR mode only). Extensive measurements of stability against temperature variations in the microwave part and in the low-frequency part of the radiometers have been carried out to assess the merits of each mode. The temperature variations have been designed to resemble those inevitably found in a satellite orbiting the Earth. Sensitivity measurements have been carried out to confirm the theoretical differences between modes. The 5-GHz radiometer was used for the exercises.
10.2 The Radiometers Used in the Experiments The 5-GHz noise-injection radiometer is basically designed according to the block diagram shown as Figure 5.10 but with the addition of a microwave preamplifier before the mixer. It has for the present task been reconfigured to
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101
operate in the Dicke mode and the total power mode. First, the noise-injection circuitry is deactivated. In the Dicke mode the gain of the LF circuit has to be reduced by 56 dB. The total power mode requires more thorough changes. The Dicke switch is deactivated and the LF circuitry substituted by a stable DC amplifier-integrator. The DC amplifier includes a stable offset to compensate for the signal caused by the receiver noise temperature. Also, the detector is replaced, and a tunnel diode detector is used due to its very low noise close to DC. The latching circulator (normally used as a Dicke switch) is now used as a calibration switch. During the stability measurements, the internal 313-K load was connected to the radiometer input for 12 seconds each 24 seconds (i.e., the radiometer measures 12-second TA, 12-second TR, 12-second TA, and so on). The 17- and 34-GHz radiometers were used without modifications (NIR mode only).
10.3 The Experimental Setup For calibration, sensitivity, and stability measurement purposes, the input of the radiometer must be connected to stable, well-known signal sources. In all measurements to be reported later, the radiometer was connected either to a microwave load in a freezer (see Figure 9.1), or to a commercial, liquid nitrogen cooled load (5 GHz only). The load in the freezer is a termination submerged in a suitable liquid. The temperature can be varied down to –30°C, and it is measured by a thermometer and by the digital thermometer of the radiometer. Typically temperatures around +20°C (293K) and around –25°C (248K) were used during the measurements. In addition, the liquid nitrogen load enabled measurements with a 77-K input to the radiometer (5 GHz only). During sensitivity measurements (5 GHz only), the radiometer was allowed to reach thermal equilibrium (it takes several hours), and a few minutes of recording were made in each mode (DR, NIR, TPR) and for each input (∼293K, ∼248K, ∼77K). During stability measurements much longer time series were used—up to 8 hours. Again, the radiometer was allowed to reach thermal equilibrium before the start of the measurements, in order to reach a well-defined starting point, but also to ensure that the temperatures in the front end were inside the rather narrow range of the digital thermometer (38°C to 46°C). Two types of stability measurements were carried out: stability versus front-end temperature and stability versus the temperature of the LF section of the radiometer. The front-end temperature, being electronically regulated, is changed simply by adjusting a potentiometer. The back-end temperature was
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raised from its nominal ambient around 23°C to some 35°C by a heater-blower arrangement.
10.4 5-GHz Sensitivity Measurements The sensitivity measurements were, as already described, carried out for three different input temperatures: +20°C, −25°C, and 77K. An integration and sampling time of 64 ms was used. The results are shown in Table 10.1. The expected sensitivities (see Chapter 6) are 0.41K for the Dicke type modes and 0.20–0.21K for the total power mode. A reasonable agreement between measured and expected values are found, considering the statistical nature of the results. The total power mode especially shows good agreement. The DR and the NIR show slightly, but probably statistically significant, larger values than expected. A possible explanation is given next. It has been suggested that rapid gain fluctuations in the radiometer (fluctuations faster than the integration time) would contribute in a deteriorating fashion to the sensitivity of the radiometer [1, 2]. This mechanism would, however, especially affect the total power mode and thus cannot explain the observed differences. The present measurements cannot support the existence of said fluctuations. Another suggestion shall be brought forward: The fundamental difference of the factor 2.0 between Dicke and total power mode stems from the square wave modulation of the signal in Dicke radiometers. If, however, the “square wave” signal is limited in bandwidth—which it is in the present radiometer—the factor 2 increases, eventually up to a factor of 2.22 in a sinusoidally modulated radiometer (the AF amplifier has a very narrow bandwidth around the Dicke switch frequency). See [2]. In the present radiometer, the AF bandwidth has been measured to 100 Hz–13 kHz. The square wave signal before the synchronous detector can be expressed as follows: Table 10.1 Measured Sensitivities (5 GHz) Calibration Temperature
Radiometer Mode
+20°C
0.45K
0.49K
0.22K
−25°C
0.45K
0.48K
0.22K
77K
0.53K
0.47K
0.21K
Sensitivity and Stability: Experiments with Basic Radiometer Receivers
f (t ) =
103
4 sin t sin 3t sin 5t ⋅ + + + K π 1 3 5
normalized so that the effective value is 1. If only the first harmonic is let through the AF amplifier, the effective value of the signal is E =
4 1 ⋅ = 0.90 π 2
leading to an increase of the factor 2 to 2/0.90 ~ 2.22, as stated before. In the 5-GHz radiometer, where the Dicke frequency is 2.225 kHz and the AF bandwidth is up to 13 kHz, the three first terms must be considered. Hence, the effective value is calculated from: 2π
E
2
2
1 42 1 1 = ⋅ 2 ⋅ ∫ sin t + sin 3t + sin 5t dt 2π π 0 3 5
which can be evaluated, and the result is E 2 = 0.9331 or E = 0.9659. Having found a measured sensitivity for the TPR of ∼0.22K, the expected sensitivity for the Dicke type modes is thus 0.22 · 2/0.9659 = 0.46K, which is quite close to the observed values. In conclusion, it can be stated that the basic radiometer sensitivity formula gives a good estimate of the performance.
10.5 Stability Measurements During the stability measurements the 5-GHz radiometer was configured in either DR or TPR mode, while the NIR mode was represented by the 17- and the 34-GHz radiometers. Only the 17-GHz results are shown herein, as the 34-GHz results are almost identical. 10.5.1
Discussion of the 5-GHz DR Results
An example of the stability measurements is shown by the curves in Figure 10.1. First, the notation on the curves shall be explained. The abscissa is time in 24-second increments; 24 seconds is the update rate of housekeeping data and hence temperatures from the digital thermometer. The graph thus corresponds to 254 · 24 seconds ∼1 hour and 42 minutes of recording. The band of eight thin, solid, or broken lines show the temperature of the eight important components in the front end, and refer to the left-hand scale in counts. Recall that the physical
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temperature is found from: T = counts/32 + 38.0°C. Table 6.1 shows the correspondence between component and sensor numbers, which are included on Figure 10.1, but otherwise only when needed in the discussion of the curves. The curves separate somewhat due to fact that some components are active and generate heat (see curve 7, the noise-injection diode, in Figure 10.1, for example). The temperature of the front end has been forced to oscillate in a fashion that could resemble the oscillations found in a satellite orbiting the Earth. The enhanced curve named DR shows the output of the radiometer in the Dicke mode. The output is calculated as follows: Sensor 2 gives the temperature of the reference load TR. Then the radiometer output is found by subtracting the digital output multiplied by a calibration constant (actually found during the sensitivity measurements described earlier). The curve is shown on a relative scale (see the right-hand side of Figure 10.1), as we are only interested in deviations from stable levels and not in the absolute level. Although the results were recorded with 64-ms integration and sampling time, a computer integration to 12-second time slots has been carried out. This corresponds to a sensitivity of: ∆T = 0.41 ⋅ 0.064 12 = 0.030K The standard deviation of a noisy curve can be estimated by using a rule of thumb: The peak-to-peak amplitude on the curve is roughly 0.1K. The standard deviation for such a signal is roughly:
250 DR 7
200
6 5
150 1K 5
100 7
6 0 1 5
50
4
4 3 25
0
0
Figure 10.1 5-GHz DR. TA = −25°C.
1H 42 Min
254
Sensitivity and Stability: Experiments with Basic Radiometer Receivers
σ = 01 .⋅
1 2 2
105
= 0.035K
which is in good agreement with the expected value. It is immediately observable from Figure 10.1 that the DR shows a large variation in its output, which correlates very well with the general front-end temperature—especially with the temperature of the mix-preamp as measured by sensor number 5. The DR results are very reproducible. This graph represents only one example out of many recorded during the experiments and they all display the same features down to a quite detailed level. The DR results can be explained by considering gain variations with temperature in microwave amplifiers. In [3], it is stated that the gain of amplifiers, like the ones used here, typically decreases with temperature by 0.013 dB/°C/stage at 45°C physical temperature. The present radiometer has two stages in the RF preamplifier and one stage in the mixer-preamplifier. The peak change in front-end temperature during the experimental oscillations is roughly 5°C. Thus, we expect a gain change of: ∆G = −0.013 ⋅ 3 ⋅ 5 = 0.2dB ∆G = 0.046 (4 .6% ) In the present case, with TA = −25 °C and TR = 42°C, we find a change in the output of the radiometer due to gain variation of: δDR = 0.046 ⋅ (42 + 25) = 31 .K which is seen to fit very well with the results in Figure 10.1. It is also clear that when temperature increases, the gain decreases and hence the difference TR − TA decreases. As TR is the reference in the radiometer, this means that the output (which is a measure of TA ) increases.
10.5.2
The 5-GHz DR with Correction Algorithm
Figure 10.2 shows the results of the experiment that were originally displayed as Figure 10.1. As noted before, the DR curve seems quite well correlated with the general temperature level in the front-end. Figure 10.3 shows this correlation more clearly. Here the radiometer output (vertical relative scale as on Figure 10.2) has been plotted versus the front-end temperatures as measured by sensor 02 (reference load) and sensor 05 (mixer-preamplifier). It is seen that the correlation is best with sensor 05, but certainly not perfect.
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Microwave Radiometer Systems: Design and Analysis
250
DR 200
DRC
DRC
150
DR
1K
100
50
0
0
1H 42 Min
254
Figure 10.2 5-GHz DR with correction. TA = −25°C.
As already discussed in Section 10.5.1, the variations in the output of the DR can be explained by considering the gain variation with temperature in microwave amplifiers. A typical gain change of δG = 0.013 · 3 dB/°C ∼0.009/°C was quoted. In Figure 10.2 the curve marked DRC represents a corrected output, using a δG = 0.008 and the reading from sensor 05. The output of a Dicke radiometer is found as: V OUT = b ⋅ (T R − T A ) ⋅G where b is a constant. In the present radiometer with A/D conversion the output is a digital number N. Hence: N = c ⋅G ⋅ (T R − T A ) or: T A = T R − N c ⋅G which can be expressed as: DR = T 02 − N ⋅CAL
Sensitivity and Stability: Experiments with Basic Radiometer Receivers
107
1K
0
Dicke load (02)
255
1K
0
Mix-preamp. (05)
255
Figure 10.3 5-GHz DR scatter plots.
DR being the notation on the curves, T02 is the reference temperature (sensor 02), and CAL is the radiometer calibration constant. With gain variations present, the output of the radiometer is expressed as V OUT = b ⋅ (T R − T A ) ⋅G ⋅ (1 + ∆G ) where ∆G is the relative change in G (usually a small figure). Again, N = c ⋅G ⋅ (T R − T A )(1 + ∆G )
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Microwave Radiometer Systems: Design and Analysis
or: T A = T R − (1 − ∆G ) ⋅ N c ⋅G inserting again CAL for 1/c · G and recalling that ∆G is known as gain change per centigrade, we get T A = T R − N ⋅CAL + N ⋅ δG ⋅ δT ⋅CAL δT is the temperature deviation from normal (steady state) where the calibration of the instrument was carried out. In this case we consider the output of sensor 05 having a nominal value of 112 counts = 41.5°C. Returning to present notation we find DRC = T 02 − N ⋅CAL + N ⋅ 0.008 ⋅ (T 05 − 415 . ) ⋅CAL It is seen from Figure 10.2 that this very simple correction algorithm accounts for a large part of the output fluctuation, but the result is not perfect as would already be expected from the scatter plots in Figure 10.3. The problem is of course that none of the existing temperature sensors adequately describe the temperature inside the three microwave amplifier stages. In a future design this could easily be accommodated and a better correction would be possible. Figure 10.4 shows the results from another experiment designed to show the general behavior of the Dicke radiometers subjected to front-end temperature oscillations. This time a very low input temperature of 77K was used, and this should enhance the problems with DR operation: The low temperature means greater difference TR − TA enhancing changes due to gain variations. Indeed this is observed: note the five times coarser scale necessary to keep the curves inside the frame. In this case we now expect a change in the output of the radiometer due to gain variations of: δDR = 0.046 ⋅ (42 + 273 − 77 )K δDR = 11K which is seen to fit well with the results. Again the simple correction as discussed earlier has been applied, and the result (curve DRC) is a suppressed output fluctuation: some 2K as opposed to the original 12K (apart from the narrow peak at the rapid temperature increase to the left in Figure 10.4, where the lack of appropriate and intimate temperature sensors is most severe).
Sensitivity and Stability: Experiments with Basic Radiometer Receivers
250
109
DR
200
DRC
150
DR 5K
100
50
0
0
1H 42 Min
254
Figure 10.4 5-GHz DR with correction. TA = 77K.
10.5.3
The 17-GHz NIR Results
Figure 10.5 shows the results of a thermal cycle in the 17-GHz NIR. Note the good correlation with temperature. Figure 10.6 shows the correlation more clearly. A good correlation is found between the output and the temperature of the reference load (sensor 01 in this case), but an almost perfect correlation exists between the output and the temperature of the noise diode (sensor 07). This is quite pleasing because the feature is easily explained: A temperature change in the noise diode causes a change in output power, which again translates directly into a change in radiometer output. The high degree of correlation ensures that a good correction is possible. The output, N, of the noise-injection radiometer is a direct measure of the injected noise: T I = N ⋅CAL where again CAL is the calibration constant. The input brightness temperature is found as: T A = T R − N ⋅CAL or with the present notation:
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Microwave Radiometer Systems: Design and Analysis
250
200 NIR 150 NIRC
1K
100
50
0
0
1H 42 Min
254
Figure 10.5 17-GHz NIR with corrections. TA = −25°C
NIR = T 01 − N ⋅CAL The injected noise can be expressed more thouroughly as: T I = N ⋅ K ⋅T D (1 + ∆T D ) where TD is the output from the noise diode, ∆TD is the relative deviation with temperature, and K accounts for losses in the noise-injection circuitry. It is seen that actually CAL = K · ∆TD and we find: T I = N ⋅CAL (1 + ∆T D ) and T A = T R − N ⋅CAL (1 + ∆T D ) or T A = T R − N ⋅CAL − N ⋅CAL ⋅ δT D ⋅ δT where δTD is the relative deviation per centigrade and δT is the temperature deviation from nominal value (where the calibration was carried out) concerning the noise generator, that is, sensor 07 (nominal value 150 counts corresponding to 42.7°C). Returning to the present notation, we find:
Sensitivity and Stability: Experiments with Basic Radiometer Receivers
111
1K
0
Noise diode (07)
255
1K
0
Dicke load (01)
255
Figure 10.6 17-GHz NIR scatter plots.
NIRC = T 01 − N ⋅CAL − N ⋅CAL ⋅ 0.007(T 07 − 42.7 ) The value of δTD = 0.007 has been found empirically to give the best correction, and indeed, when observing the curve marked NIRC in Figure 10.5, a very satisfactory correction has been obtained. 10.5.4
Discussion of the TPR Results
Figure 10.7 shows the behavior of the 5-GHz total power radiometer when subjected to temperature oscillations in the RF front end. The input temperature to
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Microwave Radiometer Systems: Design and Analysis
250 INT EXT
200 EXT
DIFF
150
EXT INT
INT
100
5K
EXT
DIFF
50 INT
0
0
1H 42 Min
254
Figure 10.7 5-GHz TPR. TA = 77K.
the radiometer is 77K. Recall that the radiometer measures the internal reference load and the antenna signal alternatively with a 24-second period. The curve named INT is the measurement of the internal load, and the noise level in the radiometer is TR + TN = 313 + 527K = 840K (527K corresponds to the 4.5-dB noise figure of the radiometer). EXT is the measured antenna temperature, and the signal level is TA + TN = 77 + 527K = 604K. The two curves subtracted give the curve named DIFF, and this corresponds to the output from a total power radiometer with frequent calibration—in this case with 24-second period. DIFF is seen to look very much like DR—the output from the Dicke radiometer—in Figure 10.4 (just turned upside down as a result of a different sign convention). This is not surprising, when considering that the difference carried out on the computer (as part of the data treatment) in the total power case, corresponds exactly to the difference performed in an analog fashion in the Dicke radiometer. However, in the Dicke radiometer, the “calibration rate” is 2 kHz, while in the total power radiometer it is 42 mHz (1/24 second), but the present instrument is so stable with time that this does not matter. The variation in the curve named DIFF can of course be explained as in the Dicke case as a result of a gain variation of 0.2 dB (4.6%) due to a physical temperature change of 5°C. The measurement of the internal reference is subject to the same gain variation resulting in an expected change of 0.046 · 840K = 38.6K. However, this time an opposite mechanism must also be considered: If temperature increases, gain decreases, resulting in a lower output, but at the
Sensitivity and Stability: Experiments with Basic Radiometer Receivers
113
same time receiver noise temperature increases, resulting in a larger output. Microwave amplifiers, with noise figures like the one in the present radiometer, typically exhibit an increase in noise of 0.014 dB/°C, that is, 0.07 dB or 1.6% for the 5°C temperature change. This results in an output change of 0.016 · 527K = 8.4K, and the total change as a result of the temperature variations, is thus expected to be 38.6 − 8.4 ∼ 30K. It is seen from the figure that the variation in INT is roughly 25K, not quite the expected value, but still a satisfactory agreement is noted. Likewise, the change in EXT is expected to be: 0.046 · 604 − 8.4K ∼ 19K, and the observed value is roughly 13K. Overall, it looks like the typical noise figure change with temperature used for the calculations is not quite large enough to fit the present amplifier. 10.5.5
Back-End Stability
In Figure 10.8 we find the response of the DR and the NIR to temperature variations in the low frequency part of the radiometer. The temperature is constant (23°C) until a certain moment, when 35°C warm air is forced into the LF circuitry. After a period, the heating is turned off again. It is seen that the Dicke mode shows a quite substantial response to the heating. This is the result of a combination of gain changes and drift with temperature in the DC coupled part
250
200 DR
150 5K 100 NIR
50
0
0
1H 42 Min
Figure 10.8 5-GHz DR and NIR. LF temperature variations. TA = 77K.
254
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Microwave Radiometer Systems: Design and Analysis
of the LF circuitry. As expected, the NIR is quite invariant to LF temperature changes, due to the closed loop operation of this radiometer type. The total power radiometer’s response, when subjected to temperature variations in the low-frequency part of the instrument, is also well behaved, and again the variations are the result of gain changes and drift with temperature.
10.6 Conclusions For the three investigated radiometer types (DR, TPR, and NIR), measured sensitivity agrees well with theoretical predictions, and we note especially that the TPR exhibits a sensitivity that is superior by a factor of 2 compared with that of the other radiometer types. It is also noted that the simple, well-known formula for radiometer sensitivity is confirmed: No degradation from rapid gain fluctuations was experienced. Regarding the stability of the DR against thermal variations in the microwave front end, this instrument is well behaved. Variations in output for a constant input brightness temperature are noted, they are reproducible from experiment to experiment, they show good correlation with the temperature of the microwave amplifiers, and they can be explained (and modeled) by amplifier gain variation with temperature. A correction algorithm has been implemented based on the model and a good, but not perfect, correction is possible. An even better correction is expected to be possible if temperature sensors in close contact with the amplifier stages are available. The TPR may also be regarded as well behaved. The variations in output are explainable as in the DR case, and overall the behavior of the TPR in many ways resembles that of the DR. Stability is good, and single point calibration every 24 seconds is adequate to bring the accuracy to the same level as that found for the DR. As in the Dicke case, a correction for gain variation is possible. Regarding the NIR, a very positive conclusion is reached, namely, that even subjected to relatively large thermal variations in the RF front end, the NIR represents the ultimate design regarding stability. The output variations encountered are simply a result of varying output from the noise diode and can be corrected with great accuracy. Also, the stability of the three radiometer modes against temperature variations in the low frequency part has been investigated. The NIR is completely invariant to such variations as is to be expected. The DR and the TPR in the present design are relatively sensitive to such thermal variations. It is, however, a matter of careful design to alleviate this problem. In all three cases (DR, NIR, TPR) a calibration each half minute or so (depending on the rise and fall times of possible thermal variations) will ensure
Sensitivity and Stability: Experiments with Basic Radiometer Receivers
115
good stability without the need for modeling based on gain or noise generator output variations. However, it is certainly a positive feature that such modeling is possible as a backup, and furthermore, it may reduce the rate at which calibration is required. The present work can in a certain sense not support the use of the traditional Dicke radiometer for future space systems. If the ultimate in stability and accuracy is required, the noise-injection concept is the candidate. The penalty is circuit complexity and loss of sensitivity by a factor of 2, compared with the total power radiometer. When the ultimate in sensitivity is required, the total power radiometer is the candidate. The penalty is slightly inferior stability and the requirement for frequent calibration (at least once per minute). Hence, the total power radiometer is especially well suited for mechanically scanned imagers where frequent calibration (once per scan) is easily accommodated without loss of useful data, and the noise-injection radiometer is recommended for push-broom applications where long periods between calibration are wanted (see Chapter 11). Further information about stability can be found in [4, 5].
References [1]
Ulaby, F. T., R. K. Moore, and A. K. Fung, Microwave Remote Sensing, Vol. 1, Dedham, MA: Artech House, 1981.
[2]
Tiuri, M. E., “Radio Astronomy Receivers,” IEEE Trans. on Antennas and Propagation, Vol. 12, No. 7, 1964, pp. 930–938.
[3]
Miteq, Miteq Amplifier Handbook, Miteq, 125 Ricefield Lane, Hauppauge, NY 11788, 1986.
[4]
Hersman, M. S., and G. A. Poe, “Sensitivity of the Total Power Radiometer with Periodic Absolute Calibration,” IEEE Trans. on Microwave Theory and Techniques, Vol. 29, No. 1, 1981, pp. 32–40.
[5]
Tanner, A. B., and A. L. Riley, “Design and Performance of a High-Stability Water Vapor Radiometer,” Radio Science, Vol. 38, No. 3, 2003, p. 12.
11 Radiometer Antennas and Real Aperture Imaging Considerations The purpose of the antenna is to collect the emitted energy from a target and present it to the radiometer input.
11.1 Beam Efficiency and Losses The ideal antenna has a certain gain within its field of view and zero gain outside. Figure 11.1(a) shows the polar pattern for such an idealized antenna. The measurement situation becomes very simple: If an extended target is viewed by the antenna, this collects energy from the target and not from anything else in the world. However, such an antenna cannot be realized. First, the sharp cutoff of the beam is not possible. Figure 11.1(b) shows a more realistic beam. To define the beamwidth, it is now necessary to refer to a certain level on the beam compared to the peak gain. The −3-dB points are normally used. Actually even this pattern is not possible in real life. Sidelobes picking up energy from directions far away from the main beam direction cannot be avoided [see Figure 11.1(c)]. By careful design they can be minimized but never avoided. An important antenna property is the so-called beam efficiency η defined as the ratio between the energy received through the main beam and the total energy received by the antenna (main beam + all sidelobes). The antenna in Figure 11.1(a) has a beam efficiency of 100%. To fully describe the beam efficiency for a realistic pattern, η is often quoted for several levels on the main beam (i.e., η = 90% within the −10-dB points means that 90% of the total energy received
117
118
Microwave Radiometer Systems: Design and Analysis 0
0
0
180 (a)
180 (b)
180 (c)
Figure 11.1 Antenna polar patterns: (a) idealized sector shape, (b) realistic main beam, and (c) realistic pattern.
by the antenna is received within the −10-dB points of the main beam). An antenna with η = 95% within the −20-dB points is about the best you can get. To get a flavor of the problems associated with beam efficiency, let us consider an example, where an antenna having η = 95% (total main beam) senses an ice floe on the surface of the sea. The ice floe is just the size of the area on the ground illuminated by the main beam. See Figure 11.2. To simplify the situation, only downward looking sidelobes are assumed present. In case of a lossless antenna we find: T A = η ⋅T B + (1 − η ) ⋅T SL Typical values are TB = 270K (ice) and TSL = 100K (sea), which together with η = 95%, gives:
Radiometer Antenna (η, T0, ᐉ)
TSL TB Ice
Figure 11.2 Antenna measuring an ice floe.
Sea
Radiometer Antennas and Real Aperture Imaging Considerations
119
T A = 0.95 ⋅ 270 + 0.05 ⋅100 = 262K which is quite far from the value of 270K, which we expected to measure. Fortunately, Figure 11.2 displays a situation with extreme contrasts. In general, the ice floe may extend for several footprints, and the sea around it will contain other ice floes elevating the spurious signal TSL. In total, smaller errors may be expected. However, it should be noted that imaging near coastlines is in general a problem due to the large radiometric contrast between land (warm ~270K) and sea. In Figure 11.2 it is noted that the antenna itself may have a loss ᐉ. This will have to be treated exactly as described in Section 3.3. It is, however, possible to make antennas with very small losses.
11.2 Antenna Types Three main types of antennas shall be considered, namely, horns, phased arrays, and reflector antennas. Figure 11.3 shows a horn, a phased array, and three often-used reflector antenna types. Horns are low-gain devices, and as such are not used as primary remote sensing antennas in spaceborne systems. They are often used for
(a) Feed network (b)
(c)
(d)
(e)
Figure 11.3 Antenna types: (a) horn; (b) phased array; (c) front-fed paraboloid; (d) Cassegrain; and (e) offset paraboloid.
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Microwave Radiometer Systems: Design and Analysis
laboratory measurements (calibration), in airborne systems, and as feeds in reflector antennas. Although the horn antenna is illustrated as a square, pyramidal horn in Figure 11.3, this is not optimal due to relatively poor patterns. Potter horns have almost ideal patterns with very low sidelobes and identical in the E and H planes. Also, corrugated horns are well suited and in addition to good patterns they feature large bandwidth. Phased arrays are generally not used as radiometer antennas, as they are relatively lossy, one-frequency devices. Figure 11.3 shows a slotted waveguide phased array. Microstrip patch antenna arrays can also be considered. Both are widely used in radar systems. It is possible to make an electronically steerable antenna by incorporating phase shifters in the feed network. Due to this feature (and the flatness of the structure), phased arrays do find use for special purposes. Regarding the reflector antennas, the simple front-feed paraboloid is not the best solution due to the losses in the long feed waveguide. The Cassegrain antenna may be used, although it has some problems with sidelobes, due to reflections and refractions in the subreflector and the struts that carry it. The offset paraboloid antenna shown in Figure 11.3(e) is the ideal radiometer antenna. The feed can be connected directly to the radiometer (low losses), and no aperture blockage is present. The offset reflector geometry is further evaluated in Figure 11.4. Drive assembly Reflector
Aperture
Vertical
Vertex 50° 30° 30° 50° Focal point Feed horn
Axis of parabola
Figure 11.4 Offset paraboloid reflector geometry.
Radiometer Antennas and Real Aperture Imaging Considerations
121
The reflector is a section of a normal paraboloid, not including the vertex. The feed horn is (as usual) in the focal point, but turned to illuminate the cutout section. A special feature of the offset system is that if the reflector is rotated about an axis equal to the horn axis, the antenna beam will be scanned (leave the plane of the paper in Figure 11.4), but the reflector will still be properly illuminated by the horn. For the antennas discussed here, where the electrical aperture is roughly equal to the physical aperture, it is very simple to estimate the width of the main beam. The 3-dB beamwidth is slightly larger than the reciprocal of the aperture measured in wavelengths of the operating frequency: θ∼14 . ⋅λ ∆
(11.1)
Many readers will know this rule-of-thumb equation with a factor 1.2 ahead of λ/D. The factor 1.4 is used here to reflect the radiometer’s need for high beam efficiency, which generally results by a careful design having a low aperture edge illumination (and hence a wider beam compared to other situations). A 1-m Cassegrain antenna used at 30 GHz (1-cm wavelength) will thus have a 0.014 ( = 0.8°) beamwidth. Looking straight down from an airplane at 2,000-m altitude, the footprint on the ground is FP = θ · H = 28m, and from a satellite at 80-km altitude, the footprint (looking straight down) will be 11.2 km. Note that here, and in the following, the footprint is taken as the intersection between the ground plane and the three-dimensional antenna pattern at the –3-dB level (other definitions are possible though rarely used).
11.3 Imaging Considerations A remote sensing device, like the microwave radiometer, obviously points toward airborne or spaceborne operation. If a radiometer with its antenna is mounted on a satellite, and the antenna points straight down, the forward movement of the satellite (∼7.5 km/sec) will facilitate measurements on the ground along a straight line (the nadir path of the satellite). Coverage of the entire Earth by such “profiles” will require an enormous number of orbits! A dramatic increase in mapping efficiency results from scanning the antenna (see Figure 11.5). In the line scanner the antenna swings back and forth around a rotation axis parallel to the satellite velocity vector. The footprint will thus move back and forth across the nadir path, and as the satellite moves forward, a certain area (swath) on the ground is covered by the antenna beam.
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Antenna scan
Satellite velocity vector
Nadir path
Swath Antenna footprint
Figure 11.5 Satellite-borne line scanner.
The swath width is dependent on the scan angle of the antenna (and on satellite altitude). It is clear that certain relationships must exist between swath width, footprint, and scan speed: the scan speed must be large enough to ensure contiguous ground coverage with given footprints and swath width. Likewise, it is clear that because the footprint rapidly moves to a new position, only a certain time is available for each brightness temperature measurement, that is, there is a certain constraint to the integration time of the radiometer. There will be more information about this in Section 11.4 and Chapter 12. The line scanner is often used (especially in airborne systems), but it has one serious drawback: the varying incidence angle across the swath. For many applications (especially scientific measurements), this is not acceptable, as brightness temperatures are often strongly dependent on incidence angle. Figure 11.6 shows a scanning system that gets around this problem by employing a conical scan. An antenna, with the geometry shown in Figure 11.4, scans about a vertical axis. Again, the footprint will scan across the swath, but this time with constant incidence angle. The conical scan is used in several high quality radiometer systems like the DTU airborne radiometer system. Also, the scanning multichannel microwave radiometer (SMMR) on the U.S. Nimbus 7 satellite, the first and very successful spaceborne multifrequency imaging system for Earth surface sensing, used a conical scan as well as a range of newer systems like SSM/I. Satellite builders dislike moving masses such as scanning antennas, as they disturb the stability of the satellite movement (the satellite mass is not very, very large compared to the antenna mass). A moving mass, which has to oscillate, is
Radiometer Antennas and Real Aperture Imaging Considerations
123
Antenna scan Satellite velocity vector Nadir path
Swath Antenna footprint
Figure 11.6 Conical reciprocating scan.
especially unpopular. Therefore, scanning the antenna in a continuous rotating movement is often used (see Figure 11.7). Measurements are only taken as the antenna looks at the swath in the forward direction. This may seem an awful waste of measurement time, as the antenna clearly looks away from the useful swath for the greater part of the rotation period. The situation is, however, that the rotating scan should not be compared to an idealized zigzag scan, but to a real life ditto: In real life the zigzag scan cannot take advantage of an antenna that moves across the scan with constant angular velocity, stops immediately at the scan edge, then moves back again with constant angular velocity. Rather, the antenna has to come to a gentle stop at the scan limit, and has to be gently accelerated for the backward scan (sinusoidal variation of scan angle as function of time). Thus, a rather large amount of time is wasted at the scan edges for accelerating the antenna. Figure 11.8 illustrates the trade-off between the rotating and the sinusoidal scan. The ratio of the resulting sensitivities ∆TREC/∆TROT for a certain radiometer in the reciprocating/rotating case is shown as a function of scan half-angle (maximum scan angle in the reciprocating case, equal to the angle defining the useful swath in the rotating case). It is seen that small scan half-angles favor the reciprocating scan, while approaching 50° reduces the penalty for using a rotating mode. The break-even mark is found at 57°. SMMR used a 25° scan half-angle and a sinusoidal movement, which is clearly justified in Figure 11.8, but the scanner to be described in Chapter 13 will use a 60° half-angle and a fully rotating antenna.
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Microwave Radiometer Systems: Design and Analysis
Antenna scan Satellite velocity vector Nadir path
Useful swath Antenna footprint
Figure 11.7 Conical scan by rotating antenna.
Note that in some cases it is highly desired to use also the aft look (to have two different look directions). This may not be a problem for the radiometer, but it may be for the spacecraft designer as it is now required to have unobstructed field of view both fore and aft. The users in general want small footprints (or better ground resolution, to put it differently). Small footprints mean large antennas or high frequencies. As technology evolves, high-resolution systems become possible, but a small footprint results in rapid rotation and in very short integration times, which, through our radiometer sensitivity formula, directly translate into poor sensitivity. The solution to this fundamental problem is offered by the so-called push-broom concept illustrated in Figure 11.9. In the push-broom radiometer system, a multiple beam antenna covers the swath while the satellite moves forward. A host of radiometer receivers are connected to an equal number of antenna feeds, producing individual beams to sense the Earth simultaneously. The obvious advantages of the push-broom system compared to a scanning system are: • No moving antenna (makes the satellite builder happy); • Much larger dwell time per footprint, hence better sensitivity (the foot-
prints do not have to time share a single radiometer receiver). The obvious problems areas are:
Radiometer Antennas and Real Aperture Imaging Considerations
125
1.4 1.3 1.2 1.1 1.0 0.9 0.8 ∆TREC ∆TROT
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0°
10°
20°
30°
40° 50° Scan half-angle
60°
70°
80°
90°
Figure 11.8 Trade-off between a reciprocating and a rotating scan.
• Complicated antenna; • Many receivers (one per antenna beam).
The problems with the antenna can be solved, and as technology moves forward, cheap and lightweight receivers can be built. So, for future advanced space-borne radiometer systems, the push-broom concept is to be seriously considered. A detailed description of the push-broom system is given in [1]. See also [2, 3].
11.4 The Dwell Time Per Footprint Versus the Sampling Time in the Radiometer In an imaging radiometer system the antenna footprint moves across the scene to be sensed, and the dwell time per footprint is defined as the time taken by the antenna beam to move a distance of one footprint. When the antenna beam scans a scene with a certain brightness temperature distribution, this results in a certain variation in the input signal to the associated radiometer; hence, there
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Microwave Radiometer Systems: Design and Analysis
Satellite velocity vector Nadir path
Swath Antenna footprints
Figure 11.9 Push-broom imager.
are certain requirements for the sampling in that radiometer. Quite clearly the spectrum associated with these input variations to the radiometer heavily depends on the dwell time per footprint: The faster the scan, the quicker the variations, or, to put it differently, the wider the spectrum. However, as will be shown next, the actual shape of the antenna pattern plays an important role. In mathematical terms the sensing of the scene by the moving antenna corresponds to a convolution of the antenna pattern with the brightness temperature distribution of the scene. Hence, to find the transfer function H(f ) associated with that process, it is assumed that the antenna beam sweeps across a delta function in the scene distribution. Then H(f ) is simply found as the Fourier transform of the antenna pattern (transformed to the time domain by means of the scan velocity , or the dwell time per footprint). Figure 11.10 shows a host of idealized antenna patterns. The patterns have been normalized to have an equal 3-dB width, and (without loss of generality) this has been assumed to be 2 seconds (i.e., the footprint dwell time is 2 seconds). Curve A represents a sector shaped pattern (often used for overview considerations). B is the main beam of a (sin x)/x pattern. It may seem odd to include that, as it is a completely unreal antenna having negative sidelobes. (Note that we are dealing with power patterns since the brightness temperature to enter the
Radiometer Antennas and Real Aperture Imaging Considerations
dB
A:
Sector
B:
sin 1.9 t 1.9 t
0
127
2
( ( ( ( ( ( sin 1.4 t 1.4 t
C: −3
4
sin t t
D:
t2 exp − 1.43
E: −10
A
−20
B
1
C 2
D
E t(sec)
Figure 11.10 Antenna power patterns (only one half shown).
antenna is a power measure.) The reason is purely academic and will emerge later. The next two curves represent far more realistic patterns, namely, a ((sin x)/x)2 having −13-dB sidelobes and ((sin x)/x)4 with −26-dB first sidelobes. This statement is supported by Figure 11.11, which shows normalized patterns of two actual antennas: one with a 140λ aperture (e.g., 1.4m at 30 GHz) and one with a 600λ aperture (e.g., 2m at 90 GHz). When compared with Figure 11.10, the two curves lie nicely between curves C and D. Finally, curve E is a Gaussian pattern, also sometimes used as a reference for overview considerations. As previously mentioned, the transfer function of the scanning antenna is found simply by Fourier transforming these power patterns and the results are shown in Figure 11.12. The sector shaped pattern transforms into a |(sin x)/x| with zeros at n · 1/(2 seconds) = n ⋅ 0.5 Hz. Likewise, the (sin x)/x pattern transforms into a box shape having a total width of 1.9/π = 0.6 Hz. The transform of the ((sin x)/x)2 pattern can be found by a convolution in the frequency domain of two box patterns and it is a triangle extending out to ±1.4/π = ±0.45 Hz. Again the transform of the ((sin x)/x)4 can be found by a convolution of two triangles, or by consulting tables of Fourier transforms. The result is:
128
Microwave Radiometer Systems: Design and Analysis
dB
0 −3
−10
600 λ
140 λ
−20 2
1
t(sec)
Figure 11.11 Two real-life patterns. 3 3 2 2 for 0 ≤ f ≤ 1 π 3 4 ⋅ π ⋅ f − 3 2 ⋅ π ⋅ f + 1 3 3 2 2 H ( f ) = − π 4 ⋅ f + 3 2 ⋅ π ⋅ f − 3 ⋅ π ⋅ f + 2 for 1 π ≤ f ≤ 2 π 0 for 2 π ≤ f
Finally, the Gaussian pattern transforms into another Gaussian curve: H (f
)=
143 . ⋅ π ⋅ exp(−143 . ⋅π2 ⋅ f
2
)
(Note that the two last transforms (D and E) cannot be separated in the graphical representation of Figure 11.12.) Now the appropriate sampling of these spectra shall be discussed, taking −20-dB aliasing as criterion. Traditionally, two different attitudes have been taken: either a sampling time equal to the dwell time per footprint [4, 5], or (by a kind of Nyquist argument) sampling twice per dwell time [6]. The first corresponds to a sampling frequency fs = 1/2 Hz in our case; the second corresponds to fs = 1 Hz. As will become clear shortly, a more reasonable answer lies between these figures.
Radiometer Antennas and Real Aperture Imaging Considerations
dB
129
H(f)
B
0 C
D A & E
−10 A
−20
1 0.5
1
f(Hz)
Figure 11.12 Antenna transfer functions.
If one makes overview considerations using the sector antenna (A), it is correct that ∼1 Hz sampling is required; and even with this high rate, some aliasing must be endured due to the large lobe around 0.7 Hz (some filtering could alleviate the problem). The other extreme is found using the awkward antenna pattern (B): This is, from a sampling point of view, the ideal pattern having, in the frequency domain, a sharply limited and quite narrow form. A sampling frequency of 0.6 Hz is adequate and no aliasing is present. Considering the more realistic patterns C, D, and E, we see that a sampling frequency around 0.7–0.8 Hz is required, depending on which amount of aliasing can be accepted. Note that in no case is 0.5 Hz (i.e., equal sampling time and dwell time) adequate. Figure 11.13 displays the total situation HTOT for an antenna transfer function HA corresponding to the realistic patterns D and E (and approximately for C), having selected a sampling frequency fs of 0.7 Hz and including the transfer function HRAD of the radiometer (from Figure 5.9, scaled to proper frequency). The transfer function of the radiometer slightly modifies the antenna response and the level of aliasing is very low: maximum −20 dB (and lower near to 0 Hz).
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Microwave Radiometer Systems: Design and Analysis
05 0
fs
1
f(Hz)
HRAD HA −10
HTOT
−20 dB
H(f)
Figure 11.13 Transfer functions of the radiometer system.
Hence, as a rule of thumb, in an imaging radiometer system with a 2-second dwell time per footprint, a sampling time of 1/0.7 Hz = 1.4 seconds is required, or, in general, a sampling time of 0.7 times the dwell time per footprint is required. Finally, it shall be stated that finding the upper limit of the sampling time is interesting in an attempt to keep the data rate from a given radiometer system as low as possible. This may, however, not be the most important issue as data rates from radiometers are comparatively modest due to generally coarse ground resolution as compared with other sensors. The radiometer integration time is, however, closely related to the necessary sampling time (in the radiometers discussed in this book the sampling time and the integration time are equal). Hence, finding the maximum sampling time is also finding the maximum integration time, thereby an important parameter in the achievable radiometric sensitivity.
11.5 Receiver Considerations for Imagers The total power receiver exhibits the best obtainable sensitivity properties, given a certain noise figure of the radiometer. Moreover, it is a simple receiver type,
Radiometer Antennas and Real Aperture Imaging Considerations
131
not needing a low loss, fast electronic switch (the Dicke switch) in the input circuitry. On the other hand, the total power receiver is inferior to the switching type of radiometers (Dicke radiometer and noise-injection radiometer) regarding stability. The total power receiver has to be calibrated at frequent intervals, at least once per minute. For traditional, mechanically scanned radiometer systems, the requirement for receiver sensitivity is severe. At the same time, frequent calibration is easily achieved: once per scan, while the antenna is looking away from the swath anyway, the receiver is calibrated. Hence, the total power radiometer is an obvious candidate for such systems. For the push-broom system, requirements for receiver sensitivity are greatly relaxed due to the much lower data rate per receiver as compared to the single receiver situation. At the same time, frequent calibration is not attractive, as all receivers are always busy sensing the Earth. A well-designed Dicke radiometer, or a noise-injection radiometer, only requires perhaps daily calibration. Hence, the push-broom situation seems to favor a trading of sensitivity for stability and, in conclusion, the Dicke types of switching radiometer is preferred.
References [1]
Künzi, K., N. Skou, and K. Pontoppidan, Study of Push-Broom Radiometer Systems, Final Report, ESTEC Contract No. 5792/84/NL/GM(SC), Electromagnetics Institute, R 298, 1984.
[2]
Harrington, R. F., and C. P. Hearn, “Microwave Integrated Circuit Radiometer Front-Ends for the Push-Broom Microwave Radiometer,” Government Microcircuit Application Conference, Orlando, FL, 1982.
[3]
Harrington, R. F., and L. S. Keafer, “Push-Broom Radiometry and Its Potential Using Large Space Antennas,” Large Space Antenna Systems Technology, NASA Langley Research Center, 1982, pp. 81–104.
[4]
Gloersen, P., and F. T. Barath, “A Scanning Multi-Channel Microwave Radiometer for Nimbus-G and SEASAT-A,” IEEE Journal on Oceanic Engineering, Vol. 2, No. 4, 1977.
[5]
The Nimbus-7 Users’ Guide, NASA Goddard Space Flight Center, Greenbelt, MD, 1978.
[6]
Hollinger, J. P., and R. C. Lo, “Low-Frequency Microwave Radiometer for N-ROSS,” Large Space Antenna Systems Technology, NASA Conference Publication 2368, 1984, pp. 87–95.
12 Relationships Between Swath Width, Footprint, Integration Time, Sensitivity, Frequency, and Other Parameters for Satellite-Borne, Real Aperture Imaging Systems The following considerations serve as an illustration of the trade-off between important parameters as spatial resolution and integration time, hence sensitivity, as well as of the differences between scanning systems and push-broom systems. The satellite case is covered; an analysis of an aircraft imager would follow the same lines yet be simpler due to a simpler geometry (no curved Earth to take into account). Only the rotating scan is considered. The angle of incidence at the ground is 53°, an often-used value (used in well-known systems like SSM/I and TMI). The satellite altitude is assumed equal to 800 km—a typical figure for remote sensing satellites. Note that: S = swath width H = satellite height F = frequency D = antenna diameter (aperture) FP = footprint (geometric mean of footprint along track and across track) TD = dwell time per footprint τ = radiometer integration time 133
134
Microwave Radiometer Systems: Design and Analysis
∆T = radiometer sensitivity NE = number of footprints across the swath R = Earth radius (6378 km) VS = satellite velocity X = radius in the circle on which the footprints are situated Y = slant range from satellite to footprints β = half scan angle
12.1 Mechanical Scan From an inspection of Figure 12.1, and using straightforward geometric considerations and inserting known distances, we find: Y = 1,219 km α = 45.2° X = 865 km The swath width is easily calculated (see Figure 12.2) from: S = 2 ⋅ X ⋅ sin β The maximum useful swath can be reasonably defined by setting β = 60°. This is no sacred value, but it is clear from Figure 12.2 that beyond 60° the increase in effective swath is very limited, while the number of footprints and hence data rate increase proportionally with β; 60° seems a good compromise. See also discussion in Section 11.3. Thus, we find: S M = 1498 , km
(12.1)
The total 360° perimeter of the scan circle is: C = 2 ⋅ π ⋅ X = 5,435 km The antenna 3-dB beamwidth is found using (11.1): θ = 14 . ⋅λ D where λ is the observational wavelength and D is the antenna diameter (aperture). Using c = F · λ (c is the speed of light), we find:
Satellite-Borne, Real Aperture Imaging Systems Relationship
135
Satellite
Velocity vector α H Y 50° X
R
R
Figure 12.1 Conical scan geometry, side view.
θ = 14 .
c 0.42 = ( F in GHz, D in m ) F ⋅D F ⋅D
The 3-dB footprint in the scan direction is now simply: FPS = Y ⋅ θ =
512 (km) F ⋅D
The 3-dB footprint in the along track direction is in satellite coordinates the same, but when projected onto the ground it is:
136
Microwave Radiometer Systems: Design and Analysis
Velocity vector
X
X β
C
β
Satellite
S
Figure 12.2 The satellite and the swath seen from above.
FPL =
FPS 851 = (km) sin 37° F ⋅ D
As a single, representative figure for spatial resolution, the geometrical mean of the footprint dimensions in the along track and across track directions can be worked out: FP = FPS ⋅ FPL =
660 (km) F ⋅D
so we have: FPS = 0.776 ⋅ FP FPL = 129 . ⋅ FP Quite often it is really the footprint that is given, and the antenna size that must be calculated. Hence, D (m ) =
660 F (GHz ) ⋅ FP ( km )
(12.2)
Satellite-Borne, Real Aperture Imaging Systems Relationship
137
The number of footprints for contiguous coverage along the scan circle C is: 2π ⋅ X FPS
N FP =
The number of swaths per second (contiguous coverage) is calculated from: NS =
V SSP FPL
(12.3)
where VSSP is the velocity of the subsatellite point on the surface of the Earth. These values correspond to just consecutive footprints, which may not be quite what we require. Hence, the number of footprints to be covered per second is: N F = N FP ⋅ N S 2π ⋅ X ⋅V SSP NF = FPS ⋅ FPL The velocity of the subsatellite point is found from the following set of equations well known from orbital mechanics texts: gs 0.00981 =R ⋅ R +H R +H R = VS ⋅ R +H
VS = R ⋅ V SSP
Inserting relevant values in the present case, we find VSSP = 6.625 km/sec and the following expression for the number of footprints to be covered per second: NF =
36,034 FP 2
and the dwell time per footprint is: TD =
1 FP 2 = N F 36,034
138
Microwave Radiometer Systems: Design and Analysis
Following the discussion in Section 11.4, the sampling and integration time τ of the associated radiometer should be equal to the dwell time per footprint multiplied by 0.7. This corresponds to a 30% footprint overlap in the scan direction. Requiring also a 30% overlap in the along-track direction, to avoid aliasing also in this case, means that: τ = T D ⋅ 0.7 2 =
FP 2 (sec) 73,538
(12.4)
Now typical sensitivities can be estimated. For a total power receiver the sensitivity is: ∆T =
T A +T N B ⋅τ
TA could, for Earth-oriented sensing, typically be 230K. A current and realistic spaceborne receiver at middle frequencies around 20 GHz (see Section 13.3.4) may have a noise figure of 3 dB (noise figure of the preamplifier: 2 dB; losses of components such as a prefilter, antenna feed, waveguides, all preceding the preamplifier: 1 dB); 3 dB is equivalent to a noise temperature of: T N = 290 ⋅ (NF − 1) = 290 ⋅ ( 2.0 − 1) T N = 290K Again, at frequencies around 20 GHz, a bandwidth of 200 MHz could be typical for a spaceborne radiometer. Hence, the sensitivity may be estimated as: ∆T =
230 + 290 200 ⋅10 6 ⋅
∆T =
FP 2 73,538
10 (K ) ( FP in km ) FP
(12.5)
At higher frequencies TN will tend to increase, but this is compensated by the larger possible bandwidth of the receiver. At lower frequencies the opposite is the case: Lower TN is compensated by the fact that lower bandwidths are required due to interference problems. So the rule-of-thumb figure for sensitivity obtained from (12.5) can be used in the frequency range 5–100 GHz. Below 5 GHz only quite narrow bandwidths are available for passive remote sensing due to many active services, and sensitivities must be assessed individually using the calculated integration time and actual bandwidths.
Satellite-Borne, Real Aperture Imaging Systems Relationships
139
A single figure of merit for a radiometer receiver is the radiometer constant C defined as the sensitivity corresponding to an integration time of 1 second. So the receivers considered here have a radiometer constant of: C=
230 + 290
200 ⋅10 6 ⋅1 C = 0.037K The revolution speed of the rotating reflector can be found from the number of swaths per second, NS, divided by 0.7 due to the fact that we require 30% footprint overlap as already discussed: RS =
0.7 0.7 ⋅ FPL = NS V SSP
(12.6)
or in the present case: R S = 0136 . ⋅ FP (sec. rev.) ( FP in km) This can also be expressed in revolutions per minute: ω=
60 441 = (rpm) RS FP
(12.7)
12.2 Push-Broom Systems The maximum useful swath width can be worked out exactly as for the scanning system as SM = 1,498 km. For a push-broom system there is, however, an important trade-off between swath width on one side and on the other side the number of channels plus reflector complexity, hence cost. Thus, it is certainly viable to consider a system having a swath smaller than the maximum useful one as quoted earlier. The relationship between actual swath width and the number of footprints (channels) can be estimated as: S = N E ⋅ FPS ⋅0.7 The factor 0.7 reflects the usual 30% footprint overlap. As for the scanner: FPS = 0.776 ⋅ FP
140
Microwave Radiometer Systems: Design and Analysis
so we find S = N E ⋅ 0.54 ⋅ FP (S and FP in km)
(12.8)
The dwell time per footprint is calculated from: T D = FPL V SSP However, FPL = 129 . ⋅ FP and as before τ = 0.7 ⋅T D Hence: τ=
129 . ⋅ FP ⋅ 0.7 (sec) 6.625
or τ = 0136 . ⋅ FP (sec)
(12.9)
Assuming the same receiver performance and conditions as in the rotating case, but now with a Dicke type radiometer, the sensitivity will be: ∆T = 2 ⋅
230 + 290
. 200 ⋅10 6 ⋅ 0136 ⋅ FP 0.20 ∆T = (K) (FP in km) FP
(12.10)
12.3 Summary and Discussion Given a representative orbit height of 800 km, the measurement frequency F (GHz), and the ground resolution FP (km), the following formulas have been worked out for: maximum useful swath width SM (km) (corresponding to a half
Satellite-Borne, Real Aperture Imaging Systems Relationship
141
scan angle β = 60°), antenna aperture D (m), radiometer integration time τ, typical radiometer sensitivity ∆T (K ), and the revolution time for the rotating antenna RS (seconds)—also expressed as revolutions per minute ω. For the mechanical scanner it has been assumed that ground coverage with a 30% footprint overlap both across track and along track shall be obtained by a single receiver with one antenna beam by a fully rotating antenna giving a conical scan with an incidence angle on the ground equal to 53°. The receiver has a radiometer constant (sensitivity for 1-second integration time) equal to 0.037K, and it is implemented as a total power radiometer. For the push-broom system it is assumed that NE footprints (hence NE receivers) cover the actual swath S simultaneously, the receivers have a radiometer constant of 0.074K, and are implemented as Dicke type switching radiometers. Again 53° incidence angle on the ground is assumed. The typical radiometer sensitivity ∆T quoted can only be taken as a rule-of-thumb figure in the frequency range 5–100 GHz. Outside this range, and if accurate estimates are needed, the sensitivity must be calculated on a case by case basis using the expression for the integration time τ, and actual radiometer noise figures and bandwidths. Moreover, the typical sensitivity is given for a typical scene brightness temperature of 230K. Especially for high-end systems having a low noise figure, the resultant sensitivity will be quite dependent on the actual scene brightness temperature intended to be measured by the radiometer in question. For both systems, the ground resolution FP is defined as the geometric mean of the footprint along track and across track: FP = FPS ⋅ FPL meaning that FPS = 0.776 · FP and FPL = 1.29 · FP in the present geometry. See Table 12.1. In Figure 12.3 a comparison between mechanically scanned systems (MS) and push-broom systems (PB) is shown. Sensitivities for the two systems are Table 12.1 Summary of (F in GHz, FP in km)(∆T estimate valid for 5 < F < 100)
SM D τ ∆T
Scanner
Push-Broom
1,498 km (β = 60°) 660 (m) F ⋅ FP FP 2 (ms) 73.5 10 (K) FP
1,498 km (β = 60°) 660 (m) F ⋅ FP
S RS
0.136 · FP (sec/rev.)
ω
441/FP (rpm)
0.136 · FP (sec) 0.20 (K) FP NE 0.54 · FP (km)
142
Microwave Radiometer Systems: Design and Analysis ∆T (K) & N/10 10 9 8 MS 7 6 5 4 3 2 N
1 PB 0 0
20
40
60
80
100
FP (km)
∆T (K) & N
100.00
N 10.00
MS 1.00
PB 0.10
0.01 1
10
100
FP (km)
Figure 12.3 Comparison (lin and log scales) between ∆T for mechanical scanner (MS) and for push-broom system (PB). N = ∆T(MS)/∆T(PB). H = 800 km.
Satellite-Borne, Real Aperture Imaging Systems Relationship
143
shown as functions of desired footprint as well as an improvement factor N defined as the ratio between sensitivities for the two systems for a given footprint. Large N favors push-broom systems. It is obvious from the curves that for small footprints (a few kilometers), the scanner cannot give reasonable sensitivities, while the push-broom imager certainly can. N becomes very large as an indication of this.
12.4 Examples Following the discussions in Sections 12.1 through 12.3, three mission-oriented systems will be covered as illustrations of the differences between the scanner and the push-broom system. 12.4.1
General-Purpose Multifrequency Mission
Consider the 18.7-GHz channel of an SSM/I-like multifrequency radiometer system. A 1-m aperture is assumed (this is a typical size for such a system). The ground resolution will be: FP = 35.3 km. For the scanner we find: τ = 16.9 ms ∆T = 0.28K RS = 4.8 seconds/rev. corresponding to 12.5 rpm. while the push-broom system parameters are: τ = 4.8 seconds ∆T = 0.03K NE = 79 corresponding to the maximum swath SM A radiometric resolution of 0.28K will satisfy most users and a revolution time of 4.8 seconds for a 1-m reflector is not frightening. Surely the push-broom system offers better sensitivity but at the expense of complexity (79 receivers and a more complicated antenna system). Hence, the trade-off between scanner and push-broom in this case favors the first. A scanner will be discussed further in Chapter 13. 12.4.2
Coastal Salinity Sensor
A ground resolution of, say, 16 km is compatible with narrow seas and enclosed waters. The generally accepted frequency for the purpose is 1.4 GHz. A radiometric sensitivity of a fraction of a Kelvin is required. For a scanning system we find:
144
Microwave Radiometer Systems: Design and Analysis
D = 30m τ = 3.35 ms RS = 2.1 seconds/rev. corresponding to 28 rpm Only some 20 MHz of bandwidth is available in the L-band protected band, and a realistic receiver noise temperature is 170K. The ocean brightness temperature is typically 130K (vertical polarization around 50° incidence angle). Hence, the sensitivity is: ∆T =
130 + 170
20 ⋅10 6 ⋅ 0.00335 ∆T = 12 . K Not only are the requirements for sensitivity far from being fulfilled but also the spacecraft designer is left with the problem of having a 30 m dish rotating with one revolution per 2.1 sec. Clearly not a feasible solution. For a push-broom system we find: τ = 2.1 seconds NE = 177 corresponding to the maximum swath SM Bearing in mind that for this demanding application, a noise injection radiometer is probably the candidate radiometer option, the sensitivity can be assessed from (4.7) assuming a reference temperature of 300K: ∆T = 2 ⋅
300 + 170
. 20 ⋅10 6 ⋅ 21 . K ∆T = 015 which fulfills the requirements. The cost is receiver and antenna system complexity; 177 identical receivers are needed, but integrated techniques can be used, thus greatly facilitating mass production, and at the same time keeping volume and mass to reasonable levels. The antenna system must include 177 individual feeds and have an unusually shaped and sized reflector. There will be more information about such issues in Chapter 14. 12.4.3
Realistic Salinity Sensor
The 30-m aperture just discussed is indeed ambitious by all standards, and is primarily included to illustrate the significant differences between scanners and push-broom systems. A more realistic salinity sensor could assume a 10-m
Satellite-Borne, Real Aperture Imaging Systems Relationship
145
aperture, which in turn results in a ground resolution of 47 km. Again, a radiometric sensitivity of a fraction of a Kelvin is required. For a scanning system we find: τ = 30 ms RS = 6.4 seconds/rev. corresponding to 9.4 rpm. The conditions are as before, and the sensitivity is calculated as: ∆T =
130 + 170
20 ⋅10 6 ⋅ 0.03 ∆T = 0.4 K Even a 10-m reflector is a mighty big antenna to scan with 9.4 rpm, and the sensitivity is not impressive. Also in this case the scanner is not a feasible solution. For a push-broom system we find: τ = 6.4 seconds NE = 59 corresponding to the maximum swath SM The sensitivity is: ∆T = 2 ⋅
300 + 170
20 ⋅10 6 ⋅ 6.4 ∆T = 0.08K which fulfills all reasonable requirements. A system along these lines is studied in more detail in Chapter 14.
13 First Example of a Spaceborne Imager: A General-Purpose Mechanical Scanner 13.1 Background In 1978 the Scanning Multichannel Microwave Radiometer (SMMR) was launched on the U.S. satellite Nimbus-7. SMMR represented a new and very successful concept: the multifrequency passive imager that has played a dominating role within remote sensing of the Earth’s surface. SMMR measured the two polarizations of the brightness temperature from the Earth at the frequencies: 6.6, 10.69, 18.0, 21.0, 37.0 GHz. It used a ±25° conical reciprocating scan with an incidence angle on the ground of 50°. The antenna aperture was 79 cm and the footprints were: 79 × 121, 49 × 74, 29 × 44, 25 × 38, 14 × 21 (FPS × FPL in kilometers) [1]. Data from the SMMR has been widely used through the years and the established applications are in Table 13.1. The life of SMMR came to an end in 1987 (many years after the anticipated date) and replacements or upgrades were studied by the space agencies. In 1979/1980 the ESA Imaging Microwave Radiometer (IMR) was studied [2]. It employed the frequencies of 6.84, 10.65, 15.3, 23.8, 36.5, and 90 GHz and a 1.26-m aperture. Thus, it was basically an upgraded version of the SMMR concept, with the addition of a 90-GHz channel for high-resolution (∼6 km) sea ice mapping. A distinct difference between the two instruments deserves mentioning, however. The SMMR used a scanning reflector illuminated by one, fixed, multifrequency feed-horn. This is a very elegant solution but has serious drawbacks: The feed is quite lossy, and being fixed causes polarization mixing when the reflector scans away from neutral position. IMR used a set of 147
148
Microwave Radiometer Systems: Design and Analysis
Table 13.1 SMMR Applications Ocean parameters
Sea surface temperature Wind speed
Atmospheric parameters Water vapor Liquid water Rain intensity Cryopheric parameters
Sea ice (fractional ice coverage, ice boundary, ice type classification) Perennial snow (on ice caps and glaciers) Seasonal snow (area, water equivalent, water runoff)
Land parameters
Permafrost Soil moisture Vegetation characteristics
single-frequency horns in a feed cluster and had the feeds (plus the radiometers) rotate with the reflector. This is less elegant but gives a better performance. Also in the United States, SMMR successors were studied by NASA. Two candidates, both using a 4-m antenna, have been assessed: the advanced SMMR for the National Oceanic Satellite System (NOSS) and the Large Antenna Multifrequency Microwave Radiometer (LAMMR). Both employ frequencies between 4 and 37 GHz, and the NOSS system also includes a 91-GHz channel. These systems reflect optimism, as a 4-m antenna was about the largest solid reflector to fit inside launchers, so why not go for the ultimate solution? The optimism was not shared by decision-makers, and none of these systems materialized. In the meantime, SMMR performed quite well within sea ice studies and the preferred algorithms used only the 18-GHz and 37-GHz channels. Hence, a dedicated—and realistic—sea ice sensor, having a 61-cm aperture and featuring the frequencies 19.35 and 37 GHz for classification, 22.235 GHz for atmospheric correction, and 85.5 GHz for ice edge detection, was designed and eventually launched in 1987 [3]. It is called the Special Sensor Microwave/Imager (SSM/I) and is part of the U.S. Defense Meteorological Satellite Program (DMSP). The SSM/I also features a rotating antenna having the feed system and the radiometers rotate with the antenna. In addition to this, a revolutionary and elegant concept for in-orbit calibration was devised. The system has proven highly successful, and several instruments have been launched ensuring continuous data availability to the present and beyond. Europe was also caught by the 4-m antenna optimism, and the first versions of the ESA Multifrequency Imaging Microwave Radiometer (MIMR) featured such a large reflector. MIMR was an ESA program of considerable endurance, and over the years it became more realistic and ended being largely
First Example of a Spaceborne Imager: A General-Purpose Mechanical Scanner 149
an upgraded and much improved IMR using a 1.6 × 1.4-m reflector. The project was carried to the point where a full instrument was developed and evaluated before the program was cancelled. As an example of how such multifrequency imagers can be designed, a generic system having a 1-m electrical antenna aperture will be worked through in the following. The starting point of the study is the following requirements: • Frequencies: 10.65, 18.7, 23.8, 36.5, and 89 GHz; • Polarizations: vertical and horizontal; • Sensitivity: corresponding to the receiver model used in Chapter 12,
but also evaluated for actual parameters; • Spatial resolution (footprint): corresponding to 1-m aperture; • Incidence angle on the Earth: 53° (conical, rotating scan); • 800-km orbit; • Radiometric dynamic range: 0–313K.
13.2 System Considerations 13.2.1
General Geometric and Radiometric Characteristics
The instrument to be designed in this chapter utilizes a 1-m aperture antenna. But before focusing on that size, a broader discussion is warranted, and apertures ranging between 0.5m and 4m are considered. The background is the set of formulas derived in Chapter 12 and summarized in Table 12.1. In Table 13.2, calculations based on these formulas are carried out for the given frequencies and antenna sizes. The notation in the table is self-explanatory when referring to Chapter 12. The table includes instrument options ranging from relatively simple systems with small antennas resulting in benign resource demands to the host satellite, to difficult systems with large antennas and indeed severe resource requirements. The lowest frequency has the largest footprint; the longest integration time and hence the best associated sensitivity; and the least severe requirement of antenna rotation rate for contiguous Earth coverage. In a multifrequency system, the antenna rotation rate will have to be selected to suit the highest frequency. In that case the integration time per instantaneous footprint for the lower frequencies will be shorter than originally calculated. However, simultaneously the swath is oversampled proportionally, and the original integration time (hence, sensitivity) can be restored by suitable integration in the data analysis.
150
Microwave Radiometer Systems: Design and Analysis
We can clearly see from the table that a system with a 4-m antenna being illuminated by one 90-GHz feed with one associated receiver leads to an impossible situation: Not only is the sensitivity at 90 GHz unsatisfactory (a realistic receiver performance was assumed for the calculations), but also the spacecraft designer is left with the problem of having a very large antenna dish rotating at four revolutions per second. There are two possible approaches to this problem: underillumination of the reflector at the higher frequencies, or multiple antenna beams (and receivers) at the higher frequencies. Hybrid solutions are also possible. 13.2.1.1 Underillumination
In this case a certain lower limit is set for the footprint size. To simplify the discussion a 3-m antenna is considered. Assume, for example, that a footprint of 9.1 × 15.2 km (corresponding to the full illumination of the reflector at 18.7 GHz) can satisfy all reasonable user requirements. At the higher frequencies the reflector is suitably underilluminated to obtain the same resolution, and the sensitivity and antenna revolution time quoted in Table 13.2 for 18.7 GHz will also hold for the total multifrequency system—in this case, 0.8K and 37 RPM. The advantage of the principle is that it is easy to implement; the drawback is that the full resolution capability of the antenna is not utilized. A second advantage deserves to be mentioned. Several channels will have equally sized footprints, simplifying subsequent data analysis; oftentimes, geophysical retrievals are based on data from several channels, including several frequencies. Basically this requires all channels be processed to have identical footprints before retrieval algorithms are applied. But again: since a variety of applications normally are to be served by any one mission, and these applications use different frequency combinations, it is not very satisfactory to exclude the use of the full resolution power of the antenna system. 13.2.1.2 Multiple Beams
In this case more than one feed horn, each with its individual receiver, produce several antenna beams to sense the swath simultaneously. The antenna rotation rate can be lowered proportionally with the number of beams at a given frequency. For example the use of five beams at 89 GHz reduces the rotation rate to that required by the 18.7-GHz channel. Two receivers at 36.5 GHz can easily do the job at this frequency. The 23.8-GHz channel cannot give contiguous ground coverage with one receiver, but, as it does not sense the ground anyway (but rather the atmosphere), this may be acceptable. Otherwise, two receivers are needed, or a slight underillumination can be an attractive solution. The advantage of this concept is that full use of the reflector is made at all frequencies. The disadvantage is complexity.
First Example of a Spaceborne Imager: A General-Purpose Mechanical Scanner 151 Table 13.2 Using the Information in Table 12.1 for an Imager with Certain Frequencies and a Range of Antenna Sizes
D(m) FPS(km) FPL(km)
(msec) RPM
T(K) F(GHz)
0.5 0.7 1 1.2 1.5 2 3 4
96.2 68.7 48.1 40.1 32.1 24.1 16.0 12.0
159.9 114.2 79.9 66.6 53.3 40.0 26.6 20.0
209.1 106.7 52.3 36.3 23.2 13.1 5.8 3.3
3.6 5.0 7.0 8.5 10.7 14.2 21.3 28.4
0.08 0.11 0.16 0.19 0.24 0.32 0.48 0.65
10.65
0.5 0.7 1 1.2 1.5 2 3 4
54.8 39.1 27.4 22.8 18.3 13.7 9.1 6.9
91.0 65.0 45.5 37.9 30.4 22.8 15.2 11.4
67.8 34.6 17.0 11.8 7.5 4.2 1.9 1.1
6.2 8.7 12.5 15.0 18.7 24.9 37.4 49.9
0.14 0.20 0.28 0.34 0.42 0.57 0.85 1.13
18.7
0.5 0.7 1 1.2 1.5 2 3 4
43.0 30.7 21.5 17.9 14.4 10.8 7.2 5.4
71.5 51.1 35.8 29.8 23.8 17.9 11.9 8.9
41.9 21.4 10.5 7.3 4.7 2.6 1.2 0.7
7.9 11.1 15.9 19.0 23.8 31.7 47.6 63.5
0.18 0.25 0.36 0.43 0.54 0.72 1.08 1.44
23.8
0.5 0.7 1 1.2 1.5 2 3 4
28.1 20.1 14.0 11.7 9.4 7.0 4.7 3.5
46.6 33.3 23.3 19.4 15.6 11.7 7.8 5.8
17.8 9.1 4.5 3.1 2.0 1.1 0.5 0.3
12.2 17.0 24.3 29.2 36.5 48.7 73.0 97.4
0.28 0.39 0.55 0.66 0.83 1.11 1.66 2.21
36.5
0.5 0.7 1 1.2 1.5 2 3 4
11.5 8.2 5.8 4.8 3.8 2.9 1.9 1.4
19.1 13.7 9.6 8.0 6.4 4.8 3.2 2.4
3.0 1.5 0.7 0.5 0.3 0.2 0.1 0.0
29.7 41.6 59.4 71.2 89.0 118.7 178.1 237.5
0.67 0.94 1.35 1.62 2.02 2.70 4.05 5.39
89.0
152
13.2.2
Microwave Radiometer Systems: Design and Analysis
Instrument Options
Let us now return to the 1-m aperture system to be covered in this chapter. For this size of antenna, a rotation rate around 40 RPM is deemed practical. A radiometric resolution around 0.5K can serve most applications adequately (around 1K acceptable at 89 GHz). A range of options having different combinations of underillumination and multiple beams can be devised as illustrated in the following. 13.2.2.1 Option 1
This is just the straightforward, basic option as assumed in Table 13.2 for a 1-m antenna. The spatial resolutions, sensitivities, and other salient features are repeated in Table 13.3. The sensitivity requirements are not quite fulfilled for the two higher-frequency channels, and even worse, the antenna rotation rate is unacceptably high. Each frequency has one dual polarized feed horn and basically two receivers. As indicated, the two polarizations at the lower frequencies may be measured by just one receiver, due to the rather high oversampling of the Earth: The antenna rotation rate is determined by the highest-frequency channel. A multiplex switch must be inserted between the two antenna ports (H and V polarization) and the receiver input, but for redundancy and system reliability reasons, two individual receivers may very well be preferred anyway. Likewise, it is indicated that in fact two receivers may not be needed at 23.8 GHz as this channel senses the atmosphere where two polarizations may not be needed, but again system reliability may dictate the use of two receivers. Therefore, in total there will probably be 5 × 2 = 10 receivers. 13.2.2.2 Option 2
The reflector is underilluminated at 89 GHz so that this channel will feature the same ground resolution as the 36.5-GHz channel. This solution is illustrated in Table 13.4. Table 13.3 Key Figures for the Basic Option
F (GHz)
Footprint (km)
Number of Feeds
Number of Receivers
Antenna RPM
10.65
48 × 80
0.16
1
2 (1)
59
18.7 23.8
27 × 46
0.28
1
2 (1)
22 × 36
0.36
1
2 (1)
36.5
14 × 23
0.55
1
2
89.0
5.8 × 9.6
1.4
1
2
T (K)
First Example of a Spaceborne Imager: A General-Purpose Mechanical Scanner 153 Table 13.4 Key Figures for the Underillumination Option
F (GHz)
Footprint (km)
10.65
48 × 80
18.7 23.8
Number of Feeds
Number of Receivers
Antenna RPM
0.16
1
2
24
27 × 46
0.28
1
2
22 × 36
0.36
1
2
36.5
14 × 23
0.55
1
2
89.0
14 × 23
0.55
1
2
T (K)
The sensitivities as well as the antenna revolution rate are satisfactory. The solution is simple, but as already argued it may not be satisfactory not to utilize the full resolution potential of the antenna. As before, each frequency has one dual polarized feed horn and two receivers, in total 5 × 2 = 10 receivers. 13.2.2.3 Option 3
Again the reflector revolution time is fixed at 24 RPM (i.e., to suit the 36.5-GHz channel), but now the 89-GHz channel must use more than one feed horn to cover the swath. It is clear from Table 13.2 that two channels at 89 GHz will not quite assure the required 30% footprint overlap along track, as 2 · 9.56 km (the 89-GHz FPL) = 19.12 km, that is, somewhat less than the 23.32 km (the 36.5-GHz FPL) just fulfilling overlap requirements. The actual overlap is: (19.12 − 23.32 · 0.7)/19.12 = 0.15, that is, 15%. This may well be considered acceptable in view of the high cost of implementing a third 89-GHz channel that would be required if requirements should be strictly adhered to. The implication of having only 15% overlap will, in most cases, be small. The aliasing errors can in general not be quantified, as they are scene-dependent. For many natural scenes (or brightness temperature distributions), even poorer overlap causes low aliasing errors: It depends of the contents of high frequencies in the spatial frequency domain, and this is often moderate for natural scenes. However, it can be stated—based on experience with system simulators—that the 30% overlap requirement ensures alias free operation in all practical cases. It should be noted that a slight underillumination at 89 GHz of the antenna reflector, in order to yield a footprint of 11.66 × 7.02 km (i.e., half of that at 36.5 GHz), will bring us back in line with the 30% overlap requirement and completely alias free operation. This must be a user choice in each individual case. The option is illustrated in Table 13.5. The numbers in the table are largely as in the previous two tables, apart from the important fact that
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Microwave Radiometer Systems: Design and Analysis
Table 13.5 Key Figures for the Multiple Beam Option
F (GHz)
Footprint (km)
10.65
48 × 80
18.7 23.8
Number of Feeds
Number of Receivers
Antenna RPM
0.16
1
2
24
27 × 46
0.28
1
2
22 × 36
0.36
1
2
36.5
14 × 23
0.55
1
2
89.0
5.8 × 9.6
0.86
2
4
T (K)
acceptable rotation rate and sensitivity at 89 GHz are achieved by having two feed horns, hence antenna beams at this frequency. The 89-GHz sensitivity is found by taking the value from Table 13.2 (1.35K) and realize that it is improved by the square root of the ratio between the 59.4 RPM (what would be needed using one single channel) and 24.3 RPM (actually employed). (Note that the integration time is directly enlarged by this ratio, meaning that the sensitivity is divided by the square root of the ratio.) The sensitivities as well as the antenna revolution rate are satisfactory. The solution is still relatively simple: The price to pay is a doubling of the feed and the receivers at the highest frequency, but these are of modest size and weight, so the penalty is moderate. As before, most frequencies have one dual polarized feed horn and two receivers, while the 89-GHz channel employs the double of that, in total 6 × 2 = 12 receivers. 13.2.2.4 Option 4
This option is included to show that it is possible to obtain a slower antenna rotation rate and improved radiometric sensitivity at the higher frequencies at the expense of system complexity. The reflector revolution time is fixed at 12.5 RPM to suit the 18.7-GHz channel. Five feeds are required at 89 GHz to ensure complete Earth coverage. Two feeds at 36.5 GHz are adequate, while one receiver at 23.8 GHz is probably acceptable, as some undersampling may be all right for this atmospheric channel (also, a slight underillumination is a possibility). See Table 13.6. Again, the sensitivities at the channels beyond 18.7 GHz are found by taking the appropriate values from Table 13.2 and divide them by the square root of the ratio between the original RPM (what would be needed using one single channel) and the 12.5 RPM actually employed. The number of receivers has now increased to 10 × 2 = 20. It is seen that good sensitivities and low rotation rate is indeed a possibility, but at the expense of a great many receivers and many feeds possibly leading to severe real estate problems in the feed area.
First Example of a Spaceborne Imager: A General-Purpose Mechanical Scanner 155 Table 13.6 Key Figures for Enhanced Multiple Beam Option Footprint F (GHz) (km)
Number T (K) of Feeds
Number of Antenna Receivers RPM
10.65
48 × 80
0.16
1
2
18.7
27 × 46
0.28
1
2
23.8
22 × 36
0.32
1
2
36.5
14 × 23
0.40
2
4
89.0
5.8 × 9.6
0.62
5
10
12.5
13.2.2.5 Summary
Option 1 is relatively simple. It has a limited number of feed horns and receivers. Each feed is dual polarized, so, in general, two receivers (a dual receiver unit) are required per feed horn. However, at the lowest frequencies the oversampling of the Earth is such that both polarizations may be multiplexed into one receiver. For redundancy reasons two receivers are still desired. At 23.8 GHz two polarizations are not really required as this channel only senses the atmosphere. Again, for redundancy reasons, a dual receiver unit is preferred. The radiometric sensitivity at 89 GHz leaves something to be desired, but, worse, the antenna rotation rate is unacceptably high. Option 2 is also simple. It solves the problem with a marginal radiometric resolution and with a high antenna rotation rate. Option 2 will fulfill many geophysical requirements, but certainly not all. For example, sea ice boundary mapping requires the best possible spatial resolution while requirements to radiometric resolution are less stringent. It is thus quite unsatisfactory not to aim at ultimate spatial resolution (not make full use of reflector) at all frequencies. Option 3 is a good compromise between requirements and complexity. The option will serve many geophysical requirements concerning both spatial resolution and radiometric sensitivity. It makes full use of the antenna resolution capability, and it must be recalled that the user can always trade spatial resolution for sensitivity in the data analysis by proper integration, and thus at the same time achieve equal footprints at different frequencies. The implementation of the option is relatively straightforward as it only requires one extra feed horn and two extra receivers. Option 4 is included only to show that it is possible to obtain slower antenna rotation and better radiometric sensitivity at the expense of hardware complexity. The slow rotation time found for option 4 can probably not warrant the extra hardware complexity. The horn area will especially suffer from real estate problems.
156
Microwave Radiometer Systems: Design and Analysis
Only option 3 will be considered in the following. 13.2.3
Baseline Instrument Specifications
Table 13.7 summarizes the key parameters for the multifrequency, conically scanning imager to be discussed in the subsequent sections. Horizontal and vertical polarization is sensed at each frequency, and two simultaneous beams are employed at 89 GHz to achieve a reasonable antenna rotation rate as well as acceptable radiometric sensitivities at all frequencies. Each frequency is served by one dual polarized feed horn and two receivers, apart from the 89-GHz channel where twice that is needed—in total 6 feeds and 12 receivers. The incidence angle on the Earth is 53°, and the orbit altitude is 800 km. 13.2.4
Instrument Layout and Receiver Type
The multifrequency conically scanning radiometer system is illustrated in Figure 13.1. The offset parabolic reflector antenna and the drum holding the radiometers and the cluster of feed horns rotate around a vertical axis, thus ensuring constant incidence angle on the ground. Following the discussions in Section 11.5, total power receivers are assumed. The superior sensitivity of the total power radiometer, as compared with other radiometer types, is certainly needed for this application as evident from the ∆T figures in Table 13.7. At the same time frequent calibration— once per antenna revolution—is readily achieved. The total power radiometer requires two calibration points: one cold and one hot. The cold calibration point is actually the cold space brightness temperature, and each time the feed cluster is passing under the tilted mirror indicated in Figure 13.1, the beam is diverted towards cold sky. A little later the feed cluster passes under a bucket holding an ambient temperature absorber, thus providing the hot calibration Table 13.7 Key Figures for the Baseline Instrument
F (GHz)
Footprint (km)
Number of Feeds
Number of Antenna Receivers RPM
10.65
48 × 80
18.7
27 × 46
0.16
1
2
0.28
1
2
23.8
22 × 36
0.36
1
2
36.5
14 × 23
0.55
1
2
89.0
5.8 × 9.6
0.86
2
4
T (K)
24
First Example of a Spaceborne Imager: A General-Purpose Mechanical Scanner 157
Figure 13.1 Scanner. (Courtesy of the European Space Agency.)
point. This elegant solution ensures a very satisfactory calibration where only the reflector is outside the calibration loop—and reflectors can be made with very low losses that will not deteriorate calibration fidelity [4]. This is in contrast to early systems like the SMMR, which used calibration switches, calibration loads, and dedicated sky-looking horns in front of the receivers. Thus, losses and reflections were different when imaging and when calibrating, and minute accounting for those was a necessity (and a difficulty).
13.3 Receiver Design The radiometers of the system are used in pairs: H and V polarization, frequency for frequency (two pairs at 89 GHz). Hence, it is practical to construct them as dual receiver units: a pair of receivers for one given frequency. Following the discussion in Section 5.1.1, the receivers operating at 10.65 to 36.5 GHz will be designed as direct receivers: Microwave amplifiers covering the frequency range are readily available, as well as good quality tunnel diode detectors; requirements to filter selectivity are not overwhelming for these broadband applications (which would otherwise favor the superheterodyne principle with its IF filter possibilities); and finally, for spaceborne applications, it is a strong argument to get rid of the power consuming local oscillator. The situation is not quite so favorable for the 89-GHz channel, and it will be designed as a DSB superheterodyne receiver without preamplifier. 13.3.1
The Direct Receivers (10.65–36.5 GHz)
The design and layout of the direct total power receiver is very close to that of the SSB receiver as discussed in Section 5.4.2, and it is illustrated in Figure 13.2. The input calibration switch is not present in this design where the calibration switching process is taken care of as part of the antenna scan. The mix-preamp and the local oscillator are not present and the IF filter is omitted. This has the consequence that all filtering takes place at the RF level, and thus the
158
Microwave Radiometer Systems: Design and Analysis
TA
RF
∼ ∼ ∼
Isolator RF
RF
DC Square law detector
Filter Analog to digital converter
∆/Σ
-x.x mV Offset
DC
∫ Integrator
Data ck
Figure 13.2 Direct receiver layout.
requirements to the RF filter may well be tighter than normally found in superheterodyne designs. In general, this is no problem due to the rather wide frequency bands normally used in radiometers. The IF amplifier is substituted by an RF amplifier. With these changes, the design is just as before: RF amplification is determined so that proper signal levels are achieved at the detector, the DC amplification is determined so the proper signal levels are present on the A/D converter, the offset is determined so that proper use of the A/D converters’ range is achieved. The A/D converter is a 12-bit converter, giving a digital resolution of the 0–313-K input signal of below 0.1K.
13.3.2
The 89-GHz DSB Receivers
The design and layout of this DSB total power receiver is as discussed in Section 5.4.1 and illustrated in Figure 5.11. As earlier, the input calibration switch is not present in this design where the calibration switching process is taken care of as part of the antenna scan. The local oscillator architecture warrants some discussion. As already described, the receivers are arranged two by two as dual receiver units. It is an obvious idea to use one LO to drive both mixers in a dual receiver unit, but this results in a potential single point failure: loss of the oscillator incapacitates both receivers. Moreover, the local oscillator is deemed one of the components in a radiometer most likely to fail. Hence, an arrangement with two oscillators driving the two mixers through a quadrature hybrid (magic tee at this high frequency) is proposed (see Figure 13.3). Only one oscillator is operating, and if this stops working, DC power is removed and switched to the other oscillator. Whenever possible, dielectric
First Example of a Spaceborne Imager: A General-Purpose Mechanical Scanner Ant. V
∆
∼
LO 1
Σ
∼
LO 2
QH 3 Ant. H
Out
RX 1 2
RX 2
159
Out
Figure 13.3 Dual receiver unit.
resonator oscillators should be used. They have adequate frequency stability for radiometer use, and they are far more power-efficient than other oscillator types. 13.3.3
Integrated Receivers: Weight and Power
For three decades now, we have seen a variety of imaging microwave radiometer systems in space, and technology has developed over the years resulting in smaller, lighter, and more power-efficient microwave systems. For spaceborne systems this is very important. The famous SMMR launched in 1978 represents the technology of the 1970s. It had 10 radiometers spanning a frequency range from 6.6 GHz to 37 GHz. The receivers had a weight of 30 kg and consumed 65W of power (i.e., 3 kg and 6.5W per receiver on average). The radiometers were constructed using individual waveguide components joined together using sections of waveguide. The 1980s saw the development of the SSM/I series of multifrequency, imaging radiometers. The same technology was used, now featuring 3 kg and 5W per receiver. A dramatic change happened during the 1990s where MMIC technology became practical even at higher microwave frequencies. The JASON radiometer system serves the frequencies 18.2, 23.8, and 34 GHz, and features individual receiver units about 9 × 6 × 3 cm in size, with a weight of 400g and a power consumption of 2W. A unit includes everything from a Dicke switch to an A/D converter. TRW has designed and built these MMIC radiometers. Recent developments for a next generation JASON-like instrument saves additional resources by combining several receivers into one package: A three-radiometer Dicke system (18.7, 21, and 34 GHz) is integrated into one unit about 8 × 10 × 2.5 cm with a weight of 550g and consuming 4W. This breadboard unit was developed by Quinstar Technologies under a JPL contract. Again, everything from Dicke switches to A/D converters is included (Table 13.8). Based on the Quinstar specifications, it is safe to assume that for the frequencies 10.65 GHz to 36.5 GHz radiometers, dual receiver units having a weight of 500g and a power consumption of 2.6W can be developed for the
160
Microwave Radiometer Systems: Design and Analysis
Table 13.8 Weight and Power History
Year
Name
Number of Receivers
Weight (kg) Power (W)
Weight and Power Per Receiver
1978
SMMR
10
30
65
3 kg and 6.5W
1987
SSM/I
7
24
35
3 kg and 5W
1999
JASON
3
1.2
6
400g and 2W
2001
Quinstar
3
0.55
4
180g and 1.3W
present purpose. This is actually a conservative assumption, as no Dicke switches and no input multiplexing, as implemented in the Quinstar unit, are required. Also, at 89 GHz it is safe to assume the weight of 500g for a dual receiver unit, but the power requirement is increased by 1W to a total of 3.6W for a dual receiver unit in order to reflect the presence of a local oscillator. 13.3.4
Performance of the Receivers
Until now, the radiometric performance of the system has been based on the typical bandwidths and noise figures as assumed in Chapter 12 for overview calculations. In each actual case, proper calculations of the resulting sensitivity must of course be carried out based on the actual bandwidths and noise figures. In the following it is assumed that the bandwidths as indicated in Table 13.9 have been established. The stated bandwidths are, as throughout this book, the predetection bandwidth (i.e., the bandwidth that is used in the radiometer sensitivity formula). For direct receivers and single-sideband (SSB) receivers, this is also the input RF bandwidth. However, for double-sideband (DSB) receivers, the input Table 13.9 Actual Sensitivity Issues
F (GHz)
Bandwidth Noise (MHz) Figure (dB)
Integration Time (ms)
10.65
100
2.5
52.3
0.20
18.7
200
2.8
17.0
0.27
23.8
200
3.0
10.5
0.36
36.5
300
3.1
4.5
0.46
89.0
500
5.0
1.8
0.90
T (K)
First Example of a Spaceborne Imager: A General-Purpose Mechanical Scanner 161
RF bandwidth is twice the predetection bandwidth. Thus, in the present case, the input bandwidths are as quoted in Table 13.9 for all channels but the 89 GHz channel, where it is 1 GHz. The TRW MMIC radiometers used in JASON exhibit 2.8 dB noise figure at 18.2 GHz, 3.0 dB at 23.8 GHz, and 3.1 dB at 34 GHz. For the present purpose, these are still realistic figures, bearing in mind that the JASON radiometers include a lossy Dicke switch that is not present here, while, on the other hand, a small loss (hence noise figure degradation) accounting for a small section of input waveguide and the feed horn should be added. A 2.5 dB is assumed reasonable at the lower 10.7 GHz. Using the prescribed bandwidth (300 MHz) and integration time (4.5 ms) from Table 13.9, we find for the 36.5-GHz channel: T = 0.46K. For the lower frequencies we can also assess the sensitivity using the bandwidths and integration times from the table, but then it must be recalled that the calculated sensitivity will be the sensitivity after proper ground preprocessing, in which integration is carried out both across track and along track to reflect the larger footprint compared with the one (36.5 GHz) on which the actual sampling is based. This results in the following figures: ∆T = 0.36K at 23.8 GHz, ∆T = 0.27K at 18.7 GHz, and ∆T = 0.20K at 10.65 GHz. A state-of-the-art, but realistic, noise figure for an 89-GHz spaceborne radiometer is 5 dB corresponding to a 626-K noise temperature. The integration time is the 0.75 ms from Table 13.2, modified to reflect the lower antenna rotation rate: τ = 0.75 · 59.4/24.3 ms = 1.8 ms. As a result, ∆T = 0.90K. It is seen that the actual sensitivities as shown in Table 13.9 compare quite well with the typical sensitivities derived in Chapter 12, and displayed in Table 13.7. However, it must be emphasized that, especially at the higher frequencies, there is some freedom to adjust the bandwidth and thus obtain other sensitivities. At the lower frequencies there are so many active services that relatively narrow protected bands must be adhered to, but at the higher frequencies, especially in the 90-GHz range, there are possibilities for an input bandwidth of several gigahertz without severe radio interference threats from active services. 13.3.5
Critical Design Features
Overall, it is fair to state that microwave radiometers, of the type and in the frequency range discussed here, employ mature technology and design features. However, a few critical areas shall be pointed out in the following. Microwave radiometers are very sensitive to front-end losses and reflection coefficients. As these cannot generally be avoided (although they can be minimized), they must be known and stable with time so that corrections are possible. Hence, careful waveguide design has been the dominant technology until
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Microwave Radiometer Systems: Design and Analysis
recently. As stated earlier, MMIC technology is now a viable option, generally characterized by good stability in addition to the other virtues to which we already alluded. Stability is greatly enhanced by a stable thermal environment. Hence, it is required that the dual receiver units are thermally stabilized to some given mean temperature ±1°C or so. This stabilization is easier the smaller the receiver, so once again the MMIC technology offers clear advantages. The mean temperature need not be the same for all receivers, the absolute level does not matter (as long as it is within reasonable operating levels for electronics), and the stability is to be understood as short-term stability (typically orbital variations). A long-term drift over weeks and years is of no concern. The temperatures in the dual receiver units must be carefully monitored and form part of the housekeeping data. The only lossy components outside the temperature-stabilized enclosures are the antenna waveguides and feeds. All possible effort must be put into the mechanical design to keep waveguide lengths as short as possible. Their losses must be known, and their temperature monitored carefully at several points along each waveguide run. The reflection coefficients of the antenna ports must be kept to very low values, but this is generally no problem for offset reflector antennas with feed horn illumination. The mechanical layout must take into consideration thermal expansion and contraction of the relatively rigid antenna waveguides. Flex-guides cannot be recommended due to poor stability. The LF section of total power radiometers is very sensitive to low frequency noise (from DC up to, and somewhat above, 1/τ). The smallest integration time in question here is 1.8 ms, corresponding to 560 Hz. Hence, power supply noise and ripple should be avoided below about 5 kHz. Switch mode power converters should generally be avoided, but, as they exhibit superior efficiency as compared with linear supplies, they will have to be used in space systems. They must be carefully designed for low noise and carefully evaluated with the radiometers. The local oscillators in radiometer receivers generate harmonics that may be emitted through the feed horns and find their way to other radiometers at higher frequencies. Hence, local oscillator frequencies must be arranged in such a fashion that no radiometer input band include harmonics of any local oscillator. This is not a problem in the present system where only the 89-GHz radiometers employ local oscillators, but generally it should be remembered. Apart from the above-mentioned internal EMC problem, compatibility with other sensors and services of the carrying satellite must be ensured. Surely no radio transmission can be allowed in any of the radiometer input bands. Also, harmonics from any transmitter must be considered. The frequency of major transmitters should be selected so that harmonics do not intercept any radiometer input band, or they must be reduced to very low levels at the source
First Example of a Spaceborne Imager: A General-Purpose Mechanical Scanner 163
13.4 Antenna Design Only a few comments shall be brought forward for the sake of completeness, the subject being outside the scope of this book. The general antenna geometry is shown in Figure 13.4. The geometry is equivalent to the one shown in Figure 11.4, with a 50° offset angle. The reflector has a 100-cm circular aperture and the focal length is 75 cm. The antenna term: “F/D ratio” is 0.30 (note that in this context D is not the aperture but the total diameter of the paraboloid from which the offset section may be cut out). The total dimensions of the reflector are 100 × 112 cm. The feed axis is tilted 50° with respect to the parabola axis. Typical Potter horns are assumed at the lower frequencies, and multiflare horns at 89 GHz. The Potter and the multiflare horns are light, compact designs with very thin walls (hence little difference between inner and outer diameter of the horn aperture). Table 13.10 shows the outer diameter of the horn apertures for a set of Potter/multiflare horns.
140
cm
120
100
80
Aperture Aperture 100cm cm DD==100
60
40
20 30° 30°
−20
20
40
Figure 13.4 Antenna geometry.
60
80 F=75 F = 75cm cm
100
120
140
160 cm cm
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Microwave Radiometer Systems: Design and Analysis
Table 13.10 Horn Dimensions
F (GHz)
d (mm)
10.65
88
18.7
50
23.8
40
36.5
27
89.0
11
The offset reflector is scaled for an illumination angle of 30°. At this angle the typical horn patterns are down by 20–21 dB. Adding roughly a 1-dB space attenuation results in an edge illumination of the reflector in the −21- to –22-dB range, meaning that the factor 1.4 in the beamwidth equation (11.1) is justified (ensuring low sidelobes and good beam efficiency). Figure 13.5 shows a possible horn layout. The relative horn dimensions are as shown in Table 13.10. The X between the 89-GHz horns marks the focal point of the reflector. Note that no angular orientation is given. This must be determined so that the antenna beams from the two 89-GHz horns give contiguous coverage (with 15% overlap). All horns should be as close to the focal point (measured in wavelength at the individual frequency) as possible. This means that the highest frequency horns should be placed near the focal point first.
18.7
10.7
89
89 23.8
36.5
Figure 13.5 Antenna feed layout.
First Example of a Spaceborne Imager: A General-Purpose Mechanical Scanner 165
Due to the fact that the feeds are not all at the prime focus of the reflector, the footprints on the ground will be displaced from one another. As long as the displacements are known (which they are), this is no problem, but some geometrical corrections will have to be carried out as part of data processing after the instrument is operating. The feed positions are not critical as seen from an antenna performance point of view (although they are for determining the footprint positions). It is clear that displacements in the focal plane of several wavelengths are required to enable the cluster. Still, good performance can be achieved. In order to ensure the required 53° incidence angle on the ground from the satellite altitude, the whole antenna system (reflector plus feeds) must be tilted forwards by 4.8° (the line in Figure 13.4 from the focal point to the center of the reflector, equal to the feed axis, is not vertical but tilted by 4.8°) according to the scan geometry as shown in Figure 12.1. Alternatively, the antenna design could directly have used a 45.2° offset angle and no additional tilt. This may not be so practical, however, as it would—in real life—imply that a whole range of antenna designs would be required to serve different satellite altitudes (the 800 km selected here is only a typical example). In all cases rotation is around a vertical axis.
13.5 Calibration and Linearity 13.5.1
Prelaunch Radiometric Calibration
The basic calibration is carried out to find the calibration curve of the radiometer receivers, that is, the relationship between known input levels and corresponding digital output counts. Primarily, this is done with the receivers subjected to their nominal environment. During such exercises, the linearity of the receivers must be verified and the sensitivity (defined as the standard deviation of the output signal for a constant input level) checked. Having calibrated the receivers, these, together with proper calibration sources, can be used to measure the losses in antenna reflectors, feeds, and waveguides. However, the receivers cannot be expected to operate under a nominal, constant temperature when in orbit. First, a thermal analysis might show that the temperature within the radiometer instrument will oscillate by typically up to several degrees during an orbit cycle. Second, unforeseen thermal gradients may be experienced in orbit. So it is necessary to investigate radiometer performance under nonideal thermal conditions. The results from the experiments in Chapter 10 show that it is possible to find the true brightness temperature at the antenna when the radiometer temperature is different from its nominal value. To do this, each receiver must be calibrated subject to different temperature levels and temperature oscillations.
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Microwave Radiometer Systems: Design and Analysis
These oscillations shall be planned to resemble as much as possible the oscillations that may occur in orbit. Many temperature sensors must be embedded in each receiver and their output recorded during calibration exercises, and included in the housekeeping data transmitted from the satellite. Sensors must also measure the temperature of the antenna horns, antenna waveguides, and hot loads. Adequate sensors must be employed to ensure a reasonable picture of the thermal conditions within the instrument. Having the calibration data for the receivers, the losses of waveguides and horns, and the housekeeping data, it is possible to calculate the brightness temperatures as viewed by the antenna. A different calibration approach is also possible. After the manufacture and integration are done, the total instrument is subjected to representative thermal oscillations and levels, with different, known radiometric input signals. A multiple regression is performed on the input and output signals (the output signals being the radiometer counts and the housekeeping data) and calibration equations will emerge. It can be useful to perform both calibration techniques and it will increase the correction possibilities in case of unforeseen thermal or other problems in space. One may ask: Why bother about the prelaunch calibration (apart from the initial calibration and linearity check of the individual receivers), because we have both a hot point and a cold point available for frequent calibration once in orbit? The reason is that for space instruments fallback solutions should always be implemented as far as possible. In case of unforeseen problems, it is of great value to be able to calculate corrected brightness temperatures based on models and prelaunch exercises (as was discussed in Chapter 10). Here the fallback solution does not require extra hardware or resources in the satellite (apart from temperature sensors which do not contribute to weight, power, and data rate by any significant amount). Only some thermal exercises before launch are needed (which may, however, be expensive and time-consuming). 13.5.2
On-Board Calibration
The present scanner with fully rotating antenna/feed/receiver assembly will employ the hot load/cold sky reflector calibration layout as mentioned in Section 13.2, and as also found in well-known systems like the SSM/I and the MIMR. The principle is illustrated in Figure 13.6. While the antenna rotates, at a certain time while the antenna beam would look away from the useful swath anyway, the ray path between the feed and the main reflector is interrupted by the hot load, and likewise for the sky reflector. Thus, the switch indicated in Figure 13.6 is actually not physically present, and an almost perfect two-point calibration is carried out; only reflectors are outside
First Example of a Spaceborne Imager: A General-Purpose Mechanical Scanner
167
TC Out * TB
Out * TH
In Radiometer
Figure 13.6 Calibration schematics.
the calibration loop. As already mentioned, the loss of present-day, high-performance reflectors is so low that it can be neglected, and, if this for some reason is not the case, the loss can be measured extremely accurately by radiometric means, and corrected. The calibration method as described earlier assumes that the radiometer receiver’s transfer function is linear. This is generally the case for a well-designed radiometer when we discuss relatively standard requirements as in the present case: Linearity must be viewed upon relative to the required sensitivity and absolute accuracy (which are typically of the same size), here around 0.5K. Linearity has been a matter of discussion for future high-accuracy systems requiring a fraction of Kelvin accuracy, but in the present case adequate linearity fidelity is obtainable by careful design—especially concerning the detector circuit. These issues were discussed in Section 9.4. Experiments with real hardware show that present-day, well-designed radiometers are indeed linear to within a fraction of a Kelvin. Also, it is well known that often the major contributor to nonlinearities is the detector (not very surprising), and by proper detector design (tunnel diode with correct loading) these can be held at a very low level.
13.6 System Issues 13.6.1
System Weight and Power
The weight and power of the radiometers have already been discussed in Section 13.3.3. Another important resource driver is the antenna reflector. Low-weight structures have been built, and it is known that a 2-m carbon fiber composite dish weighing 12 kg has been launched into space. Similarly, a 3-m dish for a future ocean salinity mission has been designed with a weight of 21 kg. So, a present rule of thumb states an antenna reflector weight around 3 to 4 kg per square meter with proven technology. Hence, the present reflector would weigh around 3 kg. With this low reflector weight, the struts and other structure to carry the reflector and the associated feeds become a significant part of the total antenna weight, in the present case around 5 kg.
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Microwave Radiometer Systems: Design and Analysis
Finally, a complete radiometer system of course includes several other units than what have been discussed above, and a total power and weight budget could look as it does in Table 13.11.
13.6.2
Data Rate
The data rate can be estimated by assuming 16-bit data words from the receivers (4 bits for label, 12 bits for radiometric data). The rate per receiver is determined by the integration time, which is equal to the sampling time. To simplify the situation, the sampling rate of the 10.65- to 23.8-GHz channels is assumed to be equal to the sampling rate of a 36.5-GHz channel (the frequency that determined the antenna rotation rate). As the footprint is larger at these lower frequency channels compared with the 36.5-GHz channel, some on-board integration could be carried out to lower the data rate. The estimates are thus conservative. It must be recalled that the useful swath, where the receivers are sampled at nominal speed, only corresponds to 120° out of the full 360° rotation. In addition, the radiometers are sampled while the feeds pass under the cold sky reflector and the hot load, let us assume 2 × 30° of rotation. Thus, the receivers are sampled at nominal rate during 180° out of the 360° rotation. For the 10.65- to the 36.5-GHz channels (4 × 2 = 8 receivers in total), the data rate is: Table 13.11 Power and Weight Budget Power:
Receivers
18W
Data handling
5W
Scan
10W
Power supply Total power Weight:
Total weight
6W 39W
Antenna including struts
8 kg
Receivers
3 kg
Feeds
2 kg
Data handling
2 kg
Power supply
2 kg
Calibration
6 kg
Scan motor
5 kg
Deployment
6 kg 34 kg
First Example of a Spaceborne Imager: A General-Purpose Mechanical Scanner
D1 =
169
16 ⋅ 8 180 ⋅ = 14 .2 Kbps 0.0045 360
For the four 89-GHz radiometers, the rate is: D2 =
16 ⋅ 4 180 ⋅ = 17.8 Kbps 0.0018 360
or in total: 32 Kbps. (Housekeeping and calibration data add to this figure by an insignificant amount.) It is clear that a typical radiometer system in not a data rate resource driver when compared with most other remote sensing systems (not surprising when considering the multikilometer spatial resolution of microwave radiometers in contrast to the multimeter resolutions of synthetic aperture radar and optical systems).
13.7 Summary A general-purpose, multifrequency mechanically scanned radiometer system has been described. The major characteristics of the system are: • Orbit height: 800 km; • Swath width: 1,498 km; • Polarization: H and V; • Incidence angle: 53°; • Antenna aperture: 1m; • Antenna rotation rate: 24 RPM; • Radiometric dynamic range: 0–313K.
Further specifications are found in Table 13.12. Twelve total power receivers are used, and the system requires the following resources: • DC power: 39W; • Weight: 34 kg.
The data rate from the radiometers is estimated to 32 Kbps.
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Microwave Radiometer Systems: Design and Analysis
Table 13.12 Summary of Specifications Footprint Bandwidth Noise Integration F (GHz) (km) (MHz) Figure (dB) Time (ms)
T (K)
Feeds
Receivers
10.65
48 × 80
100
2.5
52.3
0.20
1
2
18.7
27 × 46
200
2.8
17.0
0.27
1
2
23.8
22 × 36
200
3.0
10.5
0.36
1
2
36.5
14 × 23
300
3.1
4.5
0.46
1
2
89.0
5.8 × 9.6
500
5.0
1.8
0.90
2
4
References [1]
Gloersen, P., and F. T. Barath, “A Scanning Multi-Channel Microwave Radiometer for Nimbus-G and SEASAT-A,” IEEE Journal on Oceanic Engineering, Vol. 2, No. 4, 1977.
[2]
“IMR, Imaging Microwave Radiometer—Phase A Study,” ESA Document Ref. ESS/SS 1006, 1980.
[3]
Hollinger, J. P., and R. C. Lo, SSM/I Project Summary Report, NRL Memorandum Report 5055, Naval Research Lab., 1983.
[4]
Skou, N., “Measurement of Small Antenna Reflector Losses for Radiometer Calibration Budget,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 35, No. 4, 1997, pp. 967–971.
14 Second Example of a Spaceborne Imager: A Sea Salinity/Soil Moisture Push-Broom Radiometer System This chapter will show how to arrive at the design of a system, the aim of which is to measure certain geophysical parameters with certain accuracies and resolutions by using the guidelines set forth in the previous chapters.
14.1 Background A frequency of 1.4 GHz is generally accepted for measuring sea salinity and a ground resolution around 50 km is acceptable. From Table 12.1 it is seen that this results in an antenna aperture of some 10m. It is clear that a mechanical scanner with this size of antenna would be very demanding concerning satellite resources, as already discussed in Section 12.4.3. The push-broom concept offers a much more viable possibility, and high capacity spacecraft can carry structures of the size in question. The technical specifications for the design to be carried out in the following are: • A frequency around 1.4 GHz; • An antenna aperture of 10m; • A satellite altitude of 800 km; • Incidence angle on ground: 53°.
171
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Microwave Radiometer Systems: Design and Analysis
Using the formulas in Section 12.3, we find: • Maximum swath width: 1,500 km; • Footprint: 47 km (FPS = 36 km, FPL = 60 km); • Integration time: 6.4 seconds; • Number of receivers: 59.
A trade-off between swath width and the number of receivers is possible. In the present design it is decided to opt for 21 receivers, giving a swath of 530 km. Such a decision reflects a compromise: A wide swath provides better (more frequent) ground coverage, but requires more resources (many receivers, large antenna). This is a quite frequent situation when planning a spaceborne sensor system: There is a delicate balance between user wishes or requirements and the available resources (in the end often boiling down to financial resources).
14.2 The Brightness Temperature of the Sea The brightness temperature of the sea depends on several parameters: frequency, incidence angle, polarization, sea surface temperature, wind speed (actually surface roughness), and salinity. Disregarding surface roughness, the brightness temperature can in fact be calculated in a relatively straight forward manner assuming the sea surface to be a plane boundary between two media, water and air, and then evaluate the Fresnell reflection coefficients knowing the dielectric constant of water. The Klein & Swift computerized model for the brightness temperature of the sea [1] does that, and it has been run for a range of these parameters, keeping the incidence angle fixed at 53°. Based on the output from the model, the following can be concluded. Only at rather low frequencies is a response to salinity present, especially at low sea surface temperatures. The sensitivity to salinity increases with decreasing frequency well into the UHF range. As the crowded UHF band is approached, however, insurmountable problems with interference from active radio services arise, and it is generally accepted that the lowest possible frequency band for radiometer work is the protected radio astronomy band 1.400–1.427 GHz. At 1.4 GHz the vertical brightness temperature depends on sea surface temperature (SST ) and salinity (S) as illustrated in Figure 14.1. It is noted that the sensitivity to salinity is best at warm temperatures. It is also noted that some dependence on temperature is evident especially for low salinity water. Fortunately, we are in the situation that a large part of the Earth’s oceans are in the best possible category: moderate-to-warm temperatures and high salinity around 35 practical salinity unit (psu) (1 psu is in effect equal to 1
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173
160 0 psu 150 14 psu 22 psu
TV 140
30 psu 130 38 psu 120 0
5
10
15
20 SST (°C)
25
30
35
Figure 14.1 Vertical brightness temperature (TV) as a function of sea surface temperature with salinity as parameter. Wind speed is zero.
part per thousand). Arctic oceans and brackish seas are more difficult to deal with. Dealing only with the open-ocean/high-salinity case, the curves in Figure 14.1 reveal a brightness temperature sensitivity to salinity at best approaching ∆TB/∆S = 1K/psu (warm water at 30°C), and the sensitivity will be better than ∆TB/∆S = 0.5K/psu for moderate to warm water (above 10°C). For the same conditions the brightness temperature sensitivity to sea surface temperature never exceeds ∆TB/∆SST = 0.2K/°C. The horizontally polarized brightness temperature shows inferior response to salinity and will not be considered further in the present context. However, as already alluded to, the brightness temperature also depends on sea surface roughness, which in turn is a result of winds. Traditionally, a direct relation is assumed, so that an expression for the brightness temperature as a function of wind speed can be quoted. This is certainly true at the higher microwave frequencies as evidenced by the many spaceborne sensors like wind scatterometers and imaging radiometers yielding highly useful wind data over the oceans on a routine basis. Also, at L-band such a direct dependence is assumed, but unlike the salinity and temperature dependence, it is difficult to accurately model it, and it is necessary to resort to experimental data. Hollinger has provided a very useful data set [2], which has later been scrutinized and compared with others [3]. The relevant data is shown in Figure 14.2. The figure shows how much the brightness temperature in a given situation changes with wind speed assuming a linear dependence. It is seen that at the 53° incidence angle used here the wind dependence is quite small for the vertical polarization, only about 0.1K per meters per second.
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Microwave Radiometer Systems: Design and Analysis
0,6
Sensitivity (K per m/sec)
0,5 0,4 H pol 0,3 0,2 0,1 V pol 0 −0,1
0
10
20
30
40
50
60
70
80
−0,2 −0,3 Incidence angle (deg.) Figure 14.2 The brightness temperature dependence on wind speed at vertical and horizontal polarization as functions of incidence angle.
This is a highly warranted feature for a mission where the wind signal is a disturbing signal to be corrected. In conclusion, it is seen that at 1.4 GHz the vertical polarization brightness temperature responses (∆TB) to salinity changes (∆S ), sea surface temperature changes (∆SST ), and wind speed changes (∆WS ) are for most open ocean conditions (a sea temperature above 10°C) approximately: • ∆TB/∆S ∼ 0.5K/psu; • ∆TB/∆SST ∼ 0.2K/°C; • ∆TB/∆WS ∼ 0.1K per meters per second.
It is clear that, to measure salinity with good accuracy, a sensitive radiometer is required, and corrections for wind and sea temperature must be carried out. It must be noted that these conclusions only hold as long as the models on which they are drawn hold. It may be questioned whether the existing models can be exploited to the accuracy levels required for the present task. It is thought that the models for the brightness temperature as a function of salinity and sea surface temperature are quite reliable. Similar models to those used here, and precise radiometers at 1.4 GHz, have been demonstrated to enable airborne salinity and sea surface temperature measurement accuracies to better than 1 psu and 1°C by researchers at the NASA Langley Research Center [4–6]. In 2002 a
Second Example of a Spaceborne Imager
175
pool experiment specifically set up to test the Klein & Swift model confirmed its accuracy [7]. The RMS difference between measured and modeled brightness temperatures was found to be around 0.1K. The wind speed sensitivities are slightly less well founded. A recent experiment [8] has largely confirmed the Hollinger figures used here, but error bars associated with the data of both experiments are quite big, so the quoted sensitivity of 0.1K per meters per second can only be regarded as a guideline for system considerations.
14.3 The Brightness Temperature of Moist Soil Laboratory measurements of the dielectric constant of moist soil show a very large change with varying water content, as seen from Figure 14.3 [9]. This is not very surprising when considering that dry soil typically has a dielectric constant of around 3 for the real part with a low imaginary part. Water, on the other hand, has at 1.4 GHz a very high dielectric constant of around 80 (real) with an imaginary part strongly dependent on the contents of salts. When mixing soil and water, the resulting dielectric constant exhibits a very large variation with water contents (i.e., soil moisture). Assuming the soil surface as a flat interface between soil and air, the brightness temperature as sensed by a downwards looking radiometer can be calculated just as was explained for the calm sea surface, and it will show a large variation with soil moisture. Of course, the surface of the Earth is not a smooth, flat interface, and furthermore it is normally not bare. Thus, many experiments have been carried out over the years to investigate the merits of radiometers in a realistic context. It can be concluded that a frequency below 2–3 GHz is required for soil moisture measurements. This is primarily due to the masking effect of the vegetation cover at higher frequencies. However, there is a lower limit to the usable frequency set by interference (as was discussed in the previous section) and a generally accepted compromise is 1.4 GHz. Horizontal polarization is preferred over vertical. This stems from the fact that vegetation has predominant vertical structures and therefore affects the vertical polarization most, but at 1.4 GHz vertical polarization is certainly also usable. Even at 1.4 GHz dense vegetation is not transparable, and brightness temperature corrections based on models with biomass input is required. The biomass may be estimated by other spaceborne measurements for example in the optical region. The brightness temperature of soil is also dependent on surface roughness, and this parameter cannot easily be measured independently. However, the time scale for roughness changes is very different from the time scale for soil moisture changes. Concerning farmland, for example, the roughness changes dramatically only a few times each year, when the farmer prepares the fields. Hence, the time
176
Microwave Radiometer Systems: Design and Analysis 35 Yuma sand, wt = 0.17
Vernon clay, wt = 0.28 Miller clay, wt = 0.33
30
Dielectric constant
25
20
15
ε’
10
5 ε’’ 0 0
0.1 0.2 0.3 0.4 3 0.5 3 Volumetric water content, cm /cm
0.6
Figure 14.3 Laboratory measurements at L-band of the real and imaginary parts of the dielectric constant for typical soils as functions of moisture contents. (From: [9]. © 1983 IEEE. Reprinted with permission.)
histories of soil moisture variations can generally be monitored without roughness disturbances. The brightness temperature of soil is also dependent on the physical temperature of the material from which the emission originates. At 1.4 GHz the majority of the brightness power is emitted from a soil layer 2–5 cm beneath the surface. The physical temperature of this layer is not easily measured by remote sensing. It must be taken from climatological and meteorological sources plus models for the influence of such parameters on the needed temperature. The problem can be considerably alleviated by selecting a Sun-synchronous orbit, so that the radiometric sensing is always carried out at one specific local time in the day. Typically, an early morning (6 a.m.) orbit is selected, and the direct Sun heating is largely avoided. These considerations, and the fact that typical brightness temperature responses are as large as 40–60K, ensure that soil moisture assessment can be carried out with good accuracy, in some cases without physical temperature correction, and in others with corrections based on climatological and meteorological data.
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177
14.4 User Requirements for Geophysical and Spatial Resolution 14.4.1
Salinity Measurements
A summary of user requirements is found in [10]. For the open ocean spatial resolution is not the big issue as salinity generally only changes over large distances, and 50 km is certainly very useful. However, there are stringent requirement to salinity measurement resolution: 0.1 psu will provide new input to oceanographers of very high value, while 1 psu would be of little interest (can almost be taken from existing salinity maps based on point measurements from buoys and ships). The design target in this chapter will be 0.1 psu. Recalling a typical sensitivity of the brightness temperature to salinity changes of ∆TB/∆S = 0.5K/psu, this translates directly into a radiometric resolution of better than 0.05K. Then a perfect knowledge of sea surface temperature and wind speed is assumed. A 1°C error in SST translates into a 0.2-K error in the brightness temperature, and 1-m/s error in wind speed changes the brightness temperature by 0.1K. Although these seem to be small numbers, they lead to brightness temperature contributions that in this demanding case must be quantified and corrected for. This, in turn, leads to certain requirements to companion measurements of sea surface temperature and wind speed. 14.4.2
Soil Moisture Measurements
Rainfall variations have roughly a 10-km scale, and a ground resolution around that value would be appreciated by users, but this leads to systems with antenna aperture sizes in the 50-m range, which is impossible with today’s technology. A pragmatic view leads to the notion that a 50-km ground resolution will indeed be very useful as this fits the grid sizes of present climatology and meteorology models—and soil moisture input to these models is actually of paramount interest. Requirements for radiometric resolution and accuracy are modest, and 1K would be sufficient.
14.5 A 1.4-GHz Push-Broom Radiometer System 14.5.1
Sensitivity Considerations
It is clear that the salinity mission is the design driver. The requirement for resolution of the salinity measurement is 0.1 psu, which in case of full knowledge of wind speed and physical temperature translates into a radiometric sensitivity of 0.05K as already noted earlier. This sensitivity is seen to be almost in line with the typical sensitivity of 0.08K as calculated in Section 12.4.3. Assume a 0.08-K radiometer sensitivity and uncertainties in temperature and wind speed of 1°C
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Microwave Radiometer Systems: Design and Analysis
and 1 m/s, respectively. The temperature uncertainty results in a radiometric uncertainty of 0.2K and the wind speed uncertainty gives a 0.1-K uncertainty. As the three uncertainties are statistically independent, the total standard deviation of the radiometer measurement will be: ∆T tot = 0.08 2 + 0.2 2 + 01 . 2 = 0.24 K resulting in a 0.48 psu uncertainty in salinity, which is far from fulfilling the requirements. It is obvious that the dominating factor is the uncertainties in the disturbing geophysical parameters, especially sea temperature, and it would help little to strive for a better radiometric resolution. Fortunately, the oceans surface temperature is quite well known from satellite sources like infrared radiometers augmented by buoy measurements. In the following it will be assumed that the radiometric sensitivity is still 0.08K, the temperature of the sea is known to within 0.3°C, and the wind speed is known to be within 1 m/s. This results in a measurement sensitivity of 0.14K, which again transforms into a 0.28-psu uncertainty in retrieved salinity. This is still not fulfilling the original requirements, but there is little to do about it, as sea surface temperature and wind speed cannot be known to better accuracy than assumed here. The only remedy is spatial or time averaging as part of postprocessing of the data once transferred to ground. In the present case this is a viable solution; as already stated, ground resolution is generally not the great issue concerning ocean salinity, and 100 km would serve adequately most users. This means that four footprints can be averaged, and with the reasonable assumption that measurement uncertainties are statistically independent from footprint to footprint, the uncertainties are reduced by a square root of 4 (i.e., to 0.14 psu), which is quite satisfactory. If a user would prefer to retain the 50-km ground resolution, another integration scheme is possible, namely, to integrate over four consecutive orbits over the area in question. This is possible since sea salinity is generally a slowly varying parameter. Actually, even further time averaging may be possible, which would reduce the salinity uncertainty to below the 0.1 psu target value. All of this, of course, requires a radiometer stability and calibration accuracy well below 0.1K, which surely is challenging. There are, however, off-line, postlaunch methods like vicarious calibration that may alleviate the problems [11]. 14.5.2
The 1.4-GHz Noise-Injection Radiometer Receiver
Following the discussion in Section 11.5, a Dicke-type switching radiometer will be employed. Due to the extreme requirements to performance set forth by the sea salinity mission, the noise-injection radiometer is the candidate receiver
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type. The design follows the guidelines set forth in Chapter 5, and assuming a realistic receiver noise temperature of 170K as already mentioned in Section 12.4, the values indicated in Figure 14.4 are found. Compared with the generic noise-injection radiometer design shown in Figure 5.10, the major differences are that the receiver, being a direct detect receiver, has no mixer and LO and hence no IF circuitry. The consequence is more RF amplification and more stringent requirements to the RF filter. Also, it is indicated that the Dicke switch for this low microwave frequency design is not a latching circulator but rather a PIN diode switch. Latching circulators are too big at this frequency, so the slightly larger loss of a semiconductor switch must be accepted. A completely different design option is a very viable candidate at this relatively low frequency, namely, the digital radiometer (see Figure 14.5). The digital radiometer uses no detection but sampling and A/D conversion directly at the RF frequency, here around 1.4 GHz. This does not imply that the sampling frequency has to be twice this RF frequency, bearing in mind that according to Nyquist the sampling frequency has to be twice the bandwidth—which in this case is only 19 MHz. So allowing for some overhead, the sampling in this example is chosen to be 63.5 MHz as also indicated in Figure 14.5. Actually, the sampling frequency cannot be chosen freely above twice the bandwidth: A thorough frequency planning, taking all sideband products into account and avoiding aliasing, must be carried out.
1423 MHz
29900K
−20 dB
1 mV/µW
∼ ∼ ∼ 1404 MHz
RF
TA 0K
6.6µVpp
1K
299 K
30 dB
RF 46 dB
0.66Vpp
300 K −3 dB Noise switch
100 dB AF
0.5 VDC/1 Vpp
95%
−1 dB
10 V = 100% ∆/Σ
9.5 V
±1
0.33 V 1.50 sec
DC 29 dB
−3.7 dB Noise diode ENR = 28 dB
Figure 14.4 The noise-injection direct receiver.
DATA CK
FS
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1K
299 K
1423 MHz RF
TA 0K 29900K
−20 dB
30 dB
∼ ∼ ∼ 1404 MHz
RF 30 dB
26 dB RF
300 K −3 dB
Noise switch −1 dB
95% Processor
Fast A/D
DATA
CK: 63.5 MHz
−3.7 dB Noise diode ENR = 28 dB
FS
Figure 14.5 The digital receiver with noise-injection.
The digital radiometer as described here actually carries out the downconversion in the sampling process, and it is also named: radiometer with subharmonic sampling. The system relies on the fact that fast A/D converters, having an analog input bandwidth encompassing L-band frequencies and a time jitter low enough to suit sampling of the same frequencies, are available, for example, the Maxim MAX104. For more information about digital radiometers, see [12, 13]. The output from the A/D converter is immediately integrated suitably in a fast field programmable gate array (FPGA), thus slowing down the data rate to more common radiometer data rates. This FPGA is named “processor” in Figure 14.5 as it also includes algorithms controlling the noise switch. The processor can actually also carry out other important tasks. Provided some further oversampling is done, digital filtering becomes an option. This would make it possible to relax on the analog RF filter (which can become clumsy at L-band) and at the same time ensure very good out-of-band suppression, which is important at L-band where many active services are close by. In addition to this attractive feature, the advantage of the digital radiometer is that it represents the ultimate reduction in analog hardware. On the other hand, it must not be forgotten that the stability of the A/D converter (sampling circuitry and reference voltage especially) becomes a very important issue, and fast converters are power consuming. Nothing is free. Based on the considerations in Chapter 13, where it was found that a dual receiver unit at middle microwave frequencies might have a weight of 500g and
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consume 2.6W, it can be estimated that an L-band noise-injection receiver might have a weight of 500g and consume 2W. The size of microwave circuitry, and hence the weight, increases slightly when going to lower frequencies due to microwave components like filters and isolators. The power consumption of the more complicated noise-injection radiometer is slightly larger than for the total power radiometers considered in Chapter 13. In total for 21 channels, we thus assume 11 kg and 42W.
14.5.3
Antenna Considerations
It is not within the scope of the present book to discuss the design of the antenna in any detail. However, a few comments shall be made for the sake of completeness. Details can be found in [14]. Earth surface observation systems normally require that the antenna beam be scanned around a vertical axis (conical scan with fixed incidence angle on the ground). This applies to the present case, and the word “scan” will be used also in conjunction with the push-broom concept although no movement is involved. For Earth observation systems half-scan angles up to 60° are often desired; here a ±18° scan is employed. For this reason it is considered necessary that the reflector be made rotationally symmetric around a vertical axis in order to preserve antenna beam fidelity. This is obtained by the so-called torus antenna, in which the reflector surface is generated by rotating a section of a parabolic arc around an oblique axis (see Figure 14.6). By this rotation, the feed point of the parabolic segment traces out a “focal curve” for the torus reflector, and the antenna feed horns are placed on this focal curve. For practical reasons the horns must be arranged in two rows as illustrated, since their physical size exceeds the distance between positions required for proper beam squinting corresponding to correct footprint position on ground. This, in turn, results in minor beam squinting along track, but that effect is easy to correct in the data processing. The rotation axis is in space oriented to be vertical, and the horizontal axis of the drawing indicates the direction of the ray leaving the reflector. The focal length (f ) is seen to be rather long compared with the aperture (D). This is necessary to avoid performance degradation as each horn illuminates a reflector surface that is parabolic in one plane and circular in the orthogonal plane.
14.5.4
Layout of the System
A layout of the radiometer system is shown in Figure 14.7. The photo shows an airborne demonstration model scaled to a frequency of 36.5 GHz. The instrument was flown in conjunction with a mechanically scanned imager having the same ground resolution in order to validate the push-broom concept [15].
182
Microwave Radiometer Systems: Design and Analysis W = 18.6 m
D = 10m
Rotation axis = vertical axis
45.2° f = 13.2 m
Figure 14.6 Push-broom torus antenna with 21 feeds.
Figure 14.7 The push-broom radiometer demo system.
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The main antenna dimensions for the space system are: • Aperture diameter: D = 10m; • Focal length: f = 13.2m; • Reflector width: W = 18.6m.
For many years the huge antenna structures as considered here have been an insurmountable problem, but substantial developments have taken place recently, and now there is no doubt about the feasibility. A 12-m mesh antenna, having a weight of 85 kg and being able to serve an L-band radiometer, has been flown in space (see Figure 14.8). A communication satellite having two 19 × 17-m antennas has been designed and the antennas demonstrated. A 14-m inflatable parabolic reflector antenna with a weight of 60 kg has been built and successfully deployed in space. In parallel herewith a 27 × 36-m inflatable torus reflector antenna, intended for push broom applications, has been designed. The weight is 211 kg. Based on these numbers, a 10 × 19-m mesh antenna could have a weight of around 150 kg including feed mast and structure, while a fair guesstimate concerning an inflatable antenna is 100 kg. The feeds require a few comments. So far, horn antennas have been assumed as feed elements, and indeed the scaled demo model shown in Figure 14.7 employs horns. For the spaceborne L-band instrument, it must be realized that horns become very big, in the present case with an aperture around 80 cm and of considerable length. Such horns can be fabricated as light and stiff structures, but the weight per unit will probably be around 10 kg, in total for the horns: 210 kg.
Figure 14.8 ASTRO 12-m mesh reflector. (Courtesy of Astro Aerospace, Northrop Grumman Space Technology.)
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An alternative to the horns is microstrip patch antennas. In general, these will have higher losses than horns do, but considering the considerable bulk of the horns, it may well be an option worth investigating. The losses in patch antennas are largely associated with the feed network, so every effort towards a low-loss design must be pursued, for example, using air suspended stripline.
14.6 Calibration Calibration, in this section, means checks while the radiometer instrument is flying in space. In addition to this, a fundamental calibration is carried out before launch, using the principles described in Chapter 9 and further discussed in Section 13.5. As mentioned several times, it is reasonable for push-broom radiometer receivers to trade sensitivity for stability to ease calibration. Hence, Dicke-type switching radiometers are selected. Such radiometers only need one, low temperature calibration point, and, equally important, may only need calibration daily (given proper electrical, mechanical, and thermal design). The cold calibration point is for ground-based (and airborne) radiometers achieved by cooling a load to a low temperature, often by liquid nitrogen. This is not at all practical in a spacecraft (today, at least). However, other cooling methods are available: Peltier cooling and radiation cooling. Temperatures around 200K are possible with both methods. For applications where the measured brightness temperatures are comparatively high (e.g., sea ice measurements), this could be fine. For others involving low brightness temperatures (oceanography), it is not quite satisfactory. Each of the two cooling methods has its more serious technical drawback: The Peltier elements are power-consuming; the passive radiator is large and requires unobstructed view to free space (away from the Sun). However, the methods may play a role for very high-frequency radiometers, where hardware is small (i.e., little weight and volume to cool). Another promising possibility for a low temperature calibration point is the so-called active cold load. This is, in fact, an FET transistor amplifier where the input acts as a matched load having a noise temperature much lower than the physical temperature (actually comparable with the noise of the circuit when used as an amplifier). In [16, 17] such devices having noise temperatures in the 60–70-K range are discussed. In [18] the performance of a 120-K active cold load is presented. For satellite radiometers an antenna pointing toward free space is a very attractive cold calibration point. The cold space temperature can be launched into the radiometer input in two different manners: by switching the input away from the main antenna to some smaller antenna (sky horn) pointing toward free space, or by diverting the main antenna beam away from the Earth’s surface
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(including the limb of the atmosphere) through the use of some steerable mirror. The sky horn method is a possible and proven technique for single receiver systems. In the push-broom case, with a host of receivers, this solution is not quite as attractive. The many sky horns would have to be mounted on the surface of the satellite to pick up radiation from free space and require a substantial amount of waveguide and switch hardware. The method of diverting the main beam toward free space involves a mirror being moved slowly along the front of the feed horns, diverting the beams one by one. • Problem 1: Moving parts. However, the movement is slow, the moving
mass is small, and the action is not very frequent. • Problem 2: Architectural constraints for the spacecraft designer. Both
the normal antenna beam and the sky beam must be unobstructed by other sensors (equivalent to the sky horn situation described earlier). • Great advantage: A very satisfactory calibration is carried out. The cali-
bration includes the total sensor (apart from the main reflector) and no extra loss and complexity is introduced in the signal path through the use of calibration switches. Until now schemes have been discussed in which all radiometer receivers are individually calibrated to absolute accuracy. If this is deemed impossible, due to some of the problems already mentioned, another fundamentally different calibration scheme can be proposed, namely, a two-step process: (1) relative intercalibration of all sensors, and (2) absolute calibration of one (or a few) of the sensors. 1. Relative intercalibration. This is done entirely in the data analysis process after the radiometer system is operating in space. Incorrect intercalibration will result in banding in the radiometer imagery. By along-track integration, channel for channel, of long passes over open ocean, a calibration vector arises. This integrated information is used to adjust the calibration constants of the different receivers relative to each other. 2. Absolute calibration of one or a few sensors. A small mirror beneath the ray path to direct the beam toward free space, or a calibration switch leads the signal from a sky horn into the receiver input. In this case the sky horn solution is attractive, as it employs no moving parts and only requires a single sky horn and one switch. Care must be exercised when selecting this switch with regard to loss. Possibly a
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coaxial relay could be used as it only has to be operated a few times per day. The key question in this proposed scheme is whether the relative intercalibration can be carried out satisfactorily based on data analysis alone. This problem has been addressed by computer simulation: Based on SMMR imagery from the Pacific Ocean, synthesized push-broom data with calibration errors have been generated. Even rather simple algorithms selecting a long North-South track, discarding the worst rain showers and heavy clouds, and avoiding land masses have, by the described integration approach, given very accurate calibration adjustment constants. Using these adjustments on the distorted image, the original was found with great fidelity.
14.7 A Disturbing Factor: The Faraday Rotation The measurement accuracies discussed so far have included uncertainties imposed by the instrument itself: the radiometric sensitivity, as well as the fundamental fact that the radiated brightness temperature may depend on a range of geophysical parameters in addition to the one toward which it is being aimed. However, modifications to the received brightness temperature introduced by the intervening atmosphere and ionosphere, as well as sky radiation reflected in the sea surface, must be accounted for. This section will cover the most prominent ionospheric effect, namely, the Faraday rotation. The discussion will go into some detail as the effect and the methods to correct for it/circumvent it will have instrument design consequences. The remaining disturbing effects will be briefly discussed in Section 14.8.
14.7.1
The Faraday Rotation
Usually, within radiometry, ionospheric effects are ignored, but in the present case the frequency is so low and the measurement requirements so stringent that an investigation is necessary. The plane of polarization of microwave signals propagating from Earth through the ionosphere to a satellite is rotated by an angle θ. The amount of rotation depends on the direction and location of the ray path with respect to the Earth’s geomagnetic field and on the state of the ionosphere. To get a feeling for the magnitude of the polarization rotation angle θ, a mean daytime value can be estimated from: θ = 17/F 2 (F in GHz) taken from [19]. Hence, the average daytime rotation is found to be θ = 8.7° at 1.4 GHz, and furthermore it is illustrated why the effect generally can be ignored at higher frequencies.
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A more in-depth consideration of the Faraday rotation is found in [20]. From this, Figure 14.9 is taken. It shows the worst-case average rotation on 12.00 UTC March equinox. The average over one month of the daytime maximum rotation is estimated to 28°, whereas monthly maximum averages at 6 a.m. are around 5°. In addition, day-to-day variations can reach values within +100% to −50% of the averaged values due to the unpredictable nature of the ionosphere. Proposed missions generally have a 6 a.m. orbit, so from these considerations it is clear that the radiometer system has to cope with at least 5°, possibly up to 10°, Faraday rotation. The polarization rotation will result in a slight mixing of the true vertical (TBV) and horizontal (TBH) brightness temperatures. A dual polarized radiometer will thus measure: T BV′ = T BV ⋅ cos 2 θ + T BH ⋅ sin 2 θ T BH′ = T BV ⋅ sin 2 θ + T BH ⋅ cos 2 θ
(14.1)
Typical values are TBV = 132K and TBH = 66K. Assuming θ = 10°, we find: T BV′ = 130.0K and T BH′ = 68.0K The 2-K error in TBV translates into an error in retrieved salinity of about 2–4 psu (depending on sea temperature), which is totally unacceptable.
14.7.2
Correction Based on Knowing the Rotation Angle
The set of equations (14.1) can be solved with respect to TBV, for example. After some reductions, the following expression is found: T BV =
T BV′ − T BH′ ⋅tg 2 θ 1 − tg 2 θ
(14.2)
Hence, if both the local vertical (T BV′ ) and horizontal (T BH′ ) brightness temperatures are measured, and θ is known, the true vertical brightness temperature can be found. The rotation angle can be calculated from the total electron contents (TEC) maps available from a variety of sources. However, a self-standing mission not dependent on the availability and accuracy of such external sources can also be conceived as will be done in the following sections.
Figure 14.9 One-way Faraday rotation in degrees at 1.4 GHz for March equinox, 12.00 UTC, azimuth worst case. (From: [20]. © 1986 ESA. Reprinted with permission.
188 Microwave Radiometer Systems: Design and Analysis
Second Example of a Spaceborne Imager 14.7.3
189
Correction Based on the Polarization Ratio
The true and the local polarization ratios are defined as: T BV T BH T′ R ′ = BV T BH′ R=
(14.3)
Inserting the expressions for the local brightness temperatures into the expression for the local polarization ratio leads after some reductions to the following expression for the angle of rotation: tg 2 θ =
R −R′ R ⋅R ′ − 1
(14.4)
Hence, if the true polarization ratio is known, the Faraday rotation can be found from measurements of the local polarization ratio. Figures 14.10 and 14.11 have been generated from the model for the brightness temperature emitted from the sea already discussed in connection with Figure 14.1, including the wind responses shown in Figure 14.2 (0.1K per m/s at V pol and 0.3K per m/s at H pol). From Figure 14.10 it is seen that the 2.100 38 psu
2.080
30 psu
2.060
22 psu
2.040
14 psu
2.020 R 2.000
0 psu
1.980 1.960 1.940 1.920 1.900 0
5
10
15
20 SST (°C)
25
30
35
Figure 14.10 Polarization ratio (R) as a function of sea surface temperature (SST) with salinity as parameter. Wind speed is zero.
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Microwave Radiometer Systems: Design and Analysis
2.100 2.080 2.060 2.040 2.020 R 2.000 1.980 1.960 20 °C
1.940
10 °C
1.920
0 °C
1.900 0
5
10
15
20
25
WS (m/sec)
Figure 14.11 Polarization ratio (R) as a function of wind speed (WS) with sea surface temperature as parameter. Salinity is 34 psu.
true polarization only exhibits a marginal dependence on salinity and temperature: R varies between 2.00 and 2.09 for SST ranging from 0–30° and salinity ranging from 0–38 psu. The variations are typically much less for realistic conditions where approximate temperature and salinity values for a given area are known (from climatology and from other measurements). For example, for SST = 21 ± 1°C and for S = 35 ± 1 psu, R varies between 2.061 and 2.068 corresponding to a 0.3% variation. Figure 14.11 shows a much stronger dependence on wind speed with R variations from 2.06 down to 1.94 for wind speeds between 0 and 20 m/s (20°C and 34 psu), that is, a 6% variation. Hence, if the wind speed is known, the true polarization ratio (R ) can be estimated with good fidelity. By measuring the local ratio (R ′), θ can then be found, and finally having this, the true vertical brightness temperature is found using the formulas shown earlier. Similarly, the true horizontal brightness temperature may be found. Simple Example with No Measurement Errors
Consider the following example: • S = 34 psu; • SST = 20°C;
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• WS = 10 m/s.
From the ocean model is then found: • TBV = 132.65K; • TBH = 66.40K; • R = 1.998.
Assuming a 10° Faraday rotation, the measured (local) brightness temperature values are found to be: • T BV′ =130.65K; • T BH ′ = 68.40K.
If these values are used without correcting for the Faraday rotation, the retrieval would be incorrect. The H-pol value points towards lower salinity while the V-pol value points towards higher salinity (bearing in mind that it is steadily assumed that the wind speed is known from other sources). The measured local polarization ratio is R ′ = 1.910, the true polarization ratio R is known as the wind speed is known, so the Faraday rotation is found from (14.4) to be θ = 10.02°, and from (14.2): TBV = 132.65K, meaning that the correct value of the 1.4-GHz vertical brightness temperature is recovered, and good quality geophysical parameters may be found. 14.7.4
Consequences for Instrument Design
Note that in order to correct for Faraday rotation, the radiometer system must measure both vertical and horizontal polarizations. This doubles the number of receivers (weight and power consequences) and requires the feeds to be dual polarized (design complexity but marginal influence on weight and power). The antenna reflector serves both polarizations without problems. It is noteworthy that a dual polarized system actually is optimum for the combined sea salinity/soil moisture mission as this solves the problem that basically sea salinity is primarily dependent on vertical polarized measurements while the optimum polarization for soil moisture is horizontal. 14.7.5
Circumventing the Problem by Using the First Stokes Parameter
As it is obvious from the previous discussion, the radiometer needs to measure both the vertical and the horizontal polarizations and by the addition of those
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Microwave Radiometer Systems: Design and Analysis
we have the first Stokes parameter [see (7.4)]. This parameter represents the total power in the electrical field, and it is totally invariant to Faraday rotation. Hence, if the geophysical parameters in question (here salinity) can be retrieved as well from the first Stokes parameter as from the vertical polarization, the Faraday problem is solved and need no further concern. This is largely the case: Salinity is found from the first Stokes parameter with good sensitivity, but the influence of wind is slightly larger. Thus we are faced with a choice: having to correct for both wind and Faraday each with their uncertainties (see Sections 14.7.2 and 14.7.3), or just correcting for the wind with a slightly larger uncertainty (first Stokes). There is more information about this in [21].
14.8 Other Disturbing Factors: Space and Atmosphere As already mentioned in Section 14.7, which deals with Faraday rotation in some detail since this effect has important consequences for instrument design, there are other disturbing factors that must be taken into account in order to obtain correct measurements of the radiated brightness temperature: space radiation and atmospheric effects. They will only be mentioned briefly here as the effects and the way to correct for them has no consequences for the design of the L-band radiometer—which is the subject of this chapter—although there may be important consequences for the data processing once the instrument is flying in space. More detailed information can be found in [22–24]. 14.8.1
Space Radiation
Microwave power emitted from space will generally enter the antenna main beam through reflection in the sea surface. Three contributions must be considered: 1. The cosmic radiation is isotropic at a constant level of 2.8K, and this bias does not affect measurement accuracy. 2. The galactic noise exhibits a great variation, depending on whether the antenna beam reflected in the sea surface looks toward the galactic pole or the galactic center (0.8K and 16K, respectively, at 1.4 GHz). This effect must certainly be taken into consideration. Corrections must be carried out on the measured data, which is possible as the galactic noise is well mapped. 3. Sun glint. The Sun is a very intense microwave emitter, with a brightness temperature dependent on solar activity, but always on the order of 100,000K or more at the frequencies in question here. Direct Sun reflection in the sea surface must be avoided, which is best done by
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choosing an early morning, Sun-synchronous, near polar orbit, for example, a 6 a.m. orbit. This, in short, means that the equatorial ascending passing takes place at sunrise, and the Sun will be almost 90° away from the look direction of the radiometer (forward-looking assumed). However, this is only a crude assessment, and at high latitudes—additionally bearing in mind that the radiometer has a certain swath width, and that under rough sea surface conditions, scattered solar radiation will be received from directions away from the specular direction—some pixels will probably be contaminated by reflected Sun radiation. This requires detailed analysis and pixel flagging as part of the data processing once the instrument is flying. 14.8.2
Atmospheric Effects
Absorption by water vapor is generally of great concern within microwave radiometry. However, for the low frequencies considered here, this effect can be neglected. Also oxygen contributes to the atmospheric effects. The loss and reradiation due to oxygen contributes around 4.5K to the received brightness temperature, and must be corrected for. Moreover, the contribution is dependent on surface pressure and temperature, but with a low sensitivity, which makes it easy to correct. Typical clouds and rain rates give very low contributions and can be neglected (see [25].
14.9 Summary A sea salinity/soil moisture sensor with a 1.4-GHz push-broom radiometer system as the core instrument has been described. The major characteristics of the system are: • Antenna aperture: 10m; • Polarization: vertical and horizontal; • “Scan” angle: ±18°; • Swath width: 530 km; • Footprint: 36 × 60 km (47 km average); • Number of channels: 21; • Integration time: 6.4 seconds.
The system senses the Earth from an early (6 a.m.) morning Sun-synchronous 800-km orbit, and 2 × 21 = 42 noise-injection radiometers are used. The detailed characteristics are:
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Microwave Radiometer Systems: Design and Analysis
• Frequency: 1,404–1,423 MHz • Noise temperature: 170K • Sensitivity: 0.08K (for 6.4-second integration)
The radiometer system will consume 112W of prime power (84W for receivers, 10W for data handling, and 18W for power supply). The main antenna dimensions are: • Reflector size: 10 × 18.6m; • Focal length: 13.2m.
The total system weight is assumed to be 392 kg (150 kg for antenna, 210 kg for feeds, 21 kg for receivers, 11 kg for miscellaneous electronics + calibration). The 1.4-GHz radiometer system can measure sea salinity (S ) to better than 0.3 psu, provided that sea surface temperature (SST ) is known to within 0.3°C and wind speed (WS ) to within 1 m/s. This resolution in the salinity measurement corresponds to a snapshot measurement over the 47-km footprint. Spatial or time averaging is possible in order to improve radiometric resolution as sea salinity in the open ocean is generally a slowly varying parameter both in time and space. Averaging to 100-km ground resolution enables close to a 0.1-psu resolution in salinity measurements. The 1.4-GHz radiometer system is well equipped for soil moisture measurements over land. The radiometric resolution is ample, and the 50-km ground resolution respectable—fitting well the resolution of present climatology and meteorology models, for which the L-band data will be an important input.
References [1]
Klein, L. A., and C. T. Swift, “An Improved Model for the Dielectric Constant of Sea Water at Microwave Frequencies,” IEEE Trans. on Antennas and Propagation, Vol. 25, No. 1, 1977, pp. 104–111.
[2]
Hollinger, J. P., “Passive Microwave Measurements of Sea Surface Roughness,” IEEE Geoscience Electronics, Vol. 25, No. 2, 1971, pp. 165–169.
[3]
Sasaki, Y., et al., “The Dependence of Sea-Surface Microwave Emission on Wind Speed, Frequency, Incidence Angle, and Polarization over the Frequency Range from 1–40 GHz,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 25, No. 2, 1987, pp. 138–146.
[4]
Blume, H. -J. C., and B. M. Kendal, “Passive Microwave Measurements of Temperature and Salinity in Coastal Zones,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 20, No. 3, 1982, pp. 394–404.
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[5] Blume, H. -J. C., B. M. Kendall, and J. C. Fedors, “Measurement of Ocean Temperature and Salinity Via Microwave Radiometry,” Boundary-Layer Meteorology, Vol. 13, 1978, pp. 295–308. [6] Blume, H. -J. C., et al., “Radiometric Observations of Sea Temperature at 2.65 GHz over the Chesapeake Bay,” IEEE Trans. on Antennas and Propagation, Vol. 25, No. 1, 1977, pp. 121–128. [7] Wilson, W. J., et al., “L/S-Band Radiometer Measurements of a Saltwater Pond,” IEEE Proc. of IGARSS’02, 2002, pp. 1120–1122. [8] Champs, A., et al., “Sea Surface Emissivity at L-Band: Derived Dependence with Incidence and Azimuth Angles,” Proc. of EuroSTARRS, WISE, and LOSAC Workshop, ESA SP-525, 2003, pp. 105–116. [9] Schmugge, T. J., “Remote Sensing of Soil Moisture: Recent Advances,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 21, No. 3, 1983, pp. 336–344. [10] Gudmandsen, P., N. Skou, and B. Wolff, (eds.), Spaceborne Microwave Radiometers, Final Report, ESTEC Contract No. 4964/81/NL/MS/(SC), Electromagnetics Institute, Tech. University of Denmark, R 267, 1983. [11] Ruf, C. S., “Vicarious Calibration of an Ocean Salinity Radiometer from Low Earth Orbit,” American Meteorological Society, J. of Atmospheric and Ocean Technology, Vol. 20, No. 11, 2003, pp. 1656-1670. [12] Fischman, M. A., and A. W. England, “Sensitivity of a 1.4 GHz Direct-Sampling Digital Radiometer,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 37, No. 5, 1999, pp. 2172–2180. [13] Rotbøll, J., S.S. Søbjærg, and N. Skou, “A Novel L-Band Polarimetric Radiometer Featuring Subharmonic Sampling,” Radio Science, Vol. 38, No. 3, 2003, pp. 11-1–11-7. [14] Pontoppidan, K., and N. Skou, Microwave Radiometry Study Concerning Push-Broom Systems, Final Report, ESTEC Contract NO. 6374/85/NL/GM(SC), Vol. 1: Electromagnetics Institute, R 332, Vol. 2: TICRA A/S, 1986. [15] Skou, N., and S. S. Kristensen, “Comparison of Imagery from a Scanning and a Pushbroom Microwave Radiometer,” IEEE Proc. of IGARSS´91, 1991, pp. 2107–2110. [16] Frater, R. H., and D. R. Williams, “An Active ‘Cold’ Noise Source,” IEEE Trans. on Microwave Theory and Techniques, Vol. 29, No. 4, 1981, pp. 344–347. [17] Forward, R. L., and T. C. Cisco, “Electronically Cold Microwave Artificial Resistors,” Trans. on Microwave Theory and Techniques, Vol. 31, No. 1, 1983, pp. 45–50. [18] Randa, J., L. P. Dunleavy, and L. A. Terrell, “Stability Measurements on Noise Sources,” IEEE Trans. on Information and Measurement, Vol. 50, No. 2, 2001, pp. 368–372. [19] Hollinger, J. P., and R. C. Lo, Low-Frequency Microwave Radiometer for N-ROSS, Large Space Antenna Systems Technology, NASA Conference Publication 2368, 1984, pp. 87-95. [20] Svedhem, H., Ionospheric Delay and Faraday Rotation at Microwave Radiometer Frequencies, ESTEC Report TRI/075/HS/mt, 1986. [21] Skou, N., “Faraday Rotation and L-Band Oceanographic Measurements,” Radio Science, Vol. 38, No. 4, 2003, pp. 24-1–24-8. [22] Yueh, S. H., et al., “Error Sources and Feasibility for Microwave Remote Sensing of Ocean Surface Salinity,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 39, No. 5, 2001, pp. 1049–1059.
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[23] Le Vine, D. M., and S. Abraham, S., “The Effect of the Ionosphere on Remote Sensing of Sea Surface Salinity from Space: Absorption and Emission at L Band,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 40, 2002, pp. 771–782. [24] Le Vine, D. M., and S. Abraham, “Galactic Noise and Passive Microwave Remote Sensing from Space at L Band,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 42, 2004, pp. 119–129. [25] Skou, N., and Hoffmann-Bang, “L-Band Radiometeres Measuring Salinity from Space: Atmospheric Propagation Effects,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 43, No. 10, 2005, pp. 2210–2217.
15 Examples of Synthetic Aperture Radiometers 15.1 Introduction This chapter gives a brief discussion of the trades involved in designing a synthetic aperture radiometer for Earth remote sensing and then illustrates the concepts with two synthetic aperture radiometers. The first is an existing aircraft sensor called, ESTAR. ESTAR played an important role in the development of this technology for remote sensing and provided data to demonstrate the potential for remote sensing of soil moisture from space. A brief overview is given of the hardware and the techniques employed for image reconstruction and calibration. An image is shown from the soil moisture experiment at the Walnut Gulch Watershed an experiment that was critical in demonstrating the viability of this technology. The second example is a sensor called HYDROSTAR. This is an instrument that was proposed for remote sensing from space. Although HYDROSTAR was never actually flown, it does illustrate the potential of aperture synthesis for remote sensing from space. Design parameters are given together with expected performance. This instrument is similar in principle to the aircraft instrument, ESTAR; however there are many ways in which aperture synthesis could be implimented in space. In fact, at the time of this writing, a mission called SMOS that uses synthesis with small antennas arranged in the form of a Y is being built by the European Space Agency (ESA) for remote sensing of soil moisture and ocean salinity from space.
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15.2 Implementation of Synthesis The primary penalty paid for employing aperture synthesis is a decrease in signal to noise for each measurement (baseline) compared to a filled aperture. This occurs because each measurement in the synthesis array is presumably made with antennas much smaller than a single antenna with resolution equivalent to that of the synthesized array (e.g., to take advantage of array thinning that is possible with synthesis). The result is a potential worsening of radiometric sensitivity (RMS noise) in the image [e.g., see (8.7)]. However, since no scanning is necessary in aperture synthesis, the time per measurement can be increased, which improves the time-bandwidth product. Also, the image is comprised of many measurements (baselines). Because of these two factors, it is possible even with minimum redundancy configurations (configurations with a minimum of repeated baselines) to approach the radiometric sensitivity of an equivalent real aperture radiometer [1, 2]. The art in applying aperture synthesis is finding configurations that permit substantial thinning of the array (e.g., to save mass in remote sensing from space) and at the same time achieving radiometric sensitivity commensurate with the science requirements for the observable. In practical remote-sensing situations observation, time is limited by the motion of the spacecraft (about 7 km/sec in low Earth orbit) or by the time constant of the observable. Figure 8.3 illustrated a concept suitable for remote sensing from geosynchronous orbit where, because there is no relative motion of the spacecraft, the time to form an image and the size of the synthesis array (number of baselines) is limited by the time constant of the geophysical observable. On the other hand, Figure 15.1 illustrates two configurations that are practical when the spacecraft is moving rapidly with respect to the surface as, for example, in remote sensing from low Earth orbit. The example in Figure 15.1(a) is a combination of a real and a synthetic aperture antenna. The real antennas are “stick” antennas oriented with their long axis in the direction of motion. The stick antennas produce a narrow fan beam with good resolution along track and essentially no resolution in the across track dimension. Resolution across track is obtained using aperture synthesis. A configuration of this type can reduce the antenna aperture needed in space by about 80% and still obtain radiometric sensitivity comparable to a real aperture [1–3]. This is the configuration used in the aircraft prototype ESTAR and proposed for HYDROSTAR, the instrument proposed for measuring soil moisture from space. The example in Figure 15.1(b) is a concept for employing aperture synthesis in both dimensions. In this example small antennas are arranged along the arms of a cross and the necessary baselines are obtained by making measurements between all independent pairs of antennas. This configuration can have spatial resolution comparable to a filled aperture with the dimensions similar to those of the arms. The compromise one makes in using
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(a)
Small antennas
(b)
Figure 15.1 Two configurations showing how aperture synthesis might be implemented for remote sensing from space. (a) A hybrid that uses aperture synthesis only in the across-track dimension. (b) A configuration employing small antennas along the arms of a “cross” that uses aperture synthesis in both dimensions.
aperture synthesis in a configuration such as this is a potential loss of radiometric sensitivity because the array is so highly thinned. There is also increased processing complexity because the number of products that must be measured grows rapidly as the array is thinned. However, the advantage in terms of weight and mechanical simplicity of such a senor can be very important. Many variations on this theme are possible. Aircraft instruments with antennas arranged in “Y” and “U” configurations are being built [4, 5] and an instrument in space is being built using the “Y” configuration [6]. The “Y” is an important configuration because it minimizes the number of redundant baselines, although it is not
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necessarily the most efficient in terms of the number of antennas needed for a given resolution.
15.3 Airborne Example: ESTAR 15.3.1
Hardware
To illustrate how aperture synthesis can be implemented in practice, the airborne sensor called ESTAR will be used as an example. This is an existing instrument that is important because it helped to demonstrate that aperture synthesis was practical for passive microwave remote sensing and in particular for sensing soil moisture and ocean salinity. ESTAR was developed at NASA’s Goddard Space Flight Center in Greenbelt, Maryland, and at the University of Massachusetts in Amherst, Massachusetts [7, 8]. It is an L-band radiometer in the hybrid configuration shown in Figure 15.1(a). It was designed for remote sensing of soil moisture where the need for large apertures is greatest because the measurement of soil moisture is best done at long wavelengths. (Long wavelengths are needed to penetrate into the soil and through the vegetation canopy.) The hybrid configuration was adopted because it is practical for application in space and because it involves relatively simple processing compared to configurations that employ thinning in both dimensions. The real antennas that comprise the thinned array in ESTAR are linear arrays of horizontally polarized dipoles. In operation, these antennas are oriented with their long axis in the direction of motion [Figure 15.2(a)]. The stick antennas produce a narrow fan beam with good resolution along track but essentially no resolution in the across track dimension. The resolution across the track is obtained using aperture synthesis. ESTAR has five stick antennas that are spaced at integer multiples of a half-wavelength (about 10.6 cm at the center frequency of 1.413 GHz). Each stick antenna consists of a row of eight dipoles [Figure 15.2(b)]. With this configuration of sticks employed in ESTAR, it is possible to obtain seven unique baselines plus one at the zero spacing. The result is a synthesized beam with a width of about ±4° at nadir in the cross track dimension. The resolution in the along track dimension is determined by the real aperture and is about ±8°. An image is formed by placing the across-track images edge to edge during successive integration periods. This is similar to a raster scan in a conventional cross-track scanner except that in the synthesis radiometer the cross-track image is created in software and there is no mechanical motion of the sensor. The actual antenna hardware is shown in Figure 15.3. The instrument is shown in Figure 15.3(a) as it was installed on an Orion P-3 aircraft in preparation for test flights. The white structure at the bottom of the instrumentation box is a radome covering the stick antennas. The RF circuitry is housed inside
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Resolution cell (a)
R.F. front end
Complex correlator
Local oscillator and calibration source
(b)
Figure 15.2 (a) The ESTAR array consists of stick antennas oriented in the direction of flight. (b) The stick antennas are linear arrays of horizontally polarized dipoles spaced at multiples of a half-wavelength.
the box. The correlators, the computer, and the power supplies are mounted on racks inside the airplane’s passenger compartment. In Figure 15.3(b), the same box is shown with the radome removed (and upside down) so that the individual stick antennas can be seen. ESTAR has five antennas spaced in multiples of λ/2. With the configuration shown in Figure 15.3 (antennas at positions N λ/2 with N = 0, 1, 3, 6, 7), it is possible to obtain all baselines which are multiples of λ/2 from 0 to 7.
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(a)
(b)
Figure 15.3 (a) The ESTAR antenna array. (b) The ESTAR array with the radome removed so that the stick antennas can be seen. At the top is the box mounted in the bomb bay of an Orion P-3 ready to fly.
The dimensions of this particular instrument were determined by the size of a radiometer it replaced on the aircraft because it had to fit into the same space. It was not intended to be an optimum structure. In fact, among the interesting problems in aperture synthesis are issues of optimization such as: (1) determining the configuration that gives the maximum baseline with a given number of antennas; or, conversely, (2) determining the minimum number of antennas needed for a given maximum baseline. In each of these problems, the spacing is a multiple of a fixed minimum and it is required that all baselines are measured at least once. For example, if size were not a problem what would be the optimum configuration for ESTAR if it had six antennas and wanted maximum resolution? Solutions to these problems can be found by trial and error, and there tend to be many solutions. Unique solutions have been found only for a few very simple special cases. Hence, there is a lot of variability possible even in optimum designs.
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The raw data output in ESTAR consists of seven complex voltages (the in-phase and quadrature output from the correlators at each of the seven independent, nonzero baselines), plus a total power measurement at the zero spacing. These can be expressed analytically using (8.3) specialized to the case of synthesis in one-dimension. Denoting the measurements with the integer m (i.e., m = 0, 1, 2, …, 7) corresponding to the length of the baseline in multiples of λ/2, and substituting into (8.3), the correlator output, V(m), can be written in the form: V (m ) = C m
+π 2
∫T ( θ )P (m , θ )e
jmπ sin ( θ )
d θ + Dm
(15.1)
−π 2
where θ is the incidence angle in the across-track dimension measured from nadir, T(θ) is the microwave “brightness” temperature of the scene, and P(m, θ) is the product of the “voltage” patterns of the two antennas employed in this baseline. When the antennas are identical, P(m, θ) reduces to the conventional “power” pattern of the antenna and is proportional to its gain. The constant Cm is a scale factor which includes the gain of the RF system and must be determined as part of the calibration procedure. The coefficients Dm are constants which were added in the analysis of ESTAR to accommodate the circuitry used for the zero spacing channel (a noise injection radiometer) and to account for biases (offsets) present in the early versions of the correlator circuitry. Another reason for including the offsets is the possibility of coupling between receivers as explained by Corbella et al [9]. The Dm are small except in the case of the zero-spacing and are determined during calibration. Equation (15.1) is complex and the coefficients C and D are in general complex (representing phase differences in the signal paths for each receiver). In the ideal case when P(m, θ) and Cm are independent of m, a change of variables such as employed to write (8.5) permits (15.1) to be written in the form of a Fourier transform. In this case it is possible, at least in principle, to invert the transform to find T(θ) in terms of the correlator outputs V(m) and biases, Dm. This is the theoretical basis for aperture synthesis. However, in the actual case, several obstacles must be overcome to achieve the inversion. First, V(m) is not known at a continuum of points spanning the desired spectral domain. For example, in ESTAR V(m) is known only at a relatively small subset of discrete points corresponding to the seven baselines. Second, the unknown scale factors, Cm, are not known a priori and may be different for each baseline (because the gains and phase paths are different) and may change (because gains drift). Third, the individual antenna patterns are not truly identical (e.g., because of mutual coupling and coupling to the structure). In ESTAR the P(m, θ) are different for each antenna pair [10]. Finally, the offsets Dm may not be
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zero and must be determined for each baseline. One procedure to account for these deviations from the ideal is to perform a numerical inversion of (15.1) using parameters of the instrument measured in the laboratory. This procedure is outlined in the following sections. 15.3.2
Image Reconstruction
In the case of ESTAR an inversion was obtained by replacing the integral in (15.1) by its approximating sum and, thereby, reducing (15.1) to a matrix of algebraic equations. In this procedure, the scale factors, Cm, are written Cm = Co αm, where Co is a constant, independent of m, which converts the ESTAR output to units of brightness temperature. The αm represent differences in gain and phase among channels (baselines). Absorbing the unknowns αm into the matrix, G, (15.1) becomes: V k = C 0 ∑ i G kiT i + D k
(15.2)
where the symbol Σ i means that the sum is over the index “i”. The odd values of k (i.e., k = 2m + 1) correspond to the in-phase output of the correlator [real part of (15.1)] in which case G ki = αk P (m , θ i ) cos[m π sin ( θ i )]∆θ
(15.3a)
and the even values of k (i.e., k = 2m) correspond to the quadrature output of the correlator, in which case G ki = αk P (m , θ i ) sin[m π sin ( θ i )]∆θ
(15.3b)
In the case of the zero spacing radiometer, m = 0, k = 1 and (15.3a) applies. In ESTAR there are 15 values Vk (one for the zero spacing and two each for the seven nonzero baselines). In this case, Gki is a matrix with 15 rows (K = 15) and N columns where N is the number of terms in the approximating sum for the integral in (15.1). The number, N, is somewhat arbitrary. In ESTAR, N = 91 which corresponds to ∆θ = 2° in the approximating sum. Compare this with the synthesized beam which has a beam width (distance between zeros) of about 8° and is an indication of the resolution of the instrument (see Section 8.3). The feature that makes (15.2) useful is that the Gki are measurable parameters of the instrument. They are the impulse response of the sensor and can be measured in a conventional antenna chamber by looking at a point source. In such a situation, N is determined by the number of positions at which the point source is observed.
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Assuming that the Gki have been measured, an image is formed by solving (15.2) for the N values of Ti. The data are the K measurements, Vk. This system of equations is underdetermined (N > K ); however, a solution can be found by imposing a secondary condition (e.g., minimizing the square error when compared to the ideal solution). In particular, the matrix equation, V = GT where G is N × K with N > K, has a minimum least square solution T ′ of the following form [11]:
{
T ′ = G t [GG t ]
−1
}V
(15.4)
where G t[GG t ]−1 is called the “pseudo” inverse (and the superscript “t” denotes the transpose of the matrix). In most of the work done with ESTAR, image reconstruction in the form of Equation 15.4 has been employed. The image is:
{
T = G t [GG t ]
−1
}[V − D ] C
0
(15.5)
In (15.5), V is a vector of measured “visibilities,” G is a characteristic of the instrument (and measured in the laboratory), and D and Co are unknowns that are determined by looking at known sources during “calibration.”
15.3.3
Calibration
In an ideal system (Co = 1 and Dk = 0) the rows of G are just the instrument output, V, when the input, T, is a point source (a vector with zeros everywhere except at one position, θi = θi = n ). Hence, the elements, Gki, can be measured in the laboratory by letting the instrument view a point source and then moving the point source sequentially to positions from −90o < θ < 90o so as to move through the columns of G. In practice this is done in an antenna chamber by putting a source at one end, and rotating the antenna array at the other end while continuously monitoring the output, Vk, from each of the channels. One must also account for system biases, D, and the background radiation emanating from the chamber. One way of doing this is to take the difference of measurements, first with the source on and again with the source off. For example, assume that the background is constant (a good assumption if the measurements are made in an antenna chamber). Letting this constant be TBB, one obtains the following with the source off: V k (Off
) = C oT BB ∑ iG ki + D k
(15.6a)
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When the source is on, the instrument also receives radiation from the source Ts. Thus: V k (On ) = C o [T BB ∑ i G ki + T s G kn ] + D k
(15.6b)
where it is assumed the source is in position, n. Taking the difference, one obtains G kn = (1 C oT s
){Vk (On ) − Vk (Off )}
(15.7)
By changing the position “n” of the source relative to the antenna array, one can determine all the columns of Gki. For example, ESTAR uses 91 positions of the point source, corresponding to source positions from +90o to –90° in two-degree increments. The ESTAR instrument records the output from all the baselines simultaneously. Hence, in the anechoic chamber measurements are actually made of all the k-rows of Gki at the same time. This is important because it means that relative differences between channels are correctly represented even though the constants, Co and Ts, may not be known. Phase and gain introduced in the RF path are removed using an internal reference (calibration) source. One possibility is a stable noise source with a switch at the antenna terminals that periodically switches from the antennas to the noise source. While in the “calibrate” mode the instrument output, Vk, is proportional to the complex gain of each correlator channel [in effect proportional to the αk in (15.3)]. By dividing the raw ESTAR data by the output signal when in the calibrate mode, the αk are in effect canceled and only one gain constant, Co, remains to be determined. A similar procedure, although with a more complex distribution network has been adopted for the spacecraft sensor being developed for the SMOS mission [4, 12]. The remaining step is to determine the constants Co and Dk in (15.2). This can be achieved by viewing two scenes with known brightness temperature. The constants are determined by comparing the measured output Vk with the theoretical output of the test scene. This is analogous to calibration in a conventional total power radiometer, except that “calibration” constants must be determined for several channels (one for each Vk). In practice, a linear regression is used in which values of Co and Dk are chosen which give an optimum fit of the measured visibilities to the theoretical values. For example, test scenes used for ESTAR have been scenes such as a blackbody (e.g., the antenna chamber) and water (e.g., a large lake). The former is warm (300K) and the later cool (around 100K) at L-band.
Examples of Synthetic Aperture Radiometers 15.3.4
207
Discussion
Let G ′ = Git [GG t ]−1 denote the pseudo-inverse and let Vk′ be a set of visibilities normalized by subtracting Dk and dividing by Co as in (15.5). Then, the solution of (15.1) is: T i ′= ∑ k G ki′V k ′
(15.8a)
= ∑ j [G ′G ]ij T j
(15.8b)
where Tj is the matrix of brightness temperatures representing the actual scene. In the ideal case (identical antennas and receivers), the rows of [G ′G ] are identical but shifted and (15.8b) has the form of a discrete-valued convolution: the convolution of the ith row of the matrix [G ′G ] with the scene Tj. In this case (15.8b) is the discrete analog of the conventional expression for the response of an antenna with power pattern P(θ) to a thermal source (incoherent radiation) with effective temperature T(θ) [13]: T ′( θ ) = ∫ P ( θ − θ ′ )T ( θ ′ )dθ ′
(15.9)
Writing (15.9) as a sum (i.e., replacing the integral by its approximating sum) and comparing with (15.8b), one sees that each row of [G ′G] corresponds to P(θ – θ′) at a particular value of θ. In other words, the rows of [G ′G] represent the power pattern of the “synthesized” antenna. Figures 15.4 through 15.6 show examples for an ideal ESTAR. Figure 15.4 is a plot as function of θ of the numbers in the rows of the matrix G corresponding to a baseline with spacings of 2λ and 7λ/2 (m = 4 and 7). The solid curve is the even term (in phase) and the dashed curve is the odd term (quadrature). Examples of the synthesized antenna pattern are shown in Figure 15.5. These are examples of the rows of [G ′G]. Curves are shown for the rows corresponding to viewing angles of 0°, ±20°, and ±30°. For comparison the ideal pattern of one of the stick antennas (a linear array of eight dipoles) is shown in Figure 15.6 plotted with the synthesized beam at nadir (0°). The two have been normalized to have the same peak value. The pattern (power pattern) of the stick is approximately ±8° wide at the half-power points (a linear array of eight dipoles spaced λ/2 apart). The pattern of the nadir pointing beam synthesized by ESTAR is narrower at half-power by about a factor of two (±4°). This is a characteristic of interferometers that is possible because of the complex conjugate baselines. Notice the large sidelobes of the synthesized pattern. This is also a characteristic of aperture synthesis. The sidelobes can be reduced at the expense of resolution (broadening of the main beam) by weighting the visibilities during
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1 0.5
Amplitude (relative)
0 −0.5 −1 −50
−40
−30
−20
−10
10
20
30
40
50
−40
−30
−20
10 −10 0 Angle (degrees)
20
30
40
50
0
1 0.5 0 −0.5 −1 −50
Figure 15.4 Rows of the matrix G for a spacing of (a) 2λ and (b) 7λ/2 corresponding to m = 4, 7 respectively in (15.1). The solid line is the inphase term and the dashed line is the quadrature term.
image reconstruction [11]. Also notice (see Figure 15.5) that not all of the synthesized beams are identical. Noticeable broadening occurs at large viewing angles. Examples for the actual ESTAR instrument are shown in [8]. If one limits the field of view of the synthesized image to angles for which the synthesized beams are essentially identical, then one can think of the image reconstruction described above as a scan of an effective antenna beam (e.g., the solid line shown in Figure 15.6) across the scene. The important point is that this scan takes place in software (i.e., instantaneously) and one does not have to account for scan time as in a conventional cross-track scanning radiometer. 15.3.5
Example of Imagery
The ESTAR instrument was an important step in demonstrating the potential of aperture synthesis for passive microwave remote sensing at long wavelengths, and it played an important role in the development of remote sensing of soil moisture. It provided data to support development of algorithms to retrieve soil moisture in experiments such as at the Little Washita Watershed in 1992 [8, 14]
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1
0.8
Amplitude (relative)
0.6
0.4
0.2
0
−0.2
−0.4 −50
−40
−30
−20
−10
0 10 Angle (degrees)
20
30
40
50
Figure 15.5 Examples of the synthesized antenna pattern. Patterns are shown with pointing angles (boresite) of 0, ±20 and ±30 degrees. The units on the ordinate are relative amplitude.
and the Southern Great Plains experiments in 1997 and 1999 [15, 16]. It also played an important role in demonstrating the potential for remote sensing of sea surface salinity in experiments such as the Delaware Coastal Current Experiment [17]. Figure 15.7 is an image made by ESTAR in Viginia, south of the border with Maryland. The Chesapeake Bay is to the left and the Atlantic Ocean is to the right and the land area is called the “Delmarva” Penninsula. The axes are labelled in latitude (abscissa) and longitude (ordinate). As a reference, 37.5°N latitude is approximately due east of Richmond, Virgina. Images such as this were made as part of calibration and instrument checks prior to major campaigns such as the Southern Great Plains experiments mentioned earlier. This is a good region to test an imaging L-band radiometer because of the high radiometric contrast between land and water and the abundance of detail to test image quality. This image is a composite of data collected on five different occasions from September 1995 to August 1999. The regions can be distinguished by the slightly different mean brightness temperatures. (See [18] for a color
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Microwave Radiometer Systems: Design and Analysis
1
0.8
Amplitude (relative)
0.6
0.4
0.2
0
−0.2
−0.4 −50
−40
−30
−20
−10
0 10 Angle (degrees)
20
30
40
50
Figure 15.6 Comparison of the synthesized beam (solid line) with the power pattern of a linear array (dashed line) of similar size (7 half-wavelengths).
image.) Each subimage consists of about four lines flown East-West at an altitude of 2,000 feet. The ESTAR brightness temperature map has been superimposed on the geographical map indicating the peninsula boundaries and streams. Another example is shown in Figure 15.8. This is an example from measurements made at the USDA’s Walnut Gulch watershed near Tombstone, Arizona, during soil moisture measuring experiments in 1991 [8, 14]. This was an important experiment because it demonstrated that images of scientific quality could be obtained with this technique. ESTAR made two flights during this experiment, one on August 1 and again on August 3. Prior to August 1, a small localized rainfall event occurred at the watershed very near the center of the study area. On the afternoon preceding the second flight (August 3), a large thunderstorm occurred over the watershed centered near the western edge of the study area (left-hand side of Figure 15.8). This storm was localized to the western two-thirds of the watershed. The eastern edge of the watershed received very little rainfall during this storm. The rainfall patterns are evident in the image. The effect of the small, isolated rainfall event prior to the flight on August 1 is
Examples of Synthetic Aperture Radiometers
211
Brightness [K] 71
103
131 145 159 173 187 201 215 229 243 257 271 285 299 313
37.70
Latitude
37.65
37.60
37.55
37.50 −75.90
−75.80
−75.70
−75.60
Longitude Figure 15.7 ESTAR images of the Delmarva Peninsula. This is a composite from five different flights conducted from 1995 to 1999.
clearly evident near the center of the image for August 1 (top). Similarly, the left side of the image for August 3 clearly shows the effects of the thunderstorm in the western portion of the watershed. Comparison of the two images shows a dramatic decrease in brightness temperature on the western edge of the watershed (left) due to the rainfall and an increase in brightness temperature on the eastern side of the watershed (right) indicative of the drying which took place over this portion of the watershed between the two flights. For a quantitative comparison of the ESTAR data with ground truth, see [8, 16], and for a color version of this image, see [8].
15.4 Spaceborne Examples 15.4.1
HYDROSTAR
A synthetic aperture radiometer designed to obtain global maps of soil moisture and sea surface salinity from space was proposed to NASA in the late 1990s in response to a call for Earth System Science Pathfinder missions. The instrument was called HYDROSTAR and was patterned after ESTAR. It employed
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August 1
August 3
Brightness [K] 195
285
Figure 15.8 ESTAR images of the Walnut Gulch Watershed during flights on August 1 and August 3, 1991. The cool temperatures are an indication of an increase in the moisture in the soil following a thunderstorm prior to the flight on August 3.
aperture synthesis in the across track dimension, operated at L-band with horizontal polarization, and employed electronics and calibration schemes validated by ESTAR. By employing aperture synthesis in the cross-track dimension, the aperture needed in space was reduced to less than 20% of that needed for a filled aperture of the same resolution, and the need for mechanical or electrical motion (scanning) was eliminated. The salient features of HYDROSTAR are summarized in Table 15.1. The science objectives of the HYDROSTAR mission were primarily driven by the requirements for the measurement of soil moisture. Hence, the mission called for observations at a constant local time (Sun synchronous orbit) with a revisit time with global coverage of 3 days or less. The HYDROSTAR mission called for a 670-km orbit with a 6 a.m. equatorial crossing and it achieved the desired revisit time by processing in the cross track dimension to ±35°. HYDROSTAR is shown in its deployed configuration in Figure 15.9. The instrument was composed of three major subsystems: the antenna system, which includes the stick antennas and the deployment structure, the RF system, which includes the front end and other radiometer RF electronics, and the signal
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213
Table 15.1 Parameters of the Proposed HYDROSTAR Mission Mission
Instrument
Coverage
Global
Frequency
Revisit
3 days
Polarization
Horizontal
Orbit
670 km
FOV
±450 km
Sunsynchronous
Pointing
Nadir
6 a.m. ascending
L-band (1.413 GHz)
Dimensions
5.8 × 9.5m
Antennas
16 waveguide sticks
Resolution
30 km (15 km across track)
Sensitivity
1K
Accuracy
3K (or better)
Mass
500 kg
Power
350W
processing system, which includes the A/D conversion and digital correlators. All of the radiometer electronics with the exception of the RF front ends are located together near the spacecraft. The RF front ends are located at the antennas and are connected to the radiometer electronics at the spacecraft with low-loss coaxial cable. In its normal operating mode, the integration time per image is 0.5 second and a noise diode is used for internal calibration as in ESTAR. Absolute calibration is accomplished using reference scenes in a manner similar to that described above for ESTAR. HYDROSTAR employed 16 antennas arranged in a minimum redundancy. The minimum spacing is a half-wavelength and the antenna array has 90 independent baselines at integer multiples of a half-wavelength. The array spans 9.5m in the across-track dimension. Each antenna in the array is a rectangular waveguide stick 5.8m long. The waveguide has 36 slots inclined to produce horizontal polarization and cut in the narrow wall of the guide. Each stick has an along track beamwidth of 2.3° at band center corresponding to a resolution of about 30 km at nadir from the 670-km orbit. Because wave guides are narrowband devices, operation over the desired bandwidth is obtained by subdividing each stick into four resonant subarrays of nine slots, each coupled together with a flexible combining network. The antennas are fabricated in composite to minimize weight and maximize rigidity and thermal stability. The resolution across-track matches the along-track resolution at the swath edge (±35o). At nadir, the across-track resolution of the synthesized beam has a peak-to-null beamwidth of 1.2° corresponding to about 15-km resolution.
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Figure 15.9 HYDROSTAR in its deployed configuration. The synthesis array consists of 19 waveguide antennas. Each antenna is comprised of four subelements.
For launch, the antennas are folded and the array compressed. The deployment sequence on orbit is shown in Figure 15.10. For launch, the waveguides are collapsed into two wings of eight waveguides each. Each antenna consists of four subantennas and, in the stowed position, the outer segments of each waveguide are folded 180° and rest on the inner segments. To deploy the antenna array, three separate steps are required. First, the spring-loaded waveguide outer segments immediately rotate 180° and latch to their full extension. Next, each wing is rotated into the observing plane (rotated 90°). Finally, the waveguides are extended on the hinged truss to the required position. 15.4.2
SMOS
Although HYDROSTAR was a viable sensor and development proceeded to the point of testing a full-sized scale model of the antenna array, it was never built. However, a synthetic aperture radiometer has been selected by the European Space Agency (ESA) and is under development as the second Earth Explorer Opportunity Mission within ESA’s Living Planet Program. This is also an L-band instrument designed for remote sensing of soil moisture and ocean salinity. It employs aperture synthesis in two dimensions and is dual-polarized [6, 12]. The instrument in its original design, called MIRAS (Microwave Imaging
Examples of Synthetic Aperture Radiometers
215
2.
1.
3. 4.
Figure 15.10 The deployment sequence for HYDROSTAR. Deployment starts at the top left (1). The sticks unfold (2), rotate (3) and the spread to their final positions (4).
Radiometer using Aperture Synthesis), was also dual frequency (L-band and C-band); however, in the final design, only the L-band channel was kept. The mission is called SMOS (Soil Moisture and Ocean Salinity) and is scheduled for launch in 2007. Figure 15.11 is an artist’s concept of the SMOS spacecraft showing the instrument and the deployment sequence. The sensor employs an array of antennas arranged in a “Y” configuration. Each row in the “Y” consists of 21 contiguous antenna elements uniformly spaced at 0.875 wavelength. There are a total of 69 antenna elements in the array. The remaining six antenna elements are arranged in pairs between the arms in the central “hub.” The innermost element in each pair is connected to a noise injection radiometer and provides the dc value of the image (that is, the zero-space baseline). The outer element in each pair is a correlation radiometer and is also used in the image reconstruction. In the deployed position the plane of the Y is tilted with respect to nadir. The plane of the Y is tilted forward at about 32.5°. This was done in order to increase the incidence angles at the surface and thereby enhance the difference between the two polarizations. The antennas are dual-polarized and the instrument can operate in two modes: dual polarization in which it measures both
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Microwave Radiometer Systems: Design and Analysis
Figure 15.11 The SMOS mission showing the deployment sequence and the MIRAS instrument in its deployed configuration. The small circles along the arms of the “Y” are the individual antennas in the synthesis array. [Courtesy of EADS (European Aeronautic Defense and Space)–CASA Espacio and ESA.]
vertical and horizontal polarization and fully polarimetric in which the cross term is also measured. Internal calibration is provided by a distributed noise signal. Mechanically the instrument consists of the central hub and three deployable arms. Each arm consists of three sections that are folded at launch. Figure 15.11 shows the solar panels and arms as they deploy after launch and also the final configuration when fully deployed. The length of each arm is 4.0m. The effective resolution on the ground varies across the footprint because of the large range of incidence angles. On average the resolution is on the order of 43 km and the useful swath across-track is about 1,060 km. The antenna spacing and forward-looking geometry present some interesting issues for SMOS. In particular, the antenna spacing admits grating lobes in the reconstructed image so that only a portion of the field of view is useful [12]. Because of the large amount of thinning, the RMS noise in each snap shot (one integration period) is relatively large. However, because many pixels appear in more than one snap shot, averaging is possible to reduce the noise. Another interesting feature of this instrument is the use of 1-bit digital correlators for each of the baselines. This introduces additional noise, but reduces the complexity and power requirements of the correlator circuitry. It also requires a different type of radiometer for the zero spacing to provide the dc signal. As mentioned earlier, a noise injection radiometer (see Chapter 4) has
Examples of Synthetic Aperture Radiometers
217
Table 15.2 Characteristics of SMOS Mission
Instrument
Coverage
Global
Frequency
Revisit
3 days
Polarization
H & V with an option for polarimetric
Orbit
763 km
FOV
±450 km
Sunsynchronous
Pointing
32° (forward)
6 a.m. ascending
L-band (1.413 GHz)
Dimensions
4.3m per arm
Antennas
21 per arm (69 total; 0.875 λ spacing)
Resolution
30–90 km
Sensitivity
0.8–2.2K
Accuracy
3K (or better)
Mass
370 kg
Power
525W
been chosen for this application. Finally, in its deployed configuration, the sensor is very big. This makes direct measurement of its impulse response (the G-matrix discussed in Section 15.3.2) in an antenna chamber very difficult. Alternatives such as modeling from measurements of the instrument subsystems with verification by observing reference targets on orbit are being considered. The characteristics of the instrument and mission are summarized in Table 15.2. Monolithic microwave integrated circuits (MMICs) are employed for the receivers, which amplify and downconvert. The baseband signals are digitized at 1 bit and routed via optical fiber to a central processor. Approximately 3,500 complex correlations are required. The antennas are dual-polarized dipoles implemented with multilayer microstrip circuitry. They are about 16.5 cm in diameter. The estimated overall mass of the instrument is 370 kg and the power consumption is 525W. The sensor will be launched into a sunsynchronous orbit at an altitude of 763 km and is scheduled for 3 years of operation with an option to extend the mission for an additional 2 years.
References [1]
Le Vine, D. M., “The Sensitivity of Synthetic Aperture Radiometers for Remote Sensing Applications from Space,” Radio Science, Vol. 25, No. 4, 1990, pp. 441–453.
[2]
Ruf, C. S., et al., “Interferometric Synthetic Aperture Radiometery for Remote Sensing of the Earth,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 26, 1988, pp. 597–611.
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[3] Le Vine, D. M., “A Multifrequency Microwave Radiometer of the Future,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 27, No. 2, March 1989, pp. 193–199. [4] Le Vine, D. M., “Synthetic Aperture Radiometer Systems,” IEEE Trans. on Microwave Theory and Technique, Vol. 47, No. 12, December 1999, pp. 2228–2236. [5] Le Vine, D. M., M. Haken, and C.T. Swift, “Development of the Synthetic Aperture Radiometer ESTAR and the Next Generation,” Proc. Internat. Geosci and Remote Sens. Sympos. (IGARSS), Anchorage, AK, September 2004. [6] Kerr, Y., et al., “Soil Moisture Retrieval from Space: The Soil Moisture and Ocean Salinity (SMOS) Mission,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 39, No. 8, August 2001. [7] Le Vine, D. M., et al., “Initial Results in the Development of a Synthetic Aperture Microwave Radiometer,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 28, No. 4, 1990, pp. 614–619. [8] Le Vine, D. M., et al., “ESTAR: A Synthetic Aperture Microwave Radiometer for Remote Sensing Applications,” Proc. IEEE, Vol. 82, No. 12, December 1994, pp. 1787–1801. [9] Corbella, I., et al., “The Visibility Function in Interferometric Aperture Synthesis Radiometry,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 42, No. 8, 2004, pp. 1667–1682. [10] Griffis, A., “Earth Remote Sensing with an Electronically Scanned Thinned Array Radiometer,” Ph.D. dissertation, Dept. of Elec. Engin., Univ. of Mass., February 1993. [11] Tanner, A. B., “Aperture Synthesis for Passive Microwave Remote Sensing: The Electronically Scanned Thinned Array Radiometer,” Ph.D. dissertation, Dept. of Elec. Engin., Univ. of Mass., February 1990. [12] Kerr, Y. H., et al., “The Soil Moisture and Ocean Salinity Mission: An Overview” in Microwave Radiometry and Remote Sensing of the Earth’s Surface and Atmosphere, P. Pampaloni and S. Paloscia, (eds.), Zeist, the Netherlands: VSP, 2000, pp. 467–475. [13] Kraus, J. D., Radio Astronomy, New York: McGraw-Hill, Ch. 6, 1966. [14] Jackson, T. J., et al., “Large Area Mapping of Soil Moisture Using the ESTAR Passive Microwave Radiometer in Washita-92,” Remote Sens. Environ., Vol. 53, 1995, pp. 27–37. [15] Jackson, T. J., et al., “Soil Moisture Mapping at Regional Scales Using Microwave Radiometry: The Southern Great Plains Hydrology Experiment,” IEEE Trans. on Geoscience and Remote Sensing, Vol 37, No. 5, September 1999, pp. 2136–2151. [16] Le Vine, D. M., et al., “ESTAR Measurements During the Southern Great Plains Experiment (SGP99),” IEEE Trans. on Geoscience and Remote Sensing, Vol. 39, No. 8, 2001, pp. 1680–1685. [17] Le Vine, D. M., et al., “Remote Sensing of Ocean Salinity: Results from the Delaware Coastal Current Experiment,” J. Atmos. and Oceanic Tech., Vol. 15, 1998, pp. 1478–1484. [18] Le Vine, D. M., C. T. Swift, and M. Haken, “Development of the Synthetic Aperture Microwave Radiometer, ESTAR,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 39, No. 1, 2001, pp. 119–202.
Acronyms AC
Alternating Current
AF
Audio Frequency
CORRAD Correlation Radiometer DC
Direct Current
DR
Dicke Radiometer
DRO
Dielectric Resonator Oscillator
DSB
Double Sideband
DTU
Technical University of Denmark
EMC
Electro Magnetic Compatibility
ENR
Excess Noise Ratio
ESA
European Space Agency
ESTAR
Electronically Scanned Thinned Aperture Radiometer
FPGA
Field Programmable Gate Array
IF
Intermediate Frequency
IMR
Imaging Microwave Radiometer
INS
Inertial Navigation System
IR
Infrared 219
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Microwave Radiometer Systems: Design and Analysis
LAMMR
Large Aperture Multifrequency Microwave Radiometer
LF
Low frequency
LO
Local Oscillator
MIMR
Multifrequency Imaging Microwave Radiometer
MIRAS
Microwave Imaging Radiometer with Aperture Synthesis
MMIC
Monolithic Microwave Integrated Circuit
NASA
National Aeronautical and Space Administration
NIR
Noise-Injection Radiometer
NOSS
National Oceanic Satellite System
psu
practical salinity unit (= parts per thousand)
RF
Radio Frequency
S
Salinity
SMMR
Scanning Multichannel Microwave Radiometer
SMOS
Soil Moisture and Ocean Salinity
SSB
Single Sideband
SSM/I
Special Sensor Microwave / Imager
SST
Sea Surface Temperature
TEC
Total Electron Contents
TPR
Total Power Radiometer
UHF
Ultra High Frequency
WS
Wind Speed
Index Digital radiometer, 178 Digital thermometer, 50 Direct receiver, 25–26, 157–58 DSB receiver, 26–27, 40–42 Dual receiver unit, 158–59 Dwell time, 125–30, 137
Absolute accuracy, 9–11 Active cold load, 184 AF amplifier, 33 Aliasing, 37, 128 Antenna, 117–21, 163–65, 181 Antenna beamwidth, 121 Antenna geometry, 120, 163, 181 Antenna rpm, 134–39, 152–53 Antenna target calibration, 82–83 Antenna temperature, 7 Aperture synthesis, 69, 72–73, 75–76, 198–200, 200–4, 208–11, 214–17
Faraday rotation, 186–92 Footprint, 121, 134, 152–53 Fringe washing, 74 IF circuitry, 31–31 Image reconstruction, 197, 204–5, 207–8 Integrated receiver, 159–60 Integration time, 9, 34, 138, 140–41 Integrator, 33–34
Baseline, 69–71, 74, 75, 76–78, 200–4,204–5, 205–6, 213 Beam efficiency, 117–19 Brightness temperature, 7, 75, 203, 207, 209–11
LF circuitry, 33–34 Linearity, 87–96, 165–67 Line scanner, 121–25
Calibration, 81, 96–98, 165–67, 184–86, 205–06 Calibration load, 82–84 Calibration target, 82–85 Complex correlator, 19, 57–62, 65 Conical scanner, 122–23, 134–35, 143, 147 Correlation radiometer, 18–20, 60–62, 64–68, 69
MMIC technology, 159–60, 217 Multiple beams, 150 Noise diode, 39, 92–93, 97, 109–11 Noise-injection radiometer, 16, 38–40, 47–53, 109–11, 178–81 Noise temperature, 9, 29–30 Offset paraboloid, 119–21, 163–65
Data rate, 168–69 Detector, 30–31, 40–42 Dicke radiometer, 14–16, 27–37, 104, 131
Polarimetric radiometer,55–68, 96–98 Polarimetry, 55–57
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Polarization, 55–57, 173, 189–91 Polarization combining radiometer, 57–60 Preamplifier, 25–27, 40–42, 42–43 Pseudo inverse, 204–5 Push-broom imager, 121–25, 139–40, 177–84 Radiometer receiver, 7 Receiver noise figure, 29–30, 134–39, 160–61 Receivers for imagers, 130–31 Sampling, 37, 38, 125–30 Sea salinity, 172–75, 209, 214–15 Sea surface temperature, 172–75 Sensitivity, 7–9, 14–16, 17–18, 62–64, 73, 75–76, 102–3, 141, 198–200, 212–13, 217 Sensitivity measurements, 102–3 Sky calibration, 85–86, 156–57, 166–67, 184–86 Sky horn, 157, 184–86 Soil moisture, 69, 175–76, 200–4, 208–11, 211–14, 214 Space radiation, 192–93 Spatial frequency, 71, 73–74
SSB receiver, 26–27, 42–43 Stability, 9–11, 43–44, 47–53, 103–14 Stability measurements, 103–14 Stokes parameters, 55–57 Superheterodyne receiver, 25–27 Swath width, 121–25,134–36, 140–41 Synchronous detector, 33–34 Synthesized beam (antenna pattern), 76–78, 200–4,204–5, 207–8 Synthetic aperture radiometer, 197, 211–14, 214–217 Temperature stabilized enclosure, 49 Torus reflector, 181 Total power radiometer, 13–14, 40–43, 111–13, 130–31, 157–58 Weight and power, 159–60, 167–68, 178–81, 183, 194, 211–14, 214–17 Wind speed, 172 Visibility, 70, 75, 205, 207–8 Visibility function, 75 ∆/Σ converter, 34–37
The Artech House Remote Sensing Library Fawwaz T. Ulaby, Series Editor
Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation, Ian G. Cumming and Frank H. Wong Digital Terrain Modeling: Acquisitions, Manipulation, and Applications, Naser El-Sheimy, Caterina Valeo, and Ayman Habib Handbook of Radar Scattering Statistics for Terrain, F. T. Ulaby and M. C. Dobson Handbook of Radar Scattering Statistics for Terrain: Software and User’s Manual, F. T. Ulaby and M. C. Dobson Magnetic Sensors and Magnetometers, Pavel Ripka, editor Microwave Radiometer Systems: Design and Analysis, Second Edition, Niels Skou and David Le Vine Microwave Remote Sensing: Fundamentals and Radiometry, Volume I, F. T. Ulaby, R. K. Moore, and A. K. Fung Microwave Remote Sensing: Radar Remote Sensing and Surface Scattering and Emission Theory, Volume II, F. T. Ulaby, R. K. Moore, and A. K. Fung Microwave Remote Sensing: From Theory to Applications, Volume III, F. T. Ulaby, R. K. Moore, and A. K. Fung Radargrammetric Image Processing, F. W. Leberl Radar Polarimetry for Geoscience Applications, C. Elachi and F. T. Ulaby Understanding Synthetic Aperture Radar Images, Chris Oliver and Shaun Quegan Wavelets for Sensing Technologies, Andrew K. Chan and Cheng Peng
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