Industrial Color Physics

Springer Series in

OPTICAL SCIENCES founded by H.K.V. Lotsch Editor-in-Chief: W.T. Rhodes, Atlanta Editorial Board: A. Adibi, Atlanta T. Asakura, Sapporo T. W. Hänsch, Garching T. Kamiya, Tokyo F. Krausz, Garching B. Monemar, Linköping H. Venghaus, Berlin H. Weber, Berlin H. Weinfurter, München

154

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OPTICAL SCIENCES The Springer Series in Optical Sciences, under the leadership of Editor-in-Chief William T. Rhodes, Georgia Institute of Technology, USA, provides an expanding selection of research monographs in all major areas of optics: lasers and quantum optics, ultrafast phenomena, optical spectroscopy techniques, optoelectronics, quantum information, information optics, applied laser technology, industrial applications, and other topics of contemporary interest. With this broad coverage of topics, the series is of use to all research scientists and engineers who need up-to-date reference books. The editors encourage prospective authors to correspond with them in advance of submitting a manuscript. Submission of manuscripts should be made to the Editor-in-Chief or one of the Editors. See also www.springer.com/series/624 Editor-in-Chief William T. Rhodes, Ph.D. Professor Emeritus, Georgia Institute of Technology Professor of Electrical Engineering and Associate Director, Imaging Technology Center Florida Atlantic University Boca Raton, FL 33431 USA E-mail: [email protected] Editorial Board Ali Adibi Georgia Institute of Technology School of Electrical and Computer Engineering Atlanta, GA 30332-0250, USA E-mail: [email protected] Toshimitsu Asakura

Max-Planck-Institut für Quantenoptik Hans-Kopfermann-Straße 1 85748 Garching, Germany E-mail: ferenc [email protected] Bo Monemar

Hokkai-Gakuen University Faculty of Engineering 1-1, Minami-26, Nishi 11, Chuo-ku Sapporo, Hokkaido 064-0926, Japan E-mail: [email protected]

Department of Physics and Measurement Technology Materials Science Division Linköping University 58183 Linköping, Sweden E-mail: [email protected] se

Theodor W. Hänsch

Herbert Venghaus

Max-Planck-Institut für Quantenoptik Hans-Kopfermann-Straße 1 85748 Garching, Germany E-mail: [email protected]

Fraunhofer Institut für Nachrichtentechnik Heinrich-Hertz-Institut Einsteinufer 37 10587 Berlin, Germany E-mail: [email protected]

Takeshi Kamiya Ministry of Education, Culture, Sports Science and Technology National Institution for Academic Degrees 3-29-1 Otsuka, Bunkyo-ku Tokyo 112-0012, Japan E-mail: [email protected]

HorstWeber Technische Universität Berlin Optisches Institut Straße des 17. Juni 135 10623 Berlin, Germany E-mail: [email protected]

Ferenc Krausz

HaraldWeinfurter

Ludwig-Maximilians-Universität München Lehrstuhl für Experimentelle Physik Am Coulombwall 1 85748 Garching, Germany and

Ludwig-Maximilians-Universität M Sektion Physik Schellingstraße 4/III 80799 München, Germany E-mail: [email protected]

Please view available titles in Springer Series in Optical Sciences on series homepage http://www.springer.com/series/624

Georg A. Klein

Industrial Color Physics

13

Georg A. Klein Herrenberg Germany

ISSN 0342-4111 e-ISSN 1556-1534 ISBN 978-1-4419-1196-4 e-ISBN 978-1-4419-1197-1 DOI 10.1007/978-1-4419-1197-1 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009940329 © Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Translated from German by Todd Meyrath and the author.

In memoriam of Dr. Hartmut K.A. Pauli

Preface to the English Edition

Colors arise only in the brain, normally originating from electromagnetic waves from the outside world.

This book is based on courses given by the author in the Department of Colors, Paints and Plastics at the University of Applied Sciences in Stuttgart and continued at the University of Applied Sciences in Esslingen, Germany. The development of color physics in industry began in the middle of the 19th century with the large-scale manufacturing of natural colors. Since that time, a great variety of new, especially synthetic, colorants have been produced in order to meet increasing demands for non-self-luminous colors with regard to color applications. The rapid progress in color physics and accompanying applications over the last three decades are the reasons for this work. Here, the fundamentals of color physics are outlined and the most important recent developments and applications in the color industry are discussed. In comparison to the first German edition,1 all chapters of the book have been revised and expanded with regard to effect pigments. After the introductory chapter, the optical fundamentals of absorbing and effect colorants are discussed. The exceptional spectral and colorimetric properties of effect pigments are detailed in combination with further characterizing parameters. Color spaces are presented as well as the efficiency of recent color difference formulas. In addition to the normal spectral measuring methods for absorbing colorants, modified procedures for effect colorations are outlined. The typical angle-dependent properties of pearlescent, interference, and diffraction pigments as well as mixtures with metallic pigments are clarified by measurements. In addition, criteria for estimation of measurement errors as well as the statistics of color difference values are detailed.

1 Klein, G.A.: “Farbenphysik für industrielle Anwendungen”, Springer, Berlin, Heidelberg (2004).

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The directional two-flux approximation with directional rays is introduced and allows for the creation of the optical triangle. Some characteristic triangle parameters enable the demonstration of the performance of the two-, three-, and multi-flux approximations up to a maximum of n = 256 fluxes. Based on these different concepts, the fundamentals of the classical color recipe prediction methods are described. These topics are completed with the most important modern methods for recipe prediction for all known sorts of colorations. This edition has only been realized through the kindness of many people, and I am happy to express my thanks to them. First, I owe a special debt of gratitude to Dr. Todd Meyrath (Ventura, CA, USA). Not only did he translate from German, he also offered numerous ideas – most of which have been realized in the text. Possible translation errors in the book should be attributed to the author. A lot of suggestions concerning radiative transfer came from friendly discussions with Dr. Hartmut Pauli (Basel, Switzerland). Many thanks go to Dr. Peter W. Gabel (Darmstadt, Germany), Dr. Alfried Kiehl (Velden, Germany), Dr. Changjun Li (Leeds, UK), Mike Nofi (Santa Rosa, CA, USA), Francis Powers (Shawbury, Shropshire, UK), Ian Wheeler (Leven, UK), Dipl.-Ing. Gerhard Wilker (Frankfurt am Main, Germany), and Dr. Klaus Witt (Berlin, Germany) for their encouragement and, in many cases, the kind permission to reproduce some light and scanning microscope images of colorants. Thanks to Klaus-Juergen Woyczehowski (Frankfurt am Main, Germany) for timely help with these; I very much appreciate his kindness. Last but not least, sincere thanks go to my family. Herrenberg, Germany May 2009

Georg A. Klein

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 8

2 Light Sources, Types of Colorants, Observer . . . . . . . . . . . . . 2.1 Optical Radiation Sources and Interactions of Light . . . . . . . . 2.1.1 Visible Spectrum and Colors . . . . . . . . . . . . . . . . 2.1.2 Types of Light Sources . . . . . . . . . . . . . . . . . . 2.1.3 Technical Light Sources . . . . . . . . . . . . . . . . . . 2.1.4 Illuminants . . . . . . . . . . . . . . . . . . . . . . . . 2.1.5 Geometric Optical Interactions . . . . . . . . . . . . . . 2.1.6 Interference of Light . . . . . . . . . . . . . . . . . . . . 2.1.7 Diffraction from Transmission and Reflection Gratings . . 2.2 Absorbing Colorants . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Types and Attributes of Absorbing Colorants . . . . . . . 2.2.2 Pigment Mixtures and Light Transmittance . . . . . . . . 2.2.3 Description of Color Attributes . . . . . . . . . . . . . . 2.2.4 Color-Order Systems . . . . . . . . . . . . . . . . . . . 2.2.5 Surface Phenomenon . . . . . . . . . . . . . . . . . . . 2.3 Effect Pigments . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Types of Metallic Pigments . . . . . . . . . . . . . . . . 2.3.2 Morphology of Metallic Particles . . . . . . . . . . . . . 2.3.3 Coloristic Properties of Metallic Pigments . . . . . . . . . 2.3.4 Sorts of Pearlescent and Interference Colorants . . . . . . 2.3.5 Interference Pigments Consisting of Multiple Layers . . . 2.3.6 Spectral Behavior of Pearlescent and Interference Colorants 2.3.7 Opaque Films Containing Absorbing and Effect Pigments . 2.3.8 Colors of Diffraction Pigments . . . . . . . . . . . . . . 2.4 Observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Color Perception and Color Theories . . . . . . . . . . . 2.4.2 Color Perception Phenomenon . . . . . . . . . . . . . . . 2.4.3 Subtractive and Additive Mixing of Colors . . . . . . . . 2.4.4 Tristimulus Color-Matching Experiments . . . . . . . . .

11 11 12 14 18 23 25 34 38 43 43 48 51 57 59 63 65 69 76 82 85 91 101 104 109 110 114 116 120

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2.4.5 Determination of Tristimulus Values . . . . . . . . . . . . 2.4.6 CIE 1931 and CIE 1964 Standard Colorimetric Observers . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Systems of Standardized Tristimulus Values, Color Qualities, Chroma of Effect Pigments . . . . . . . . . . . . . . . . . . . 3.1 Systems of Standardized Tristimulus Values . . . . . . . . . 3.1.1 CIE 1931 Tristimulus Values . . . . . . . . . . . . 3.1.2 Chromaticity Coordinates and Chromaticity Diagram 3.1.3 CIE 1976 Color Spaces . . . . . . . . . . . . . . . 3.1.4 DIN99o Color Space . . . . . . . . . . . . . . . . . 3.2 Color Difference Metrics and Color Tolerances . . . . . . . 3.2.1 CMC(l:c) Color Difference Formula . . . . . . . . . 3.2.2 CIE94 Color Difference Expression . . . . . . . . . 3.2.3 CIEDE2000 Color Difference Equation . . . . . . . 3.2.4 Efficiency of Color Difference Formulas, CIE Color Appearance Models . . . . . . . . . . . . . . 3.2.5 Color Tolerances . . . . . . . . . . . . . . . . . . . 3.3 Color Constancy and Metamerism . . . . . . . . . . . . . . 3.3.1 Chromatic Adaptation and Color Constancy . . . . . 3.3.2 Index of Color Inconstancy . . . . . . . . . . . . . 3.3.3 Kinds of Metamerism . . . . . . . . . . . . . . . . 3.3.4 Special Metamerism Indices . . . . . . . . . . . . . 3.4 Specific Qualities of Colorants . . . . . . . . . . . . . . . . 3.4.1 Build-up and Coloring Potential . . . . . . . . . . . 3.4.2 Strength and Depth of Color . . . . . . . . . . . . . 3.4.3 Covering Capacity . . . . . . . . . . . . . . . . . . 3.4.4 Transparency and Coloring Power . . . . . . . . . . 3.4.5 Color Fastness and Turbidity . . . . . . . . . . . . . 3.4.6 Stability of Effect Pigments . . . . . . . . . . . . . 3.5 Chroma of Effect Pigments . . . . . . . . . . . . . . . . . 3.5.1 Coloristic Quantities of Effect Pigments . . . . . . . 3.5.2 Color Difference Equation for Metallics . . . . . . . 3.5.3 Chroma of Pearlesence and Interference Pigments . . 3.5.4 Mixtures of Effect Pigments . . . . . . . . . . . . . 3.5.5 Color Development of Diffraction Pigments . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Measuring Colors . . . . . . . . . . . . . . . . . . . . . 4.1 Measurement of Reflecting and Transmitting Materials 4.1.1 Measurement of Colors and Visual Judgment . 4.1.2 Measurement Geometries . . . . . . . . . . . 4.1.3 Sample Requirements . . . . . . . . . . . . . 4.1.4 Transparent, Translucent, Opaque Colors . . .

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159 161 164 164 166 169 172 175 176 179 185 189 192 197 200 201 206 209 214 221 228

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233 234 235 239 248 250

Contents

4.1.5 Color Matching . . . . . . . . . . . . . . . . . . 4.1.6 Acceptability and Tolerance Agreement . . . . . . 4.2 Measuring Methods . . . . . . . . . . . . . . . . . . . . 4.2.1 Tristimulus Colorimeter . . . . . . . . . . . . . . 4.2.2 Spectrophotometer . . . . . . . . . . . . . . . . . 4.2.3 Accuracy of Spectrophotometers . . . . . . . . . . 4.2.4 Reflectance and Transmittance of Layers . . . . . 4.2.5 Auxiliary Optical Methods for Effect Pigments . . 4.2.6 Fluorescent, Thermochromic, Photochromic Colors 4.3 Uncertainties of Spectral Color Measurement . . . . . . . 4.3.1 Qualitative Errors . . . . . . . . . . . . . . . . . 4.3.2 Quantitative Errors and Error Distribution . . . . . 4.3.3 Normal Distribution in Three and More Dimensions 4.3.4 Statistical Testing of Color Differences . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .

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252 255 257 257 259 263 266 271 274 278 279 280 284 287 292

5 Theories of Radiative Transfer . . . . . . . . . . . . . . . . . . . 5.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Basic Concepts and Definitions . . . . . . . . . . . . . 5.1.2 Absorption and Scattering . . . . . . . . . . . . . . . . 5.1.3 Single and Multiple Scattering . . . . . . . . . . . . . . 5.1.4 Radiative Transfer Equation . . . . . . . . . . . . . . . 5.1.5 Radiative Transfer in Plane Parallel Layers . . . . . . . 5.1.6 Phase Function for Anisotropic Scattering . . . . . . . . 5.2 Directional Two-Flux Approximation . . . . . . . . . . . . . . 5.2.1 Reflection and Transmission . . . . . . . . . . . . . . . 5.2.2 Optical Special Cases . . . . . . . . . . . . . . . . . . 5.2.3 Optical Triangle . . . . . . . . . . . . . . . . . . . . . 5.2.4 Determination of Optical Coefficients . . . . . . . . . . 5.3 Theory of Kubelka and Munk . . . . . . . . . . . . . . . . . . 5.3.1 Empirical Approach . . . . . . . . . . . . . . . . . . . 5.3.2 Exceptional Optical Cases . . . . . . . . . . . . . . . . 5.3.3 Determination of Optical Constants . . . . . . . . . . . 5.3.4 Boundary Layer Correction . . . . . . . . . . . . . . . 5.3.5 Limits of Kubelka–Munk Theory . . . . . . . . . . . . 5.4 Three-Flux Approximation . . . . . . . . . . . . . . . . . . . 5.4.1 Conception of Three-Flux Theory . . . . . . . . . . . . 5.4.2 Reflection and Transmission . . . . . . . . . . . . . . . 5.4.3 Optically Different Materials . . . . . . . . . . . . . . 5.4.4 Correction of Surface Effects . . . . . . . . . . . . . . 5.4.5 Special Cases of External Reflection and Transmission . 5.5 Approximation of Radiative Transfer by Multi-Flux Theory . . . 5.5.1 Exact Solutions for Internal Reflection and Transmission

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295 295 296 299 302 306 308 313 316 317 319 321 324 326 327 329 331 332 337 340 341 343 345 348 352 356 357

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5.5.2 5.5.3 5.5.4

Surface Boundary Corrections . . . . . . . . . . . . Total Reflection and Optical Extreme Cases . . . . . Boundary Conditions, Matrices of Reflection and Transmission . . . . . . . . . . . . . . . . . . Directional and Diffuse Reflection and Transmission Inclusion of Total Reflection . . . . . . . . . . . . . Corrected Optical Triangle . . . . . . . . . . . . . .

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370 372 373 377 379

6 Recipe Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Classical Method . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Calibration Series with Absorbing Colorants . . . . . . . . 6.1.2 Calibration and Reference Colorations for Effect Pigments 6.1.3 Determination of Absorption and Scattering Coefficients . 6.1.4 Optical Path and Albedo . . . . . . . . . . . . . . . . . . 6.1.5 Coefficients of the Phase Function . . . . . . . . . . . . . 6.1.6 Accuracy of Predicted Recipes . . . . . . . . . . . . . . . 6.2 Strategies for Recipe Prediction . . . . . . . . . . . . . . . . . . 6.2.1 Numerical Methods . . . . . . . . . . . . . . . . . . . . 6.2.2 Spectrometric Strategy . . . . . . . . . . . . . . . . . . . 6.2.3 Colorimetric Method . . . . . . . . . . . . . . . . . . . 6.2.4 Balanced Color Differences . . . . . . . . . . . . . . . . 6.3 Realization of Recipes . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Selection of Suitable Recipes . . . . . . . . . . . . . . . 6.3.2 Sensitivity and Correctability of Color Recipes . . . . . . 6.3.3 Numerical Procedures for Recipe Correction . . . . . . . . 6.3.4 Databases . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.5 Modified Expert Systems . . . . . . . . . . . . . . . . . 6.3.6 Neural Networks . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

381 382 384 390 393 397 399 400 403 404 409 414 417 420 421 424 427 431 435 441 445

Appendix . . . . . . . . . . . . . . . . . . . . . . A.1 Non-colored Applications of Effect Pigments A.1.1 Metallic Pigments . . . . . . . . . . A.1.2 Pearlescent Pigments . . . . . . . . A.2 Chromatic Adaption Transform CAT02 . . . A.2.1 Forward Mode . . . . . . . . . . . . A.2.2 Reverse Mode . . . . . . . . . . . . A.3 Two-Flux Approximations . . . . . . . . . . A.3.1 Directional Fluxes . . . . . . . . . . A.3.2 Diffuse Fluxes . . . . . . . . . . . .

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447 447 447 448 448 448 450 451 451 453

References in Alphabetic Order . . . . . . . . . . . . . . . . . . . . .

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Name Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5.5.5 5.5.6 5.5.7 References

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Chapter 1

Introduction

Colored objects influence our lives each and everyday. Within physics the term color is used ambiguously and is in no way restricted to the field of optics. In solid-state physics, the origin of the colors of crystals is certainly of interest; in particle physics the so-called quarks carry electrical charges which are astonishingly called red, green, and blue, yet have no relation to any real colors! The well-known colors of light as well as the various phenomena of non-selfluminous colors belong to the field of optics. Non-self-luminous colors result if suitable colorants such as dyes or pigments are mixed into an organic or inorganic medium. This book confines itself to non-self-luminous colors, their physical and colorimetric qualities as well as their typical industrial applications. Modern colorants can be divided into two groups: absorption colorants and effect pigments. Non-self-luminous colors are only perceived when they are illuminated by light or other energy source. Being a perception, the color impression of the observer is thereby of central importance. Amazingly, our vision – from which we obtain about 80% of the information from our surroundings – is provided by nature with the capability of distinguishing more than 10 million colors. At this stage, we must stress that color is a perception; it is not a physical quantity but rather a purely psychophysical response, usually to visual light after entering the eye. It is, therefore, not measurable by normal engineering methods. It is possible, however, to describe colors in an objective manner by quantifying them with three distinct numbers. These numbers are called color values and are dimensionless quantities. The values can be interpreted, for example, as lightness, chroma, and hue of the relevant color. Certainly, the three values are only representatives of a specific color; they do not describe the color perception itself. From a geometrical point of view, these three color quantities can be taken as coordinates of a point in a three-dimensional color space. Hence, a color space can be considered as an isolated part of a three-dimensional Cartesian coordinate system. On the other hand, each space is obviously characterized G.A. Klein, Industrial Color Physics, Springer Series in Optical Sciences 154, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-1197-1_1, 

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1 Introduction

by the coordinate system and the metrics chosen. Therefore, the so-called colorimetry describes the metrics between the color quantities in a predefined color space. Since color vision arises exclusively from a neural-induced perception and not directly from a physical effect, colorimetry is used to compare colors of similar or nearly identical hue, among other things. Our modern scientific and technical knowledge about colors follows a long historical development. The oldest surviving colored documents created by humans are the rock and cave paintings from the Paleolithic period found worldwide and dating from the time between about 40,000 and 8,000 years ago [1]. Already during this period, humans decorated their skin and cloths with natural colors. In the following epochs until the Egyptians, refinement was limited to merely the application of natural colors. Even from modern antiquity, no fundamental or new findings about color properties are known, simply some unsuccessful attempts for color theories can be found. The first systematic experiments with color phenomenon were made by Newton with sunlight in the year 1671: with a simple prism he proved that sunlight is comprised of colored parts. In 1704, he concluded: “For the Rays to speak properly are not coloured. In them there is nothing than a certain Power and Disposition to stir up a Sensation of this or that Colour”. His knowledge and experience in optics are concentrated in the work “Opticks”, in which he already began treating terms such as refraction, reflection, and interference [2]. In his color theory of 1810, Goethe criticized this apparent overemphasis of the physical aspects of color; in particular, he stressed the physiological components of color vision [3]. However, the physical statements of his theory were subsequently disproved. Fundamental scientific understanding of colors goes back to Young. In 1802, he created the spectrograph for measuring the intensity distribution of light sources. Young additionally introduced the term wavelength of light and established the first physically and physiologically founded trichromatic theory of color vision [4]. A physiologically determined systematic of color sensation was defined by Grassmann in 1853 with four empirical laws of additive color mixing. They form the basis of modern colorimetry [5]. Moreover, Grassmann was the first to characterize colors by quantities. These quantities are composed of numbers for hue, lightness, and saturation, which are similar to the above description. With these, he has introduced the principle of color values – an essential method in modern industrial color physics. The modern trichromatic theory was established already in 1867 by Helmholtz [6]; it is based on the earlier ideas of Young [4] and Maxwell [7]. With the so-called Young–Helmholtz theory, the psychophysically induced color stimulus can be described numerically by physical and physiological factors. The underlying trichromatic theorem – confirmed experimentally in 1964 – is that color stimulus is caused by the fact that the retina in the eye contains three receptors with photopigments of different sensitivities for the primary colors

1 Introduction

3

red, green, and blue. Only these three receptors are responsible to initiate color sensation [8]. Independently in 1878, Hering formulated the so-called opponent color theory. According to this model, the rear of the retina contains three different channels for the opponent color pairs of red and green, yellow and blue as well as the opponent achromatic colors black and white, which are able to produce all color sensations [9]. These ideas were finally proven in 1956 [10, 11]. The retinex theory, introduced by Land in 1959, starts from the hypothesis that the retina and the visual cortex (located at the rear areas of both brain lobes) are connected by three separate channels. In these channels, the arriving neural signals are compared according to their trichromatic lightness contribution so that color sensation is stimulated [12, 13]. The three aforementioned color theories outlined here are not only of interest for research of color perception but also for the application of their established results to the evaluation of the visual and colorimetric properties of colors and colorants. Of great importance in this development is the so-called high colorimetry, formulated (in vector algebra) by Schroedinger in 1920, since then it is abbreviated as colorimetry. Our actual colorimetric methods are based on these ideas [14]. With this formalism, it is possible to make statements about the complete identity of color sensation. Moreover, we are able to obtain information about the similarity of visually different color impressions. These phenomena are relevant for color matching and comparison of nearly identical colors [15–17]. There has been great delay in the implementation of most of the above insights and accumulated knowledge into the industrial setting. About 80 years after the beginning of large-scale production of modified natural and increasingly synthetic absorption colorants, in 1931 the first conventions were set out by the Commission Internationale de L’Éclairage (CIE, International Commission on Illumination) to describe colors with uniform quantities [18]. With these decisions, an essential step toward better communication between manufacturers and users of absorption colorants was initiated. In the proposals of the CIE, ideas of the trichromatic theory have been adopted. This concept was thoroughly revised in 1974 and elements of the opponent color theory as well as colorimetry were taken into consideration. Two years later, parts of this program – named CIELAB system – were recommended for global application [19]. On the basis of the experiences achieved with these proposals, the recommendations have been built up and modified since this time [20–23]. Apart from the higher color physical requirements on today’s industrial colorants, their production, improvement, and processing are of primary interest. Among others, important properties are the total miscibility of the utilized colorants, components, and additives, their chemical and physical compatibility, as well as their durability against shear, pressure, or temperature, all of which might depend, for instance, on the chosen process technology. The principally desired characteristics for most technological applications include: high color

4

1 Introduction

constancy against different climatic environments, electromagnetic, radioactive, and even cosmic radiation, as well as fastness – meaning resistance – against chemical changes. Beyond these, the innocuousness concerning toxicological and ecological criteria is increasingly important. For testing the aforementioned and additional coloristic properties, spectral and colorimetric methods are used. With the CIELAB system and later adjustments, colorimetric criteria are applied in color industry, for example: – to specify colors and colorants; – to characterize the typical color producing properties of colorants; – to quantify and assess the color differences of similar or nearly equal colors; – for suitable estimation and assessment of the altered color sensation caused by substitution of colorants, change in illumination or observer conditions; – for recipe prediction of colored samples of unknown colorant compositions. The treatment of these and similar applied problems in an economic fashion was realized only during recent decades. Three reasons are responsible for this: first, the development of complex microstructures in semiconductors (actually reduced now to nanodimensions); second, computers with faster computing speed and larger storage density since 1970; and third, the increased accuracy and simultaneously improved reproducibility of the developed components for instruments to measure colors. The resulting progress has led to extensive and fundamental knowledge about color physical problems of absorption and effect pigments. Until now, effect pigments have been intentionally excluded from our considerations. These flake-shaped particles with a diagonal dimension of about 5–100 μm produce exceptional color sensations, differing essentially from those of absorption colorants. Effect colors result optically either from metallic reflection, interference, or diffraction. Effect pigments are produced industrially to an increasing extent only since the middle of the last century. Two main reasons are responsible for this late distribution: first, effect pigments passed through an autonomous technical development in comparison to absorbing colorants; second, the completely unusual colors and optical interactions produced by this kind of colorant. Metallic reflection, interference, and diffraction are not comparable with selective absorption or scattering, which generate the used colors of absorbing colorants. Effect pigments can be divided into four groups: metallic, pearlescent, interference, and diffraction pigments. In Table 1.1 various sorts of modern colorants are listed together with their dominant color producing interactions. Typical for metallic pigments is the metallic gloss, which is absent in traditional absorption pigments. The beginning of metallic pigments goes back to the beating of gold; a skill practiced in Egypt as early as 5,000 years ago [24]. At that time, gold was beaten into foils with minimal thickness of 1 μm (1 μm

1 Introduction

5

Table 1.1 Modern sorts of colorants and main optical interactions Type of colorant

Colorant

Dominant light interaction

Absorption colorants

Dyes Absorption pigments

Absorption Absorption, scattering

Effect pigments

Metallic pigments Pearlescent, interference pigments Diffraction pigments

Reflection Interference Diffraction

corresponds to 10–6 m) for commodities and pieces of jewelry as well as parts of buildings with a precious and protective surface. Since about 200 BC in China, Japan, and India, Buddha statues were embellished with slices of gold. From there, the art of gold-beating reached Rome, where this skill was even mentioned briefly by Plinius Secundus the Elder in the first century AD; the topic is treated in more detail in the Lucca Manuscript. This document is a recipe collection gathered by Greek monks of the 9th century. The most important confirmed last historical discourse on the technology of gold-beating is represented by a manuscript from the 12th century of the German monk Theophilus . Two centuries after the founding of various centers in northern Germany, the town Nuernberg became the primary center of the gold-beating technology. During the period that followed, increasing demand for gold led to ever thinner metallic foils which unfortunately resulted in a greater failure rate. This is why they were embedded in protective binders ever since. From those flakes, the so-called gold flitter, over the last centuries led to today’s gold and metallic pigments. For reasons of economy and excessive demand, it was finally necessary to find a replacement for gold. This led to gold-colored brass, a material which shows an optical behavior similar to gold in the visible range. Brass is well known since the 3rd century BC in Babylon and Assyria, but vanished thereafter and was rediscovered in Roman times. Since the year 1820, brass has been produced on the large scale in Germany by alloying copper (56–90%) with zinc. A similar history is responsible for the replacement of bright silver–bronze, an alloy of silver with tin, by a less expensive metal: aluminum, which shows a metallic reflection comparable to that of silver–bronze. Pure aluminum has been obtained economically using the technology of melt-flow electrolysis since 1886 and can be produced in the shape of metallic pigments. Certainly aluminum pigments have shown an increased acceptance only since 1970, because since that time it has been possible to realize the desired formulations with this kind of effect pigment on the large scale. Aluminum pigments are preferentially applied for mono- and multi-layer coatings, plastics, or printing inks. Metal flakes for colorants – with mean diameters between 5 and 50 μm – have been called

6

1 Introduction

metallic pigments only for some decades. Now, metallic flakes are being produced in various geometrical shapes and even various colors with the addition of absorption pigments fixed on the surfaces of the particles. Pearlescent pigments, the second group of effect pigments, imitate the nacre luster of natural pearls. The colored effect seems to rise from the depths to the surface of the pearl and results from constructive interference at the various internal interfaces. In order to duplicate this color phenomenon, in Paris in 1656 Jacquin produced and processed the so-called essence d’orient (pearl essence) – a suspension consisting of tiny plates of guanine and hypoxanthine – acquired from fish scales [25]. The use of this cost-intensive production process ceased in 1920: during the following two decades some suitable inorganic compounds were crystallized with increasing success in layers of various thicknesses, which completely imitate the luster of pearls. Modern pearlescent pigments mostly consist of metal oxides fixed on natural or synthetic mica substrates. In the middle of the 20th century the economic upturn allowed for the development of pearlescent pigments in a similar range of application as metallic pigments. In addition to mono-layer pearlescent pigments, transparent or opaque twoand multi-layer pigments have also been realized. Their striking chromatic and brilliant colors result mainly from interference at the combined multi-layers: that is why they are called interference pigments. Sometimes the colors of interference pigments change greatly with the angle of observation. This is principally a consequence of the great difference in refractive index of the layers, which consist of different metals, metal oxides, or even liquid crystal structures [25]. The individual films have thicknesses between about 20 and 200 nm (1 nm corresponds to 10–9 m), therefore, on the high side, nearly the size of visible wavelengths, a requirement for optical interference among other things. The typical size of interference pigments extends from some microns to nearly one millimeter. This is about one to three orders of magnitude greater in size compared to absorption pigments. More recently, new types of effect colorants, called diffraction pigments, have been manufactured. Their production is based on knowledge and materials of nanotechnology. The color effect of these pigments is initiated by diffraction – again a consequence of the wave properties of light – and is extremely angle dependent. Compared with interference pigments, they even show extreme color changes ranging from violet up to red – over the entire visible spectrum. The diffraction effect is a consequence of the periodic grating structure engraved in the particles; the pigments have diameters of about 20–100 μm. Without a doubt all kinds of effect pigments increase enormously the available colors in industry, but the methods of characterizing and measuring them are less than satisfactory. This is no surprise given the fact that the methods for measuring and characterization of colors have thus far only be developed for absorbing colorants. These methods are in general unsuited to qualify and

1 Introduction

7

quantify the characteristic color properties and angle-dependent colors of effect pigments. The development of adequate measuring methods for these colorants is ongoing. It is known that new findings and applications in modern natural sciences are improved by interaction between theory and experiment. Since the introduction of digital computers after 1960, the methods of numerical simulation have greatly progressed. Right from the beginning, computers were applied in industrial color physics to simulate the light interactions of colorants. For an adequate optical theory, it is necessary to describe the relevant optical processes in colored materials in a suitable manner. Strictly speaking, the various single or combined optical interactions have to be taken into account. At least two optical principles are used for this: single and multiple scattering. Single scattering was first developed by Mie [26], who postulated that color is caused only by a single interaction of light with the electric charges of the colorant particles. In contrast, in multiple scattering light continues to interact until it is absorbed or it leaves the material. These ideas were finally formulated by Chandrasekhar [27]. Although both concepts of single and multiple scattering produce similar results, the formalism of Mie is to this day much too extensive and time consuming for industrial color applications. In industrial applications, the theory of radiative transfer of Chandrasekhar is mostly used, modified with a well-established method in physics: the continuous radiative field of the light inside and outside of a colored layer is divided into discrete light cones. Two cones represent a two-flux theory and so on, until we get the multi-flux theory with any positive integer number n > 2 of cones. The special case of two fluxes with diffuse radiation corresponds to the theory of Kubelka–Munk [28], which certainly has only limited validity. With finer adjustment of the subdivision, the cone model seems to correspond more closely with reality. At least the multi-flux formalism is a reliable apparatus in color physics and related fields. Although the relevant formalisms are merely approximations, with these and further approximations, the color industry has nonetheless gained economic advantage to a large extent. One of the most important applications of this procedure is the numerical recipe prediction for colorants. Since about 1970, this method has developed itself into an established and particularly efficient tool in the color industry. With this procedure, a color of unknown colorant composition can be matched with available colorants only by calculating their approximate concentrations. Recipe prediction is nowadays an easy and effective aid. This is in contrast to the past, when previous generations were forced to select some suitable samples only visually from extensive series of experiments in a long-term empirical manner. But now, classical recipe calculation delivers a multitude of equivalent or alternative color recipes, and with the added benefit of a considerable shorter development time. The experience with the multitude of varied recipes, generated by this method, has made it necessary to catalog them, for example, with

8

1 Introduction

regard to the constituent colorants. To manage the enormous number of ancient recipes, modern software databases or expert systems are used. Today, these systems are often combined with numerical recipe prediction, in particular, to match colors containing both absorption and effect colorants. Clearly, all existent theoretical concepts aside, the visual sensation of the observer will always be the final authority on all efforts in the color industry. The neural processes in the brain are known to behave nonlinearly; the neural signals coming from the retina are gathered and modulated in different areas of the brain lobes until the signals reach the visual cortex. Consequently they are extremely difficult and complex to detect. It is, without a doubt, desirable to bridge the gap to the understanding of the neurological and the neurophysiological processes in the brain responsible for color sensation. In this context, only interdisciplinary research is able to make a considerable step forward [29]. Otherwise nearly all methods for characterizing, qualifying, or comparing colors remain on the contemporary, empirical level. In any case, it is definite that a perceived color depends on three criteria: the source of light, the illuminated color sample, and the color sensation of the observer. These three factors together constitute the fundamentals of color physics, colorimetry, and relating industrial applications described in this book.

References 1. Guthrie, RD: “The Nature of Paleolithic Art”, University of Chicago Press, Chicago (2005) 2. Newton, SI: “Opticks: or, a Treatise of the Reflections, Refractions, Inflections and Colours of Light; Also Two Treatises of the Species and Magnitude of Curvelinear Figures”, repr edition London 1704; Culture et Civilisation, Bruxelles (1966) 3. Goethe, JW von: “Zur Farbenlehre”, repr 1st vol ed Tuebingen in 1810, Harenberg, Dortmund (1979) 4. Young, T: “On the theory of light and colours”, Philos Trans Lond 92 (1802) 12 5. Grassmann, HG: “Zur Theorie der Farbenmischung”, Annalen der Physik 89 (1853) 69; original translation in English: Philosophical Magazine 7, Ser 4 (1854) 254; further: MacAdam, DL, Ed: “Selected Papers in Colorimetry – Fundamentals”, SPIE Milestone Series MS 77 (1993) 10 6. Helmholtz, H von: “Handbuch der physiologischen Optik”, 2nd rev ed, Voss, Hamburg (1896) 7. Maxwell, JC: “On the theory of compound colours and the relations of the colours of the spectrum”, Philos Trans R Soc Lond 150 (1860) 57 8. Brown, PK, Wald, G: “Visual pigments in single rods and cones of the human retina”, Science 144 (1964) 45 9. Hering, E: “Outline of a Theory of the Light Sense”, (1920), Transl.: Hurvich LM a. Jameson D; Harvard University Press, Cambridge, MA (1964) 10. Svaetichin, G: “Spectral response curves of single cone”, Acta Physiol Scand 39 Supply 134 (1956) 17 11. Hurvich, LM, Jameson, D: “Some quantitative aspects of an opponent colors theory”, I, II, III; J Opt Soc Am 45 (1955) 546, 602; ibid. 46 (1956) 405 12. Land, EH: “Experiments in color vision”, Sci Am 200 5 (1959) 84 13. Land, EH: “Recent advances in retinex theory”, Vision Res 26 (1986) 7

References

9

14. Schroedinger, E: “Grundlinien einer Theorie der Farbenmetrik im Tagessehen I., II., III.”, Annalen der Physik 63 (1920) 397, 427, 481 15. Richter, M: “Einfuehrung in die Farbmetrik”, 2nd ed, W de Gruyter, Berlin (1981) 16. Wyszecki, G, Stiles, WS: “Color Science”, 2nd ed, Wiley Classics Library, New York (2000) 17. Judd, DB, Wyszecki, G: “Color in Business, Science and Industry”, 3rd ed, Wiley, New York (1975) 18. CIE 1931: “Proceedings of the Eighth Session”, Cambridge, England 1931; Bureau Central de la CIE, Paris (1931) 19. CIE No 15.2: “Colorimetry”, 2nd ed, Commission Internationale de L’ Éclairage (CIE); Bureau Central de la CIE, Wien (1986) 20. CIE No 116: “Industrial Colour-Difference Evaluation”, Commission Internationale de L’Éclairage (CIE), Bureau Central de la CIE, Wien (1995) 21. CIE No 142: “Improvement to Industrial Colour-Difference Evaluation”, Commission Internationale de L’Éclairage (CIE), Bureau Central de la CIE, Wien (2001) 22. CIE No 15.3: “Colorimetry”, 3rd ed, CIE, Bureau Central de la CIE, Wien (2004) 23. Schanda, J, Ed: “Colorimetry: Understanding the CIE System“, Wiley, Hoboken, NJ (2007) 24. Humpl, I: “Blattgold”, C Winter, Heidelberg (1990) 25. Pfaff, G: “Special effect pigments”, in: Smith, HM, Ed: “High Performance Pigments”, Wiley-VCH, Weinheim (2002) 26. Mie, G: “Beitraege zur Optik trueber Medien, speziell kolloidaler Metalloesungen”, Annalen der Physik, 25, 4th ser (1908) 377 27. Chandrasekhar, S: “Radiative Transfer”, repr 1st ed 1950, Dover, New York (1960) 28. Kubelka, P, Munk, F: “Ein Beitrag zur Optik der Farbanstriche”, Zeitschr Techn Physik 12 (1931) 593 29. Backhaus, WGK, Kliegel, R, Werner, JS, Eds: “Color Vision: Perspectives from Different Disciplines”, W de Gruyter, Berlin (1998)

Chapter 2

Light Sources, Types of Colorants, Observer

In this chapter, the fundamental conditions for color production are discussed. In simplified terms, the visual color impression of non-self-luminous colors is ultimately due to three independent components: the light source, the colorants of the color pattern, and the observer. The color perception depends, therefore, on the specific properties of these factors. Factors of particular importance are as follows: – the spectral power distribution emitted of the light sources used; – the light interactions with the colorants of the color sample, especially the resultant absorption, scattering, reflection, transmission, as well as interference or diffraction; – the color perception capability of the observer. We will go into these three factors in more detail in the following sections. To begin with, we deal with the most important light sources used for color assessment and the most simple light interactions of colorants. The composition and the typical spectral properties of industrially applied colorant sorts are described in detail. The explanation of color sensation of the observer seems initially to be out of scope; however, this theme is necessary to consider for at least two reasons: first, some phenomena of the human color sense really stand out. These have to be taken into account during color assessment. Second, color perception is affected by the law of additive color mixing, upon which the entire colorimetry and the corresponding applications of industrial color physics are founded.

2.1 Optical Radiation Sources and Interactions of Light Without light there exists no color. The concept of color is bound to visible wavelengths. Therefore, we turn at first toward the typical properties of natural

G.A. Klein, Industrial Color Physics, Springer Series in Optical Sciences 154, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-1197-1_2, 

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2 Light Sources, Types of Colorants, Observer

and man-made light sources because the spectral power distribution of an illuminant affects the color impression. Due to ever-present changes in natural daylight, such a source is unsuited for producing a consistent color sensation with an unchanging non-self-luminous color. On account of this uncertainty, we are forced to rely on man-made sources of constant and reproducible light emission – normally in the visible range. For a reliable assessment of colors in industry, the spectral power distributions of two commonly used man-made light sources have been standardized. The actual physical processes producing color appearances can be described by elements of simple geometrical optics as well as some effects of wave and quantum optics. In this section, these interactions are described in so far as they are significant for better understanding of the color physical properties of modern industrial colorants.

2.1.1 Visible Spectrum and Colors The electromagnetic spectrum covers an enormous range of wavelengths λ from, for example, values such as λ ≈ 1 fm (1 fm corresponds to 10–15 m) for cosmic radiation to λ ≈ 10 km for radio waves, therefore a range of around 19 orders of magnitude; see Fig. 2.1. On the other hand, the visible range of humans is only a small part of the spectrum of electromagnetic waves. Merely wavelengths in the very small interval from 380 to 780 nm are normally perceived by humans as visible light. Wavelengths at the left end of the range between

10–15

10–12

10–9

10–6

10–3

1

λ m

103

1 2 3 4 5

6 7 8 9 10

Violet Green Orange Blue Yellow Red 380 nm

f Hz

1021

1018

780 nm 1015

1012

109

106

Fig. 2.1 Spectrum of electromagnetic waves: 1 cosmic radiation, 2 gamma radiation, 3 Xray radiation, 4 ultraviolet radiation, 5 near-ultraviolet radiation; 6 infrared radiation, 7 radar waves, 8 VHF waves, 9 television waves, 10 radio waves

2.1

Optical Radiation Sources and Interactions of Light

13

380 and 440 nm are perceived as violet. With increasing wavelength, the color impression changes to blue, green, yellow, orange, and finally red. Red is perceived at wavelengths above 600 nm. The associated wavelengths are subject to individual variations in color perception. The so-called spectral colors are the purest producible colors. They are characterized by a wavelength width of less than 1 nm (i.e., with a laser). On the other hand, if the radiation contains nearly all wavelengths of the visible spectrum and of equal intensity, the resulting color impression is white light (e.g., white clouds). For the entire range of visible light between about 380 and 780 nm to be perceived, there must be sufficiently high intensity. Under normal illumination conditions, the wavelength interval that can be seen by humans is restricted to between about 400 and 700 nm. Many modern color measuring instruments work in this limited range [1]. Apart from its wave character, light also exhibits simultaneously particlelike properties. To this day, perhaps, this dualism is not understood in terms of everyday human experience. The corresponding particles of electromagnetic radiation, and therefore of visible light, are the so-called photons. Photons in the visible range carry a sufficient amount of energy for selective stimulation of the photosensitive pigments in the retina of the eye to initiate color impression. The eyes should, however, be protected from dangerous ultraviolet (UV) or infrared (IR) radiation. However, radiation of wavelengths near the visible range which cannot be directly perceived by humans can, in conjunction with suitable colorants, cause different physical effects. Luminescence colorants, for example, absorb energy at UV wavelengths and then emit most of this energy at longer wavelengths – usually within the visible or IR range. The needed transitions from energetic steady states occur either spontaneously by fluorescence or delayed by phosphorescence. The energy surplus is converted into molecular vibration energy and leads macroscopically to a temperature increase. The energy absorption of normal absorption colorants in the visible or IR range is also transformed into molecular vibration energy. If this energy conversion is accompanied by a color change, such kinds of colorants are denoted as thermochromic. Moreover, colorants are termed as phototropic, if the color change is only caused by energy absorption at visible wavelengths. On the other hand, excessively high UV or IR radiation energy is sometimes able to initiate irreversible molecular changes, which result in bleaching or total loss of color. In contrast to the above-mentioned colorants, overall the greatest percentage of industrially used colorants contain absorption and effect colorants. In absorption colorants, the incident energy is sufficiently high to initiate partial absorption or scattering. Physically, light absorption in colorant molecules occurs only for certain transitions between quantum energy levels – therefore, in special wavelength regions of visible light. The corresponding processes are called selective absorption or scattering. On the other hand, scattering of light depends on the electrical charge distribution and the geometry of the colorant

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2 Light Sources, Types of Colorants, Observer

particles. In contrast to absorption pigments, dyes do not normally show any scattering because the size of the isolated molecules in solution is too small for such an interaction. The light reflected in the direction of the eye initiates in the retina signals which are perceived usually as non-self-luminous colors. The color separation of pearlescent, interference, and diffraction pigments is a consequence of the wave nature of light. In order to produce a suited interference effect, the pigment particles are built up of layers with different refractive indices of which the light waves interfere constructively or destructively depending on optical path length. The layer thicknesses are smaller than the interfering wavelengths. In contrast, the particles of diffraction pigments show an embossed regular grating structure at which suited wavelengths are diffracted. The distance between two light-transferring slits is about 1 μm.

2.1.2 Types of Light Sources The perception and assessment of non-self-luminous colors requires illumination with a suitable light source. Depending on the mechanism of light generation, optical radiation sources have different spectral power distributions. On the basis of the emitted spectrum, illuminants can be divided into two categories: temperature and luminescence radiators. The most important luminous sources of both classes are given in Table 2.1. In the following, we discuss details of both categories because the illumination of color samples is our primary context. In the near future, semiconductor diodes and lasers are expected to replace, in part, the light sources used to date. Therefore, we also discuss on these sources even though they are, thus far, rarely applied in color industry despite a multitude of advantages. Table 2.1 Kinds of optical light sources Temperature radiator

Luminescence radiator

Natural

Artificial

Artificial

Sunlight, Scattered light of the Earth atmosphere, stars, galaxies

Blackbody radiator, incandescent lamp, arc lamp

Gas discharge tube, fluorescent lamp, light emitting diode (LED), source of coherent light (laser)

For a common characterization, optical radiation source output distributions are often compared with the spectral energy distribution or temperature of a so-called blackbody radiator – also denoted as blackbody or cavity radiator. At lower temperatures, metals emit heat energy in form of IR radiation; gradually, with increasing temperature, dark-red glow emanates. With a further increase

2.1

Optical Radiation Sources and Interactions of Light

15

of temperature, the color changes to orange and yellow, finally to bluish white. During this process, both the radiation energy and the brightness of the emitted light increase. The wavelength with the most energy shifts to smaller wavelengths, i.e., a blue shift. For an ideal blackbody, this radiation is generated inside the cavity of a blackbody radiator and the outside of the cavity walls absorb all external electromagnetic waves. The ideal situation, therefore, is the emission of only the cavity radiation according to its temperature. The radiation power S(λ,T)dλ of a blackbody radiator at wavelength interval dλ is given by the Planck law of radiation [2]: S(λ,T)dλ =

λ5

c1  dλ. · {exp [c2 (λT)] − 1}

(2.1.1)

The radiation constants c1 and c2 have values of c1 = 2πhc2 = 3.74185 × m2 and c2 = hc/k = 1.43884 × 10−2 m K. In Equation (2.1.1), the wavelength λ should be in units of meters and the temperature T in units of Kelvin. The radiation constants contain the velocity of light in vacuum c and the Boltzmann constant k. For derivation of Equation (2.1.1), Planck introduced h – now called the Planck constant. Figure 2.2 shows the spectral power distribution in wavelength given by Planck’s law. As can be seen, at a temperature of 500 K, the peak of spectral power is in the IR range. For an increase to much higher temperatures, i.e., to greater than 104 K, this peak shifts over the visible range into the UV range. For temperatures of about 7,600 and 3,700 K, the peak of the spectrum lies at the respective edges of the visible range. The Planckian formula (2.1.1) contains 10−16 W

109

Energy density / W.m–2.nm–1

Visual range g

a: 500 K b: 1,000 K c: 2,000 K d: 4,000 K e: 6,000 K f: 10,000 K g: 20,000 K

106 f e d

103

c b

100

a 10–3 101

102

103

104

Fig. 2.2 Spectral power distribution of blackbody radiator of different temperatures

λ

nm

16

2 Light Sources, Types of Colorants, Observer

two limiting cases: for short wavelengths Wien’s law of radiation and for long wavelengths Rayleigh–Jeans radiation formula. Before the quantum hypothesis was established, both laws lead to inconsistent infinite energies in the UV range (“UV catastrophe”). The primary assumption made by Planck is that a radiating system exchanges energy with the surrounding radiation field only with an integer multiple of the quantum energy E=

hc = hf . λ

(2.1.2)

In this formula, f is the frequency of the corresponding wavelength. Both the continuous spectra of temperature radiators and the discontinuous line spectra of luminescence radiators are based on the emission of light quanta that are identical with the already mentioned photons. Because the color of the spectrum emitted by a blackbody radiator changes with temperature, it is useful to introduce the term color temperature. With this quantity, the emitted light of a source is compared with that of a blackbody radiator and thus characterized. The color temperature of an illuminant corresponds to the temperature of the blackbody radiator which emits the maximum of light at the same color as the actual illuminant. Strictly speaking, only a temperature radiator can be assigned a color temperature. Other optical radiators, such as luminescence radiators, are characterized by a so-called similar or correlated color temperature. The most well-known temperature radiator is the Sun. Inside the Sun, at temperatures higher than 107 K, deuterium is converted to helium by nuclear fusion (Bethe–Weizsäcker cycle) [3]. For generation of 1 mol helium, the gigantic energy of 1.55 × 102 GJ is released. The total solar fusion energy results in a Sun surface with a mean temperature of about 5,800 K and an exceptionally high radiation power of about 63.3 MW/m2 . Merely a small fraction of this power, namely the so-called solar constant with value 1.37 kW/m2 , reaches the Earth’s atmosphere. This value reduces to about 1.12 kW/m2 if the Sun is at its zenith and the atmosphere is free of clouds. Already these considerations indicate the necessity of carrying out outdoor exposure tests of industrial colors (Section 3.4.5). Along the way to the Earth’s surface, the light interacts with particles of the atmosphere; its intensity is reduced by absorption and scattering. The light scattering is caused by the molecules in the air and this is responsible, for example, for the blue sky. According to the Rayleigh law J=

V π 2 (n − 1) 2 · · E · cos2 ϑ, N r 2 λ4

(2.1.3)

short wavelength blue light is scattered more strongly than the long wavelength red light because λ is contained in the denominator of this expression. The

2.1

Optical Radiation Sources and Interactions of Light

17

further quantities in Equation (2.1.3) are defined as follows: J the intensity of the scattered light, N the number of scattering particles per unit volume V, n the refractive index of the scattering medium, r the particle radius, E the amount of the electric field strength, and cos2 ϑ the phase function (see Section 5.1.5); ϑ denotes the scattering angle with regard to the incident intensity. The Rayleigh law is only valid for wavelengths λ which are longer than the particle radius r. In contrast to the blue color of the sky, sunrise and sunset are caused by scattering and absorption of light in the atmosphere, more precisely due to the air molecules as well as to aerosols (water drops, dust particles, etc.). On the long and nearly tangential optical path of the light through the layer of air, blue wavelengths are more strongly scattered and absorbed. The remaining blue light, therefore, reaches the observer on the Earth with considerably less intensity as compared with the much less scattered long wavelength red light. The Sun and the sky, therefore, appear reddish. In addition to dependence on daytime, received sunlight changes due to weather conditions, geographical latitude, season, and due to the approximately 11-year sunspot cycle. Accordingly, the color temperature of daylight is subject to substantial variations and takes values in the range of 5,500 K for direct sunlight to more than 14,000 K for blue zenith skylight. Simultaneously, the spectral power distribution changes. This is shown in Fig. 2.3 with curves normalized at the wavelength 555 nm. At this wavelength, the sensitivity of the human eye is at its highest (Section 2.4.6).

a

Relative spectral energy

b

400

c d e

500

600

λ

700

nm

Fig. 2.3 Relative spectral energy distribution curves of daylight, normalized at 555 nm: (a) cloud-free zenith skylight, (b) cloud-free north skylight, (c) overcast skylight, (d) medium daylight, and (e) direct sunlight [4]

18

2 Light Sources, Types of Colorants, Observer

The daylight variations mentioned above create extra complexities for the unambiguous visual and objective assessment of non-self-luminous colors and their typical properties. A single color sample can produce a completely different color impression simply due to a changing illumination condition. In the practice of color physics, it is necessary to use reproducible artificial light sources which have nearly constant spectral power distributions. These artificial light sources are often referred to as technical sources. This corresponds to a constant color temperature if aging effects are neglected. From an economic point of view, the sources should also have a reliable working life of more than 1,000 operating hours. These standards are fulfilled by most of the technical illuminators of importance in the color industry; in the following section, we turn toward such kinds of sources.

2.1.3 Technical Light Sources For solving coloristical problems of non-self-luminous colors, technical light sources are used exclusively. The main reason for this is the high reproducibility of the generated spectrum. In technical temperature radiators, a metal of high melting point is heated up by an electric energy supply to such an extent that a continuous spectrum is emitted in the visible range; this spectrum is similar to that of a blackbody radiator of the same temperature. A temperature radiator in widespread use is the tungsten filament lamp; its color temperature is essentially dependent on the filament thickness, the applied voltage, and the kind of gas filling of the bulb. The so-called tungsten–halogen bulb contains bromine or iodine which increases the light efficacy, the working life, as well as the color temperature from about 2,800 to 3,000 K. The tungsten filament lamp of color temperature 2,856 K is named standard illuminant A by the CIE. The gradual loss of filament thickness in normal tungsten lamps is slowed down by the included halogen: the vaporized tungsten combines with the halogen, cools down at the surrounded quartz bulb, and reaches – by convection – the hot filament surface; there it dissociates so that tungsten is removed. Tungsten filament lamps typically emit light of yellowish color. The accompanying spectral energy distribution is shown in Fig. 2.4. Furthermore, in a tungsten arc lamp with an argon atmosphere, both tungsten electrodes are heated by an arc discharge in such a way that a radiation distribution is produced similar to that of the tungsten filament lamp; the accompanying color temperature amounts to about 3,100 K. A carbon-arc lamp shows a color temperature of 6,000 K and a very high luminance of about 1.6 Gcd/m2 .1

1 The unit candela (cd) is defined as the luminous flux radiated from 1/60 cm2 of a blackbody with temperature 2.042 K.

2.1

Optical Radiation Sources and Interactions of Light

19

200

Spectral energy distribution S (λ)

A

150 D65 100

50

0 300

400

500

600

λ

nm

Fig. 2.4 Spectral energy distribution of a tungsten filament lamp (CIE standard illuminant A) and a UV-filtered xenon lamp (CIE standard illuminant D65)

The term luminescence radiators represents a group of radiators including so-called discharge lamps, as well as photoluminescence radiators [5, 6]. In contrast to temperature radiators, luminescence radiators emit either a line spectrum of discrete wavelengths or a band spectrum of broader wavelength intervals. Line spectra are exclusively generated by gas discharge lamps. The physical mechanisms for generating line spectra are first to accelerate charge carriers by an electric field; during collision with the gas atoms, excitation energy is transferred to the outer electron orbits of these atoms. On the basis of the quantized energy of the electron shells, the electron transition into the ground level results in emission of light with discrete wavelengths λ according to Equation (2.1.2). The actual temperature of luminescence lamps is clearly far lower than the surface temperature of temperature radiators of the same light color. Among the technical gas discharge lamps, only the filtered light of xenon or mercury vapor lamps is of major importance for visual assessment or spectral measurement of colors. The emission of light in gas discharge lamps is based on the same physical mechanisms as in luminescence radiators. At first an electric voltage pulse in a xenon atmosphere causes free charge carriers. In a highpressure xenon lamp under pulsed or constant voltage, the charged particles generate a nearly continuous spectrum in the visible range. This is accompanied by a small amount of UV radiation. The spectral energy distribution shows a flat peak at a wavelength of about 450 nm and the emitted spectrum shows only a

20

2 Light Sources, Types of Colorants, Observer

slight decrease in magnitude for longer wavelengths. Therefore, the perceived light appears slightly but insignificantly bluish; this can be seen in Fig. 2.4, curve D65. The radiation distribution is similar to that of diffuse daylight at midday on cloudless north sky, cf. Fig. 2.3, curve d. For these reasons, a UV-filtered xenon lamp of color temperature 6,500 K is used in the color industry to simulate midday light. The spectral energy distribution of this xenon discharge lamp is standardized; it is termed by the CIE as standard illuminant D65. The CIE recommends the use of xenon lamps with color temperatures of 5,000, 5,500, or 7,500 K, if the standard illuminant D65 is not available. The mercury vapor discharge lamp generates a line spectrum with emission wavelengths of 405, 436, 546, 577, and 579 nm, as well as in the UV range of 254, 314, and 365 nm. Because of the energetically high UV amount, this discharge lamp is utilized in a so-called light booth for visual assessment of fluorescence colorants, artificial color fastness tests, and in fluorescence microscopy. A light booth consists of a small one-sided open compartment with one or two small platforms to lay down the color samples to compare, as well as different non-glare light sources which can be individually switched on. The abovementioned emission wavelengths are also used for wavelength-scale calibrations of color measuring instruments. The UV fraction of the mercury spectrum is furthermore applied to stimulate the phosphorus in fluorescent lamps in order to initiate photoluminescence in the visible range. The spectral composition of the resulting band spectrum or the resulting light color depends on the chemical structure and the mixing ratio of the involved phosphorus. For color assessment of special importance, there is the cold white light of the fluorescent lamp CWF (identical with illuminant FL 2) and the light emission of the so-called three-band lamp TL 84 (identical with FL 11); the three-band lamp has radiation maxima at wavelengths of about 440, 550, and 610 nm; see Fig. 2.5. These wavelengths have spectral colors of blue, green, and red and cause trichromatic a neutral white light color. Fluorescent lamps are in widespread use only because of economic reasons: they have a luminous efficacy and a physical life which are about eight times higher than those of tungsten filament lamps, cf. Table 2.2. Light sources of principle importance in the near future are expected to be light emitting diodes (LEDs) and lasers, which greatly ripened technically in the 1960s. The central component part of an LED consists of a p–n semiconductor junction. A voltage between 1 and 15 V in conducting direction and a current of order 50 mA release photons in the p–n region. These photons are generated by an energy surplus from recombining electrons and defect electrons (holes). Available luminescence diodes doped with suited chemical compounds can emit quite monochromatic light with half-widths of 6–25 nm, for example, at wavelengths of 400 nm (gallium-nitride diode), 600 nm (gallium-arsenicnitride diode), and 660 nm (gallium-phosphide-zinc-oxide diode). The benefits of LEDs are the short switching time of about 5 ns, the small spectral

2.1

Optical Radiation Sources and Interactions of Light

21

Spectral energy distribution S(λ)

80

60

FL 11 40

FL 2 20

0

400

500

λ

600

nm

Fig. 2.5 Spectral energy distribution of fluorescent lamps: cool white fluorescent CWF (illuminant FL 2) and three-band lamp TL84 (illuminant FL 11) Table 2.2 Properties of five selected illuminants Color Correlated color rendering temperature/K index

Light efficacy/ lm/W

2,856

100

12

Tungsten filament lamp

CIE standard D65 illuminant D65, middle daylight

6,500

94

35

UV-filtered xenon lamp

Cold white daylight

FL 2

4,230

64

70

Fluorescent lamp CWF, cool white fluorescent

Bluish white daylight

FL 7

6,500

90

80

Broadband fluorescent lamp

4,000

83

90

Three-band lamp TL84

CIE CIE illuminant abbreviation CIE standard illuminant A, evening light

A

White daylight FL 11

CIE simulator

22

2 Light Sources, Types of Colorants, Observer

half-width of the emitted intensity, the high degree of optical efficiency, and the long working time. Disadvantages up to now have been the low illumination intensity in comparison to traditional light sources. Improvements in these respects, at the time of this writing, are the subject of ongoing research and development. The term laser is an abbreviation of “light amplification by stimulated emission of radiation.” A laser is, therefore, an optical amplifier which is based on the principle of stimulated emission of light. To initiate stimulated emission of light2 , an irradiating field, in some sense, forces the emission of light in atoms, molecules, or ions of gases, liquids, or solids. The incident field of frequency f has photon energy according to Equation (2.1.2). The primary requirement for stimulated light emission is that this photon energy is at least the natural energy difference of the medium. In such cases, the medium that has some population in an excited state has some return to the ground state. This emitted energy is incorporated into the incident field. In order to obtain an amplification of radiation by stimulated emission, the energetically higher levels or bands of a medium should maintain a state with a greater degree of filling. This greater electron number or population in the upper energy state is usually maintained using an energy supply such as flash lamps, other laser pump sources, currents in semiconductor laser, or atom/electron collisions. Typical classification of lasers is along the lines of the physical state of the gain medium: solid state (crystals), semiconductor, liquid (usually organic dyes), or gas lasers, for example. The ruby laser with emission wavelength of λe = 694.3 nm is a solid-state laser. Semiconductor lasers are, for example, indium-gallium-phosphide (In1-x Gax P) or aluminum-gallium-arsenide lasers (Alx Ga1-x As); the emitted monochromatic wavelength of each usually lies in the range 500 and 1,000 nm depending on the content x of the indicated element. Dye lasers are the dominant class of liquid lasers; typical laser mediums are dyes such as coumarin (460 nm ≤ λe ≤ 560 nm) or rhodamine (535 nm ≤ λe ≤ 630 nm). The most well-known gas lasers are the helium–neon laser (632 nm) and the argon-ion laser (wavelengths of highest intensity 488.0 nm and 514.5 nm). The advantages of lasers are clear, considering the outstanding features of the emitted light: constant frequency, highly monochromatic, spatial and temporal coherence, high beam directivity, and adjustable energy density. In the color industry, lasers have been successfully used for the determination of surface gloss, covering capacity and glittering of effect colorants, as well as size distribution of pigment particles in powders, among other things. In the following section, we concentrate on specific properties of light sources which are of special interest for colorimetric applications.

2 The opposite is

absorption, or, more precisely, stimulated absorption.

2.1

Optical Radiation Sources and Interactions of Light

23

2.1.4 Illuminants In the previous section, the physical basics of light emission and the applications in technical light sources have been introduced. Now, we direct our attention toward the special handling of light sources in colorimetry or color matching. Unquestionably, the vast variety of technical light sources complicates the unambiguous visual assessment of colors: colored objects are exposed to changing natural as well as artificial illuminations such as daylight, evening light, or fluorescence light. The change in illumination can alter the visual color impression (see below). The CIE has, therefore, recommended the most representative light sources to use for color assessment applications. For clearness and better communication, four terms should be identified. These terms describe the different kinds of light sources: 1. CIE illuminant: this corresponds to a theoretical source of a tabulated relative spectral power distribution S(λi ); 2. CIE standard illuminant: only two illuminants are standardized by the CIE, illuminant A and illuminant D65; 3. CIE source: corresponds to a technically realized CIE illuminant; 4. CIE simulator: is a technical source which approximately corresponds to the desired CIE illuminant. The first and second terms need some further explanation. The CIE specified several representative illuminants [7], among them are the following: a. three temperature radiators designated D50, D55, D75 with color temperatures of 5,000, 5,500, and 7,500 K, respectively; b. twelve fluorescent lamps designated from FL 1 to FL 12; the illuminants FL 1–6 emit line spectra, FL 7–9 broadband, and FL 10–12 narrowband spectra. Among these, FL 2, FL 7, or FL 11 are preferably used in colorimetry. In Fig. 2.5, only the spectral power distribution of illuminants FL 2 and FL 11 are shown; c. in the end, five high-pressure lamps designated as HP 1–5, of which two are sodium vapor lamps and three metal halide lamps; these are normally not significant in colorimetry but rather in lighting engineering. The two CIE standard illuminants are characterized by the following features: the spectral power distribution S(λi ) of standard illuminant A is given by the Planck law of radiation (2.1.1), whereas that of D65 is given by tabular values [8, 9]. These values correspond to the UV-filtered emission of a high-pressure xenon lamp shown in Fig. 2.4. Standard illuminant A is recommended for simulation of room light in the evening, D65 of midday light of color temperature 6,500 K.

24

2 Light Sources, Types of Colorants, Observer

The tabular values of a CIE illuminant are generally used for computation of color values. The corresponding simulation illuminant serves for visual assessment of color patterns. In other words, the real light source which is used to illuminate a color sample is, for the purpose of calculation, substituted by a theoretical simulation source, consisting of discrete wavelengths and power emission. This can clearly be a reason for deviation between the visual assessment and the colorimetric result. A further deviation can result from the so-called CIE standard colorimetric observers. This is not discussed until Section 2.4.6. The five most commonly used illuminants in colorimetry are D65, A, FL 2, FL 7, and FL 11; a selection of their properties is given in Table 2.2. While the standard illuminant A is assigned a true color temperature, the illuminant D65 and the fluorescent radiators have only correlated color temperatures. These are for the luminescence sources FL 2 –11: 4,230, 6,500, and 4,000 K, respectively. In most cases, the change of illumination also results in a change of perceived color. This can be caused either by the colorants themselves or by the light source used. If the spectral power distribution is responsible for color changes, this is attributed to the color rendering of the illuminating source. The yellowish light of the sodium vapor lamp HP 1, for example, bathes each chromatic color in a pale yellow. This is because sodium emits only two closely spaced wavelengths of 589.0 and 589.6 nm in the visible range. The CIE proposed the dimensionless color rendering index Ra to characterize the grade of color rendering of light sources [10–12]. This index takes values in the range 0 ≤ Ra ≤ 100. The sodium vapor lamp HP 1 has an Ra value of 20; this indicates that colors are quite distorted. In contrast, the CIE standard illuminant A takes the highest possible value of 100. An additionally used characteristic, which has a meaning in terms of energy, is the light efficacy of a radiator. This economic quantity is defined as the ratio of emitted luminous flux of a light source to the input power of unit lm/W.3 As can be seen from Table 2.2, the displayed fluorescence lamps show a higher light efficacy than temperature radiators of equal or lower color temperature. From a comparison of the spectral power distributions shown in Figs. 2.4 and 2.5, it is possible to understand how the change of a source alters the color impression. Consider Fig. 2.4: using source A, the color sample appears more yellow and red compared with illumination of a D65 simulator. This is because of the continuously increasing radiation energy characteristic of the source A from yellow to red wavelengths with quite small values at short wavelengths. Consider now Fig. 2.5: the same color sample is rendered bluish white with FL 2 source, or with FL 11 source, redder in comparison to D65 simulator. Colors 3 By definition, the unit lumen (lm) is the luminous flux which a point light source of emissiv-

ity 1 cd (candela) emanates evenly in all directions in a solid angle of 1 sr (steradian): 1 lm = 1 cd sr; 1 steradian corresponds to a solid angle Ω – of even circular cone with center point in a sphere of radius 1 m – which cuts an area of 1 m2 out of the sphere surface, cf. Fig. 5.1.

2.1

Optical Radiation Sources and Interactions of Light

25

illuminated with a D65 or FL 7 source are rendered and perceived in a similarly balanced way as under midday light. This is because of the nearly constant and high values of the corresponding emission spectra in the visible range.

2.1.5 Geometric Optical Interactions There are various possible interactions between incident light and atoms, molecules, particles, or crystals. Of these interactions, we are primarily interested in the color appearances that result. In a plane electromagnetic wave, the electric and magnetic vectors E and H are perpendicular to one another, and, in addition, mutually perpendicular to the propagation direction. The so-called wave vector k is oriented in the propagation direction. The electromagnetic wave carries the energy flux density in the direction of k, given by vector S (named as Poynting vector) and relation S = E × H.

(2.1.4)

Figure 2.6 shows the connection between the three vectors E, H, and S. In the figure, the electric and magnetic vectors are shifted a quarter wavelength in phase with respect to one another. E

S

H Fig. 2.6 Electric and magnetic field of a stationary wave

The amount of energy flux density S carried by such waves, also termed as flux density, or short flux, is the origin of interactions with the molecules or particles of colorants to produce colors. Color production of non-self-luminous colors can be caused by simple or multiple reflection, refraction, absorption, scattering, interference, and/or diffraction. When the wavelength of the light (order 0.4 to about 1 μm) is much smaller than the size of the objects that it interacts with (i.e., macroscopic objects), the light no longer behaves strongly as a wave, but rather propagates in straight lines according to geometrical optics. Reflection, refraction, absorption, or scattering can occur simultaneously if the light is incident on macroscopic boundary surfaces consisting of mediums with different optical densities. The polarization

26

2 Light Sources, Types of Colorants, Observer

of light can intensify normal color appearance. This can appear especially for some absorption pigments and liquid crystal pigments. Materials can be illuminated by directional, diffuse, or mixed light. Quite simple, but of great importance, is the directional reflection – also denoted as specular reflection. Directed reflection arises from directional light at smooth, polished, or glossy surfaces, for example at organic binders, synthetic polymers, glasses, metals, as well as colorations with absorption and effect pigments. According to the reflection law, the angles of the incident ϑi and reflected light ϑ r , measured with respect to the normal of the reflecting surface, are equal: ϑi = ϑ r . Additionally, both rays and the normal of the reflecting surface lie in the same plane, that of the paper in Fig. 2.7. It is important to note that for visual assessment of colorations of glossy surfaces one must strictly avoid observations in the direction of the specular angle. For visual inspection of absorption colorations with collimated light, the surface should be illuminated from the side and the observation performed perpendicular to the sample surface. In contrast, the visual assessment of effect colorations requires a sophisticated procedure, cf. Figs. 2.29 and 2.30.

ϑi

ϑr

Fig. 2.7 Depiction of the reflection law with incident and reflected beams, as well as angle of incidence, and specular angle, each from normal to the surface

If the medium behind the glossy surface is transparent and of different refractive index than the first medium, the beam is additionally refracted into this medium. The refracted ray deviates from the original direction, see Fig. 2.8a, b, due to the different indices of refraction in the two media. The angle of refraction ϑ 2 depends on the angle of incidence ϑ 1 and the ratio of refractive indices n2 /n1 of the adjoining mediums according to Snell’s law of refraction sin ϑ1 n2 = =n sin ϑ2 n1

(2.1.5)

(original W. Snel van Royen, 1621). In general, the refractive indices are also wavelength dependent, this normally results in violet light being refracted at a steeper angle than red light. This property is called dispersion [2] and results in prism effects.

2.1

Optical Radiation Sources and Interactions of Light

27

ϑ1

ϑ2

n1

n1

n2

n2

ϑ2

ϑ1

a)

b)

Fig. 2.8 Refraction of light at the boundary surface of (a) an optically thinner medium and (b) an optically denser medium

The reflected fraction r(μ, n) of the directional beam at the boundary surface follows from the Fresnel equation      1 μn − w 2 μ − nw 2 r(μ,n) = + , (2.1.6) 2 μn + w μ + nw where μ = cos ϑ ,

w2 = 1 − (1 − μ2 )n2

(2.1.7)

[13, 14]. Equation (2.1.6) can be derived from Maxwell equations of electrodynamics [14]. The reversal of light direction does not change the reflected fraction nor the law of refraction. The reversibility of the light path without change of effect is a general principle of geometrical optics [15]; this principle is used in color measuring methods among other things (Section 4.1.2). In the case of light incident perpendicular to the surface, the special reflected fraction is given by   n−1 2 . (2.1.8) r(1, n) = n+1 This follows from Equations (2.1.6) and (2.1.7) using μ = 1. For air with refractive index n1 ≈ 1.0, for example, and plastics or binders with a typical value n2 = 1.5, using n = n2 /n1 , the normal incidence reflected fraction is r = 0.04.4 In other words, under these conditions, 4% of the incident light is immediately 4 The cited refractive indices in this book represent values which – as usual – belong to the wavelength of the sodium line of 589.0 nm.

28

2 Light Sources, Types of Colorants, Observer

reflected from the surface of a colored sample; this amount is not available for further light interactions in the volume of a color sample. The reflectance of pure metals follows from Maxwell’s equations as well, provided that the complex refractive index nˆ is introduced: nˆ = n(1 + iκ).

(2.1.9)

The quantity nˆ is divided into the real part n for the refraction and the imaginary part nκ describing the light absorption at the interface. The quantity κ is √ named attenuation coefficient. In Equation (2.1.9), i is the imaginary unit (i = −1). For directional light incident perpendicular to the metal surface, the reflected total amount is given by r(n, κ) =

(n − 1)2 + (nκ)2 . (n + 1)2 + (nκ)2

(2.1.10)

For κ = 0, this formula reduces to Equation (2.1.8). The product nκ is termed as absorption coefficient; some measured values of n, nκ , and r(n, κ) for metals used for metallic pigments are listed in Table 2.7. A further sort of reflection occurs if a light beam enters an optically thinner medium coming from an optically denser medium. Note that the refracted ray cannot exceed an angle ϑ 2 = 90◦ ; see Fig. 2.9. For a refractive index n = 1.5, the corresponding incidence angle is ϑ 1 = 41.8◦ . In general, from the law of refraction (2.1.5), it follows that rays, with angles of incidence with γcr ≥ arcsin (1/n), are totally reflected back into the optically denser medium. The quantity γcr is called the critical angle of total reflection or in short critical angle. If

ϑ2 n1 n2

ϑ1 γcr

γcr

Fig. 2.9 Critical angle γcr at a boundary surface of different refractive indices

2.1

Optical Radiation Sources and Interactions of Light

29

the total reflected light cannot immediately leave a colored layer, it participates further in the interactions with the color-producing particles until it is absorbed or leaves the layer. Total reflected rays of angles γ ≥γcr are called partly directed in this text. For unpolarized light, a further property follows from the law of refraction with regard to the refracted ray. In the case that the reflected and the refracted rays make a right angle, the light of the reflected ray is linearly polarized, in fact perpendicular to the plane of incidence; see Fig. 2.10. This special angle of incidence is denoted as Brewster angle ϑB and is given from the law of refraction (2.1.5) with ϑ 2 = 90◦ – ϑB : tan ϑB = n.

(2.1.11)

Fig. 2.10 A reflected beam of Brewster angle ϑB is linearly polarized perpendicular to the plane of incidence

ϑB

n1 n2

ϑ2

The Brewster angle depends only on the ratio of the refractive indices at both boundary surfaces. For a ratio of n2 /n1 = n = 1.5, the Brewster angle of ϑB = 56.31◦ results. The critical angle γcr and the Brewster angle ϑB are shown in dependence on n in Fig. 2.11. Polarized light produces always more intensive colors than unpolarized light; polarized light is generated in some absorption colorants and especially in liquid crystal pigments. In addition to that from Equation (2.1.6) and the above considerations, the reflection coefficient of directional light depends on the direction of polarization parallel to the plane of incidence. These properties also follow from Fresnel equations [14]. This is shown in Figs. 2.12 and 2.13 for a refractive index value of n = 1.5 in dependence on the angle of incidence ϑi . The outer reflectance coefficient at the boundary of the optically thinner medium begins to differ from one another for the two rectangular linear polarizations already for small angles

30

2 Light Sources, Types of Colorants, Observer 100

Angle / degree

80

60

γcr

40

ϑB 20

0 1.0

1.2

1.4 1.6 Refractive index n

1.8

2.0

Fig. 2.11 Critical angle γcr and Brewster angle ϑB in dependence of refractive index n

Outer reflection coefficient

1.0

0.8

Polarisation: parallel normal

0.6 n = 1.5 0.4

0.2

0

0

20

40

60

80

Angle of incidence ϑ1

Fig. 2.12 Outer Fresnel reflection factor as function of angle of incidence for polarization parallel and perpendicular to the plane of incidence

of incidence (Fig. 2.12). This difference increases strongly with the angle of incidence. The inner reflection coefficient at the inner boundary of the optically thicker medium shows the same behavior but is compressed into the angle range 0 < ϑ2 < 41.8◦ ; see Fig. 2.13. The high increase of this reflection coefficient is caused by the critical angle of total reflection. Consider now diffuse illumination instead of directional light. This alters the reflection character. The majority of natural and artificial light propagates diffusely. Because of this, it is, perhaps, most reasonable to measure and visually

2.1

Optical Radiation Sources and Interactions of Light

31

Inner reflection coefficient

1.0

Polarisation

0.8

parallel normal 0.6 n = 1.5

0.4

0.2

0

0

20

60 40 Angle of incidence ϑ2

80

Fig. 2.13 Inner Fresnel reflection factor as a function of angle of incidence for polarization parallel and perpendicular to the plane of incidence

judge color samples under diffuse illumination. Ideal diffuse light is in the forward direction inside an angle range of ±90◦ and of equal energy over the entire range of these angles. Because of that the radiation power, the optical interactions, and specially the reflection conditions at the boundary surfaces are changed. The reflection coefficients for diffuse radiation follow from energetic considerations leading to the relation 1 − rd∗ n22

=

1 − rd . n21

(2.1.12)

The quantity rd∗ denotes the reflection coefficient of diffuse light at the boundary of the optically thinner medium with n1 and rd stands for the reflection coefficient of the optically denser medium. In Fig. 2.14, the reflection coefficients for diffuse light are represented schematically by arrows for simplicity. For diffuse illumination from air of n1 ≈1.0 in a layer of refractive index n2 = 1.5, the appropriate reflection coefficients rd∗ = 0.09178 and rd = 0.59635 come from

Fig. 2.14 Reflection coefficients of diffuse radiation at a boundary surface of different refractive indices (schematically)

32

2 Light Sources, Types of Colorants, Observer 1.0 rd

Reflection coefficient

0.8

0.6

0.4

rd∗

0.2 r 0 1.0

1.2

1.4 1.6 Refractive index n

1.8

2.0

Fig. 2.15 Three sorts of reflection coefficients in dependence on refractive index n: r for directional illumination perpendicular to the surface, rd∗ for outer diffuse illumination, and rd for inner diffuse illumination of a material

the literature [13]. The reflection coefficients for diffuse light rd∗ and rd as well as for directional light at perpendicular illumination r are shown in Fig. 2.15 in dependence of the refractive index n. The boundary surface reflection certainly complicates the visual and measuring assessment of colored samples: this surface reflection is superimposed on the entire visual impression as well as the spectrometric measuring results. But the essential and interesting parts of color sensation are generated by the light interactions in the volume of a colored layer. For the following, we define the reflection of an optical medium as the amount of incident radiation energy which is backscattered from the volume and this is superimposed by the surface reflection energy. Correspondingly, the transmission is the amount of the incident light energy which overcomes the interactions in the volume and exits the second boundary surface of the optical medium. The accompanying energies are called reflection and transmission energy; these are abbreviated by WR and WT . The electromagnetic field of a light wave can drive vibrations of suitable charge carriers in atoms or molecules of absorption colorants. This additional absorption of energy leads sometimes to emission of secondary radiation; this process is denoted as scattering. The scattering is elastic if the wavelengths of the incoming and scattered light are equal. This is the case especially within non-self-luminous colors but also for Rayleigh and Mie scattering (Sections 2.1.2 and 5.1.3, respectively). Inelastic scattering, however, produces a change of scattered wavelengths such as in Raman and Brillouin scattering [16].

2.1

Optical Radiation Sources and Interactions of Light

33

In addition to scattering, a part of the incoming light energy is normally absorbed by the charge carriers of the colorant molecules and not scattered. This causes an increased molecular vibration energy and, therefore, a temperature increase of the coloration. The absorption of energy of amount WA is finally absent from the reflected, transmitted or scattered light. In the most colored layers, scattering and absorption occur simultaneously in different amounts, and additionally dependent on wavelength. The three mentioned energy components WR , WT , WA come from the incident energy Wi . Therefore, the energy conservation law, in our case, amounts to Wi = WR + WT + WA .

(2.1.13)

1 = R + T + A.

(2.1.14)

Division by Wi results in

The quantities R, T, A are denoted as follows:  R = WR Wi reflectance,

(2.1.14a)

 T = WT Wi transmittance,

(2.1.14b)

 A = WA Wi absorption.

(2.1.14c)

These quotients are, for simplicity, also denoted as reflection, transmission, and absorption but also reflection factor, transmittance factor, and absorption factor, respectively. The law of energy conservation is an axiom of physics and is of fundamental importance; in the above formulation, it plays a central role in the entire radiative transfer of optical systems. The energy conservation law is even valid for each single wavelength, therefore, valid independent of the irradiated spectral power distribution. Furthermore, this law is independent of any specifications concerning the interacting particles of the optical medium. From that follows a basic realization, which is of great importance for the further discussions in this text: The resulting values of reflection, transmission, or absorption are characteristic quantities of the optical medium; in our case, they are essentially caused only by the colorants of the chromatic color. Reflectance and transmittance are determined with suitable color measuring instruments (Sections 4.2.1 and 4.2.2); absorption and scattering are characterized by corresponding optical constants which follow from optical models (Sections 5.1.2 and 5.1.4). Absorption and scattering are generally the most

34

2 Light Sources, Types of Colorants, Observer

important quantities of absorption colorants. In effect pigments, however, the dominant processes are wavelength dependent such as interference or diffraction. The basic optical laws responsible for color production of pearlescent, interference, and diffraction pigments are discussed in the next two sections.

2.1.6 Interference of Light The colors produced by absorption colorants and metallic pigments are essentially based on processes such as reflection, absorption, and scattering and are occurring at the surface and in the volume of a colored sample. In contrast to that, impressive color effects are generated by interference of light waves in pigment particles composed of an appropriate sequence of layers. Interference is an effect caused by superposition of suitable waves (of, e.g., liquids, gases, electromagnetic fields, elementary particles). Interference of light is, for example, responsible for the colors of soap lamellas, oil films on water, or coated lenses [17]; the colors of opals, natural pearls, insect wings, or bird feathers are in addition based on interference. The colors of interference pigments result from light waves, which are reflected at the inner and outer layer boundaries and which superimpose with the incoming waves. The produced colors are controlled by the thickness and refractive index of the different layers among other things. The layer thicknesses vary from about 10 nm to 1 μm; see Fig. 2.40 [18]. Interference colors can be distinguished from normal absorption colors by the color change in dependence of the observation angle; this is in some way similar to diffraction colors. A necessary requirement for interference is the existence of coherence. Most of temperature and luminescence radiators emit incoherent waves, because the single atoms of the source oscillate independently from each other, only short wave trains are produced; between the single waves exists no constant phase relationship. Waves are coherent, if the time dependence of their amplitude is the same irrespective of a phase shift. In the case of harmonic waves, this means that the frequencies of the waves have to be the same; however, they can have a constant phase difference. Coherent sine-shaped waves must, therefore, be of equal frequency. Coherent waves can result, for example, from the reflection of a radiative field at a mirror. From this perspective, laser light is of nearly perfect coherence because it is amplified during multiple reflections. Interference pigments normally consist of at least two layers of different refractive indices to produce a suitable reflection at the boundary layer, cf. Equation (2.1.6). In Fig. 2.16, there is a simplified illustration of the reflection and interference of light at a plane parallel layer. The reflected waves of beams R1 and R2 interfere above the layer. The waves of R 1 initiated by R1 take a longer way to the surface and, therefore, have an optical path length difference G with regard to the waves of R 2 . In view of the different path lengths, the ratio of refractive

2.1

Optical Radiation Sources and Interactions of Light R1

R2

35 R'1

ϑ1

R'2

ϑ1

n1 n2 d

ϑ2 n3

Fig. 2.16 Interference at a plane parallel layer of different refractive indices

indices n = n2 /n1 , the refraction law (2.1.5), and the phase jump of λ/2 caused by reflection of the waves at the upper layer surface, the difference G is given by

G = 2d ·

 λ n2 − sin2 ϑ1 + , 2

(2.1.15)

where d stands for the layer thickness and ϑ1 for the angle of incidence. At some locations, the wave amplitude is increased by the so-called constructive interference of the incident and reflected waves. This occurs if G is an evennumbered multiple 2z of λ/2, fulfilling the condition: (2z − 1)λ = 4d ·

 n2 − sin2 ϑz ,

z = 1, 2, 3, ... .

(2.1.16)

Destructive interference occurs for  G = (2z + 1)λ 2,

z = 0, 1, 2, ... .

(2.1.17)

The positive integer z is called interference order. The amplifying light waves and, therefore, the corresponding colors can be modified according to Equation (2.1.16) by the material quantities d and n; this is used to a great extent for realization of different kinds of pearlescent and interference pigments. For color sensation, the additional change of color impression in dependence on the observation angle ϑz can be quite strange. The quantity ϑz belongs to the different interference orders z instead of the constant angle ϑ1 . Generally, the intensity of the amplified waves decreases strongly with the number of z.

36

2 Light Sources, Types of Colorants, Observer

Some special interference features result in the case that light is incident perpendicular to the surface of a layer. Colors of pearlescent and simple interference pigments are visually characterized by observation perpendicular to the colored surface; some important technical applications come out of this. From Equation (2.1.16) with ϑ1 = 0 for the dominant first interference order (z = 1), the simple result d = λ/4n follows. Furthermore, if the interference wavelength λ and the refractive index n are constant, the layer thickness for order z, given by  d = (2z − 1)λ 4n,

(2.1.18)

leads to constructive interference. A stepwise increase of the layer thickness by the quantity d leads to a distance of Δd = λ/2n between two adjacent intensity maxima. The same distance holds for neighboring minima. These considerations are especially used to reduce the reflection of optical systems by destructive interference. With the so-called optical coating, the optical surfaces are coated with an inorganic layer by physical vapor deposition; the refractive index nC of the coating has to satisfy the condition √ (2.1.19) nC = n1 n2 , where n1 and n2 are the refractive indices of air and of the optical material, respectively. Unfortunately, the effectiveness of reflection reduction is limited to a middle visible wavelength. To achieve a nearly regular reduced reflection of wavelengths in the entire visible range, a multi-layered coating on both sides of the optical element is necessary at the most 10 layers which are tuned with each other. This is a type of dielectric coating called an anti-reflection coating. The so-called dielectric mirror coating relies likewise on interference. For this, multi-layer coatings of alternately higher and lower refractive indices nh and n1 are produced; see Fig. 2.17. If each single layer has a constant optical thickness dh = λ/4nh or dl = λ/4nl , then the reflected waves of first order interfere constructively with the incoming light caused by the additional phase jump at the boundary of the optical denser medium. Therefore, a narrowband mirror results; the reflectivity depends on the difference of the refractive indices of the layers [17]. With change of the layer parameters, the width of the wavelength interval can be controlled. These considerations are also used to achieve suitable layer structures in pearlescent and interference pigments to produce a dominant color component. Interference colors can be further improved by multiple reflection of light between two semi-transparent mirrors at distance d, similar to the placement in a so-called Fabry–Pérot interferometer; see Fig. 2.18. One part of the reflected light is transmitted through the second layer. Multiple reflection leads to a great number of partial beams, which interfere behind the second layer. The layer distance d and the refractive index n of the medium between the layers are chosen in such a way that only a small wavelength band is transmitted; this construction

2.1

Optical Radiation Sources and Interactions of Light

37

Fig. 2.17 Layer sequences of a dielectric mirror with high and low refractive indices nh and n1

nh nl nh nl

dh =

λ 4nh

dl =

λ 4nl

Substrate

operates as an interference filter. For fixed distance d, this construction is also called an etalon. The deciding parameters for the interference efficacy are n and d of the intermediate layer. Because adjacent beams have the same geometrical optical path difference, constructive interference is given by zλ = 2nd cos αz ,

z = ±1, ± 2, ... .

(2.1.20)

The intensified wavelengths become, therefore, smaller with increasing angle of beam incidence α z . For a layer thickness d = 300 nm and refractive index n = 1.5, the wavelengths of violet and red light (400 and 700 nm) are separated for the first order by an angle difference of about 25◦ . Founded on this principle, d

L

LQ P

Q1 n Q

αz

Fig. 2.18 Fabry–Pérot interferometer: the partial waves of points Q, Q1 produce interferences of “equal inclination”

38

2 Light Sources, Types of Colorants, Observer

in particular, is the angle-dependent color effect of multi-layered interference pigments in liquid crystal structures; see Fig. 2.43.

2.1.7 Diffraction from Transmission and Reflection Gratings When light is incident on objects or boundaries with dimensions on the order of the wavelength of the light, the wave characteristics of light become very important. This is the situation, for example, at a diffraction grating. Upon passing through the grating, some portion of the light is deflected and/or is fanned out depending on the grating geometry and the wavelength. This phenomenon is an example of Fraunhofer diffraction if the light beam is incident nearly perpendicular to the grating [19]. In addition to macroscopic structured materials, diffraction pigments can be impressed with such grating structures. This leads to color effects which are also depending on the angle of observation. A simple macroscopic transmission grating is shown in Fig. 2.19, not to scale. The geometry is simply achieved by scratching or etching of equidistant grooves in a thin plane parallel glass sheet. With recent techniques, diffraction pigments can be impressed with nanostructures. Each constant groove gap d, also called grating period, contains a narrow light-transmitting slit. The reciprocal quantity of the grating period, g = 1/d, is denoted as the grating constant; its units are given in lines per millimeter (l/mm). At each of the slits – which are spaced with typically as much as 5,000 l/mm or more – the incident wave front

αz

αi

d

αi G1

αz G2

Fig. 2.19 Diffraction conditions of an optical transmission grating (schematically)

2.1

Optical Radiation Sources and Interactions of Light

39

is diffracted according to the Huygens principle, which means that each point of a wave front is assumed to be the origin of a new elementary wave [19]. Because diffraction occurs at all illuminated grating slits, a pattern of constructively and destructively interfered waves develops behind the grating. The path difference G1 + G2 of waves coming from two neighboring slits follows from Fig. 2.19 as G1 + G2 = d(n1 sin αi + n2 sin αz ),

(2.1.21)

where n1 and n2 stand for the refractive indices in front and after the grating and α i for the angle of incidence. The diffraction maxima occur for a path difference G1 + G2 equal to an integer multiple z of the wavelength λ. With Equation (2.1.21), the relation zλ = d(n1 sin αi + n2 sin αz ), z = 0, ± 1, ± 2, ...,

(2.1.22)

follows. The zeroth-order diffraction, equivalent to z = 0, contains all wavelengths of the irradiated light. Higher diffraction orders for z = 0 are generated on both sides of the zeroth order with symmetric intensity maxima and minima. The wavelengths contained in the incident light fan out by the grating in such a manner that the condition in Equation (2.1.22) is fulfilled. The grating deflects large wavelengths stronger than shorter wavelengths; this is the converse of a prism. Moreover, the diffraction spectrum of the first order is of higher intensity compared to that of a prism spectrum. In order to avoid an overlapping of the diffraction maxima of higher order, the incident angle α i and the grating period d can suitably be tuned with each other (see below). In addition to transmission gratings, reflection gratings are also commonly used – these are especially realized in diffraction pigments. These can be formed by vapor coating both sides of a nontransparent grating structure with an additional layer of a reflecting metal, cf. Fig. 2.20; this has the added bonus of a possible improvement in the mechanical stability of the thin plates. The waves reflected from the periodically arranged mirrors interfere with the incoming waves from the opposite direction. Consequently, the diffraction pattern already known from transmission gratings develops in front of the reflection grating. The cross section of the grooves can be produced as rectangular, triangular, or sine shaped. Reflection gratings are used in modern spectrophotometers and optimized diffraction pigments, among other things. Examples of diffraction particles are shown in Figs. 2.54 and 2.55. Concerning the reflection grating in Fig. 2.20, the path difference G1 – G2 of the reflected waves from adjoining grooves follows from the expression G1 − G2 = d( sin αi − sin αz ) .

(2.1.23)

40

2 Light Sources, Types of Colorants, Observer

Fig. 2.20 Diffraction conditions of an optical reflection grating (schematically)

αi G2

αi d

αz G1

αz

In analogy to the transmission grating, the diffraction maxima are given by zλ = d( sin αi − sin αz ) ,

z = 0, ± 1, ± 2, ... .

(2.1.24)

For z = 0, it follows α i = α 0 and the grating operates like a normal flat mirror, that is, the wavelengths are not separated. Generally, the use of gratings results in spectra of higher light intensity in comparison to prisms, but the incident intensity is distributed among all diffraction orders. Among them, is the maximum for z = 0, which is of highest intensity, and also generally not of interest (see Fig. 2.21). This disadvantage can be bypassed using a so-called echelette grating5 ; see Fig. 2.22. On the basis of the special geometry of such a grating, nearly the entire intensity of the diffracted light can be concentrated into a particular diffraction order, as required. To achieve this aim, the cross section of the grooves has to meet the following requirements: 1. The desired diffraction order zB is not zero; the reflecting grating elements should be tilted by an angle α B above the grating base; this angle is called the blaze angle, after the corresponding production method known as the blaze technique.

5 echelette:

French, small ladder.

2.1

Optical Radiation Sources and Interactions of Light

41

Δα

Δβ

Fig. 2.21 Angle differences of diffraction maxima

2. The angle half-width α of the diffraction fringe, caused by this kind of grating element, has to be matched with the angle distance β between two successive diffraction maxima; see Fig. 2.21. In view of the first condition, it is useful to consider the angles from the grating base normal. The blaze angle is, therefore, given by the simple relation  αB = (αi − αz ) 2,

(2.1.25)

where α i and αz are the angle of incidence and the diffraction angle of order z, respectively. In addition, these two angles are combined with Equation (2.1.24), to give zB λB = d · (sin αi − sin αz ) , Grating normal

zB = 0, ± 1, ± 2, ... .

Face normal

αB αi αz b

αB d

Fig. 2.22 Echelette grating with blaze angle α B

(2.1.26)

42

2 Light Sources, Types of Colorants, Observer

The quantity λB is called blaze wavelength and zB denotes the blaze order. According to Equation (2.1.25), the blaze angle depends on the incident and the diffraction angles. For this reason, echelette gratings can be realized with different blaze angles. From the last two expressions, the condition zB λB = d · [ sin αi + sin (2αB − αi )] ,

zB = 0, ± 1, ± 2, ...

(2.1.27)

follows. It is independent of a diffraction angle. For improved understanding, we differentiate now between two types of light incidence – from which consequently follow different blaze angles. In the first case, we assume an illumination in the direction of the grating normal; see Fig. 2.22. In this case, the angle of incidence is α i = 0 and it follows from Equation (2.1.27):   zB λB 1 , zB = 0, ± 1, ± 2, ... . αB = arcsin (2.1.28) 2 d In the second case, the light is incident in the direction of the face normal, the so-called Littrow or autocollimation configuration. In this case, then the incident angle is equal to the blaze angle α i =α B given by   zB λB (2.1.29) , zB = 0, ± 1, ± 2, ... . αB = arcsin 2d Note that because an echelette grating of sine-shaped cross section can be approximated by a series of successive isosceles triangles, the outlined considerations are also applicable to that geometry. From the second condition above, some further geometrical conclusions result. With the designations given in Figs. 2.20 and 2.22, the relation cos αz b = d cos (αz − αB )

(2.1.30)

can be derived. In other words, the triangle geometry depends on the blaze angle as well as the angle αz of diffraction order z. Additionally, according to Equation (2.1.30), the width b of a step is specified with the groove distance d. If the illumination is carried out parallel to the grating normal, from Fig. 2.22, we have the intermediate result α z = 2α B . The condition b=d·

cos 2αB cos αB

(2.1.31)

therefore follows. On the other hand, for illumination parallel to the face normal, the condition α z = α B is given and the simple formula b = d · cos αB

(2.1.32)

2.2

Absorbing Colorants

43

follows from Equation (2.1.30). In this case, the triangle of the echelette grating is right angled. The utilizable wavelength range of such kinds of gratings is roughly limited to the interval 0.7λB ≤ λ ≤ 2λB . Absorption and scattering dissipation reduce the efficiency of a blaze grating to about 70% [20]. Accordingly, the blaze technique enables the focusing of about 70% of the influx into a desired z = 0 diffraction order. Each diffraction pigment is normally optimized with regard to the first diffraction order z = ±1. This diffraction spectrum can be observed symmetrically with respect to the direction of illumination, and is followed by further orders of lower intensity, cf. Section 3.5.5. These principles apply not only to macroscopic gratings but also to diffractive pigment particles; see Figs. 2.55 and 2.56.

2.2 Absorbing Colorants After considering different light sources and basic light interactions in the previous section, the second fundamental component for color producing of non-self-luminous colors is the color sample containing the colorants. Colorants can be divided into two groups, depending on the dominant mechanism of color production: classical absorption colorants and modern effect pigments (cf. Table 1.1). Industrially applied absorption colorants consist mainly of synthesized colors of inorganic and organic compounds, and in some rare cases of modified natural colors. In this section, we characterize dyes and absorption pigments, describe the most important color attributes and the accompanying coloristic properties as well. Some of these properties are correlated with specific spectral features of the corresponding coloration. Additionally, color-order systems will be outlined. In some application cases, such systems offer an overview of the diverse-generated absorption colors. Each of these color order systems is grouped according to preset characteristic criteria. On one such system is based a special CIE color space. It is also shown that the color impression results from light interactions in the volume as well as at the surface of a color pattern. Properties of effect pigments are described in the next section, which show a typical color development in dependence of the angle of observation, a dependence that is absent in absorption colorants.

2.2.1 Types and Attributes of Absorbing Colorants According to a rough classification, colors can be produced by 15 different physical mechanisms [21]. In the case of non-self-luminous colors, these processes are entirely attributable to energetic interactions of electromagnetic waves with the bounded electrons of atoms, molecules, particles, or crystallites of the color-producing material. With regard to absorption colorants, we first outline

44

2 Light Sources, Types of Colorants, Observer

some typical phenomenological properties of absorption pigments and afterward those of dyes. The color origin of absorption pigments can be reduced to absorption and scattering processes. Such kinds of light interactions are called selective if they are effective in a narrow range of wavelengths in the visible spectrum. Light is scattered by pigment particles if at least two conditions are met: first, the particle dimensions and the wavelengths of the irradiated light are on the same order of magnitude; second, the colorant molecules show spatially separated electric charge distributions – the so-called multipoles. Details of these are given in Sections 5.1.2 and 5.1.3. Chromatic absorption pigments are also called colored pigments or sometimes merely pigments. They consist of inorganic and organic compounds which, in either case, form crystallites of sometimes different types. The crystallite dimensions are typically of the same order of magnitude lesser as the wavelengths of light. Because of the charge separations in multipoles, the morphological non-uniform crystallites sometimes conglomerate to form differently shaped particles with sizes from 10 nm to as much as 1 μm in size. All sorts of pigments – absorption as well as effect pigments – are insoluble in a binder or any polymer matrix. The pigments are usually uniformly dispersible in such materials although some need a suited additive for that. These colorants are used not only, for example, for mass coloration of plastic materials, fibers, paper but also for coloring of lacquers, pastes, and coatings of solids of quite different surfaces. In synthetic high polymers, the pigments tend to congregate in the amorphous regions and, therefore, additionally change the mechanical, thermal, or even electrical properties of the compound. Of great importance – with regard to color physical applications – are the covering capacity (also called hiding power), color strength, and tinting power. Requirements for optimized incorporation of pigments are sufficient wettability, dispersibility, as well as compatibility of the binding materials used, polymers, or additives, among other things. Inorganic pigments consist of oxides, sulfides, sulfates, silicates, chromates, carbonates, and metal complexes, for example [22]. Compared to organic pigments, they are preferentially used on account of their distinct optical scattering power and the typical high hiding power. In comparison with organic pigments, due to their simple and stable molecular structure, inorganic pigments tend to have better rheological behavior as well as increased weather resistance. Characteristically, inorganic pigments are mostly dull colors with lower color strength but with greater hiding power compared to organic colorants. A multitude of absorbing colorations with desired color properties are, therefore, achieved only with mixtures of inorganic and organic pigments. With regard to the chemical structure, organic pigments are divided into azopigments, polycyclic pigments, and anthraquinone pigments. The outstanding feature of organic pigments is their distinctive colorfulness or chroma in comparison to inorganic pigments. This generally comes with a high color strength.

2.2

Absorbing Colorants

45

Compounds of polycyclic structures, compared to molecules with azo-groups, tend to disperse better in polymer binders, have a lower migration tendency, as well as higher weather durability [23]. Table 2.3 shows the most commonly used modern inorganic and organic absorption pigments, differentiated with regard to the kind of the dominant color production mechanism. White and black pigments assume a special role in industrial color physics. White pigments stand out due to their nearly ideal scattering of light in the visible range. They are preferentially used for pure white, increase in the lightness of any coloration, or covering of a background. On the other hand, the characteristic feature of black pigments is the dominant absorption. These pigments are applied mainly in tiny amounts for black colors and for darkening of absorption colors. With calibration series of white and black pigment mixtures, the calibration of the lightness scale is, therefore, carried out between minimal scattering (pure black pigment) and maximal scattering (pure white pigment). An analog consideration holds for the case of absorption (Section 6.1.1). It is further the case that a really tiny amount of a black pigment improves the interference color of transparent pearlescent or interference pigments; this is because the black amount absorbs the complementary color produced of interference pigments. Table 2.3 lists also fluorescence and phosphorescence pigments. These are summarized by the term luminescence pigments. Both sorts absorb light normally at lower wavelengths in the range of X-rays, UV, or the visible spectrum; they often also absorb energy from electron beams. After some short time, a part of the absorbed quantum energy is reemitted but with longer wavelengths (lower energy) according to Equation (2.1.2). Fluorescence radiation is emitted spontaneously and phosphorous radiation, in particular, has a delay in the reemission. In contrast to phosphorescence (Section 4.2.6), fluorescence emission stops immediately after illumination. Unlike absorption pigments, dyes are completely soluble in a solvent or in a polymeric medium. The coloristic properties are essentially based on absorption. On account of the absence of scattering, dyes are normally transparent – notable exceptions are dark dyes in high concentrations. Dyes consist nearly exclusively of organic chemical structures. Typical groups of atoms with covalent bonds such as >C=C<, >C=O, or –N=N– (ethylene, carboxyl, or azo group, respectively), called chromophores, are typically responsible for the coloration of the organic compounds. The π-electrons6 of these covalent bonds absorb a fraction of the incoming light waves. The incorporation of further molecular groups, the so-called auxochromes, causes a color shift either to

6 In chemical compounds π -electrons form a pair of electrons which belong together to two different atoms.

Color production

Selective scattering/ selective absorption

Pigment

Absorption pigment, colored pigment Oxides Iron-II-oxide, iron-III-oxide, chromium-III-oxide, chromium-IV-oxide, chromium-VI-oxide pigments Mixtures with oxide pigments: cobalt blue, cobalt green, zinc iron brown Chromate pigments Chromium yellow, chromium orange, chromium green; chromium titanate, molybdate red, molybdate orange; copper chromate Iron blue pigments Iron cyanide blue Cadmium, bismuth pigments, ultramarine pigments

Inorganic

Typical examples

Table 2.3 Typical modern inorganic and organic absorption pigments

Azo pigments Mono-pigment, disazo-pigment, β-naphthole pigment, naphthole AS pigment, benzimidazolon pigment, disazo condensation pigment, metal complex pigment Polycyclic pigments Phthalocyanine, carbazole, quinacridone, perylene, perinone, pyrrolo/pyrrole, thioindigo pigments Anthraquinone pigments Anthrapyrimidine, flavanthrone, pyranthrone, anthanthrone, dioxazine, triarylcarbonium, quinophthalone pigments

Organic

46 2 Light Sources, Types of Colorants, Observer

Color production

Scattering

Absorption

Selective absorption, emission within 10 ns

Selective absorption, emission after 1 ms

Pigment

White pigment

Black pigment

Fluorescent pigment

Phosphorescent pigment

Pure phosphors Alkaline tungsten salts Other phosphors Alkali halogenoids, alkaline earth oxides, alkaline earth sulfides, Barium oxide: doped with Na, Mn, Ce, Sn, Cu, Ag; zinc phosphide, cadmium phosphide, gallium sulfide, zinc sulfide, cadmium selenide, gallium phosphide

Fluorite, uranylic salts, salts with metals of rare earths

Carbon black, iron oxide black, copper chromate

Titanium dioxide (anastas, rutil), zinc sulfide, zinc oxide pigments

Inorganic

Typical examples

Table 2.3 (continued)

Pure phosphors Carbazoles Other phosphors Fluorescent organic substances, embedded in crystalline matter

Oxinaphthaldazine, disazomethine

Aniline black

White plastic powders

Organic

2.2 Absorbing Colorants 47

48

2 Light Sources, Types of Colorants, Observer

higher wavelengths as with –NH2 and –OH groups (amino and hydroxyl groups, respectively) or to lower wavelengths with –NH–CO–CH3 (ethylene-acid-amide group), for example. Dyes are subdivided into natural and synthetic compounds; see Table 2.4. Dyes found in nature are generally known by common names like indigo, crimson, saffron, or alizarin, although they are prepared partial artificially today. For reasons of product constancy, generally only synthetic dyes are applied. Among synthetic dyes are azo-dye, anthraquinone dye, indigo dye, cationic dye, phthalocyanine dye, polymethine dye, triphenylmethane dye, xanthene dye, and fluorescence dye [24, 25]. Owing to their molecular double bond structures, dyes show a poorer fastness to light and weather resistance in comparison to pigments. The basic molecular interactions of fluorescence dyes and pigments are described in the literature [26]. Table 2.4 Typical examples of natural and synthetic dyes Dye

Typical examples

Natural

Indigo, crimson, saffron, alizarin

Synthetic

Azo-dye, anthraquinone dye, indigo dye, cationic dye, phthalocyanine dye, polymethine dye, triphenylmethane dye, xanthene dye, fluorescence dye

2.2.2 Pigment Mixtures and Light Transmittance The wavelengths of the visible range which are not absorbed by colorants make up a so-called complementary color. This color is the perceived color of the absorbing dye or pigment; see Table 2.5. It can be seen in the table Table 2.5 Spectral range of absorption, light color, and perceived complementary color of absorption colorants Rough spectral range of absorption/nm

Light color of the spectral range

Perceived complementary color of the colorant

380–440 440–480 480–490 490–500 500–560

Violet Blue Green blue Blue-green Green

Yellow-green Yellow Orange Red Crimson

560–580 580–595 595–605 605–750 750–780

Yellow-green Yellow Orange Red Crimson

Violet Blue Green blue Blue-green Green

2.2

Absorbing Colorants

49

that the light and complementary colors reverse their roles at a wavelength of about 560 nm. Over and above that, in Table 2.19 are given some pairs and triples of complementary colors; some of them are partly demonstrated in Color plate 1.7 These relationships concerning complementary colors are valid for uniform spectral power distributions of the irradiated light similar to a xenon discharge lamp. Complementary colors are arranged opposite (according to Hering color opponent theory) in a color plane of the CIELAB system; see Color plate 4. As mentioned in the previous section, the realization of a desired color is normally achieved with mixtures of different sorts of colorants. Apart from coloristic aspects, concerns over the compatibility and color fastness of the components are in the forefront. Colorations of lacquers, plastic materials, or textile fibers consist usually of mixtures with three up to six or more different colorants. Mixtures of different fluorescence dyes can be distorted by fluorescence extinction if the quantum emission of one dye in the visible range causes a fluorescence stimulation of a second dye in this range. For the realization of a great number of different color shades, a selection of at least 25 up to about 130 chromatic, white, and black absorbing pigments has to be made and as much as of 110 effect pigments. Among the colored absorption pigments, normally yellow and red should preponderate in comparison to violet, blue, or green shades; additionally, two to four brown colorants are normally taken into consideration. Similar considerations should be taken into account for dyes. The predicted color should match the reference color as exact as possible. In the majority of cases, there are additional properties, such as high color constancy or low metamerism, which need to be fulfilled. It is, therefore, necessary to have a broad experience with the composition of the colorant components and binding materials for mixing in order to achieve the coloristic, processing, or basic performance conditions required with regard to the reference color. Color samples are termed as transparent, translucent, or opaque in dependence on their light transmittance properties. Requirements for transparent colors are not only pure absorption and complete solubility of the used colorants but also the refractive indices of the applied colorant matrix (e.g., solvents, binding agent, or plastic materials) have to agree with those of the used colorants. Transparent optical media are characterized by the wavelength-dependent absorption coefficient. This coefficient follows from the spectrometric measurements of the transmittance and a suitable approximation of radiative transfer in optical media (Section 5.1). A transparent chromatic layer is perceived by way of not only transmitted light but also reflected light. The accompanying reflectance comes merely

7 Color plates

are inserted between Chapters 3 and 4.

50

2 Light Sources, Types of Colorants, Observer Table 2.6 Light transmittance and spectral quantities of color samples Measuring quantities

Determination quantities

Examples

Transparent

Directed, diffuse reflectance and transmittance

Absorption coefficient K

Liquids, inorganic, organic glasses

Translucent, translucent nonopaque, translucent glimmering

Directed, diffuse reflectance and transmittance

Absorption coefficient K, scattering coefficient S, phase function p

Binders, foils of partially crystalline high polymers, paper, opal glasses

Opaque

Directed, diffuse reflectance

Absorption coefficient K, scattering coefficient S, phase function p

Emulsion paints, lacquers, plastics, textiles, ceramics, leather

Light transmittance

from reflection at the illuminated outer and inner boundary surfaces which is caused by differing refractive indices. The magnitude of the reflected portion follows from Equations (2.1.6), (2.1.7), (2.1.8), (2.1.9), (2.1.10) or (2.1.12). In Table 2.6, three different sorts of color samples with regard to the degree of light transmittance are listed along with some spectral measuring and determination quantities. Translucent color patterns such as turbid films, paper, or opal glass are characterized by selective absorption and simultaneous scattering. Translucent media are only light transmitting on a small scale; nonetheless, a colored background is not completely covered. The light transmittance decreases with increasing layer thickness, this is similar to transparent layers. Some organic pigments of light yellow, orange, or red shade are translucent as are some pearlescent and liquid crystal pigments. The scattering of light occurs at the irregular surfaces or edges of the pigment particles and caused by the electromagnetic interactions with the multipoles of the pigment particles. In general, scattering of translucent colors depends on the pigment sorts used, the chemical structure of the surrounds, the refractive indices, and the structure of the boundary surfaces. Translucent colorations are particularly of interest for such coloristic applications, in which the same hue is to be realized simultaneously in a nearly transparent and almost opaque finish. In addition to reflectance and transmittance, the characteristic quantities of translucent color samples are turbidity and covering capacity (Sections 3.4.3, 3.4.4, and 3.4.5). The theoretical modeling of radiative transfer in translucent systems can actually be quite difficult. These complications are caused by the combined processes of absorption and scattering, where the latter is anisotropic in some

2.2

Absorbing Colorants

51

cases. On the basis of the different optical effects, translucent materials can be subdivided into the following groups: ideal translucent: a directional ray is partly absorbed and diffuse scattered; it exits the medium with lower intensity; translucent diaphanous: the primary ray in the optical medium is surrounded by a halo8 ; the primary ray is more attenuated than in the ideal translucent case; translucent gleaming: the energy of the primary ray is spread out in an intense halo; there is virtually no primary ray remaining at the second boundary surface. These different translucent states are best modeled with a multi-flux approximation. For this, in addition to absorption and scattering coefficients of the optical medium, some additional optical quantities such as the phase function p, for example, need to be taken into consideration (Section 5.1.5). The majority of natural and artificial non-self-luminous colors are opaque; they, therefore, appear impenetrable from the rear – a background is covered completely by this kind of colors. In all opaque systems light scattering is normally the dominant process, and it is accompanied by more or less distinct absorption. Scattering occurs isotropically without a preferred direction or, the other extreme, anisotropic with a specific preferred direction. Increasing scattering lowers the light transmittance and vice versa. The covering capacity of a coloration is, above all, caused by the scattering power of the pigment particles. The single spectrometric measuring quantity of opaque materials is the reflectance. The reflectance, in general, depends on the measuring angle for many kinds of effect pigments. Extreme optical states result in mixtures of absorption and effect pigments with different light transmittance. These are most often implemented in lacquers or plastic materials for consumer goods.

2.2.3 Description of Color Attributes Based on the discussion in the previous sections, it should be clear that the color of absorbing colorants is caused by light interactions such as scattering and absorption. On the other hand, the produced visual color sensation is by no means completely characterized by those. The variety of different combinations of wavelengths as well as the accompanying power distributions reaching the eye results in many colors, which can be described by different color attributes. For better understanding of the context, we use an analogy from acoustics. 8 This is a circular light spot encircling the primary ray; the halo of the Moon, for example, results of light refraction at the ice crystals in the atmosphere.

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2 Light Sources, Types of Colorants, Observer

A pure acoustic tone is unambiguous, physically described by its frequency and amplitude. The same tone, produced from different music instruments, is however surrounded by a typical sound spectrum. In a similar way, each nonself-luminous color is produced not simply by a single light frequency but also from various spectral values of the visible spectrum.9 The different wavelengths simultaneously entering the eye are perceived as a single color impression and not as separate single-colored wavelengths. This entire color impression can be verbally described by characteristic terms. The description or comparison of colors is used in color industry not only from physical or colorimetrical points of view but also according to coloristical attributes [27]. The following enumeration, which is not to be considered complete, gives some conventional terms for characterizing the color impression of non-selfluminous colors. The accompanying definitions and assemblies are, however, not uniformly used in the literature: hue, shade: the color property which is mainly described by adjectives such as red, green, yellow, blue; hue and shade are terms equivalent to color tone, or tint, see below; relative color strength, relative tinting strength: the color economy of an available colorant material relative to an arbitrarily chosen colorant of equal or similar color; color depth, color intensity: the color distinctiveness, which increases with enhancement of the same colorant amount; dullness: a characteristic color feature which can be described by an existing amount of gray or black; it is the converse to brightness. The quantitative determination of relative color strength is standardized based on colorimetric criteria (Section 3.4.2). These instructions underlie the formalism of the CIELAB or DIN99o color spaces. The following terms are also used to denote a color point in color space: lightness: a measure for the reflectance of a non-self-luminous colorant; the reflection ratio of absorption colorants is standardized by the so-called gray scale in which black is assigned to the value of 0 and white to the value 1; fluorescent and effect colorants often have reflectance values greater than 1, caused by the arbitrary fixing of the gray scale; selfluminous sources such as light sources or the sky are characterized by the term brightness rather than lightness; saturation: a quantity describing the colorfulness of colorants which does not change by further increase of the colorant concentration; shade, color tone: this corresponds to hue; equivalent terms are tint or tinge; 9 This metaphor is not to be confused with synesthesia, in which a physiological stimulus induces a further stimulus, for example, colors are associated with music and vice versa.

2.2

Absorbing Colorants

53

chroma: an absorption colorant loses colorfulness with lower saturation; chroma depends on both saturation as well as lightness because a tiny amount of black reduces the colorfulness of a color.10 Common for characterization of color impressions are also adjectives and their comparative forms; their meaning is somewhat equivalent to the terms already given above. Here are listed properties in opposing pairs: colored, chromatic: any color, such as yellow, orange, red, or green; it is analogous to the term hue; uncolored, achromatic: colors like white, gray, or black; light, bright: a color with a high lightness amount; light colors have a high reflectivity; dark: colors of small or even zero reflectance; brilliant, clear, pure: colors of both high hue and high lightness but missing white amount; pale, dirty, dull: colors of both minor hue and minor lightness. A great number of non-self-luminous colors containing absorption colorants can be directly manufactured with properties in the ranges of the last 12 listed extreme color states. Some of the cited characteristics correlate also with typical special features of the corresponding spectral reflection or transmission curve traces. The measured spectrum can sometimes be interpreted as a kind of “finger print” of the accompanying color. Some of these properties can be visualized by characteristic spectral reflection curves of absorption pigments, for example, in Figs. 2.23–2.27. Some of these features can also be found by the angle-dependent spectral reflection of effect pigments. The spectral reflectance of a chromatic absorption color is generally characterized by either a significant maximum (e.g., violet, blue, green) or a steep rise to higher wavelengths (e.g., yellow, orange, red) in the wavelength range of the complementary color or rather natural color; see Fig. 2.23. The highest absorption exists in a wavelength range of a distinct reflection minimum; backscattering, however, dominates in the range of maximal reflection or the plateau region of the relevant pigment. In contrast, an achromatic color shows a nearly constant spectral reflectance; see Fig. 2.24. Ideally scattering white is represented in the visible range by a constant reflection of 1.0 and ideal black of 0.0; gray takes intermediate values depending on the content of white or black. The decrease of spectral reflection for white or gray with shorter wavelengths is due to the tail of the UV absorption of the underlying TiO2 pigment. The impression of white results exclusively 10 These four color terms can be visualized by geometrical quantities in both mentioned color

spaces and further ones; see Sections 3.1.3 and 3.1.4.

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2 Light Sources, Types of Colorants, Observer

R(λ) c 0.8

d e

0.6 b a 0.4

0.2

0

400

500

600

λ

700

nm

Fig. 2.23 Spectral reflectance curves of chromatic pigments: (a) blue, (b) green, (c) yellow, (d) orange, and (e) red

R(λ)

a 0.8

0.6 b 0.4

0.2 c 0

400

500

600

700

λ

nm

Fig. 2.24 Spectral reflectance curves of achromatic colors: (a) white, (b) gray, and (c) black

2.2

Absorbing Colorants

55

R(λ) 2bt 0.8

2dk

1bt

0.6

0.4 1dk 0.2

0

400

500

600

700

λ

nm

Fig. 2.25 Spectral reflectance of bright and dark pigments: 1bt bright blue, 1dk dark blue, 2bt bright yellow, and 2dk dark yellow

R(λ)

0.8 a 0.6 b 0.4 c 0.2

0

400

500

600

700

λ

nm

Fig. 2.26 Spectral reflectance of different gray colors: (a) light gray, (b) middle gray, and (c) dark gray

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2 Light Sources, Types of Colorants, Observer

R(λ) 2br 0.8 2du 1br 0.6

0.4 1du 0.2

0

400

500

600

700

λ

nm

Fig. 2.27 Spectral reflectance of brilliant and dull pigments: 1br brilliant blue, 1du dull blue, 2br brilliant yellow, and 2du dull yellow

from regular light scattering over the entire visible range. This is the case for examples such as water vapor, clouds, or snow. Ideal black, on the other hand, is caused by absorption of entire visible wavelengths. Light (or dark) colors stand out either due to a high (low) reflection maximum or a widened (narrowed) plateau region; a light (dark) gray shows a shift of the reflection level to white (black); see Figs. 2.24 and 2.26. Most of the color-order systems and the colored calibration samples for recipe prediction are based on colored pigment mixtures with white and black colorants. It is remarkable that the human eye provided by nature is more sensitive to color differences between dark colors (violet, blue, green) in comparison to light colors (yellow, orange, red). This is correlated with a low maximum respective high reflectance plateau range. The higher and steeper the rise of the curve to the plateau region or the smaller the half-width of the reflection maximum, the more the color is perceived as brilliant, clear, or pure. Conversely, pale, dirty, or dull colors possess a spectral reflection characterized by a lower and broader maximum or overlapping maxima, compare in Fig. 2.27 curve 1br with 1du for a blue pigment. The spectral reflectance of a dull yellow, for example, shows a more flat peak profile and a lower plateau range compared to a brilliant yellow, cf. curves 2br, 2du in Fig. 2.27. The terms outlined up to now are merely used to describe some typical coloristical properties of classical absorption colors or colorants. This vocabulary

2.2

Absorbing Colorants

57

cannot be directly carried over to effect pigments. Rather than absorption and scattering, effect pigments produce new sorts of colors on account of different optical mechanisms; identical terms have, therefore, different meanings for effect pigments than for absorption colorants. Metallic pigments, for example, produce a characteristic metallic lightness, brilliance, or hue extinction. This ambiguity is discussed in Sections 2.3.3 and 3.5.1.

2.2.4 Color-Order Systems It is quite remarkable that the color sense of humans is capable of distinguishing about 10 millions of colors. It is further important to note that, in addition to the astonishing number of colors, a color can have different attributes; therefore, it seems essential to have systematic classifications for such a tremendous diversity of colors. Such classification systems serve not only as an overview but also as an improved communication about non-self-luminous colors, particularly for their use in difficult applications. From each of the established color-order systems, series of color samples exist for visualization. The antiquated color classifications are certainly not ordered after uniform criteria [28, 29]. The chronologically first systems were arranged based on features, which included the actual knowledge about colors. Among the contemporarily used color-order systems are to differentiate roughly two groups: systems on coloristic and on colorimetric basis. In the following, we sketch the common four representative examples of both groups. The most important coloristic-order system is that of Munsell, established in 1905. It is simultaneously comprised of various companion features such as, for example, precise nomenclature or systematic extension capability for additional colors [30]. The corresponding color patterns are ordered according to the three properties hue H, value V, and chroma C in three dimensions in a cylindrical coordinate system. The true significance of this collection are the colored patterns which display a nearly constant color difference between neighboring colorations. This was developed without any colorimetric background – an amazing for the beginning of the 20th century. In spite of the visually nearly equal color steps, this color-order system was not accepted until 1976 as a basis of the CIELAB system. Experience with the Munsell system has brought out critical disadvantages. Particularly unfavorable are the non-uniform perceived color differences of bright and dark colors. In remedy of these shortcomings, the Munsell system was supplemented by an additional color pattern in 1990. The natural color system (NCS) was worked out in Sweden and is standardized there; it is based on the opponent color theory of Hering and is arranged in pairs of the four chromatic colors red, green yellow, and blue as well as the achromatic colors white and black [31]. The patterns are organized in color

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2 Light Sources, Types of Colorants, Observer

spectra and color triangles after the three criteria blackness s, colorfulness c, and shade Φ. They are grouped in the form of an atlas of 1,741 color patterns. In spite of this great number, the NCS system is restricted in its applicability. It incompletely covers the color space, and additionally, colors with glossy surface are inapplicably marked. Moreover, the arrangement pattern is visually non-uniform. Without a measuring device, this color system is, therefore, only suited for rough orientation in color space. The so-called color index (C.I.) is suited for identification of colorants but represents no real color-order system as in the discussion above. It simply consists of a list with unsystematically assembled dyes and absorption pigments. These are partially denoted according to the origin (generic names) and according to the chemical constitution with natural numbers (constitution numbers) [32]. This listing offers a certain aid only in a few cases, if, for example, some of the colorants listed in the C.I. are to exchange with one another. Strictly speaking, the widely distributed color registry RAL 840 HR in Germany is also not a color-order system in a broader sense. This registry was created to ensure that industrial colors are classified uniformly with defined names and numbers for better communication between public agencies and producers of consumer goods. The color patterns were originally vaguely arranged in view of coloristic criteria; in the meantime, a modification was undertaken using the so-called DIN color chart, see below. It should be added that contemporary color systems also consist of patterns which change uniformly by a suitable technical parameter such as the concentration of the used colorants, for example. The corresponding inconstant changes of hue, lightness, or chroma certainly make color perception and color comparison more difficult. A visual ascertainment of color differences is not ensured by such systems. In contrast to the order arrangements above, the DIN color chart is a colorimetric-based color system [33]. It comes from the CIE chromaticity diagram; see Section 3.1.2 and Color plate 2. The color patterns are arranged with regard to three properties, similar to the Munsell system. These color properties are denoted as darkness D, hue T, and saturation S. They correspond to the ∗ , and chroma C∗ of the CIELAB system (Section 3.1.3). lightness L∗ , hue Hab ab The OSA-UCS system (Optical Society of America Uniform Color Scales) is principally used in the USA. It consists of a total of 588 color patterns, from which 12 colors at a time are positioned in the corners and one in the center of a cubic octahedron [34]. With this system, a multitude of visual equidistant color scales can be established; visually equidistant means that adjacent color patterns always show the same visually perceived color difference independent of color point in color space. This system cannot be directly transformed into the CIELAB system; the same holds for the Munsell system, NCS system, and the DIN color chart. A reliable determination of color differences is impossible on the basis of the OSA-UCS system.

2.2

Absorbing Colorants

59

Accordingly, it is advantageous to fall back on a universal applicable colororder system, which, for chromatic as well as achromatic colors, has the implicit metric of a color space. The RAL design system is organized on such considerations. It is based on the structure of the CIELAB system. The RAL design system enables, with good approximation, the visual determination of color differences. The corresponding color collection is established as RAL design atlas [35]. There exists also a collection of 70 RAL effect colors, which cannot be classified as a definite color-order system.

2.2.5 Surface Phenomenon The color attributes assembled in the next to last section are more or less an expression of a subjective color perception. As already mentioned in Section 2.1.5, the entire color impression is certainly composed of at least two components: the light interactions in the volume and at the boundary surface of a colored sample. In other words, the reflection or transmission from the volume is superimposed on the boundary surface reflection. This reflection is caused by different refractive indices at the boundary surface. Such kinds of boundary surfaces are present in paints, coatings, plastic materials, emulsion paints, or ceramics. This distinction cannot be made for undefined surfaces such as of textiles, uncoated papers, plasters, or suede leather. The kind of surface reflection is also influenced by the structure of the surface. A given color can exhibit a surface structure between two extremes: matt: appears a rough (or structured) surface; this appearance is caused by completely (or partly) diffuse surface reflection; high-glossy: appears a very smooth reflecting surface; such a surface induces only directed reflection, which is called specular reflection, specular gloss, or simply gloss. This behavior is described by the reflection law. Both the above surface properties should generally be interpreted as color attributes. For the illumination of a (color) pattern with directional light, the transition between matt, half-matt, glossy, or high-glossy surfaces can be characterized by the resultant diffuse or directed reflection with the aid of the reflection indicatrix. This is a plane polar diagram which represents the angle-dependent intensity distribution of the light reflected from the surface. In reality, an indicatrix is in three dimensions. Four different indicatrices are shown schematically in Fig. 2.28, each caused by a different sort of surface reflection. The diffuse and directional reflection amounts are given by the shape of the envelope curve and enveloping surface of the intensity distribution.

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2 Light Sources, Types of Colorants, Observer

Fig. 2.28 Reflection indicatrices of different surfaces: (a) matt: purely diffuse reflection, (b) half-matt: dominant diffuse, minor directed reflection, (c) glossy: predominant directed and minor diffuse reflection, and (d) high glossy: exclusive specular reflection

A diffuse reflecting surface of high roughness is achieved by various treatments, for example, with the help of suited polymer matrices or ceramics or pigment crystallites standing out non-uniformly from the boundary surface. In addition, the use of embossing dies is possible with regular geometrical surface forms such as micro-spheres and micro-prisms or irregular linen and other fabric structures. Further methods are sanding, etching, or physical vapor deposition (PVD). Certainly, the realization of ideal matt surfaces is exceedingly difficult. A matt surface appears normally somewhat lighter than a high-glossy surface of the same material. This is caused by the higher reflection coefficient for diffuse light in comparison to that of directional and perpendicular incident light, cf. Equations (2.1.8) and (2.1.12). The higher diffuse reflection is nearly independent of the absorption colorant sort. In the case of directional illumination, however, the reflection is only influenced by the degree of surface roughness. The matt surface of brilliant but dark-colored samples sometimes causes a minimal color shift. This phenomenon comes from the superimposed scattering of pigments near the surface. The entire diffuse reflection at the surface of a colored layer can, therefore, be composed of three components: – immediate reflection at the boundary surface; – scattering from particles near the surface; – anisotropic or isotropic scattering from the volume. The most of color physical problems are associated with the color component originated from the volume because this shows the interesting light interactions with the contained colorants. The result of a color measurement is, of course, composed of the volume and surface components. This result must, therefore, be corrected with regard to the surface boundary effect. This is achieved through the implementation of the various theoretical concepts detailed in Sections 5.3, 5.4, and 5.5, among other things. If the boundary surface contains no colorant particles, then the reflection is given by the refractive index of the binder. The pigments can, however, be

2.2

Absorbing Colorants

61

located in or near the surface, for example, by high pigment volume concentration (PVC), blooming, or flooding. In such cases, the arithmetic mean of the refractive indices of the involved materials is to be used. Such a surface boundary can have further color features, due to the fact that the refractive index of most colorants is dispersive. This effect is named bronzing; it can be present in printing inks, lacquers, plastic materials, or textiles, and can be avoided by appropriate measures. For unambiguous coloristic assessment of matt to high-glossy samples, it is absolutely necessary to avoid the glare caused by specular reflection. Therefore, the sample containing absorption colorants is always illuminated laterally at an angle of 45◦ and viewed perpendicular to the surface; see Fig. 2.29a. The reversed arrangement is also possible, but rarely used. In commercial light booths with lamps of different illuminants (normally D65, A, FL 2, FL 11 simulators), the light sources are arranged laterally and glare-free as shown in the mentioned figure. The color sample should be surrounded directly by a middle gray and the assessment should be performed by keeping the so-called CIE reference conditions, cf. Section 3.2.2. In contrast, the visual evaluation of the surface gloss is achieved with a fixed light source and constant line of vision by tilting of the sample over a specular Light source

Observer

Specular reflection

a)

Color pattern

> 60°

b)

Fig. 2.29 Two different configurations of the three factors for color impression of absorption colors: (a) for coloristical assessment and (b) for evaluation of surface gloss

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2 Light Sources, Types of Colorants, Observer

reflection angle range; see Fig. 2.29b. A light booth should, therefore, possibly have a tiltable support with angle scaling. The quantitative determination of surface reflection is carried out separately using a gloss meter; the reflected intensity is registered at several variable angles between normal to the surface and greater than 60◦ . In the case of curved substrate surfaces, for instance, car body components, cans, bottles, or tubes, it is possible to pursue simultaneously gloss, color blending, and change of gloss in dependence of the observation angle. To achieve comparable results, the radius of curvature of the substrate and the thickness of the coating have to be the same for all color samples of a collection. In contrast, coated curved substrate surfaces are absolutely unsuited for instrumental color measurements. The evaluation of the surface reflection of colorations containing effect pigments is particularly critical. The optical properties of a metallic paint coating, for example, are essentially caused by specular reflection at the flake-shaped metal particles. The flakes are primarily arranged parallel to the substrate surface. Therefore, specular reflection dominates, but it is superimposed by diffuse reflection coming partly from the rough particle edges. For metallic pigments, the angular distribution of the reflection depends also on the illumination angle as well as the angle of observation. As already explained in Sections 2.1.6 and 2.1.7, the color physical properties of effect pigments are also extremely angle dependent. Compared to absorption colorations, the visual assessment of such colorations needs a much more sophisticated procedure, cf. Fig. 2.30. The observation for effect pigments is also normally performed using a fixed light source, but the classical method needs two identical colorations, one kept horizontal and the other rotated by an angle < 45◦ from this position; see Fig. 2.30a. This procedure allows for the observation of the angle-dependent change of lightness intensity. For flake-shaped metallic pigments, this angledependent change in reflected intensity is typical; it is the so-called lightness flop. The color changes of interference and diffraction pigments between the two extreme observation angles is, however, termed as color flop. Figure 2.30b shows the modern arrangement for visual evaluation of effect colorations. In this configuration, the light source and the observer are fixed. Vertical movement of a color sample simultaneously changes both the angle of illumination and angle of observation. Therefore, the observation of the color flop, for example, needs only one color pattern and is carried out at the same surface spot. We have arrived thematically at the transition from absorption to effect pigments. These colorants have been used industrially since about 1970 and to an increasing extent. In the following sections, we discuss the structure, morphology, and the spectral properties of the most important sorts of these modern colorants.

2.3

Effect Pigments

63

Light source Observer

a)

Effect Color pattern

b)

Fig. 2.30 Two different configurations for assessment of colorations containing effect pigments with fixed observer: (a) classical method (tilting): lightness flop and (b) modern method (vertical movement): color flop

2.3 Effect Pigments Effect pigments have broken new ground in color physics, especially with regard to industrial-scale research, development, and application. The color production of effect colorants is predominantly caused by anisotropic processes like single or multiple reflection, interference, or diffraction. These processes are unrealized in absorption colorants. The generic term “effect pigment” is inadequate because colors generated by absorbing colorants are also based on an optical “effect”. However, flake-shaped pigment or shorter flake pigment is an accurate expression for this sort of colorants. The generated color impression of effect pigments is extremely angle dependent. This is a function of both the illumination and the observation direction. Effect pigments result in quite strange color

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2 Light Sources, Types of Colorants, Observer

sensations for human color sense because our sense has evolved to perceive only colors from absorption colorations. In a practical sense, effect colorants need more extravagant manufacture methods in comparison to absorption pigments and also a more extensive characterization, measuring techniques, application, and processing. All types of effect pigments consist of flake-shaped particles with a large range of typical lateral dimensions between 1 μm and 1 mm. This is more than 10 – 1000 times larger than that of absorption pigments. The flake thickness has values between 10 nm and 1 μm. On account of the flake form, the resultant color effect is increasingly distinct with a more uniform morphology and the more the particles are oriented in the binder parallel to the substrate or surface. Like absorption pigments, effect colorants can be of inorganic as well as organic nature. With regard to the processes of color production, they are divided into four groups (cf. Table 1.1). For historical reasons, they are named: – metallic pigment; – pearlescent pigment; – interference pigment; – diffraction pigment. In the literature, pearl luster pigments are often subsumed to the interference pigment classification [36]. The laws used to describe the optical properties of metallic pigments are essentially geometrical optics; all other sorts of effect pigments are generally described by wave optics. Metallic pigments consist normally of a metal or an alloy of metals. The typical metallic gloss is increasingly brilliant the more uniformly the flakes are oriented parallel to the boundary surfaces of a coating. The so-called metallic effect is mainly a consequence of the directional and diffuse reflection at the surface and the edges of the flakes. In contrast, pearlescent pigments consist of two or more layers with a high index of refraction difference; the values normally range from 1.5 to 2.9. The mostly used substrate is mica, but also metals or metal oxides are often applied. The specific pearl luster depends on the permutation of the layers. This luster originates from single or multiple reflections at the layer boundaries followed by interference of the light waves. Differing optical layers are behind the general function of interference pigments; this does not require the use of a mica substrate. An interference pigment subgroup is the so-called optically variable interference pigments. The high ratio of refractive indices, in conjunction with different layer thicknesses, fans out the first or more interference orders in such a way that a variety of interference colors are to observe angle dependence.

2.3

Effect Pigments

65

The grating structure of diffraction pigments deflects the incoming light. The resulting color effect can be attributed also to the wave nature of light. The substrate consists of a highly reflecting or even ferromagnetic substance. The substrate is vapor-coated symmetrically on both sides with several materials known from nanotechnology. The ferromagnetic particles can be oriented with an external magnetic field before the crosslinking of a binder. The produced unusual but often impressive colors require that effect pigments undergo a more subtle and closer examination and handling compared with absorption colorants.

2.3.1 Types of Metallic Pigments Metallic pigments, generally consisting of metal flakes, are employed mainly on account of the metallic reflection from the flake-shaped particles. This kind of reflection consists of superimposed specular and diffuse components which produce unusual color effects compared with absorbing pigments. Conventional metal flakes have mean lateral dimensions ranging from about 5 μm to nearly 50 μm, whereas the thickness varies between roughly 100 nm and 1 μm. In some extreme cases, the particles have dimensions which are up to 10 times higher. The ratio of thickness to diameter of the particle is called the form factor and it extends from 1:50 to about 1:500. Metal flakes are used in paints, lacquers, plastic materials, and inks; they are also employed in chemical products and for sinter metals, building materials, explosives, or pyrotechnics, for instance, as functional or chemically reactive particles. In this text, we are mainly interested in the metallic reflection. This property is caused, in simplified physical terms, by the fact that individual metal atoms can easily release the bonding electrons. In lattice arrangements, the metal atoms completely loose the valency electrons. These electrons form the electron gas which is distributed among the remaining ions so that each ion is fixed on a corresponding lattice position. On account of its interaction with the electrons, an external light wave from a normal source cannot penetrate the very dense electron gas. The majority of the light is rather reflected and the remaining part is absorbed within a very small penetration depth. Reflection and absorption produce the typical metallic brilliance and characteristic natural color of metals [14]. The change in electron gas density at the metal surface results in light dispersion in the visible range, among other things. This causes a light-, gray-, or low-colored metallic effect. The theoretical reflectivity of metals is given by Equation (2.1.10). In Table 2.7, the indices of refraction n, absorption nκ, reflection r(n,κ), and the melting temperature Tm are shown; these are for metals that are most commonly used for metal pigments. In this listing, the metals are arranged according to decreasing reflectivity. The given optical

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2 Light Sources, Types of Colorants, Observer

Table 2.7 Reflectivity, refractive index, absorption index for perpendicular incident light at wavelength of λ = 589.3 nm and T = 293 K as well as melting point of metals used for metallic pigments [37]

Metal

Reflectivity r (n, κ)

Refractive index (n)

Absorption index (nκ)

Melting point Tm /K

Ag Al Au Cu Zn Ni Fe Mo Ti W

0.99 0.912 0.888 0.804 0.768 0.664 0.586 0.575 0.565 0.524

0.052 1.181 0.280 0.493 2.74 1.71 2.91 3.40 2.09 2.83

3.91 6.99 2.91 2.80 5.77 3.61 3.58 3.56 3.11 3.02

1,235 933 1,336 1,356 693 1,726 1,809 2,890 1,933 3,683

quantities are for the middle of the visible Na wavelength of λ = 589.3 nm; they will generally have different values for other wavelengths. The melting temperatures of the given metals are higher than those of the highest flow temperature of normal polymer melts. The refractive index is also subject to dispersion; in cases of Ag, Au, and Cu it is valued n < 1. The phase velocity cp is, on account of cp = c/n, inside these three metals higher than the velocity of light c in vacuum; this is not in contradiction to the special theory of relativity because only the group velocity – with which energy or signals propagate – cannot exceed the velocity of light c. Clearly, the actual reflectivity is lower than the theoretical one. The real reflectivity depends on the details of morphology of the particles, especially the – surface grade and edge roughness; – particle size and particle size distribution; – flake thickness; – pigment orientation in the material of application. In the context of metallic pigments, it is useful to emphasize the fact that historical laxness in naming remains an issue. Terms such as aluminum bronze or silver bronze instead of aluminum pigments, gold bronze or even the more general metal bronzes, are still in widespread use today by pigment manufacturers, colorists, and even in modern literature [38–40]. Actually, aluminum bronze consists of copper alloyed at most 12% aluminum; silver bronze is an alloy of silver and tin; gold bronze is a solid blend of suitable amounts of copper and zinc; genuine bronze, however, consists of copper alloyed with tin.

2.3

Effect Pigments

67

Apart from dispersion and particle size, the character of the metallic color impression is influenced by further details. Among them are the chosen metal or alloy, the manufacturing and processing method of the flakes, and the wettability in binders. In the following, we give a survey of the influence of these parameters with regard to the visual perceived metallic effect. First of all, the chosen metal is responsible for the brilliance of the natural metallic pigment. The metallic colors change from light white (Ag, Ni), white (Al – as a substitute for Ag), bluish white (Zn), orange-yellow (Au), and reddish (Cu) to gray (Fe, Mo, Ti, W). These color attributes relate only to the metal gloss and, therefore, have a different meaning from that which was outlined for absorption pigments in Section 2.2.2. Additional natural metallic colors can be realized using mixtures of metallic pigments: Ni flakes lighten and Fe particles gray the metallic effect. Also alloys such as brass (alloy of Cu and Zn) are suited for gold-yellowish to reddish color, for example. Metallic pigments are manufactured with mixtures or alloys only if the required metallic effect is not achievable using only conventional metal flakes. The most commonly used metallic pigments from modern point of view are given in Table 2.8. Uncoated metal flakes based on natural metals have the most diversity. Particles with especially even surfaces can be manufactured using the PVD method. For this, a polymer foil is vapor coated in vacuum with a metal and afterward crushed at temperatures far below the glass transition temperature of the polymeric material. These flakes are termed as crushed PVD films. Due to modern developments, even colored metallic flakes can be manufactured. In these cases, a colored component is superimposed on the Table 2.8 Classification of metallic pigments Metallic pigment

Typical examples

Uncoated metal flakes

Aluminum (“aluminum bronze”, “silver bronze”), copper, zinc, copper/zinc alloys (70/30, 85/15, 90/10: “gold bronzes”), copper/aluminum alloys (4–12% Al: aluminum bronze), iron (austenitic steel, max. 11% Cr), nickel, tin, silver, gold, titanium

Crushed PVD films

Foils of polyethylene terephthalate, polystyrene, or polypropylene: vapor coated with aluminum, chrome, magnesium, copper, silver, gold (PVD procedure)

Flakes coated with absorption pigments

Inorganic or organic pigments in silicon dioxide or acrylate coating fixed on aluminum or “gold bronze” flakes as substrate (CVD procedure)

Partially oxidized and oxide-coated metal flakes

Partially oxidized from the surface aluminum flakes, copper flakes, zinc/copper flakes (“fire colors”); coated aluminum flakes: iron-III-oxide, tin oxide, zirconium oxide, iron titanate, cobalt titanate

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2 Light Sources, Types of Colorants, Observer

metallic effect. There are two different methods for manufacturing. In the first, absorption pigments are suitably fixed at the surface of the flakes by chemical vapor deposition (CVD) [38, 39]. The second method is based on metal flakes which are partly oxidized from the surface, or coated with metal oxides. Such metal flakes produce an intense color effect, sometimes called “fire colors.” These intense colors are caused by multiple reflections at the transparent outer layers with varying refractive indices; the multiple reflected waves then interfere. Technically, such colorants are not metallic pigments in the strict sense, rather just a multi-layered interference pigment on top of a metal substrate. In most cases, the original metallic brilliance of the metal substrate is lost. It must be noted that the chosen manufacturing method is of great influence to the resultant coloristical properties of metallic pigments. For shaping of natural particles, the melt is pressed through a narrow nozzle of suitable geometry with high pressure. Due to high flow velocities in the nozzle channel, often up to 400 m/s, the velocity gradient leads to an atomizing of the melt into round and contracting tiny droplets outside of the nozzle tip. After cooling, they are transformed into flake-shaped particles; these are the resulting metal flakes. The grinding of the solid particles is performed by two different processes. The wet milling method of Hall uses white mineral thinner for liquid phase. This simultaneously has the benefit of preventing dust explosions. In order to prevent clumping or welding of the particles, long-chained fatty acids are often added, typically 3–6% oleic or stearic acid. The dry milling method of Hametag, however, works in a N2 atmosphere containing at most 5% O2 . For this method, 4–6% palmitinic acid or stearic acid is often used as separators. The mentioned long-chained fatty acids, on the other hand, coat the entire surface of the resulting flakes; this certainly changes their wettability especially against binding materials. Because the end groups of the fatty acids are dependent of surface tension and behave either hydrophilic or hydrophobic, the metal flakes flood or disperse uniformly in the binding agent. Figure 2.31 gives an

Metal flakes

Coating

Substrate a) Leafing

b) Non–leafing

Fig. 2.31 Two different distributions of metallic particles in a painted layer: (a) leafing near the surface and (b) non-leafing or nearly uniform distribution

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illustration of two flake arrangements in a binder, the first is called leafing and the second non-leafing. The tendency to form the leafing arrangement is stronger with the lowering of the wetting with the surrounding polymer. Leafing flakes result from coating with stearic or palmitinic acid; non-leafing particles are usually obtained with oleic acid, for example. It is worth mentioning that the sort of wetting is generally correctable afterward with suitable additives. If the flakes are dispersed in the melt state of plastic materials, the leafing is generally avoided due to the high structural viscosity of the melt.11 A measurement method for determining the leafing behavior is detailed in the literature [41]. Leafing pigments incorporated in transparent binding agents show high brilliance due to a uniform and constant reflection. The abrasion resistance of the surface film is often reduced and, therefore, an additional top coat is usually applied. In contrast, the parallel and compact flake arrangement often behaves like an optical or mechanical barrier: in addition to visible wavelengths, it reflects UV and IR radiation and can also inhibit the diffusion of gases or vapors. Leafing flakes are, therefore, often used for reflection of UV and IR radiation as well as corrosion prevention pigments. Further non-colored applications of metallic pigments are given in Appendix 7.1.1.

2.3.2 Morphology of Metallic Particles As already mentioned, the metallic character is especially influenced by the morphology of the flakes. The wet milling procedure of Hall predominantly produces particles of irregular and uneven surfaces along with high edge errors – they are, therefore, quite accurately called cornflakes. Typical aluminum cornflakes are shown in Fig. 2.32. The picture was taken with a scanning electron microscope (SEM). The irregular particle edges result from fracture from other flakes during the milling process within the ball mill. The uneven surfaces are caused by abrasion of the coarse edges of colliding and pressed particles. At the particle surfaces shown in Fig. 2.32, it is possible to discern some remains of broken edge zones and indentation traces of striking balls. Both the uneven surface structure and the rugged particle edges are responsible for the typically increased diffuse light scattering of cornflakes. The light reflected from such flakes is composed of a directional and a superimposed scattering component. The accompanying indicatrix corresponds to that of Fig. 2.28c. The amount of diffuse reflected light is increased, therefore, with more uneven particle surfaces and rugged flake edges. With increasing particle scattering, there is a reduction of brilliance, that is, “it turns gray.”

11 Structural viscosity means that the viscosity has a nonlinear dependence on shear velocity;

this is in contrast to constant Newtonian viscosity.

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Fig. 2.32 SEM picture of typical cornflake particles of aluminum (source: Eckart Werke GmbH, Velden, Germany)

Sophisticated grinding techniques with metal brushings or polishing pastes have been used since about 1980 to reduce this brilliance loss. These techniques allow for the manufacture of thicker metal flakes with relatively plane surfaces as well as even or rounded edges. Particles of this kind are often called silver dollars, of which an example is shown in Fig. 2.33. These sorts of flakes reflect light with a dominant directional component accompanied by a considerably lower scattering. A paint film with silver dollars and clear top coat is, therefore, lighter and more brilliant than the one with cornflakes of the same metal and identical particle size distribution. Silver dollar pigments are preferentially employed in high-quality systems such as automotive coatings, the so-called metallics. They are also used in high polymer materials and printing inks. Shear stable flakes of upward 10 times the particle thickness of cornflakes can be realized in order to withstand processing techniques of high pressure or high shearing stress (e.g., ring main pumps, injection molding, blow molding, or extrusion). Particles with nearly plane surfaces and high brilliance can also be manufactured by PVD coating of thin polymer foils. They do, however, exhibit an undefined breaking edge. A representative example is shown in Fig. 2.34. In addition, it is possible to produce metallic pigments of constant thickness and of geometric regular shapes. These sorts of particles are called glitter flakes. To describe the glitter effect, the terms sparkle and glittering are also used. Both expressions are often utilized simultaneously, although they have somewhat different meanings.

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Fig. 2.33 SEM picture of silver dollar pigments of aluminum (source: Eckart Werke GmbH, Velden, Germany)

Fig. 2.34 Metallic pigments of PVD metal coated and broken polymer films (source: Eckart Werke GmbH, Velden, Germany)

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Sparkle is the property that single flake particles are directly recognized visually due to their expanded planar reflection surfaces. This is typically the case for mean particle sizes of about 30 μm and larger. The metal flakes are perceived separately on account of the surface reflection contrasting to the darker surroundings. They behave as isolated microscopic mirrors. In contrast to glittering, see below, neither the morphology nor the lateral dimensions of sparkle particles are necessarily uniform. The phenomenon of sparkle (also referred to as sparkling, optical roughness, micro-brightness, glint, or diamonds) is present in quite an assortment of effect pigments and is particularly observable with directional light; see also Section 3.5.1. In contrast, glittering is exclusively due to particles of uniform and regular geometry. These particles are manufactured in the form of squares, rectangles, rhombs, or circles by cutting or punching-out from metal foils or metallized polymer foils. In Fig. 2.35 an example of nearly quadratic aluminum glitter flakes cut from ribbons with a band knife is shown. Glitter flakes are of nearly uniform lateral dimension compared with conventional manufactured metallic pigments in ball mills. They are produced with sizes of 50 μm up to as much as 2 mm. They are generally at least 10 times thicker than usual cornflake or silver dollar particles. With regard to quadratic and rectangular glitter flakes, often specifications such as “2 × 2” or “2 × 4” are used. These can be interpreted as follows:

Fig. 2.35 Almost quadratic glitter flakes cut with a band knife from foil strips of aluminum [38] (source: Rapra Technology Ltd, Shawbury, UK)

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multiplication of each of these numbers with one thousandth inch (2.54 × 10–3 cm) gives the middle lateral extension of the corresponding particles. This means, for the given examples, that the glitter flakes have dimensions of 50 × 50 μm and 50 × 100 μm, respectively. It is also worth noting that with extreme process control in the Hall technique, it is also possible to produce spherical pigment particles with diameters as large as 700 μm. Such particles have, however, not the appearance of glitter flakes [38]. Colored metallic pigments offer an exceptional optical enlargement of usual metal pigments. These consist either of metal flakes covered by absorption pigments or metal flakes partially oxidized from the surface or oxide-coated metal particles. In the first case, the metal particles are coated with silicon dioxide or a polyacrylate containing inorganic or organic absorption pigments. In Fig. 2.36, there is an SEM photograph of aluminum flakes with a silicon dioxide coating of embedded inorganic pigment particles. This picture shows not only the coarse surface structure of the flakes but also the size proportion of the absorption pigments having only a few nanometers to the around two orders of magnitude larger sized metal flakes. From this difference in size, the typically higher scattering power of absorption pigments compared to effect pigments is also understandable. Colored metal effect pigments consist also of partially oxidized or oxidecoated flakes, which are manufactured using the CVD procedure. Partially

Fig. 2.36 Aluminum flakes coated with silicon dioxide and embedded inorganic pigment particles (source: Eckart Werke GmbH, Velden, Germany)

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20

100

10

50

Cumulative frequency curve

Relative frequency %

oxidized flakes of aluminum, copper, or zinc/copper are generally preferred. Iron-III-oxide-coated aluminum flakes are also common. All of these pigments produce particularly impressive reddish colors – and are, therefore, also called fire colors. These unusually striking colors are due to the combination of three effects: first, absorption and scattering of copper, zinc, or iron-III-oxide; second, interference caused by the layer construction; third, metallic reflection of the particles. Already the concept of the glitter flakes suggests that the character of the metallic effect is particularly dependent on the particle size. All particles, however, are not of the same size; therefore, the metallic effect is in general influenced by the particle size distribution. On the other hand, the size distribution can be controlled partly by the milling and sieving process; from these manufacturing steps, an asymmetrical particle size distribution with respect to the mean results. This distribution has a higher amount of smaller particles, cf. Figs. 2.37 and 2.38. The mean, in this context, is usually denoted by the quantity d50 or D[v; 0.5]. This quantity, for example, d50 = 25 μm, indicates that 50% volume of all particles are higher or lower in size than this near center value. The subtle properties of the metallic character even depend on the width of the distribution. In addition to the use of scanning electron microscopy, the laser granulometry method has proven quite useful for the determination of the mean particle size of effect pigments and the accompanying size distribution. The laser method is founded on scattering and diffraction of the particles suspended in a suitable liquid. This so-called laser granulometrical operation is suited only as a relative method, this is, not as an absolute method.

d50 0 10–1

0 100

101

102

d /μm

Fig. 2.37 Curves of particle size distribution and of cumulated frequency of an aluminum cornflake pigment with same value of d50 ≈ 20 μm as in Fig. 2.38

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20

100

10

50

Cumulative frequency curve

Relative frequency %

The size distribution of effect pigments is characterized by the so-called width W, which is given by the quotient W = (d90 − d10 )/d50 > 1. The quantities d10 and d90 mean that 10 and 90% volume, respectively, of the particles have lateral dimensions of Φ ≤ d10 and Φ ≤ d90 . A narrow distribution with low W produces a more brilliant metallic effect in comparison to a broader distribution of equal d50 value; see Figs. 2.37 and 2.38. The concentration of small particles is lower in a narrow distribution than in a broad distribution. However, the greater the number of small-sized particles present, the more gray and paler the metallic effect appears. Of course, with smaller flakes edge scattering preponderates, and in addition, the parallel configuration of the flakes is more distorted than with larger sized particles. The metallic reflection of typically narrowly distributed silver dollar pigments is consequently more distinct than that of traditional cornflakes. Cornflakes show a significantly broader particle size distribution. Among modern metallic pigments, silver dollar flakes of aluminum are the most light and most brilliant particles. According to Figs. 2.37 and 2.38, there is always an elevated number of particles smaller than 5 μm.12 This increased content of fine particles is unavoidably caused by the grinding process and is quite typical for the manufactured metal powders. The fine particles give rise to a scattering component which reduces the metallic brilliance. Finally, the production of the metallic effect is also influenced by the orientation of the particles in the polymeric surrounding medium. The particle

d50 0 10–1

100

101

102

0 d /μm

Fig. 2.38 Curves of particle size distribution and of cumulated frequency of an aluminum silver dollar pigment with same value of d50 as in Figs. 2.37

12 Particles

smaller than 5 μm contribute to particulate (dusty) matter.

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alignment is primarily determined by the processing techniques used. The maximum possible metallic reflection is achieved by complete flake parallelism to the bounding faces of a plane parallel layer; this is equivalent to a mirror. Local perturbations of particle alignment parallel to the paint coating can be caused by turbulent motion of the solvent during evaporation; such kinds of heterogeneity lead to mottling or flocculation. Both kinds of visible non-uniformities are also known from coatings with absorption pigments. Lacquers with low solid-state content display a more distinctive metallic effect than systems with higher solidstate content (so-called high solids). This is because the lower viscosity makes the orientation of the flakes easier. During processing of metallic or other flake-shaped pigments in printing inks, the absorbability of the stock can influence the parallel orientation of the flakes. But the slower the diffusion rate of the solvent, the more time available for parallel alignment of the particles. In high polymer materials, the flake pigments orient themselves according to the prevailing flow conditions. The alignment of the particles direct after surface formation is nearly maintained during cooling time and concurrent volume contraction. The collision of two melt fronts causes a flow line, at which the particles orient – visibly – parallel to the flow fronts. Flow lines can be avoided generally with suitable manipulation of the fusion in the mold [38].

2.3.3 Coloristic Properties of Metallic Pigments The geometry, morphology, and reflection of metallic pigments produce a variety of unusual color effects which need to be described in detail. The most important coloristic characteristics of metallic pigments are given in Table 2.9. From this apparent arbitrary division it is possible to discern two groups: in the first group, the indicated effect properties increase with expanding lateral dimension of the particles and for the second group, they decrease. This inverse behavior and the complex color attributes of metallic pigments demand a closer examination in comparison to the more simple properties of absorption pigments. First, the five special features of the first group will be discussed. The metallic character or metallic gloss depends on the ratio of the directional to the diffuse reflection. Both components are directly proportional to the quotient of the surface to the edge length of the metallic flakes. The higher this ratio, the more distinctly developed the metallic character. Small particles normally give rise to a higher edge scattering and, therefore, produce a poor and gray metallic effect. Conversely, flakes with a lateral dimension greater than 30 μm show a striking metallic character. In general, the narrower the particle size distribution, the more distinct the metallic luster.

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Table 2.9 Correlation between particle size and coloristical properties of metallic pigments (other used terms in brackets) Assessment of characteristic particle diameter d50 , non-leafing pigments Characteristic of metallic pigment

≤10 μm: fine pigments Cornflakes

≥30 μm: coarse pigments Silver dollars, glitter flakes

Metallic character (metallic gloss) Brightness (brilliance) Reflection brightness (whiteness) Sparkle, glittering (optical roughness) Graininess (coarseness, texture)

Insignificant, matt, gray

Quite distinct, brightened

Low Minor

High Enhanced

Invisible

Visually noticeable

Low

Visible

Lightness flop (flop, flip, travel, two-tone) Hue extinction Covering capacity (hiding power, opacity) Distinctiveness of image (DOI)

Light

Dark

Enhanced Enhanced

Low Low

High

Minor

The brilliance of metallic pigments is, in essence, caused by the directional reflection component. Metallic flakes, therefore, appear all the more brilliant the higher the directional reflected light amount and the lower the diffuse reflection component. The brilliance, and consequently the directional reflected component, is reduced with smaller and more uneven surfaces of the pigments, with broader particle size distributions and with greater irregularities in particle orientation in the surrounding polymer material. The reflection brightness or whiteness characterizes the lightness of the metallic effect. This property is a measure of the total reflected light and is composed of the directional and diffuse components. Consequently, reflection brightness differs from lightness of absorption pigments, which is due to scattering and absorption. In connection with effect pigments, the term reflection brightness has, therefore, a quite different meaning from the lightness of absorption colorants (although both quantities are determined with the same measuring and evaluation system). In fact, the spectral reflection of metallic pigments behaves similar to that of white/black mixtures of absorption pigments. Metallic pigments certainly show a key difference: the spectral reflection depends on the angle of illumination and direction of observation. This angle dependence is shown clearly, for example, by the reflectance of an aluminum cornflake pigment in Fig. 2.39. In this illustration, the reflectance

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R (%) 150

100 15 25 50

45 75 110

0 400

500

600

λ /nm

μas /degree

Fig. 2.39 Spectral reflectance of a cornflake aluminum pigment in dependence of the wavelength λ measured at aspecular angles of μas = 15º, 25◦ , 45◦ , 75◦ , 110◦ ; illumination angle β = 45◦

R is plotted in dependence of wavelength λ for five standardized aspecular measuring angles μas and an illumination angle of β = 45◦ .13 With increasing measuring angle, the reflectance behaves similar to that of light white and middle or dark gray, cf. Figs. 2.24 and 2.26. For angles steeper than μas ≈ 75◦ , the reflectance remains at a low level, the metallic effect appears dark gray [42, 43]. On the other hand, the reflectance increases exponentially for the aspecular angle of μas = 0◦ . This drastic change in brightness in dependence on the observation angle is characteristic for metallic flakes; it is termed as lightness flop or short flop (see below). The reflectance increase near the specular angle can be further raised, within limits, with a narrower particle size distribution or altogether larger sized flakes. Measured reflectance values higher than 100% are absolutely usual and produce no inconsistency with conservation of energy. Because of the lack of suited and corrosion-resistant metallic standards, the reflectance scale is based on the reflectance of a white (scattering) standard which is interpreted as a reflectance of 100% (Sections 2.2.3 and 4.1.2). Real effect pigments can have reflectance values up to about R = 800%.

13 For

nomenclature and counting of angles, see Section 4.1.2, Figs. 4.5 and 4.6.

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Metallic pigments of irregular lateral dimension greater than about 30 μm produce a phenomenon termed as sparkle in the last section. This effect is also called sparkling or optical roughness. For particle dimensions of this size or larger, the naked eye can distinguish single flakes of nearly equal orientation at the surface of a coating or plastic material. This is caused by the increased intensity of directionally reflected light at the larger particle surfaces (similar to parallelized crystals of an illuminated snow surface). As a consequence of the distorted orientation of the flakes, sparkling changes in dependence on both the illumination and observation angle. Leafing flakes develop no sparkling in dependence of the particle size because nearly all flakes have an alignment parallel to the surface of the coating or the plastic material. Sparkle is not restricted to metallic pigments and can be present in other sorts of flake-shaped pigments. This striking feature depends, e.g., on the size, the sort, the surface curvature, and the content of the effect pigment in a coloration. If the illumination is switched from directional to diffuse, the sparkling disappears completely and turns into a kind of graininess of the particles. Under this lighting condition, only a kind of fixed snowing picture is observable near the surface of the coating. This phenomenon is also called coarseness, texture, or vivid “salt and pepper” and is independent of observation angle. The impression of graininess depends on the size and type of the flakes, orientation irregularities, or clustering of the pigments during processing. Now, consider the second group of properties listed in Table 2.9. The abovementioned lightness flop (also light to dark flop, flop, flip, travel, two-tone) can be regarded as the most important and visually most striking property of metallic pigments. This term characterizes the decrease in lightness that a metallic coloration shows under diffuse illumination between two extreme angles of observation, especially at angles for perpendicular observation and an angle greater than 60◦ with regard to the normal of the surface (cf. Fig. 2.30a).14 The lightness flop is influenced by three primary factors: first, the flakeshaped pigment morphology, second, the surface and edge formation, and third, how well the flakes are ordered parallel to the surface boundaries of a layer. During observation perpendicular to the surface, the light enters directly the eye after interactions with the flakes. The observer registers the reference lightness. Now, for angles nearly parallel to the surface, the light path through the layer is longer. For this reason more interactions can take place with the particles of the layer, that is, at the surface or edges of the flakes. Due to this, light is increasingly scattered or reflected out of the line of observation and, therefore, only a small amount of the interacting light reaches the eye. This results in a registering of a reduction of lightness in comparison to the perpendicular observation.

14 Perpendicular observation means, in practice, that observation angles of β = ±20◦ , ν referred to the vertical, are permitted.

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This flop is termed as light if only a small lightness difference is observed between both extreme observation angles. It is, however, called dark if a large lightness difference is registered. For finer and irregularly shaped flakes (e.g., cornflakes), for broader accompanying particle size distribution, and for greater particle disorder in the layer, the flop is lighter. Conversely, the flop is the more dark, for greater evenness of the particle surfaces, for more rounded flake edges (silver dollar flakes), for narrower size distributions, and for more consistent parallel orientation of the particles to the surface boundary of the layer. The lightness flop can be altered afterward to some degree by adding inorganic or organic absorption pigments (see Table 2.10). Table 2.10 Lightness and color flop of effect colorations

Flop kind

Flop character

Effect pigment/ absorption pigment

Lightness flop

Light

Metallic pigment

Metallic pigment and absorption pigment Dark

Metallic pigment

Metallic pigment and absorption pigment Color flop

Colored

Absorption pigment

Absorption and pearlescent pigment Interference pigment

Diffraction pigment

Typical examples Fine non-leafing cornflakes, eventually with orientation distortion medium Scattering, inorganic, and organic; for example, titanium dioxide, chromium titanate Coarse non-leafing silver dollar flakes, normal silver dollar flakes, PVD flakes Transparent, inorganic, and organic Blue with green flop: phthalocyanine pigments of neutral color flop; blue with red flop: α/-phthalocyanine pigments Combination of hiding absorption and transparent pearlescent pigments, nano-titanium dioxide Interference pigments with extreme color flop: LCP, flakes coated with silicon dioxide, aluminum oxide, iron-III-oxide, magnesium fluoride Aluminum or nickel substrate PVD coated with chromium/magnesium fluoride or magnesium fluoride/silicon dioxide

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The phenomenon of lightness flop can be examined quantitatively by a gloss meter. The usual measuring angles μν = 20◦ , 60◦ , 85◦ with regard to the normal of the surface are certainly not sufficient. This is already clear from the angle-dependent reflectance measurements in Fig. 2.39. A reliable characteristic value describing the lightness flop of a single-layered metallic formulation is the so-called flop index; however, for clear-over-base paints, the so-called metallic value is used (Section 3.5.1). As mentioned, some metallic systems are mixed with absorption pigments for coloring or covering of the background. These systems have a more or less colored flop; see Table 2.10. Mixtures with absorption pigments always result in a lighter flop compared to the natural metallic pigment. This effect is generally called color flop. Mixtures of pearlescent and metallic pigments normally produce a lighter flop than the corresponding single natural pigments. However, the brilliance is usually raised at perpendicular observation. This behavior can be reversed with suitable pigment combinations. The color flop of interference and diffraction pigments is generally accompanied by a distinct color change. This change is mainly due to the interference or diffraction maximum of first order (Sections 3.5.3 and 3.5.5). A particular kind of color flop is given by a mixture of a metallic flakes with titanium dioxide, provided that nanoparticles of the rutil modification are used. The observable minor color shift caused by the nanoparticles is generated by the selective scattering of waves in the region of blue wavelengths; this special phenomenon is called frost effect [44]. Such a layer has a yellowish color at top view but for a flat angle of observation, a bluish color impression results. Accordingly, the shorter blue wavelengths are more scattered than the other longer wavelengths, in agreement with Rayleigh’s law (2.1.3). This comparatively low effect is also observed with other absorption or pearlescent pigments of lateral dimensions in the nanometer range. Altogether, the color flop of a formulation can be controlled within limits by adding small amounts of nanoparticles. Certainly, the frost effect lowers the entire brightness of the relevant coloration. The next property of interest in Table 2.9 is the hue extinction. This feature characterizes the capability of a metallic pigment to change or to cover completely the natural color of an absorption pigment incorporated into a formulation. In the literature [39], this ability is called “hue saturation,” which is again misleading, because this term implies a saturation of the relevant absorption colorant. The extent of the hue extinction is related to the covering capacity of the metallic particles. In this case, for metallic particles this term has the same meaning as it does for absorption pigments (Section 3.4.3). Both the hue extinction and the hiding power are improved with smaller cross sections of the particles, broader particle size distributions, larger flake thicknesses, and denser packing of the flakes.

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Finally, there is the so-called distinctiveness of image (DOI). In addition to lightness flop and hue extinction, this property lists among the central characteristics of single as well as clear-over-base paints of metallic coatings. The DOI value represents the uniformity of the observable metallic reflection. It depends mainly on the particle size and orientation of the flakes in a layer. The distinctiveness of image is again improved by smaller particles and more highly parallelized grade of the flakes. The DOI value of large-sized flakes nearly correlates with the glittering effect. The determination of the DOI value by measurements is outlined in Section 3.5.1.

2.3.4 Sorts of Pearlescent and Interference Colorants The color production of pearlescent and interference pigments is essentially based on constructive interference. Pearlescent pigments imitate the nacre luster of natural pearls. The brilliant colors and unique luster are due to superimposed light interactions such as absorption and multiple reflection at different boundary surfaces of the particles. Interference pigments generate substantially more brilliant colors than pearl luster pigments. The terms pearlescent and interference pigments are often wrongly used as synonyms for both pigment sorts, although only pearlescent pigments have the typical luster of natural pearls coming from the depths to the surface. The particles of pearl luster and interference pigments consist of layers with different refractive indices. The layer thicknesses are on the order of magnitude of visible wavelengths. The entire flake thickness varies from about 30 nm to 1 μm and the mean lateral dimension of the transparent to opaque pigments extends – similar to metallic flakes – from about 5 to 300 μm. Pearlescent, interference, and diffraction pigments can also exhibit sparkling. This sizedependent phenomenon is, in this case, generally darker than the sparkle of metallic pigments because the reflection is caused only by the difference of refractive indices instead of metallic reflection. The color-producing properties of pearlescent, interference, or diffraction pigments are dependent on the particle geometry, especially on the interfering light interactions, and the color physical conditions in the particle surrounding. According to Equations (2.1.15), (2.1.16), (2.1.17), (2.1.18), (2.1.19), and (2.1.20), the interference laws are functions of the wavelength λ, the refractive index n at the interface, the thickness d of each single layer, and the observation or interference angle α z . These parameters can be tuned in such a way that only the first interference order (z = 1) occurs in the range of normal observation angles. In this case, the higher orders can be neglected or are simply not to observe. The incoming light waves are partly reflected at each boundary surface of a particle, cf. Fig. 2.16. The constructive interference of the waves

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produces the matt to high brilliant color appearance. The interference color is observed at the specular angle on the illumination surface and the complementary color is transmitted by transparent flakes. Each single pigment, therefore, behaves as an interference filter, which the incoming light waves split up into a reflected interference component and a complementary transmitted or absorbed component. As a result of the different refractive indices at the interfaces as well as the morphology of the particles, the following light interactions together contribute to the color appearance of pearl luster and interference pigments: – constructive interference produces the sometimes intense colors which change in dependence of the angle of observation; the different colors and the angle dependence are given by the refractive indices, the thicknesses, and the number of layers; – single reflection at interfaces causes part of the glossiness; – multiple reflection at the different interfaces of the transparent or translucent layers causes the typical luster “from the depths” of pearlescent pigments; – scattering at the edges or rough surfaces of the particles leads to matt interference colors; – absorption reduces the brilliance; it depends on the layer material. Table 2.11 shows the customary substances from which pearlescent and interference pigments are composed. The materials are ordered according to increasing values of refractive index nD . In comparison, air at a pressure of 1.0 bar at room temperature T = 298 K has a refractive index of only n = 1.000272. The pigment particles consist of at least three different Table 2.11 Refractive index n of substances used for pearlescent and interference pigments; λ = 589.3 nm, T = 298 K [40, 45, 46] Substance

Special terms

Refractive index n

Synthetic high polymers MgF2 Proteins SiO2 Alumina silicate CaCO3 Al2 O3 Guanine, hypoxanthine Pb(OH)2 2PbCO3 BiOCl Fe3 O4 TiO2 α-Fe2 O3

Organic materials Magnesium fluoride Proteins Inorganic glasses Mica, muscovite Aragonite Aluminum oxide Natural pearl essence Basic lead carbonate Bismuth-oxide chloride Magnetite Anastas/rutil Hematite

1.35–1.70 1.384 1.40 1.458 1.50 1.68 1.768 1.85 2.00 2.15 2.42 2.5/2.7 2.88

·

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materials. Because the relevant substances are anisotropic crystalline, the indicated n values represent a mean. The refractive indices of the substances given in Table 2.11 are subject to dispersion. Table 2.12 is arranged by pigment classes: pearl luster, interference, and diffraction pigments. In other literature, these are often gathered arbitrarily under the collective name: special effect pigments [18, 40]. Our further discussion relates to the pigment classification and terms given in Table 2.12. This fixes a unified nomenclature for all sorts of pearlescent, interference, and diffraction pigments. Pearlescent pigments of the simplest structure are substrate free and form flake-shaped single crystals. The flakes consist of natural fish scales (75–95% Table 2.12 Effect pigments producing colors founded on wave properties of the light: pearlescent, interference, and diffraction pigments Sort of effect pigment

Unsystematic names

Pearlescent pigment

Platelet-like single crystals

Mica-based pearlescent pigments Interference pigment

Special interference pigments

Liquid crystal pigments (LCP) Optical variable interference pigments (OVIP)

Extended interference films Diffraction pigment

Grating pigments

Typical examples Natural pearl essence, basic lead carbonate, bismuth-oxide chloride, α-iron-III-oxide, titanium dioxide, mixed-phase pigments of aluminum oxide, manganese-iron-III-oxide Substrates: natural or synthetic muscovite layers: titanium dioxide (rutil or anastas), iron-III-oxide, chromium-III-oxide, silicon dioxide (multi-layer principle) Substrates: aluminum oxide, silicon dioxide, iron-III-oxide chromium, silicon–aluminum–boron silicate; Layers of iron-II-oxide-hydroxide, iron-III-oxide, chromium-III-oxide, titanium dioxide, chromium phosphate; chromium, iron-II-/iron-III-oxide, iron titanate, silver, gold, molybdenum Polysiloxanes in cholesteric phase, cross-linked in layers Substrates: aluminum, aluminum oxide, iron-III-oxide, silicon dioxide, glass flakes; Layers: aluminum, chromium, iron-III-oxide, magnesium fluoride, silicon dioxide, titanium dioxide Multi-layer film consisting of polyacrylates, polypropylene with polyethylene terephthalate, polystyrene, or polycarbonate Al substrate with symmetrical PVD layers of MgF2 or Cr/MgF2 Ferromagnetic: Ni substrate with symmetrical PVD layers of MgF2 /Al or Cr/MgF2 /Al

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guanine, 5–25% hypoxanthine), basic lead carbonate, bismuth-oxide chloride, or α-iron-III-oxide, as well as mixed phases of aluminum oxide or manganeseiron-III-oxide. On account of the lack of a mechanically stabilizing substrate, these pearl pigments will not easily survive shear and pressure flow of technical processing. They are similar to ground shells and are, therefore, limited to a small range of applications [40]. However, for the most part, the flake-shaped pearl and interference pigments consist of a symmetrically coated substrate of at least one additional layer. The most used substrates are natural or synthetic mica, aluminum, aluminum oxide, chromium, iron-III-oxide, or synthetic silicon dioxide. The lamellate center should have a great difference in refractive index compared to that of the coated layers. Pearlescent pigments are mostly based on mica substrate. This is a native depositing layer silicate, named muscovite, with total molecular formula KAl2 [(OH, F)2 AlSi3 O10 ]. Instead of natural muscovite, also synthetic mica is increasingly being used. The synthesized material shows a more uniformlayered structure and produces, therefore, more brilliant interference colors. Apart from metal oxides, further coating substances are fluorides or silicon dioxide, also cobalt and iron titanate, chromium phosphate, silver, gold, molybdenum, or chromium [18, 46–48]. The symmetric permutation of layers of the flakes is achieved by normal chemical procedures or vacuum evaporation coating by the PVD or CVD method [49, 50]. Examples of pearl luster pigments based on natural muscovite are shown in Color plates 7 and 8.

2.3.5 Interference Pigments Consisting of Multiple Layers Flake-shaped pigments based on muscovite or other substrates can be modified to produce a variety of further impressive colors. Intensified interference colors and simultaneously selective absorption, analogous to colored pigments, can be achieved by coating mica with two or more metal oxides of different refractive indices. Such kinds of flakes are also called combination pigments. Compared to single-coated mica pigments, they show more brilliant and brighter interference colors, as well as a more distinct color flop. The color flop is called distinct if a variety of interference colors are to observe. Conversely, the color flop is less distinct if only few interference colors are angle dependent to perceive. The color flop is again more distinct than with a mixture of the natural pearlescent and absorption pigments. Because of the underlying two different color production mechanisms, combination pigments are also termed as two-color pigments or color-flop pigments.15 In dependence on the observation angle, 15 Not

only combination pigments produce a color flop but rather interference pigments with other layer combinations as well as diffraction pigments, cf. Table 2.10., Section 2.3.3.

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2 Light Sources, Types of Colorants, Observer

Fig. 2.40 Cross section of a symmetrical multi-layer pigment; permutation of layers from the centered mica substrate: titanium dioxide, silicon dioxide, titanium dioxide; overall layer thickness about 500 nm (source: Merck KGaA, Darmstadt, Germany)

either the gloss is composed of the absorption and interference color or the non-self-luminous color of the absorption pigment is dominant. The most important combination pigments are TiO2 -coated mica flakes vapor-coated with further oxides such as α-Fe2 O3 (hematite modification), Fe3 O4 , or Cr2 O3 . As shown in Fig. 2.40, the muscovite substrate can be covered with two different oxide layers of TiO2 and SiO2 . On account of the six boundary layers with different refractive indices, 15 interference combinations are possible. These produce extreme interference colors which are superimposed by the absorption colors of both oxides. Mica pigments vapor-coated with TiO2 and top-coated with other metal oxides such as TiO2–x , TiOx Ny , FeTiO3 , or nanocarbon particles embedded in TiO2 generate silver gray or black pigments of improved compatibility with colored pigments. Transparent mica pigments can be produced in form of nano-sized particles by a suitable precipitation method of oxides or oxide hydrates; these colorants are called transparent colors. Moreover, modified process engineering allows for the manufacture of pigments of minor gloss [41]. The top-coat of an interference pigment can also consist of a pure metal. A substrate of a metal (Al or Cr) or metal oxide (Al2 O3 , Fe2 O3 , SiO2 ) is coated with a glassy layer of another refractive index (TiO2 , MgF2 ), as well as an evaporated semitransparent metal top-coat (Cr, Ni, or Al). The inner and outer reflecting layers form together a Fabry–Pérot etalon, cf. Fig. 2.18. This structure causes increased interference intensities and a sharp color flop by multiple reflection. An interference pigment showing a distinct color flop is generally named as optical variable interference pigment (OVIP). An example of such an OVIP of layer composition MgF2 /Al/MgF2 is shown in Fig. 2.41. In this SEM picture, it is particularly interesting to see the quite

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Fig. 2.41 SEM photograph of an optical variable interference pigment with symmetrical layer composition of MgF2 /Al/MgF2 ; cf. Color plate 9 (source: Flex Products Inc, Santa Rosa, CA, USA)

even surfaces and the sharp edges of the pigment particles. The even surfaces indicate also internally even surface boundaries and, therefore, brilliant interference colors followed by a distinct color flop. The sharp edges indicate that the flakes are broken at low temperatures and sifted out. The particles shown in Fig. 2.41 have a mean lateral dimension of d50 ∼ = 20 μm and a thickness of about 100 nm. An impression of the color flop produced by this pigment is given by comparing the two pictures of Color plate 9. Both photos show the same image field of a light microscope in bright- and dark-field illumination; bright field means illumination from the top of the surface and dark field means interference from the side of the color sample. In this case, the colored flop changes from green to violet (see also Section 3.5.3). Interference pigments of special shish-kebab layer structures and consisting of organic polymers are termed as liquid crystal pigments (LCP). A liquid crystal state is arranged without exception of rod- or elliptical-shaped polymer molecules consisting of suitable dipole moments or polarizing groups. The corresponding textures are optically anisotropic and are, for example, used in seven segment displays for more than four decades. The accompanying texture is called liquid crystalline or mesomeric phase because the molecular conformation corresponds neither to a random liquid nor to an ordered crystalline state.

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There exist altogether three different liquid crystalline textures. The corresponding molecular configurations are termed as nematic, smectic, and cholesteric: – nematic: the molecules are aligned parallel to their longitudinal axes, are arbitrary slidable in the axial direction, and are rotatable around the longitudinal axes independent of one another; – smectic: the molecules are oriented with their long axis perpendicular to each monomolecular sheet; the movement of the molecules is restricted to rotations around the longitudinal axes; – cholesteric: the molecules are arranged parallel to one another and grouped in layers; the layers are systematically turned toward each other by a specific angle; the mobility of the molecules is the same as in the nematic phase. These molecular configurations are schematically sketched in two dimensions in Fig. 2.42, but are to interpret as three-dimensional textures.

Nematic

Smectic

Cholesteric

Fig. 2.42 Schematic representation of rod-shaped polymer molecules in nematic, smectic, and cholesteric phase

The manufacture of liquid crystalline pigments of suitably layered structures normally starts with polymer molecules in the nematic phase. This state is converted into layers of cholesteric texture – for example, with silicones – at higher temperatures in the presence of a chiral additive. The single parallel layers are then cross-linked and fixed using UV radiation; see Fig. 2.43. Each layer is twisted by a constant angle relative to the adjacent layer. The nearly identical molecular conformation with regard to the initial layer is attained after passing the so-called pitch height p of about 100 nm. On account of the systematically twisted molecular conformation inside the pitch, the transmitted light is circularly polarized by this structure. The pigment particles have thicknesses

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Fig. 2.43 Parallel and cross-linked layers of polysiloxane molecules in cholesteric texture forming a half pitch of a liquid crystal pigment (schematically)

of about 5 μm, the lateral dimension normally ranges from about 7 to 90 μm. Liquid crystalline sparkling pigments can be realized up to about 500 μm. An entire pitch works optically like a Fabry–Pérot etalon [51]. The partial reflection at the pitch surfaces and the rotated molecular arrangement causes several optical effects which greatly affect the interference behavior of these pigments: – a kind of gloss coming from the depths, which is attenuated in pearl luster pigments because the light must pass through various pitches and layers; – on account of reflections between adjacent pitch surfaces, the interference wavelength λ changes according to Equation (2.1.20) for z = 1 and p = 2d; the wavelength decreases with increasing angle of observation from the vertical; an example of transparent liquid crystal pigments is shown in Color plate 10; – caused by a low pitch value, only one single interference order is observable within ±90◦ ; it is accompanied by a distinct color flop; – the reflected polarized light increases the brilliance of the interference color; – because the particles are transparent, the total color impression can be influenced by the background color or mixed absorption pigments. Furthermore, modern developments use even pure metals, metal alloys, metal oxides, or borosilicate glass for substrates of interference pigments; see Table 2.13. An example of an uncoated glass substrate and coated with TiO2 is shown in Fig. 2.44. The differences in refractive indices at the interfaces cause not only unusual brilliant and pure interference colors but also sparkle effects which are even colored. Pigments of other compositions, thicknesses, and permutation of layers cause impressive color flops. These occur nearly throughout the entire visible spectrum (see Section 3.5.3). Finally, there are the so-called extended interference films (cf. Table 2.12, previous section). The manufacturing is carried out by co-extrusion of transparent polymer foils with different refractive indices (1.48 ≤ n ≤ 1.60). The films are partly colored with absorption pigments. The original low interface reflectivity is improved by semitransparent silvering of some internal foils. The full foil sequence has a thickness of up to 400 μm and contains a maximum

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2 Light Sources, Types of Colorants, Observer Table 2.13 Some optical variable interference pigments

Substrate

Coating

Peculiarities

Al2 O3

Depending on coating thickness d TiO2 Fe2 O3 Lateral dimension 5 μm ≤ φ ≤ 30 μm

Colors: “Silver,” yellow over blue-green until blue; “Bronze,”, “Copper,” red interference colors; sparkle pigments for φ ≥ 30 μm

Ca–Al borosilicate

TiO2 , Fe2 O3 , SiO2 : SiO2 /TiO2 in multi-layers: d ≤ 1 μm, 20 μm ≤ φ ≤ 200 μm

Substrate of high transparency, “pure” interference colors without scattering, multicolored sparkle effect

SiO2

TiO2

Colored flop: “gold-silvery” to greenish, green-blue to dark-blue; more distinct with rutil compared to anastas

Fe2 O3

Layer configuration: Fe2 O3 /SiO2 /Fe2 O3 / SiO2 /Fe2 O3

Colored flop: violet to orange-“gold”; top coating of Fe2 O3 , corrosion resistant

Metals and metal alloys

Mono-layers: Al, Zn, Cu–Zn alloys; SiO2 /Al/SiO2 , α-Fe2 O3 /Al/α-Fe2 O3 Multi-layers: From the surface partially oxidized and oxides of metal flakes

Fabry–Pérot etalons; cf. Table 2.8

Fig. 2.44 (a) Uncoated borosilicate substrate, (b) coated with titanium dioxide layers; total flake thickness of about 300 nm (source: Merck KGaA, Darmstadt, Germany)

of 70 films. The multi-layer films are crushed at temperatures below the lowest glass transition temperature of the polymers used and are sieved in different fractions.

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2.3.6 Spectral Behavior of Pearlescent and Interference Colorants Pearl luster and interference pigments are either nearly transparent or opaque. The most important representatives of both groups are shown in Table 2.14. In this section, we limit ourselves to describing only transparent particles because these colorants have more interesting color shades. First, we discuss the dependence of the color impression on the background color; thereafter, we explore methods for covering coatings. As already mentioned, the interference color appears in the direction of the specular angle; this corresponds to the interference angle of first order. The complementary color is transmitted by the transparent particles and absorbed by opaque flakes. Table 2.14 Examples of nearly transparent and opaque pearlescent and interference pigments Light transmittance

Examples

Nearly transparent

TiO2 pigment, Fe2 O3 combination pigments on mica substrate; Fe2 O3 coating of Al2 O3 substrate; coated SiO2 flakes; liquid crystalline polysiloxanes

Opaque

Reduced TiO2 on white mica; multi-layer pigments: Al flakes coated with SiO2 , Fe2 O3 ; Al or Cr platelets vapor coated with MgF2 , Cr, or Ni

The total color impression of transparent interference pigments is strongly influenced by the chosen background; this is clearly shown in connection with Fig. 2.45. Because a black background absorbs the complementary color, only the interference color is observed above the coating. The interference color corresponds to the mass tone of the pigment. On account of the additional light scattering, which is generated to a greater or lesser degree by the corners or edges of the pigment particles, the surface of such coatings appears in fact dark, but rarely absolute black. On the contrary, a white background scatters, to a large extent, the transmitted complementary color and is only slightly absorbed. The interference color is then superimposed upon by the scattered amount of the complementary color in direction of the specular angle. In all other directions, only the scattered complementary color is observed. Consequently, over a black background, the natural colors of an interference pigment are observed and over a white background, the covering capacity. These uncolored background surfaces allow also for the determination of the reflectance and transmittance of a transparent or translucent layer from reflection measurements (Sections 3.4.3 and 4.2.4). In the case of a colored background, the interference color is clearly superimposed upon by that color. Because the interference and absorption colors can

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2 Light Sources, Types of Colorants, Observer Interference color

Complementary color

Black

White

Colored

Fig. 2.45 The color impression of colorations with transparent interference pigments is affected by the chosen absorbing or scattering background

be either identical or different, a variety of color flops are possible. At curved surfaces (which are always to be avoided for color measurements), the interference and the absorption color can be observed simultaneously. Transparent interference pigments mixed with colorants of complementary mass tone result in a white color according to the laws of additive color mixing. Mixtures of transparent interference pigments with other pigments of similar color produce more dull colors like the single colorants. As an alternative to a white background, a scattering silver-colored metallic or pearlescent pigment of d50 value less than 10 μm can be used. Such parameters for the pearlescent pigment normally ensure a high DOI value. Preferred bright silvery pigments for this purpose are mica flakes coated with TiO2 or aluminum cornflakes. For light gray layers FeTiO3 -mica pigments are suitable. On the basis of the scattering contribution or broad particle size distribution, the gloss is reduced. Aluminum pigments have also the tendency to reduce the chroma of pearlescent and interference pigments. This is in analogy to white in mixtures of colored absorption pigments. In the following, we consider in more detail the color systematic and the corresponding spectral reflection which result from thickness changes and composition of the layers. For this, we restrict ourselves to the pigments with layer compositions which were already discussed in the previous section, among other things. They are as follows: – titanium dioxide evaporated mica particles; – mica flakes coated with iron-III-oxide;

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93

– two mica-based combination pigments of titanium dioxide in rutil modification: top coated with iron-III-oxide or with chromium-III-oxide; – liquid crystal pigments consisting of polysiloxanes.

These pigments are typical representatives of other pearlescent and interference pigments. This goes especially for the accompanying colorimetric behavior of these pigments which show astonishing colorimetric parallels (Section 3.5.3).

2.3.6.1 Titanium Dioxide Evaporated on Mica Substrate An example of a pearlescent pigment on a mica substrate coated with rutil is shown in the upper half of Color plate 7. This picture was taken under bright field illumination. From the top view, the particles produce a yellow color impression over a black background. The non-uniform colors of the particles are caused by different layer thicknesses and by flakes tilted with regard to the image plane. This is further elucidated with the example of the red pearl luster pigment in Color plate 8. In this case, the particles in the same field are recorded in using bright and dark field illumination. The comparatively high-valued refractive index of titanium dioxide (n = 2.5 or 2.7) together with the low value of muscovite (n = 1.5) offers suitable conditions for developing neatly ordered interference colors. However, if the mica substrate is already flake shaped, TiO2 crystallizes in a thin film which is only suited for interference. Among the three possible crystal modifications of titanium oxide – rutil, anastas, and brookit – the rutil structure is preferred in this case. The dependency of the interference color on the titanium-dioxide-layer thickness is given in Table 2.15 (cf. Table 2.5). Each color impression over black background changes with increasing layer thickness from metallic “silver” over copper-red to green. These are no spectral colors because the accompanying colors are, in each case, composed of several adjoining interference wavelengths. The different wavelengths are selected by varied layer thicknesses of the metal oxide and by particles tilted differently toward the image plane (see Color plates 7 and 8). Under diffuse illumination, these pearl luster pigments produce the spectral reflectance over black background shown in Fig. 2.46. With increasing layer thickness, the peak shifts to longer wavelengths and simultaneously broadens. In the figure, this begins in the violet region. The reflectance minimum also moves to longer wavelengths, in the figure starting from the yellow range. The spectral reflectance of the “silver” pigment corresponds to that of a light gray hue or to that of aluminum cornflake pigments. This suggests the substitution of the metallic aluminum pigment by the cheaper pearlescent pigment in suitable cases.

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2 Light Sources, Types of Colorants, Observer

Table 2.15 Interference colors depending on layer thickness of titanium dioxide on mica substrate (cf. Table 2.5)

Layer thickness titanium dioxide/nm

Platelet thickness/nm

Interference color – inherent color over black background

Transmitted complementary color

40–60 60–80 80–100 90–110 120–130 100–140 120–160

120–140 140–160 230–250 250–270 280–300 310–320 370–390

“Silver” Yellow Red Copper-red Violet Blue Green

“Silver” Blue Green Blue-green Yellow-green Yellow Red

Now, assume that the peaks in Fig. 2.46 can be interpreted as interference wavelengths of first order. Clearly, this is not exact, but sufficient for the following estimations. If we use the values of the relevant refractive indices of Table 2.11 and assume perpendicular observation, then Equation (2.1.18) delivers an approximate value for the thickness of the titanium oxide layer. For the R (%) Layerthickness in nm 80

a: 40 – 60 b: 60 – 80 c: 80 – 100 d: 120 – 130 e: 100 – 140 f : 120 – 160

60

40

b a c d

20

e f

0

400

500

600

λ nm

Fig. 2.46 Spectral diffuse reflectance of mica pigments of different TiO2 coating thicknesses; measurements over black background, de:8 geometry16

16 The corresponding de:8 measuring geometry (see Section 4.1.2) simulates diffuse illumination conditions in closed rooms.

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95

last five flakes indicated in Table 2.15, this approximate calculation results in values which are in the given thicknesses intervals. The systematic changes in spectral reflectance are characteristic features of the basis pigment series: the spectral reflectance curves measured under diffuse illumination are “fingerprints” of the relevant pearl pigments. This is an analog to absorption colorants. These fingerprints are sometimes utilized for analyzing mixtures with further pigments. Using directional illumination and angle-dependent reflectance measurements, particularly important information about the properties of the relevant interference pigments can be obtained. For the moment, we restrict the discussion to only one illumination angle although the colors of pearlescent, interference, and diffraction pigments depend on the illumination as well as the observation angle. The five spectral reflectance curves in Fig. 2.47 were measured with the green pearlescent pigment, which has a peak at 507 nm in Fig. 2.46, curve (f). The film of pearl luster pigments over a black background is illuminated at an angle β = 45◦ and the spectral reflectance is measured at aspecular angles μas = 15◦ , 25◦ , 45◦ , 75◦ , and 110◦ . As can be seen, the peak reflectance reduces dramatically with increasing measurement angle and it shifts to slightly shorter wavelengths. For observations near the specular angle, the reflectance exceeds values higher than 1.0 or 100%. The chosen five measuring angles are by no means sufficient to gather the entire color dynamics of pearlescent and interference pigments [52, 53].

2.3.6.2 Iron-III-Oxide on Mica Substrate Crystalline α-Fe2 O3 has the highest refractive index of n = 2.88 among the substances listed in Table 2.11. As mentioned in the previous section, the total color impression of the layer composition with mica results from superposition of the layer-dependent interference color and the absorption color of the hematite. Iron-III-oxide produces a red to reddish-brown absorption color which is further modified by the thickness of the outer layer, see lower picture of Color plate 7. The color impression changes with increasing layer thickness from bronze colored to copper to purple or even reddish-green at the highest layer thickness. This is clear from the spectral reflectance curves shown in Fig. 2.48. In the cases of bronze, copper, and red, the reddish-brown absorption color is even amplified by the corresponding, nearly equal interference color like yellow, copper, and red. We return to the hue dependence of the layer thickness in Section 3.5.3. The superposition of interference and absorption leads to brilliant colors in the vicinity of the specular angle. Near this angle, the purple and reddish-green pearlescent pigments have a violet or green interference color caused by the relative high layer thickness of the hematite. With regard to comparable outer

96

2 Light Sources, Types of Colorants, Observer 150

R (%)

100

μas = 15°

50

25°

45°

0 400

75°

500

600

110°

λ

nm

Fig. 2.47 Spectral reflectance of the green interference pigment from Fig. 2.46 at five aspecular measuring angles μas ; measurement over black background, illumination angle β = 45◦

layer thickness, the TiO2 -mica pigments produce a broader variety of interference colors, whereas the iron-III-oxide produces diverse types of red hues. The distinct brilliance of the α-Fe2 O3 pigments comes from the slightly higher refractive index of the hematite in comparison to that of titanium dioxide. The increased covering capacity is again a consequence of the typically increased scattering of the inorganic oxide.

2.3

Effect Pigments

97

R (%)

a: Bronce b: Red-golden c: Copper d: Purple e: Red-green

80

Fe2O3Layer thickness

60

a b c

40

d

e 20

0

400

500

600

λ nm

Fig. 2.48 Diffuse spectral reflectance of mica pigments coated with Fe2 O3 of different layer thicknesses; measurement over black background, measuring geometry de:8

2.3.6.3 Combination Pigments Interference with more brilliant colors and higher absorption is generated by coating the substrate with two or more different metal oxides. A multitude of combination pigments are based on titanium dioxide-mica flakes, where the flakes are additionally vapor coated with Fe2 O3 or Cr2 O3 . These sorts of combination pigments show, in comparison to the original single-coated mica pigments, higher brilliance and a more distinct color flop. In the following, we consider the reflection behavior of mica combination pigments composed of layers of titanium dioxide in rutil modification coated with iron-III-oxide. The optical interactions between both metal oxides lead to many brilliant golden colors reaching from pale yellow-gold to rich red-gold to green-gold. With the addition of an oxide layer, a clear color extension with regard to the simple Fe2 O3 -mica particles is achieved. Furthermore, the change of the layer thicknesses of the two metal oxides generates a wealth of superimposed interference and absorption colors. The thicknesses of all three layers can be tuned with each other in such a way that the interaction of the interference and absorption components leads to a demanded coloristical effect, within limits. Similar features result from the substitution of the outer Fe2 O3 layer by Cr2 O3 . The combination of Cr2 O3 with TiO2 in anastas modification results in

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2 Light Sources, Types of Colorants, Observer

R (%) Fe2O3 TiO2 Rutil

80

60

Fe2O3 TiO2 Rutil

40 Cr2O3 TiO2 Anastas Cr2O3

20

TiO2 Anastas

0

400

500

600

λ nm

Fig. 2.49 Diffuse spectral reflectance of two combination pigments Fe2 O3 /TiO2 (rutil), Cr2 O3 /TiO2 (anastas) on mica substrate of different layer thicknesses; measurement over black background, measuring geometry de:8; the curves of Fe2 O3 /TiO2 are shifted 20 units toward higher reflectance values for better overview

high-luster blue-greenish to moss-green colors. Figure 2.49 shows the spectral reflectance curves measured under diffuse illumination of Fe2 O3 /TiO2 pigment and Cr2 O3 /TiO2 -mica pigment. Each has two different outer layer thicknesses, but the total coating thickness is constant in each case. The greater thickness of the outer oxide layer reduces the reflection. This is clearly caused by increased absorption due to greater layer thickness. In the case of a higher layer thickness of Cr2 O3 , this pigment additionally develops a clear peak in comparison to the quite broad peak belonging to the thinner outer layer. The increased influence of the Cr2 O3 layer on the interference development can be ascertained from the reflectance curve (f) in Fig. 2.46 for the green pearlescent pigment together with the two lower curves in Fig. 2.49. Altogether, titanium dioxide is responsible for the brilliance of the colors and the outer layer thickness for the interference color. The included absorption colors of iron oxide or chromium oxide exist otherwise under all observation angles. Nearly equal-colored oxide layers create a pearl luster effect of intensive colors which, at nearly all observation angles, show a noticeable color shift. However, if the color of an absorption colorant corresponds to that of the complementary color of the interference pigment, then a distinct two-colored effect is achieved, especially in the oxide combination of Cr2 O3 /TiO2 . Further inorganic absorption pigments such as Prussian blue, cobalt blue, Fe3 O4 , or carbon

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99

black generate, in combination with titanium oxide on mica substrate, unusual color effects as well. 2.3.6.4 Liquid Crystal Pigments The color flop of liquid crystal pigments consisting of polysiloxane depends on the pitch height p and causes, for example, the color pairs violet/blue, blue/turquoise, blue/green, green-blue/gold, and green/copper-red. Flakes with blue/green-flop are shown in Color plate 10 at bright and dark field illumination over black background. The noticeable sparkle particle there is already green from the top view because of the higher pitch height compared to the other flakes. To the present day, mixtures of the transparent particles with absorption or other effect pigments produce unequaled and extremely brilliant colors. As mentioned at the beginning of the section, further shades can be obtained with a suitable background color. With regard to liquid crystal pigments, this concept is underlined by the example in Fig. 2.50. The reflectance curves correspond to background colors of white, red, and black as well as each top coated with a transparent film of the same liquid crystal pigment. The reflectance peak over black at 512 nm corresponds to the green color impression from the top view. The red background leads to a minimal blue-tinged red and the

R (%)

Background alone

White

80

Layer over background

Red

60

40

20

Black 0 400

500

600

λ nm

Fig. 2.50 Spectral reflectance of a transparent liquid crystal pigment with d50 = 30 μm over white, red, and black background, as well as backgrounds alone; wavelengths of maximum reflectance over background: 512 nm (red), 531 nm (black); measuring geometry de:8

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2 Light Sources, Types of Colorants, Observer

white background creates a very light pink. The flat maximum of the white background at a wavelength of 490 nm is caused by fluorescence emission of the contained optical brightening agent (Section 4.2.6). Figure 2.51 shows the directional reflectance over a black background for illumination angle β = 45◦ and aspecular observation angles μas = 15◦ , 25◦ , 45◦ , 75◦ , 110◦ . With increasing measuring angle, the wavelength of the peak shifts from 483 to 520 nm. Simultaneously, the peak height decreases from R = 108% to about R = 2%. The angle dependence of the interference wavelength corresponds to the cosine function in Equation (2.1.20). R (%)

μas = 15°

β = 45° d50 = 30 μm

100

25° 50

45° 75° 0 400

500

λ nm

110° 600

Fig. 2.51 Spectral reflectance of a liquid crystal pigment with d50 = 30 μm for five aspecular measuring angles; measurements over black background, illumination angle β = 45◦

The brilliance of liquid crystalline pigments depends also on the average lateral dimension of the flake particles. This can be seen from the reflectance maxima in Fig. 2.52. The reflectance curves are measured for three different particle size distributions over the same black background and at constant illumination and aspecular angle of β = 45◦ and μas = 15◦ , respectively. The flakes have size distributions which correspond to the ratios of d50 /d99 = 30/90, 23/60, and 18/50 μm/μm. The reflectance maxima in Fig. 2.52 correspond to the ratios 30:23:18 of accompanying d50 values. In addition, this result is confirmed by measurements over red and blue background. The height of the reflectance maximum of liquid crystal pigments is, therefore, directly proportional to the mean flake size. Clearly, large-sized LCPs orient better to the background surface, in analogy to metallic flakes. These larger particles then show increased brilliance

2.3

Effect Pigments

101

R (%)

β = 45° μas = 15°

d50 = 30 μm 100

23 μm

50

0 400

18 μm

500

λ

600

nm

Fig. 2.52 Directional reflectance at constant aspecular measuring angle μas = 15◦ of a liquid crystal pigment in dependence on particle size d50 ; measurements over black background, illumination angle β = 45◦

compared to smaller sized flakes. The colorimetric properties of the most important pearl luster and interference pigments are outlined in Sections 3.5.3 and 3.5.4.

2.3.7 Opaque Films Containing Absorbing and Effect Pigments From discussions up until now, it is clear that the creation of new colorations by mixtures or films consisting of modern effect and classical absorption pigments represents quite a challenge. Especially needed to meet this challenge are hiding layers which consist of transparent effect pigments and covering absorption pigments. A coating is called covering or hiding, if any colored background can no longer be observed from above the film (Section 3.4.3). Covering layers with coarse metallic, transparent pearlescent, interference, or even diffraction pigments are produced by mixtures of colorants which generate suited scattering or absorption. It is also important to consider the change of the originally desired color effect with the addition of further colorants and also the compatibility with the pure effect pigment. Experience shows that covering coatings with effect pigments can, in the most cases, be manufactured with three different colorants: carbon black, suitable absorption pigments, and fine metallic pigments [54].

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2 Light Sources, Types of Colorants, Observer

A small amount of carbon black turns out to be quite effective for this. The resulting dark and sometimes even intense colors are caused by absorption of the complementary color with carbon black already inside the layer. Only a small volume amount < 1.0% of carbon black is normally sufficient. For larger concentrations, the interference color often appears too dark and the color travel (respectively, color flop) is too small or suppressed. The selective absorption and scattering of mixed in absorption pigments also result in covering layers of additionally impressive colors. Small amounts cause mostly brilliant interference colors. Larger amounts, however, can obliterate the pearl luster and interference effect: on the one hand, the interference intensity is increasingly masked and on the other hand, the complementary and part of the interference color are absorbed depending on the chroma of the absorption pigment. Finally, in the third method, the transparent pearl or interference pigment is mixed with a small amount of a special fine and, therefore, strongly scattering metallic pigment. In this case, the covering formulation is, however, accompanied by reduced brilliance, color saturation, and gloss. In all three mentioned cases, it is important to pay attention to the compatibility of the added components. Furthermore, the added amounts should be as small as possible in order to result in a coloristic effect changed only slightly. Altogether, the level of pigmentation of effect pigments in recipes depends on the desired color effect, the spreading rate of the pigment, and the molecular surroundings. For a few applications the pigment volume content is shown in Table 2.16. Apart from the application, the processability, the light, temperature, or weathering resistance, etc., additionally determine the total pigment amount of a coloration; see also Section 3.4.6. Table 2.16 Pigmentation level of effect pigments in various fields Pigment level % Employment

Metallic pigments

Pearlescent, interference pigments

Lacquers, emulsion paints Thermoplastics, thermosets Printing inks Cosmetics Toiletries

0.5–2 0.5–3 1–45 1–15 0.05–1

0.5–20 0.5–2 1–30 1–50 0.05–1

From color physical point of view, mixtures of effect pigments together or with absorption colorants obey the laws of additive or subtractive color mixing (Section 2.4.3). Mixtures or layers of effect pigments show additive color mixing if the colors of the single pigments are based on the superposition of wavelengths; see Table 2.17. But, as soon as the light interacts only with one

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Effect Pigments

103

Table 2.17 Additive and subtractive color mixing of effect and absorption pigments Pigment combination

Color mixing

Cause

Interference pigment mixed with interference pigment Interference pigment mixed with diffraction pigment

Additive

Interference pigment on absorption pigment

Additive and subtractive

Interference pigment mixed with absorption pigment

Subtractive

Absorption pigment mixed with absorption pigment

Subtractive

Superposition of reflected interference and transmitted complementary color Superposition of interference, diffraction, and transmitted complementary color Superposition interference color, absorption of complementary color and selective absorption of the colored pigment Colored pigment absorbs parts of the complementary and natural color of the interference pigment Each colored pigment absorbs parts of the influx light

Additive

absorption pigment together with any further pigment sort, the resulting color impression is based on subtractive color mixing; see also the literature [54, 55]. Additive color mixing is fundamental in the human color sense and the based on colorimetry of versatile industrial applications. Finally, we return to optical properties of interference pigments which depend on the particle size and morphology. Smaller particles show a reduced pearl luster effect in comparison with those of larger sized. This is because the higher edge scattering reduces the luster. In the case of dominant scattering, the pearl luster and gloss of interference pigments can even disappear completely. An increasing lateral size dimension up to 200 μm improves not only the brilliance but also the sparkle of the pearlescent and interference pigments; furthermore the color travel passes more wavelengths. However, with increasing flake geometry, the hiding power and DOI are reduced. The pigment properties shown in Table 2.18 correlate with related properties of metallic pigments listed in Table 2.9. In other words, comparable color properties of metallic, pearlescent, and interference pigments change in the same direction depending on the flake size. We have, thus far, still neglected opaque multi-layered pigments (Table 2.13). A considerable part of their color physical properties correspond to those of transparent effect pigments. An advantage of these pigments is the fact that the color effect is not distorted by additional colorants, but the absorption and selfscattering of the particles softens the original color. Further similarities between different effect pigment sorts are uncovered in Section 3.5.3.

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Table 2.18 Assessment of some properties of pearlescent and interference pigments in dependence of the particle size Particle size Φ/μm Property

Φ<5

5 ≤ Φ ≤ 25

10 ≤ Φ ≤ 60

30 ≤ Φ ≤ 200

Brilliance Color flop Covering capacity DOI

Low Reduced Excellent Very good

Silky Low Very good Good

Very well Striking Good Low

Sparkling Distinct Low Very low

2.3.8 Colors of Diffraction Pigments Although the diffraction of light waves has been known since the beginning of the 19th century, this phenomenon has only been used in color physics for a few years [56]. Waves are diffracted, analogous to interference, when they interact with structures of dimensions on the same order of magnitude as the wavelengths. Polychromatic light is split up by diffraction into the spectral components. Reflective diffraction pigments are the sorts that is of interest in industrial color physics. These consist of a metal substrate with a grating of embossed periodic grooves. In addition, the substrate is coated with inorganic substances; see Table 2.12. Each particle works as a reflection grating. The nano-engineering method of interference lithography can be used to produce periodic grating structures on surfaces. This method is based on the interference of two laser beams; see Fig. 2.53. With the two coherent waves from the same source, each of wavelength λL , an interference fringe pattern of parallel fringes of distance d results (Michelson configuration). This distance is given by the relation d = λL · sin ϑ,

λL

(2.3.1)

d

2ϑ

λL

Fig. 2.53 Generation of parallel structures with two coherent light rays using the Michelson configuration (schematically)

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105

where ϑ denotes the half of the divergence angle. The periodic laser fringe pattern is directed onto a metallized thermoplastic film or photoresist film so that this pattern is transferred into the film as an exposure. After removing the organic backing layer by thermal or chemical procedures, the remaining metal foil of projected groove geometry is evaporated in vacuum with further substances which are also used in nanotechniques. The substrate is coated symmetrically so that the diffraction always develops at the illuminated surface of the reflection grating. The films of up to 1 μm in thickness can be broken up into particles with lateral dimensions between 10 and 300 μm using ultrasound. The resulting flakes can be sifted by pigment size. Flakes with mean diameters of d50 = 20±2 μm are preferably used for print media and coatings [56]. The regular grating patterns consist not only of parallel but also rectangular, diagonal, or hexagonal lines. Presently, diffraction pigments are manufactured with 100 up to 5,000 equidistant parallel lines per millimeter (l/mm). The cross section of the grooves can be chosen in such a way that the first diffraction order corresponds to the geometrical direction of reflection (blaze techniques, Section 2.1.7). The diffraction particles shown in Fig. 2.54 have a grating constant of 1,000 l/mm. The substrate consists of highly reflective aluminum of about 80 nm thickness and periodic folding. Using PVD techniques, the metal film is coated on both sides with MgF2 of about 450 nm thickness; see cross section at fracture in Fig. 2.55. Diffraction pigments have been produced industrially since 2002, although symmetric grating cross sections have been used in technical optics since about 1980. The spectral reflectance of diffraction pigments with three different grating constants measured by diffuse illumination and de:8 geometry is shown in Fig. 2.56. For pigments with 1,400, 2,000, or 3,000 l/mm, the reflectance

Fig. 2.54 Diffraction pigments with periodic grating dividing of parallel lines; grating constant 1,000 l/mm (source: Flex Products Inc, Santa Rosa, CA, USA)

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Fig. 2.55 Cross section at fracture of a diffraction particle with periodic grating dividing; the surfaces of the aluminum substrate are vapor coated with MgF2 (source: Merck KGaA, Darmstadt, Germany) R (%) 3,000 l/mm

80

70

60

2,000 l/mm

50

1,400 l/mm

40

30 400

500

600

λ

nm

Fig. 2.56 Spectral reflectance of diffraction pigments of magnesium fluoride/aluminum of three different grating constants; the middle and upper curves are shifted 5, respectively 10 units toward higher scale values

is between R = 0.4 and R = 0.7. This quantity depends on the reflectivity of the metal layer, the number and thickness of the non-metallic vapor-deposited films, the accompanying refractive indices, as well as the mean particle size. The pigment with 1,400 l/mm produces a silver metallic color impression at observation perpendicular to the coating surface. The nearly flat spectral reflectance

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107

shown in Fig. 2.56 is known from silver-colored metallic or pearlescent pigments. Under diffuse illumination, particles of grating constant 2,000 l/mm appear bluish and those of 3,000 l/mm produce a yellow-orange color impression. The almost equal form of the reflectance curves in Fig. 2.57 indicates that the thickness of the aluminum substrate between 80 and 240 nm is, as to expect, of no influence with regard to the color impression. For a fixed grating constant of 1,400 l/mm, the height of the reflectance – and, therefore, the brightness – is only slightly increased with aluminum thickness. With substrate thicknesses greater than 240 nm, the surface roughness increases and, therefore, also the interface scattering. This scattering reduces, however, the intensity of diffraction. R (%)

240 nm

70 160 nm

80 nm 60

50 400

500

600

λ

nm

Fig. 2.57 Spectral reflectance of MgF2 /Al pigments with aluminum layer thicknesses of 80, 160, and 240 nm; grating constant 1,400 l/mm; the middle and upper curves are shifted 10 units toward higher scale values

Reflective diffraction pigments consisting of a ferromagnetic substrate allow for the orientation of the particles according to an external magnetic field. Preferred ferromagnetic materials are nickel, iron, cobalt, but also elements of the lanthanide series. For better understanding of the orientation of ferromagnetic particles in an external magnetic field, it is useful to make a short excursion into magnetostatics. The ferromagnetic state in solids is caused by non-compensated electron spins of the unsaturated 3d- and 4f-electron shells of metal ions. The unbalanced

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angular momentums of the electrons behave, therefore, like magnetic elementary dipoles which, in the crystal state, respond to two different forces. The first, the anisotropic force causes an alignment of the dipoles parallel to an external bounding face and the second, the exchange force forces the dipoles to parallelize to each other in the volume. In a magnetic material, anisotropic and exchange forces produce zones of equal magnetization direction. These zones have linear extensions between 1 μm and 1 mm which are called domains or Weiss areas, after their discoverer P.E. Weiss. An external magnetic field can drive two geometrical processes in the domains: a change of the threedimensional extension as well as a rotation from the original position at constant volume. Both effects are represented schematically in Figs. 2.58a–c. Figure 2.58a represents the original position of four domains in a ferromagnetic substance. A weak external magnetic field causes a shift of the domain walls; see Fig. 2.58b. An even higher external magnetic field strength turns the molecular magnets more into the direction of the external field, accompanied by a further extension of the domain volume, Fig. 2.58c. In general, domain wall shifts occur at moderate magnetic field strengths and domain rotations only at higher strengths. The basic driving mechanism for the orientation of ferromagnetic domains or particles parallel to an external field is the tendency of such systems to seek a state of minimal total energy. This is achieved by an internal demagnetization field which counteracts the external field. A sufficiently high external magnetic field strength causes a total rotation of the domains. If the lateral dimensions of free particles are on the order of magnitude of the domains, then the rotation into magnetic field direction is performed by the entire particle. This effect is

H a)

b)

H c)

Fig. 2.58 Schematic representation of Weiss domains in a ferromagnetic material: (a) without external magnetic field, (b) with weak magnetic field, and (c) with strong external magnetic field H

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known from iron filings, which align along the lines of an external magnetic field. Also ferromagnetic diffraction pigments are subject to such rotations. With the help of an external magnetic field, a nearly uniform orientation of diffraction pigments of ferromagnetic substrate can, therefore, be fixed before and during crosslinking of a binder. The both diffraction pigments given in the last line of Table 2.12 are ferromagnetic. With an additional Ni layer for the substrate, their composition corresponds to the two- and three-layered diffraction pigments one line higher in the table. The ferromagnetic particles consisting of the three different layers MgF2 /Al/Ni and grating constants of 1,400, 2,000, or 3,000 l/mm produce, under diffuse illumination, a nearly uniform silver-colored impression. A further PVD coating with chromium causes a gold-yellow color. The spectral reflectance curves of ferromagnetic diffraction pigments are of the same shape as the curves of non-ferromagnetic particles with grating constants of 1,400 and 2,000 l/mm; see Fig. 2.56. Certainly, on account of the particle orientation in a magnetic field, an angle-dependent colorimetrical behavior results, one which had not been observed before (Section 3.5.5). After a detailed description of the optical operation modes of industrially used colorants, we can conclude: between the rock and cave paintings of natural colors and the modern produced and applied colors there was, without doubt, an impressive historical development. This is accompanied by broad research as well as process and application technology in color industry. In spite of this, all presently known and also newly developed or modified colorants are merely orientated toward the color perception of humans. The human color sense is, therefore, discussed in some detail in the next section.

2.4 Observer In addition to the importance of the light source and the color pattern, the most important and final crucial factor for the emergence of color perception is the observer. His/her subjective color sensation comes from the remaining light waves that reach the retina of the eye after source light interacts with the colorants. Nearly all efforts in processing and applying natural, modified, and synthesized colorants are oriented toward the capability of human color sensation. Long ago, Newton emphasized the fact that color production is ultimately based on neural processes. This means that outside the visual cortex, colors do not exist, but only electromagnetic waves. In the following, we give a brief overview of the modern physiological and neurological understanding of color sensation [57, 58]. These connections lead directly to the fundamental Grassmann laws of additive mixing of colors. The standardized CIE color values of the years 1931 and 1976 as well as the broad color physical and colorimetrical applications are based on these laws.

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2.4.1 Color Perception and Color Theories As already mentioned in the introduction of this text, color perception is produced by psychophysical and neural processes. Color sensation is, therefore, not directly measurable with normal physical methods. The first important element contributing to overall color perception is the eye. The essential optical components of the human eye for image formation are shown in Fig. 2.59. The cornea is only 0.5 mm thick and of fixed focal length of 25 mm, the iris has a lightness-dependent aperture ratio of 28:1, and the crystalline lens is of variable focal length. This focal length amounts about 50 mm for the resting eye when relaxed for distant vision. For an eye of normal vision, these optical elements provide a clear and focused image on the retina in the area of the fovea. In the retina are located two types of photosensitive receptors: first, the rods responsible for dusk vision and achromatic colors for luminance less than 0.01 cd/m2 (scotopic vision); second, the cones for color vision for luminance higher than 10 cd/m2 (photopic vision).17 If the eye is fully adapted to darkness, just nine photons are required before a light stimulus is detected. In cases of middle illumination for luminance in the range of 0.01 and 10 cd/m2 , rods and cones are simultaneously active (mesopic vision). The retina of the human eye contains altogether about 125 million visual cells, but only 5% consist of cones. In the small area of the fovea for visual angles of about ±0.5◦ , there are only cones present. Here they are of maximum density and enable focused vision only at this spot of the retina. The majority of

lris

Crystalline lens

Cornea

Fovea Macula Optic axis

Blind Spot

{ Optic nerves

Retina

Fig. 2.59 Horizontal section of the human eye

17 For

definition of unit cd (candela) see footnote 1 in Section 2.1.3.

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111

the rods are, however, distributed outside of the macula in an area of visual angle greater than ±5◦ (for visual angle, see Fig. 2.65). At the place of the blind spot of missing visual cells, the cord of the optic nerves continues to the brain.18 The different density distributions of rods and cones in the human retina are shown in Fig. 2.60. Four different photosensitive pigments are contained within the outer zones of the visual cells: one pigment in the rods and three pigments in the cones. The photosensitive pigments consist of a protein molecule denoted as opsin to which a derivative of vitamin A1 molecule is bound. This chromophoric group is common to the four pigments. The absorption spectrum of a photosensitive pigment depends on the kind of protein as shown in the normalized representation in Fig. 2.61. The pigment in the rods, called rhodopsin, shows an absorption maximum at the wavelength of 498 nm, the tails of the maximum project into the spectral absorption ranges of the cones. The absorption maxima of the three cone pigments occur at wavelengths 437, 533, and 564 nm. These wavelengths are perceived as blue, green, and red and the corresponding cones are, therefore, called blue, green, and red receptors. In the English-speaking medical literature they are denoted as S-, M-, and L-cones, indicating the selective sensitivity at short, middle, and long wavelengths of the visible spectrum. The three cone types are not equally distributed throughout the retina. The relative distribution for blue:green:red is about 1:20:40. From the similar shapes of absorption

Number of retinal receptors × 103/mm2

Blind spot

Rods Cones

150

100

50

0 –80°

–40°

0° Angle from fovea center

40°

Fig. 2.60 Density distribution of rod and cone receptors across the human retina

18 In modern neurology,

the retina is interpreted as a part of the brain.

80°

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λ max 437

498

533

564

nm

Relative absorption

1.0

0.5

Cones Rods 0

400

500

600

λ

nm

Fig. 2.61 Normalized spectral absorption of the four different photo receptor types in the human retina [57]

curves in Fig. 2.61, it is possible to conclude that the spectral absorption mechanisms of the three cone types are basically identical, although the curves seem to be shifted along the wavelength axis. Up until now, we have assumed normal color perception, called trichromacy on account of the three different cone receptors. Some sort of color vision deficiency with at least one defective color receptor occurs in about 0.5% females and about 7% males [58–60]. Although some animal species show an evolutionary caused tetrachromacy [61], this property has almost disappeared completely of human beings. In only extremely rare cases of women a fourth color receptor was proven; such a receptor shows a maximum sensitivity in the range of yellow wavelengths [62]. The unusually varying description of defective color vision in the literature is a consequence of the fact that previous generations of researchers used the constrained color perception for indications of the neural color sensation. The following kinds of anomalous color vision can be distinguished: – color asthenopy: fast onset of tiredness during color vision; – color amblyopy: selectively reduced ability to distinguish colors; – color anomaly: caused of defective or missing color receptors. The color anomaly can be divided further into: – anomalous trichromasy: the characteristic feature is a reduced perception of one color during simultaneous observation of several varied colors. In this

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case, there are three color receptors available but one does not work normally. More concretely, there are red-, green-, and blue-yellow weakness; – dichromasy: is present if a certain color is not perceived at all; dichromasies are the most frequent anomalies in humans and can be passed on gender specifically. Dichromates have only two color receptors, leaving red-, green-, and blue-yellow blindness; – achromatopsy: this term is a synonym for complete color blindness. Affected people do not possess any of the three well-operating color receptors; such people can only differentiate lightness levels. Although the after retinal occurring neural processes are only vaguely understood for normal color vision – and surely will remain for a long time at this level understanding – we follow at least roughly the path of the neural signals in the brain. This discussion is also carried out here to indicate to the reader how difficult the search of an adequate color vision theory is. About 50 ms after photon absorption in the photo pigments, retinal signals reach the optic nerve behind the eye. Each left and right half of the retina of both eyes form a nerve fiber; see Fig. 2.62. At the position of the optic nerves crossing over, the so-called chiasma or optic chiasma, each nerve fiber coming from the left and right half of both retinas is shared to the related brain lope. In the optic chiasma, however, there is no mixing of the incoming neural signals from both eyes. The subsequent optic tract ends at the region of the so-called lateral geniculate nucleus, where Lateral geniculate nucleus

Optic radiations Optic tract

Visual cortex

Chiasma Optic nerve

Fig. 2.62 Top view of the head to the human brain with indicated path of neural signals between the two retinas and the visual cortex; the visual cortex is in no way a sharp restricted region of both brain lopes, but individually different expanded

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the separate incoming neural impulses from both eyes are united into groups. Along several optic radiators, the transformed signals directly reach the region at the back of the brain lopes. This is the location of the center of our visual perception, called the visual cortex. In one special zone of the visual cortex, the actual color perception is produced, just about 100 until 150 ms after photon absorption in the retina. On the basis of this incomplete knowledge, it is necessary to have at least an adequate theory of human color perception. Although the trichromatic color theory of Young–Helmholtz and the opponent color theory of Hering have been shown to be true on physiological basis, neither theory can concretely explain the mechanism in the visual cortex for producing color perception (cf. Chapter 1). Likewise the modern retinex theory of Land, based on studies of color constancy, delivers no usable ideas about the emergence of color impression in the visual cortex. According to the zone theory, proposed by Müller [63] and Judd [64], the first zone contains the three independent S-, M-, and L-color receptors of the trichromatic theory. In the second zone, the generated nerve impulses are transformed according to Hering’s theory into an achromatic signal and two opponent chromatic signals. The visual cortex represents the third zone. The arriving neural signals initiate the color impression including the memory. Accordingly, the zone theory merely brings together the verified and accepted basics of both theories mentioned above. On the basis of current knowledge, it is possible to distinguish 30 different zones of the brain responsible for vision. Merely five of them are assigned to the color sense, of these only one dominates for color perception. The neural processes between photon absorption in the retina and induced color impression in the visual cortex remain unclear. It is not surprising, therefore, that only the physiological confirmed theories of Young–Helmholtz and Hering lead to scientific color applications such as colorimetry. The lacking of a theory which accurately describes the human color sense turns out to be disadvantageous, in particular for quantification of visually perceived color differences. As shown in Sections 3.1 and 3.2, only empirical formulas are given to express a color difference numerically. This unsatisfactory situation has existed since the beginnings of colorimetry.

2.4.2 Color Perception Phenomenon In the previous section, we have roughly outlined how humans perceive color. Now we direct our attention at some remarkable color phenomena of the complex processes of color sensation. Among these are the so-called simultaneous contrast, negative, or positive after-images or phosphene perception. These effects are important in different color applications and need to be taken into

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115

consideration during color assessment. These are, therefore, considered briefly here. The term simultaneous contrast describes the phenomenon that the lightness and the color of the surroundings influence the color impression. We should differentiate between simultaneous lightness contrast and simultaneous color contrast. A middle gray, for example, appears darker in a white neighborhood than in a black one; this is lightness contrast. In a similar manner, differences between dark chromatic colors are resolved worse with bright-surround field than with dark-surround field; this is color contrast. For visual assessment of color differences, it is, therefore, necessary to always use the same achromatic surrounding color (Section 3.2.2). Phenomenon of simultaneous color contrast is more varied than simultaneous lightness contrast. In both cases, the contrast is amplified just at the edges of color areas. The so-called lateral inhibition is responsible for the altered color perception. This term means that the neural signals in adjacent receptors within the retina interact with one another. Changes that are caused by lightness or color alone are, therefore, felt lesser strongly; contrasts, on the other hand, are perceived amplified. An additional quite remarkable ability of human color sense is the fact that many object colors are unchanged in spite of illuminant change. For example, a blue color is still perceived as the same blue, although the spectral energy distribution of the illuminant is varied. Another property of the visual sense is combined with the so-called afterimage. This after-effect occurs, if a single-colored area of high color saturation is seen with fixed eyes during about 1 min, and without movement of the eyes or head. If the eyes are afterward adapted to a white area, the color impression remains for some time. This negative after-image is produced in the complementary color. The reason for this is that the most of the corresponding receptors are desensitized during the fixing of the chromatic surface; the remaining sensitized receptors continue to have a reinforced effect during the white impression. The contrary phenomenon becomes apparent if the eyes are closed for some minutes, and then for a short time directed toward a contrasting object and then closed again. The resulting positive after-image shows that the color sensation actually lasts longer than the original action of the light. A longer continuing involuntary persistence occurs on chromatic adaption. After-images are in particular of importance for colorists if color shades are to be judged after a bright lighting phase with monochromatic sources. Therefore, before assessment of critical hues, for example, is important to look at a large, plane, and achromatic area for several minutes in order to avoid influences of after-images. A further time-dependent characteristic of color perception is associated with a short viewing of a color stimulus. For a viewing time of less than 0.1 s, most hues appear progressively desaturated. In the case of very short stimuli of about 3 ms duration, monochromatic light in the range from 490 to 520 nm appears

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achromatic white or gray. These effects are attributed to the property that the response time of the receptors is clearly shorter for achromatic colors than for chromatic colors. Colors can be perceived, quite astonishingly, also without an outside stimulus; this phenomenon is called phosphene. After the eyes are accommodated to darkness for a sufficient time, it is normal to observe light or colored spots. The effect of outside pressure on one or both eyes results in time-dependent changing light areas or colored schlieren. Phosphene occurs in addition without dark adaption by sudden pressure or electric current. In these cases, the influence from outside the closed eyes evokes disturbances in circulation and neural transmission. There are further phenomena of color perception which depend on spatial conditions or movement of the colored object. These are not of interest to color physics and are beyond the scope of this book. With exception of phosphene, the above outlined effects enable us to perceive a world of stable colors and lightness, although we are surrounded by an even greater variety of electromagnetic waves of different frequencies and changing intensities. But these electromagnetic waves are responsible for further color effects such as additive color mixing, which is effective especially in the human eye, or subtractive color mixing which, for example, is present in absorption colorants. Both phenomena are subjects of the following section.

2.4.3 Subtractive and Additive Mixing of Colors A deeper insight into the human color sense has been obscured as a consequence of subjective color judgment and, up to now, the inability to detect directly the chromatic signals at each position from the retina to the visual cortex by objective measurements. Therefore, Grassmann tried an indirect way to come closer to the human color sense [65]. In order to describe color impressions quantitatively, he avoided some of the briefly mentioned problems by using three monochromatic light sources of different wavelengths; see Fig. 2.63. Consequently, color stimuli are generated under defined conditions and color effects can be observed and registered. Non-self-luminescent colors are unsuited for such investigations, because the colors of these light sources are required to be produced quite simply, reproducible, and additionally, they need to be mixed trouble-free with one another. For better understanding of the results achieved by Grassmann, it is useful to go into details of subtractive and additive color mixing, both of which are basic properties of color physics. Subtractive color mixing is present, for example, after polychromatic light has passed through an optical selective filter: one part of the incident light is absorbed by the filter, and, therefore, denoted as subtracted. In Table 2.19, some

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117

Red Green

Blue White screen

Observer

Black partition

Incandescent lamp

Fig. 2.63 Configuration for producing light colors for additive color mixing

examples of subtractive color mixing are listed, cf. also Color plate 1, overlapping upper colors. In the case of several simultaneously used filters, the resulting transmitted color is independent of the order of the filter. Subtractive color mixing dominates in all sorts of absorption colorants and their mixtures; the color result of a colorant mixture is, therefore, independent of addition sequence. Subtraction of light waves occurs also in special cases of mixtures with effect pigments, as well as during developing of color pictures, among other things. In contrast, additive color mixing occurs by superposition of colored lights. The likely most important example is the human color perception. Additive color mixing is subject to photons of visible light, provided they enter the retina at the same time. Superimposed, the waves or photons are denoted as added. If the retinal photo pigments are stimulated simultaneously by polychromatic light, merely one single color stimulus is induced. In this context the synonymous term “additive color mixing of light” is correct. Further examples of additive color mixture are computer or television screens. For such screens, addressable groups of closely packed red, green, and blue pixels of diameter less than 0.1 mm (of phosphorus, liquid crystals, or inert gas cells) are stimulated simultaneously to produce color points. Color pixels of such small lateral dimension cannot be perceived separately by the eye at sufficient distance; therefore, only a single color stimulus is produced. A macroscopic example is shown in Color plate 1, lower overlapping colors, cf. Table 2.19.

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Table 2.19 Examples of subtractive and additive mixing of colors; cf. Color plate 1, overlapping color segments Subtractive mixing of colors

Additive mixing of colors

Initial colors

Mixed color

Initial colors

Mixed color

Magenta, yellow Yellow, cyan Cyan, magenta Magenta, yellow, cyan

Red Green Blue Black

Green, blue Blue, red Red, green Green, blue, red

Cyan Magenta Yellow White

From the position and shape of the curves in Fig. 2.61, it is clear that the light absorption of the red, green, and blue color receptors occurs in different and partially overlapping spectral regions, although only one color stimulus is evoked in the retina. The color stimulus Φ clearly depends on wavelength λ. If the photons of the source directly reach the retina, the color stimulus Φ(λ) equals the spectral energy distribution S(λ) of the source. For non-self-luminous colors, Φ(λ) is given by the product of S(λ) and the reflection R(λ) or transmission T(λ) of the illuminated layer: Φ(λ) = S(λ) · T(λ),

(2.4.1)

Φ(λ) = S(λ) · T(λ).

(2.4.2)

Using several illumination sources simultaneously, each individual color stimulus is summed up to form an aggregate stimulus, exactly the same procedure as in the retina or in screens. All further color physical themes dealt within this book, such as color vision, colorimetry, color measurement, or color recipe prediction, are based on the fundamental empirical laws of additive color mixing formulated by Grassmann in 1853. As briefly mentioned at the beginning of this section, for his investigations, Grassmann used three monochromatic light sources emitting constant red, green, and blue wavelengths, respectively. With a similar configuration to that shown in Fig. 2.63, but without the incandescent lamp, a new light color is mixed on a white field by superposition of these three wavelengths. The experimental results show that any additive color mixing is characterized by three arbitrarily chosen primaries R, G, B, in this case lights, which are given by the corresponding color values R, G, B. They correspond to the relative luminance of the light sources used. Of importance is that each of the three color values R, G, B is not necessarily restricted to a fixed wavelength in the red, green, or blue range; they are optional. The three color values R, G, B are combined in the so-called color

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stimulus specification C, which is written as a vector in three dimensions19 C = (R, G, B)T .

(2.4.3)

Furthermore, the primaries R, G, B can be interpreted as the unit vectors of a three-dimensional space R = (1, 0, 0)T ,

G = (0, 1, 0)T ,

B = (0, 0, 1)T .

(2.4.4)

Using terms such as color values, color stimulus specification, and primaries, Grassmann summarized his results in the following three empirical laws of additive color mixture: 1. For identification of a color stimulus specification, three independent primaries, which cannot be matched by additive mixture of the other stimuli, are necessary and sufficient. 2. The result of an additive color mixture is influenced only by the color stimulus specifications, not by their spectral compositions. 3. All producible color mixing series change continuously. Now, we consider the consequences of the Grassmann laws. According to his first law, each color stimulus specification C is represented by an equation of the form C = RR + GG + BB.

(2.4.5)

It is called the color equation. Equation (2.4.5) is of central significance to all of color physics. It is valid for arbitrarily selected primaries R, G, B. The three color values R, G, B provide the contributions of the three primaries to the color stimulus specification C. In other words, the color values describe the entire color impression. This is synonymous with the statement that every color impression is given in quantitative form by three color values R, G, B. The numerical quantities of R, G, B are, therefore, representatives of a color impression. The second law of additive color mixing turns out, for example, to be applicable to all cases of color matching; it is the basis of color recipe prediction. For any color impression, it is irrelevant of which individual colorant components the corresponding coloration is composed. The same holds for the mixture of lights of different spectral distributions. If, for example, two arbitrarily given color stimulus specifications C1 and C2 are matched by three primaries R, G, B, then from the first Grassmann law, it follows 19 The exponent

T symbolizes a transposed vector.

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C1 = R1 R + G1 G + B1 B ,

(2.4.6)

C2 = R2 R + G2 G + B2 B.

(2.4.7)

According to the second law, the additive mixture of both color stimulus specifications is given by the sum of the corresponding individual color values

C = C1 + C2 = (R1 + R2 )R + (G1 + G2 )G + (B1 + B2 )B.

(2.4.8)

The additive color mixing produces a new color stimulus specification C, from which is not possible to discern whether or not it consists of several individual color components (i.e., color values). The third law of additive color mixing implies that if one or more components of the mixture are gradually changed, then the resulting color values also change gradually, that is, as opposed to changing in a discontinuous fashion. Therefore, if we assign the color stimulus specification to a point in three-dimensional space, all additively mixed color stimuli generate an own continuous and coherent color solid, the color space. Grassmann has formulated originally four laws, which in modern literature are summarized to the three given above. In the next section, we pursue the industrially important question, how we can use color values to treat color impressions objectively?

2.4.4 Tristimulus Color-Matching Experiments According to the laws of additive color mixing, a given color is characterized by three color values R, G, B. For handling of these laws, it is useful to establish the optional primaries R, G, B in such a way that at least the requirements that follow are fulfilled. The primaries should – be definite, reproducible, and computable from color measurements; – have always a positive sign; – correspond to photopic vision; – achieve numerical color differences corresponding to the visually perceived color differences. The system introduced from the CIE in 1931 meets, to a large extent, the listed first three criteria [7]. The final listed requirement is as yet not satisfactorily solved (see, e.g., Section 3.2). The CIE 1931 system rests on the results of tristimulus color-matching investigations of Wright [66] and Guild [67], which used ten and seven people, respectively. For these experiments, the complete configuration used is shown in Fig. 2.63. With a source of nearly monochromatic

2.4

Observer

121

light, a test stimulus of ±2.5 nm wavelength accuracy was generated by illuminating a bipartite white screen which was shielded against the other half. On this second field, the additive mixture of three primaries was projected. These were the matching stimuli of the three monochromatic lights. By using adjustable light controllers, the observer subjectively adjusted the light flux of the three primaries to obtain a color match between the two separated fields. Wright and Guild used three monochromatic light sources of wavelengths 700.0, 564.1, and 435.8 nm. In the case of a match, the test stimulus was characterized by the three luminance values of the primaries. Before the actual matching experiments were performed, the intensities of the three primaries were adjusted to obtain an additive mixture of achromatic white. This procedure is termed as white balance; an example is shown in Color plate 1, see lower overlapping color circles. The color values are, therefore, normalized with regard to the radiant energy density of the primaries for white balance: the accompanying color equations are valid for the so-called equienergy spectrum. Colors differing only in their lightness belong to the same chromaticity. The color stimulus specification of the test stimulus at wavelength λi is termed as Ci . The matching color values of the three primaries are called colormatching values and are assigned by ri , gi , bi ; they are valid especially for the chosen primaries R, G, B [68, 69]. Due to the subjectively different color sensation of the observers, the ri , gi , bi values fluctuate. Their mean values are denoted by r¯i , g¯ i , b¯ i . In the case of match, the color equation Ci = r¯i R + g¯ i G + b¯ i B

(2.4.9)

is fulfilled according to the first Grassmann law. However, the matching procedures certainly show that not every given spectral color can be matched with the preset primaries. For example, a blue-green color of wavelength 490 nm does not match by mixing the blue or green primaries alone. In this case, the color match of equally saturated color fields is only achieved if an amount r¯io of the primary R is directly added to the given test stimulus specification Ci . This procedure is called outer mixture and is represented by the color equation Ci + r¯io R = g¯ i G + b¯ i B.

(2.4.10)

By adding the quantity −¯rio R to each side of color equation (2.4.10), an equation analogous to Equation (2.4.9), but with negative amount −¯rio on the right-hand side, results. This is a less than satisfactory situation to which we return in the next section. For continuous wavelengths λ, the mean color-matching values r¯i , g¯ i , b¯ i turn into the color-matching functions (CMFs), which are assigned to r¯ (λ),

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2 Light Sources, Types of Colorants, Observer

Color matching function

0.4

– r (λ)

– b (λ)

0.3

g–(λ)

0.2

0.1

0 546.1

435.8

700.0

–0.1 400

500

600

λ nm

¯ Fig. 2.64 Color-matching functions r¯ (λ), g¯ (λ), b(λ) of the equienergy spectrum using wavelengths of 700.0, 546.1, and 435.8 nm for primaries R, G, B

2°

10°

50

1.8 9.1

Fig. 2.65 Visual angles of 2◦ and 10◦

¯ g¯ (λ), b(λ), and shown in Fig. 2.64. The color match on both color fields is carried out with a visual angle of 2◦ by the observer; see Fig. 2.65. Under this observation angle and at normal viewing distance of 50 cm, a circle area of 1.8 cm in diameter is perceived. In the same angular range, the fovea of the retina contains only cones (Fig. 2.60). An observer, which fulfills these conditions, is called 2◦ standard observer, abbreviated 2◦ observer, and is represented ¯ by the three CMFs r¯ (λ), g¯ (λ), b(λ). As shown in Fig. 2.64, the CMFs have unequal peak heights. This represents the different sensitivities of the corresponding three retinal color receptors. Among the CMFs, only the function r¯ (λ) has a negative amount with the dip minimum at about 522 nm. The negative proportion is a consequence of the outer mixture. If the reference color stimulus specification corresponds to the

2.4

Observer

123

wavelength of a primary, the other two primaries are not required and their corresponding CMFs are zero. This can be taken from Fig. 2.64 for wavelengths of 435.8, 546.1, and 700.0 nm. Finally, it needs to be pointed out that the trichromatic matching experiments were achieved only with few people, under photopic vision with an observation angle of 2◦ and dark surroundings. Insights for scotopic or mesopic vision, bright surroundings, or large colored fields have, up to now, not been performed.

2.4.5 Determination of Tristimulus Values In view of color measuring methods and colorimetric applications, we will use discrete wavelengths λi in the following. A trichromatic stimulus is induced, according to the explanations in Section 2.4.3, by additive mixture of all monochromatic color stimuli Φ i = Φ(λi ). In the case of non-self-luminous colors, the color stimulus Φ i follows, according to Equations (2.4.1) and (2.4.2), from Φi = S(λi ) · R(λi )

(2.4.11)

Φi = S(λi ) · T(λi ),

(2.4.12)

or

because a non-self-luminous color is to illuminate with a source of spectral power distribution S(λi ). Each retinal color stimulus Φ i is represented by a corresponding color stimulus specification Ci . If there are simultaneously i = 1, 2, . . . , N stimuli Ci , the total color stimulus specification is given by additive mixture: C=

N 

Ci .

(2.4.13)

i=1

Applying Equation (2.4.8) with N ≥ 2, C=

N  i=1

Ci =

N  i=1





Ri R +

N 

Gi G +

i=1

N 

Bi B

(2.4.14)

i=1

follows. The color values Ri , Gi , Bi correspond, on the other hand, to the product of the color stimulus Φ i , one of the respective CMFs r¯i , g¯ i , b¯ i , and the technically given wavelength interval width Δλ of the used illuminant. From this, it is possible to write the equations for the color values: Ri = Φi r¯i Δλ,

(2.4.15)

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2 Light Sources, Types of Colorants, Observer

Gi = Φi g¯ i Δλ,

(2.4.16)

Bi = Φi b¯ i Δλ .

(2.4.17)

If we insert these relations into Equation (2.4.14) and compare the new equation with Equation (2.4.5), finally the color values R, G, B of a non-self-luminous color follow from expressions:

R=

N 

Φi r¯i Δλ,

(2.4.18)

Φi g¯ i Δλ,

(2.4.19)

Φi b¯ i Δλ.

(2.4.20)

i=1

G=

N  i=1

B=

N  i=1

If the emitted wavelengths are quite closely spaced together so that infinitesimally small wavelength intervals dλ can be assumed, the discrete color stimuli Φ i can be written as the color stimulus function Φ(λ). Then, the color-matching ¯ Accordingly, the sums values r¯i , g¯ i , b¯ i also become the CMFs r¯ (λ), g¯ (λ), b(λ). in Equations (2.4.13), (2.4.14) and (2.4.18), (2.4.19), (2.4.20) should be substituted by integrals and the integration limits correspond to the lower and upper cutoff wavelengths of the visible range. In this text, the sum notation is generally preferred. Two straightforward reasons for this preference are as follows: first, the spectral power distribution S(λi ) of the most used illuminants in color industry and the CMFs of the 2◦ standard observer are tabulated for interval widths Δλ of 5, 10, and 20 nm [70–72] and second, all industrial spectrophotometers are designed to measure in one of these wavelength interval widths. Therefore, the color values R, G, B of a given color sample can be calculated from Equations (2.4.18), (2.4.19), and (2.4.20) if the accompanying reflection or transmission is known from measurement. To summarize, we emphasize that owing to additive color mixture, a given color can be described by three corresponding numerical color values R, G, B. These are merely representatives of the corresponding color and are by no means absolute values. On the basis of the experimental connections, they can be interpreted as the red, green, and blue components of a color shade. In the following section these results are finally modified for practical applications in colorimetry.

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Observer

125

2.4.6 CIE 1931 and CIE 1964 Standard Colorimetric Observers Among the indicated color values, the red component R of a color shade has a region of negative values of the CMF r¯ (λ) shown in Fig. 2.64: this is extremely unreasonable. Depending on color stimulus Φ i , the color value R can show, according to Equation (2.4.18), a positive or negative sign and, therefore, cannot be clearly interpreted in a coloristic sense. More confusing is, for example, a red coloration with a color value of R = 0. The occurrence of negative color values is due to the choice of the three real primaries R, G, B. Negative color values cannot be altogether avoided with the spectral energy distribution of technical light sources. In order to achieve only positive or zero CMFs and color values, respectively, the CIE introduced in the year 1931 – after the conclusions of Wright [66] and Guild [67] – the so-called virtual primaries X, Y, Z. These follow from a suitable numerical transformation of the previous real primaries R, G, B [7]. The virtual primaries X, Y, Z are chosen in such a way that the following criteria are fulfilled:

– X, Y, Z are by definition independent of each another, and are, therefore, not producible by mixing (the same requirement as for the real primaries R, G, B); – the new CMFs x¯ (λ), y¯ (λ), z¯(λ) always take values ≥ 0 and follow from the previous CMFs by an appropriate transformation (see below); – the virtual primaries X, Y, Z are adjusted in such a way that the corresponding tristimulus values X, Y, Z are equally valued for the chromaticity of the equienergy spectrum: X = Y = Z; – the two virtual primaries X and Z are chosen in such a way that only the color value Y is proportional to the lightness of a color.

The new color quantities X, Y, Z are called standard color values. The new CMFs x¯ (λ), y¯ (λ), z¯(λ) are named standard color-matching functions (SCMFs) ¯ and are given with the previous CMFs r¯ (λ), g¯ (λ), b(λ) by the empirical matrix equation ⎛

⎞ ⎛ ⎞ ⎛ ⎞ r¯ (λ) x¯ (λ) 2.768892 1.751748 1.130160 ⎝ y¯ (λ) ⎠ = ⎝ 1 4.590700 0.060100 ⎠ · ⎝ g¯ (λ) ⎠ . ¯ z¯(λ) 0 0.056508 5.594292 b(λ)

(2.4.21)

These SCMFs belong to the 2◦ observer, called CIE 1931 observer; the corresponding graphs are shown in Fig. 2.66 [7]. Discrete values of these functions are used to calculate the standard color values X, Y, Z, see below.

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2 Light Sources, Types of Colorants, Observer

In practice, all color samples for visual assessment have a larger sized colored area compared with the 2◦ field at the normal vision range of 50 cm (Fig. 2.65). A considerable reason for such small-sized samples is that an observation angle of 2◦ covers only the area of the fovea. Although there is the highest cone density, the induced color stimulus from this spot is insufficient for an adequate color assessment. Because of that, the CIE introduced in 1964 the so-called 10◦ observer, also termed as CIE 1964 observer, based on investigations of Stiles and Burch as well as Speranskaja with 49 and 27 people, respectively [73–75]. Recent tabular values of the SCMFs for the 10◦ observer have been given in the literature [70–72]. Whereas the primaries of the 2◦ observer are related to the wavelengths 700.0, 546.1, and 435.8 nm and the primaries of the 10◦ observer have the corresponding wavelengths 645.2, 526.3, and 444.4 nm. For the normal vision distance of 50 cm, the visual angle of 10◦ covers a circle area of 8.8 cm in diameter, cf. Fig. 2.65. In this area, the retina certainly contains rods. For this reason, the SCMFs were corrected to eliminate the influence of the rods [7]. The CIE recommended the 2◦ observer for visual angles between 1◦ and 4◦ , and the 10◦ observer for visual angles > 4 ◦ . The 4◦ limit was arbitrarily established although there exists no discontinuity of color perception at this angle. The SCMFs of the 10◦ observer x¯ 10 (λ), y¯ 10 (λ), z¯10 (λ) are distinguished from those of the 2◦ observer by the subscript 10. The values follow from a transformation similar to Equation (2.4.21) using the corresponding CMFs r¯10 (λ), g¯ 10 (λ), b¯ 10 (λ) according to the equation ⎞ ⎛ ⎞ ⎞ ⎛ r¯10 (λ) 0.341080 0.189145 0.387529 x¯ 10 (λ) ⎝ y¯ 10 (λ) ⎠ = ⎝ 0.139058 0.837460 0.073160 ⎠ · ⎝ g¯ 10 (λ) ⎠ . z¯10 (λ) 0 0.039553 1.026200 b¯ 10 (λ) ⎛

(2.4.22)

The numerical values of the components of the matrices in Equations (2.4.21) and (2.4.22) are unequal because they belong to different primaries and different observer fields. The SCMFs of both observers are together represented in Fig. 2.66. The maxima of the functions y¯ (λ) and y¯ 10 (λ) are normalized at λ = 555 nm to 1.0. Due to the different visual field of the observers, the corresponding curves do not match perfectly. For one and the same color, the standard color values corresponding to each observer are also not identical. From the nonlinear wavelength dependence of both CMFs follows that the corresponding standard color values cannot be converted into one another. Although the 10◦ observer is used to an increasing extent in color industry, in order to avoid ambiguity, the observer must be clearly indicated with the results. For the last adjustment criterion of the four listed above, it should be stated that the graph of the function y¯ 10 (λ) agrees with the measured luminous efficiency V(λ) of the human eye

2.4

Observer

127

2° 10°

Standard color matching function

2.0 z (λ) 1.5

x (λ)

y (λ) 1.0

x (λ)

0.5

0 400

500

600

700

λ

nm

Fig. 2.66 Color-matching functions of the 2◦ and 10◦ standard observers (CIE 1931 and CIE 1964 observers, respectively)

y¯ 10 (λ) = V(λ),

(2.4.23)

see Fig. 2.67.20 The standard color value Y is, on account of this adjustment, a measure for the lightness of a coloration. The curves of V (λ) and V(λ) in Fig. 2.67 correspond to the sensitivity of the eye for scotopic and photopic adaption, respectively. The curves are shifted with respect one another by about 40 nm. This is described by the so-called Purkinje effect. From the half-widths of 150 nm, it follows that the middle wavelengths of the visible spectrum are perceived with particular sensitivity under both adaption conditions. Now, the CIE standard color values X, Y, Z are simply given from the previous quantities R, G, B by substituting the discrete color-matching values r¯i , g¯ i , b¯ i of the 2◦ observer in Equations (2.4.18), (2.4.19), and (2.4.20) by the corresponding quantities x¯ i , y¯ i , z¯i :

20 Since

V(λ).

2005, the CIE’s altered recommendation [71]; since 1931 it was accepted y¯ (λ) =

128

2 Light Sources, Types of Colorants, Observer

V(λ)

Relative luminous efficiency

V '(λ) 1.0

0.5

0

400

500

600

700

λ

nm

Fig. 2.67 Relative luminous efficiency of the human eye in scotopic adaption V (λ) and photopic adaption V(λ)

X=

N 

Φi x¯ i Δλ,

(2.4.24)

Φi y¯ i Δλ,

(2.4.25)

Φi z¯i Δλ.

(2.4.26)

i=1

Y=

N  i=1

Z=

N  i=1

The standard color values for the 10◦ observer follow from the same considerations using x¯ 10, i , y¯ 10, i , z¯10, i instead of x¯ i , y¯ i , z¯i and are denoted by X10 , Y10 , Z10 . According to the last three relations, the standard color values of a coloration can be explicitly calculated if the retinal color stimuli Φ i are known from Equation (2.4.11) or (2.4.12). The spectral power distribution S(λi ) of the light source used is known from CIE tables. This means that the spectral power distribution of the real source is substituted by a corresponding artificial source for the determination of color values. The same is the case with regard to the observer: the individual observer is substituted by one of the standard observers. In addition, the measured reflection or transmission of a given color sample can differ in different color measuring devices. The retinal color stimulus values above are, therefore, idealized quantities and it is, therefore, not astonishing that color values can differ from the individual visual assessment. Nevertheless, a given coloration is unambiguously characterized by three corresponding numerical standard color values. Colors of equal standard values are

References

129

perceived as equal, even if they consist of different sorts of colorants (e.g., dyes or absorption pigments). Because of this, it is not possible to infer the constituent colorants from the numerics of the standard color values. At best, with experience, one can estimate the lightness, chroma, or hue of the color. On the other hand, a single color value alone is not of main interest in color physical applications. Of much greater importance is the color difference between two or more similar color shades. Such questions and answers to them for nearly all sorts of colors are discussed in the sections of the following chapter.

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24. Benzing, G, Ed: “Pigmente und Farbstoffe fuer die Lackindustrie”, 2nd ed, expert, Ehningen (1992) 25. Hunger, K, Ed: “Industrial Dyes”, Wiley-VCH, Weinheim (2003) 26. Valeur, B: “Molecular Fluorescence”, Wiley-VCH, Weinheim (2006) 27. Hunt, RWG: “The Reproduction of Colour”, 6th ed, Wiley, Chichester (2004) 28. Smith, KJ: “Colour order systems, colour spaces, colour difference and colour scales”; in McDonald, R, Ed: “Colour Physics for Industry”, 2nd ed, Soc of Dyers and Colourists, Bradford (1997) 29. Kuehni, RG, Schwarz, A: “Color Ordered: A Survey of Color Order Systems from Antiquity to the Present”, Oxford University Press, Oxford (2008) 30. Munsell, AH: “Atlas of the Munsell Color System”, Wadsworth-Howland & Company, Malden, MA (1915); “Munsell Book of Color”, Munsell Color Co, Baltimore, MD (1929) until now 31. Hard, A, Sivik, L, Tonquist, G: “NCS natural colour system from concept to research and applications”, Col Res Appl 21 (1996) 129 32. Colour Index International: “Pigment and solvent Dyes”, Soc Dyers Col, Bradford, England; and American Association of Textile Chemists and Colorists, Research Triangle Park, NC (1998) 33. ASTM E 308 – 08: “Standard Practice for Computing the Colors of Objects by Using the CIE-System”, American Society for Testing and Materials, West Conshohocken, PA (2008); DIN 6164: “DIN-Farbenkarte”, Part 1–3, Deutsches Institut fuer Normung eV, Berlin (1980–1981) 34. Nickerson, D: “OSA uniform color scale samples: a unique set”, Col Res Appl 6 (1981) 7 35. RAL: “RAL-Design-System”, “RAL Effect”; RAL Deutsches Institut fuer Guetesicherung und Kennzeichnung, St Augustin, Germany (2008) 36. ASTM D 16 – 08: “Standard Terminology for Paint, Related Coatings, Materials, and Applications”, American Society for Testing and Materials, West Conshohocken, PA (2008); CIE No 124/1: “Colour notations and colour order systems”, CIE, Bureau de la CIE, Wien (1997); DIN 55943: “Farbmittel – Begriffe”, Deutsches Institut fuer Normung eV, Berlin (2001) 37. Landolt-Boernstein: “Zahlenwerte und Funktionen aus Naturwissenschaften und Technik”, new series II, Vol 15b: “Metalle: Elektronische Transportphaenomene”, Springer, Berlin (1985) 38. Wheeler, I: “Metallic Pigments in Polymers”, Rapra Techn Ltd, Shawbury, UK (2003) 39. Wissling, P et al: “Metallic effect pigments”, Vincentz Network, Hannover (2007) 40. Pfaff, G: “Spezielle Effektpigmente”, 2nd ed, Vincentz Network, Hannover (2007) 41. ASTM D 480 – 88: “Standard Test Methods for Sampling and Testing of Flaked Aluminum Powders and Pastes”, American Society for Testing and Materials, West Conshohocken, PA (2008); DIN 55923: “Pigmente: Aluminiumpigmente und Aluminiumpigmentpasten fuer Anstrichfarben”, Deutsches Institut fuer Normung eV, Berlin (1983) 42. Roesler, G: “Colorimetric characterization and comparison of metallic paints”, Polymers Paint Colour J 181 (1991) 230 43. Rodriguez, ABJ: “Color and appearance measurement of metallic and pearlescent finishes”, ASTM Standardization News 10 (1995) 44. Panush, S: “Opalescent Automotive Paint Compositions Containing Microtitaniumdioxide Pigment”, Patent US 4753829 (1986) 45. Pfaff, G, Franz, KD, Emmert, R, Nitta, K, in: “Ullmann’s Encyclopedia of Industrial Chemistry: Pigments, Inorganic”, Section 43; 6th ed, Wiley-VCH, Weinheim (1998) 46. Teany, S, Pfaff, G, Nitta, K: “New effect pigments using innovative substrates”, Eur Coatings J 4 (1999) 434 47. Sharrock, SR, Schuel, N: “New effect pigments based on SiO2 and Al2 O3 flakes”, Eur Coatings J 1–2 (2000) 105 48. Maile, FJ, Pfaff, G, Reynders, P: “Effect pigments: past, present, future”, Progr Org Coat 54/3 (2005) 150

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Chapter 3

Systems of Standardized Tristimulus Values, Color Qualities, Chroma of Effect Pigments

Because the trichromatic color sense of the observer is based on additive color mixture, every color impression can be assigned three numerical color values. These color stimulus specifications are, so to speak, representatives of a color. In this chapter, the previous tristimulus values are extended, specifically in order to better meet some coloristical requirements of color industry. The empirical three color values can additionally be interpreted as points in a color space. We restrict the discussion first to the standardized systems that have been proposed for application by the CIE. The most important empirical color difference formulas in colorimetry follow from these systems. These formulas enable to calculate only the color differences of similar or nearly equal colors. In addition, we discuss the standardized DIN99o color space and the newest color appearance model which offer further methods to solve problems in industrial color physics. These formalisms allow one to better detect numerically such color deviations, which inevitably occur during production, reproduction, repair, or aging. The main focus of the effort relates to properties of absorption colors, such as color constancy, metamerism, color strength, covering power, or transparency, which are described by characteristic values. Experience shows that the related colorimetric procedures are quite efficient; however, they do have limits in their applicability. The limits in applicability of these methods are shown especially with different sorts of colorations containing effect pigments.

3.1 Systems of Standardized Tristimulus Values After introduction of the tristimulus values X, Y, Z by the CIE [1] in 1931, more than 13 different color-value systems were worked out. Each of the accompanying color spaces followed from the intention of broadening the basis of the subjective description for the increasing industrial color requirements of absorption colors. This, in no way arbitrary, variety is an expression of the fact that all of these empirical systems were incapable of sufficiently answering the most G.A. Klein, Industrial Color Physics, Springer Series in Optical Sciences 154, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-1197-1_3, 

133

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important questions in the color industry. In the following, we restrict the discussion to the three most applied contemporary color value systems. Although the color physical results with these systems are up to now quite promising, the numerical simulation of the human color sense needs further research.

3.1.1 CIE 1931 Tristimulus Values The standard color values X, Y, Z, also called CIE 1931 tristimulus values, given with Equations (2.4.24), (2.4.25), and (2.4.26), are applicable for opaque, translucent, as well as transparent non-self-luminous colors. However, the following modifications need to be taken into consideration depending on the type of light transmittance. For opaque colors, the color stimulus Φ(λ) from Equation (2.4.1) for each wavelength λi should be inserted in the above-mentioned three equations, which results in X=k Y=k

N  i=1 N 

S(λi )R(λi )¯x(λi )Δλ ,

(3.1.1)

S(λi )R(λi )¯y(λi )Δλ ,

(3.1.2)

S(λi )R(λi )¯z(λi )Δλ .

(3.1.3)

i=1

Z=k

N  i=1

In the case of translucent colors, the additional color stimulus Φ(λ) from Equation (2.4.2) is valid so that three further tristimulus values result. These are simply given by substitution of the spectral reflectance R(λi ) in Equations (3.1.1), (3.1.2), and (3.1.3) by the spectral transmittance T(λi ). For ideal transparent colors, only the transmittance values actually measured should be taken into consideration. The spectral power distribution of the source S(λi ) as well as the SCMFs x¯ (λi ), y¯ (λi ), z¯(λi ) of the chosen standard observer should be taken from standard tables for the relevant Δλ value, which is given by the measuring conditions [2,3].1 The constant k in the above equations depends on the chosen illuminant, the SMCF y¯ (λi ), and the wavelength interval Δλ. This comes from the following consideration. Independent of the wavelength λi in the visible range, an ideally scattering achromatic white field has a constant reflectance R(λi ) = 1.000. For an ideal transparent material, the set value is T(λi ) = 1.000. As explained in Section 2.4.6, the standard color-matching function y¯ (λi ) is accepted as identical to the 1 In addition to previous

recommendations, since the year 2001, the CIE also edits standards, which are designated by CIE S.

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Systems of Standardized Tristimulus Values

135

light sensitivity V(λi ) of the human eye, which is adjusted to the standard color value Y. Consequently, the standard color value is a measure for the lightness of a color. On account of this consideration, the CIE has arbitrarily assigned the ideal scattering field the value Y = 100.000 for every illuminant. Equation (3.2.1), therefore, leads to k=

100.000 N 

.

(3.1.4)

S(λi ) · y¯ (λi ) · Δλ

i=1

The choice of the constant k in this equation has a far-reaching consequence: the three standardized color values (and all further ones) are dimensionless quantities, particularly considering that the reflectance and transmittance are dimensionless; see Equations (2.1.14a) and (2.1.14b). Similar considerations are valid in view of the 10◦ observer. The corresponding formalism follows by insertion of the SCMFs x¯ 10 (λi ), y¯ 10 (λi ), z¯10 (λi ) into Equations (3.1.1), (3.1.2), and (3.1.3). In this case the constant k in Equation (3.1.4) simply results from using y¯ 10 (λi ) instead of y¯ (λi ). The accompanying standard color values are denoted as X10 , Y10 , Z10 . It should be pointed out again that for clear interpretation, all color values are to be specified with the underlying illuminant and standard observer. The standard color values X and Z are not subject to further adjustment conditions. Both quantities can, therefore, differ from 100.000. This is shown in Table 3.1 for ideal white (or ideal transparency) and common illuminants. The tabular values of Xn and Zn follow from Equations (3.1.1) and (3.1.3) by insertion of the ideal reflectance or transmittance R(λi ) = T(λi ) = 1.000. For all illuminants and standard observers, the quantity Yn = 100.000 remains. The quantities Xn and Zn are to be consequently interpreted as standard color values of the corresponding illuminant. A careful view of the sums in Equations (3.1.1), (3.1.2), and (3.1.3) confirms the conclusion which was already stated at the beginning of the previous chapter. Table 3.1 CIE standardized color values of different illuminants 2◦ standard observer

10◦ standard observer

Illuminant

Xn

Zn

Xn

Zn

D 65 A C

95.047 109.850 98.074

108.883 35.585 118.232

94.811 111.144 97.285

107.304 35.200 116.145

FL 2 FL 7 FL 11

99.186 95.041 100.962

67.393 108.747 64.350

103.279 95.792 103.863

69.027 107.686 65.607

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Each of the three standard color values X, Y, Z follows from the three external factors, which are responsible for the color impression of non-self-luminous colors: – the light source, approximated by the chosen illuminant of spectral power distribution S(λi ); – the color sample, characterized by the measured spectral reflectance R(λi ) or transmittance T(λi ); – the observer, represented by the standard observer of SCMFs x¯ (λi ), y¯ (λi ), z¯(λi ) or x¯ 10 (λi ), y¯ 10 (λi ), z¯10 (λi ). At this stage, it is necessary to point out a critical fact. Among the three factors, the reflectance and transmittance by the colorants, binders, and additives of the color pattern are clearly given. However, the spectral power distribution and the standard observer are idealized quantities: in most cases, the radiant energy of the light source used deviates more or less from the tabulated values S(λi ). In the same sense, the SCMFs x¯ (λi ), y¯ (λi ), z¯(λi ) or x¯ 10 (λi ), y¯ 10 (λi ), z¯10 (λi ) of the chosen standard observer do not necessarily agree with those of the actual observer. Consequently, the standard color values only represent the color impression of the special standard observer in combination with the chosen tabulated illuminant. In addition, it is important to remember the fact that the experimental quantities of reflectance and transmittance always have measurement errors. These critical connections should always be taken into consideration in order to avoid, for example, confusion during assessment of color values. It was already mentioned at the end of Section 2.4.5 that the sums in Equations (3.1.1), (3.1.2), and (3.1.3) are actually integrals. In reality, the optic nerves integrate over all simultaneously incoming spectral stimuli at the retina. This is independent of the width of the corresponding wavelength intervals. Nevertheless, we maintain the sum notation for the moment because the quantities of reflectance R(λi ) or transmittance T(λi ) have to be measured at a fine number N of discrete wavelengths λi . These are to be combined with corresponding tabular values S(λi ) and x¯ 10 (λi ), y¯ 10 (λi ), z¯10 (λi ), for example. The integrals are ipso facto approximated by N addends. Although the psychophysical knowledge with regard to colors is only based on empirical considerations, the color values enable an approximate quantification of the color impression, of special color properties, or of color differences at least of similar absorption colors. Such color quantities are no longer limited merely to subjective verbal descriptions. The reader should realize that every standard color value is only a representative of three special color components of a color pattern. These are exclusively valid for the chosen illuminant and the underlying standard observer.

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137

3.1.2 Chromaticity Coordinates and Chromaticity Diagram In spite of the achieved breakthrough, the CIE 1931 system lacks a level of clarity. However, before the more clear CIE 1976 and DIN99o systems are discussed, it is useful to glance over the so-called chromaticity coordinates x, y, z, which were also introduced by the CIE in 1931. These quantities are based on the standard color values X, Y, Z, upon which the above-mentioned two further systems are also based. The chromaticity coordinates of coloration are defined by the equations x=

X , X+Y +Z

(3.1.5)

y=

Y , X+Y +Z

(3.1.6)

z=

Z . X+Y +Z

(3.1.7)

Each coordinate is given by the ratio of one standard color value over the sum of all three color values of a color pattern. A unity sum of these coordinates follows: x + y + z = 1. This is why two given chromaticity coordinates determine the third quantity. Analogous formulas to Equations (3.1.5) and (3.1.6) follow for the 10◦ standard observer; the chromaticity coordinates are indicated by x10 , y10 , z10 . On the other hand, it is impossible to calculate the three standard color values of a color from two chromaticity coordinates such as x, y. For this calculation, one of the three values X, Y, Z would additionally have to be known. The chromaticity coordinates x and y represent the so-called chromaticity, which combines both terms hue and chroma of a color. The CIE has decided to use the x, y, Y system which is applicable to the 2◦ and 10◦ standard observers. Because the Y value is a measure for the lightness of a color and the primaries X and Z contain no lightness component, the quantities x, y can be taken, for example, as coordinates of a plane triangle. If these coordinates are chosen rectangular, we obtain the CIE chromaticity diagram [1]. In Color plate 2, the chromaticity values x, y of absorption colors with equal lightness are approximately represented.2 The limiting equal-sided triangle of (x, y) corner point coordinates (1, 0), (0, 1), (0, 0) is called the color triangle. Non-self-luminous colors of equal lightness are represented in the chromaticity diagram by the x, y coordinates located inside the sole-shaped area. This area is bordered by the arched spectrum locus and the straight purple boundary. The x, y chromaticity coordinates of visible spectral colors are represented by the spectrum locus. In Color plate 2, some of the corresponding 2

Color plates are inserted between Chapters 3 and 4.

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Table 3.2 Color areas of equal lightness Y in the CIE chromaticity diagram [4] 2◦ standard observer

10◦ standard observer

Illuminant

xn

yn

xn

yn

D 65 A C

0.31272 0.44758 0.31006

0.32903 0.40745 0.31617

0.31382 0.45117 0.31002

0.33100 0.40594 0.31867

FL 2 FL 7 FL 11

0.37207 0.31285 0.38053

0.37512 0.32918 0.37691

0.37928 0.31565 0.38543

0.36723 0.32951 0.37110

monochromatic wavelengths between 380 and 780 nm are indicated. The purple boundary joins the end points of the spectrum locus. The colors represented by the purple boundary are not contained in the visible spectrum, but they can be produced spectrally by additive mixture of monochromatic lights. In the case of the equienergy spectrum, the standard color values X, Y, Z are equal to one another and the chromaticity coordinates are x = y = z = 1/3. The coordinates x = y = 1/3 determine the so-called achromatic point. The quantities of the chromaticity coordinates xn , yn for ideal white or ideal transparency are given in Table 3.2 for various illuminants as well as both standard observers. The values follow from those of Table 3.1 and result from the different spectral power distributions of the sources as well as the slightly different SCMFs of the standard observers. Every point on a straight line through the achromatic point and the spectrum locus represents colors of the same hue. The greater the distance from the achromatic point, the purer the corresponding color. Because the spectrum locus represents only spectral colors, these are the purest colors which are to produce. The third coordinate of the x, y, Y system, represented by the lightness axis, is also arbitrary chosen perpendicular to the color triangle. Its value domain is always between zero for ideal black and 100.000 for ideal white. However, for black, all standard color values vanish. Because of the as-yet not fully defined Equations (3.1.5), (3.1.6), and (3.1.7), it is not so obvious how to represent black in the chromaticity diagram. On the other hand, the area included by the spectrum locus and the purple boundary decreases with increasing lightness. The corresponding entire colors tend to become achromatic until they reach white. This is represented by the chromaticity coordinates of the achromatic point as shown in Fig. 3.1. The volume contained by the surface extending along the lightness axes is called the coloring body. Within this volume, all colors possible to be produced are represented by chromaticity coordinates with the exception of ideal black. The limiting surface, except the base area, represents all pure spectral colors including their mixtures. The chromaticity diagrams in Fig. 3.1 and Color plate 2 belong to the 2◦ observer and illuminant C. In comparison, the spectrum locus for the 10◦

3.1

Systems of Standardized Tristimulus Values

139

520

y

10

540

20 30 40 50

60

560 70

0.6

80 90

580

95

0.4

600 100

620 650 770 nm

0.2 480 470

0

380

450

0

0.2

0.4

0.6

x

Fig. 3.1 Color areas of equal lightness Y in the CIE chromaticity diagram [4]

observer is only marginally shorter. This is caused by the higher and broader maxima of the corresponding SCMFs (Fig. 2.67). The chromaticity points of the illuminants D65, A, and C with correlated color temperatures and of the blackbody radiator are shown in Fig. 3.2. The solid curve section is termed as the Planckian locus. It follows, from Equations (3.1.1), (3.1.2), (3.1.3), (3.1.4), (3.1.5), (3.1.6), and (3.1.7), that this locus has the temperature-dependent Planck law of radiation (2.1.1). The chromaticity coordinates of real temperature or luminescence radiators, however, tend to be located adjacent to the Planckian locus. Although the x, y chromaticity diagram supplies an important contribution to the illustration of color values, it also reveals, however, a serious property of the human color sense which turns out to be a disadvantage in discerning the differences in equal or similar colors. According to the investigations of McAdam, similar colors, which are perceived as equal, lie inside the so-called

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520

y 540

560

0.6 500 580 A 2,000 K 2,856 K 3,500 K D65 4,500 K C 6,500 K 10,000 K

0.4

600

650 770 nm

∞

0.2 480 380

0

450

0

0.2

0.4

0.6

x

Fig. 3.2 Chromaticity coordinates of temperature radiators: standard illuminants A and D65 as well as illuminant C, and blackbody radiator

tolerance ellipses in the chromaticity diagram [4]. Some of these ellipses are shown magnified 10 times in Color plate 3. The length of the ellipse axis and the orientation are not constant; these parameters depend rather on the color locus and lightness. In the area of yellow to green colors, larger ellipses dominate in comparison to those for dark-blue colors. For dark-blue, violet, or dark red colors, the major ellipse axes are oriented nearly parallel to the purple boundary. If this line rotates counterclockwise around the endpoint corresponding to 380 nm, we nearly obtain the new alignment of the major axis in other areas of the chromaticity diagram. Color differences among dark colors are, therefore, more sensibly perceived by the human eye and with improved tolerance than color deviations for brilliant and light colors such as green, yellow, or orange. From colorimetric point of view, the chromaticity diagram gives no consistency in color differences

3.1

Systems of Standardized Tristimulus Values

141

in different color areas. Not only the color sense but even color differences behave in a nonlinear fashion and depend on the color locus in the chromaticity diagram. Consequently, also various color tolerances need to be arranged: a nonnegligible hindrance for industrial color judgment or finding out accurate color tolerance agreement. Brown and McAdam [5] showed, in addition, that Color plate 3 renders only projections of three-dimensional ellipsoids with major axes which are not necessarily located in the x, y plane. The observable lightness differences are also irregularly distributed in the color plane. In a further work, Wyszecki [6] found, however, that the semi-axes of the ellipses are smaller than those given by Brown and McAdam. The shortcomings of the x, y, Y system would really be eliminated, if one could succeed in transforming the X, Y, Z standard color values in such a way that the various ellipsoids change into spheres of equal radii. This would correspond to the uniform chromaticity scale triangle (UCS triangle and corresponding UCS color space). This goal has, until now, not been achieved. As long as it is impossible to quantitatively follow the neural processes of color perception, only the empirical approach of tracking down the so-called visually equidistant color space is possible. This empirical method forms the basis of the modern color value systems and the color appearance model in the following sections.

3.1.3 CIE 1976 Color Spaces The CIE revised several times the x, y, Y system and, in 1978, recommended the so-called CIELAB system, established 1976, for application to non-selfluminous colors [7]. The corresponding three-dimensional color space is based on the Munsell color atlas. These color patterns were characterized by spectrophotometric methods and evaluated visually to be basically equidistant [8]. At the same time, the CIELUV system was published. It is recommended for use with colored light sources and displays. Both systems are united by the term CIE 1976 color spaces. We restrict the discussion to the CIELAB system, which is applied to non-self-luminous colors and to some areas of digital image processing as well. Instead of the Munsell color attributes value V, chroma C, and hue H, the CIELAB color space is based on the following three color values: L∗ : a∗ : b∗ :

lightness or black to white contribution; red to green contribution; yellow to blue contribution.

These correspond to the three color pairs of the color opponent theory of Hering. With this, it should also be taken into account that experience shows that there

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exist no hues of absorption colors such as greenish red, reddish green, or bluish yellow. The term CIELAB is a synonym for CIE and the color values L∗ , a∗ , b∗ . The new color values follow from the empirical transformation equations L∗ = 116 · f (Y/Yn ) − 16,

(3.1.8)

∗

a = 500 {f (X/Xn ) − f (Y/Yn )} ,

(3.1.9)

∗

(3.1.10)

b = 200 {f (Y/Yn ) − f (Z/Zn )} .

These equations contain the previous standard color values X, Y, Z and those of the chosen illuminant Xn , Yn , Zn and standard observer. The values Xn , Yn , Zn are given in Table 3.1 for some illuminants. The three functions f(q) are given by  f (q) =

q1/3 for q > (24/116)3 , (841/108) · q + 16/116 for q ≤ (24/116)3

(3.1.11)

where q represents each of the ratios X/Xn , Y/Yn , Z/Zn in Equations (3.1.8), (3.1.9), and (3.1.10) [9]. The existing cubic root in Equation (3.1.11) was determined following the logarithmic change of a physiological stimulus in the Weber–Fechner law. The numbers of the linear term in Equation (3.1.11) are caused by the Pauli extension [10], with which the continuity of f(q) and the first derivative f (q) is achieved at position q = (24/116)3 . The CIELAB color space is based on the three orthogonal L∗ , a∗ , b∗ axes; see Fig. 3.3. The coordinates are arbitrarily chosen perpendicular to each other similar to the x, y, Y system of 1931. The positive L∗ axis represents achromatic colors of values between L∗ = 0 for ideal black and L∗ = 100.000 for ideal white. An a∗ , b∗ color plane of constant lightness represents the chromatic parts of a color stimulus specification. The greater the distance between the color locus and the lightness axis, the more chromatic and saturated the corresponding color. The lightness axis and its vicinity represent the color locus of achromatic colors. The lightness axis itself is, therefore, also named the achromatic axis. The trace point of this axis through any color plane is called the achromatic point. In Color plate 4, for example, a section of an a∗ , b∗ color plane representing absorption colors of middle lightness is shown. In Color plate 5, the central part of the CIELAB color space is depicted as a nearly spherical shape with corresponding achromatic and chromatic colors. The color locus represents the most frequently produced industrial absorption colors. The color values of absorption colors, capable of being manufactured, are by no means distributed over the entire mathematically defined CIELAB space. Such colors are rather limited to a sphere or ellipsoid-shaped volume including the entire achromatic axis. This volume is distorted differently depending on the sort of colorants and chosen color value system. When the McAdam ellipses from Color plate 3 are transformed into the a∗ , ∗ b color plane of the CIELAB system in Fig. 3.4, it is noticeable that the ellipses

3.1

Systems of Standardized Tristimulus Values

143

L∗ 100

White

C(L∗c , ac∗, bc∗)

Lc∗

∗ Cab

–a ∗

∗ Green ac

Yellow

bc∗

∗ hab

0

–b ∗

b∗

a∗ Black

Red

Blue

∗ , a∗ , b∗ ) is Fig. 3.3 L∗ , a∗ , b∗ axes of the CIELAB color space; the color locus C(LC C C ∗ additionally characterized by the chroma Cab and hue angle hab (see below)

are more uniform. The desired circles (respective spheres) of equal radius, however, fail to appear [11]. Although the x, y, Y and the CIELAB color space cannot be directly compared with each other, we get an idea of the effects of the transformation. Visually, the CIELAB and CIE 1931 color spaces are not equidistant. For chromatic colors, the color differences in the CIELAB space a∗ L∗ = 50 100

50

0

–50

–100 –200

–100

0

Fig. 3.4 McAdam ellipses in an a∗ , b∗ plane of the CIELAB system [11]

100

b∗

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have again greater tolerances than for achromatic dark colors. Nevertheless, with the widely accepted and applied CIELAB system, an important intermediate step on discovering the desired UCS is achieved. Properties of industrial colors are often characterized by attributes such as lightness, chroma, hue, or hue angle. The CIELAB system offers now the advantage that these properties can also be visualized and quantified. These quantities follow alternatively – instead of Cartesian coordinates L∗ , a∗ , b∗ – ∗ as the radius from cylindrical with chroma Cab ∗ Cab

 a∗ + b∗ ,

=

2

2

(3.1.12)

hue angle hab as the azimuth angle ◦

hab =

180 arctan (b∗ /a∗ ), π

(3.1.13)

and the lightness L∗ for third coordinate; see Fig. 3.3. However, also the cylinder coordinates describe more color points than existing real absorption colors. The ∗ of a color is represented in an a∗ , b∗ color plane by the distance chroma Cab between the achromatic point and the (a∗ , b∗ ) coordinates of a given color. The hue angle indicates the position inside a quadrant of a color plane. Because of this, it is a measure for the corresponding hue, cf. Color plate 4. According to the defining equation (3.1.13), the hue angle is the sole color value with dimensions given in degrees. The hue angle increases counterclockwise. Along the positive a∗ axis lies hab = 0. The CIELAB system has an additional fundamental feature. Because along each of the L∗ , a∗ , b∗ axes opponent colors change, the color difference between a sample color with color values LS∗ , a∗S , b∗S and a reference color with color values LR∗ , a∗R , b∗R is given by the corresponding difference contributions ΔL∗ = LS∗ − LR∗ , Δa∗ = a∗S − a∗R , Δb∗ = b∗S − b∗R .

(3.1.14)

These can now be interpreted in a coloristical sense. The amount and the sign of the so-called color differences ΔL∗ , Δa∗ , Δb∗ mean  > 0: lighter ΔL∗ = LS∗ − LR∗ = , (3.1.15) < 0: darker  > 0: redder , (3.1.16) Δa∗ = a∗S − a∗R = < 0: greener  > 0: yellower ∗ ∗ ∗ Δb = bS − bR = . (3.1.17) < 0: bluer

3.1

Systems of Standardized Tristimulus Values

145

L∗

ΔL∗

CS

∗ ΔEab

CR

Δb∗

b∗

Δa ∗ a∗ ∗ between color locus of a color sample C and reference color Fig. 3.5 Color difference ΔEab S CR in CIELAB color space

∗ follows, as shown in Fig. 3.5, The entire numerical color difference ΔEab from the three-dimensional Pythagorean theorem ∗ = ΔEab



(ΔL∗ )2 + (Δa∗ )2 + (Δb∗ )2 .

(3.1.18)

This color difference equation enables to indicate quantitatively the approximate value of the perceived color difference between two given colors. With the use of Equation (3.1.18), one must certainly take the following aspects into account: 1. The sign of the single color contributions is lost on account of the squares; ∗ alone it is not possible to draw any from the numerical value of ΔEab conclusions with regard to the three individual color differences. 2. As experience shows, Equation (3.1.18) holds – because of the present visually non-uniform color space – merely for small color differences in the range ∗ ≤ 5; the color values change nearly uniformly only in small of about ΔEab regions of the nonlinearly transformed color space. 3. According to the CIE proposal [7], the CIELAB color space should only be applied to non-self-luminous colors of the same size and shape; for visual assessment, the sample and reference color have to be kept in the same surroundings of a middle gray color (Section 3.2.2).

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It seems that some of the mentioned restrictions can be overcome with a color appearance model. A color difference can be alternatively expressed with the aid of the lightness ∗ and the hue difference ΔL∗ in combination with the chroma difference ΔCab ∗ difference ΔHab ; see below. The contribution of the chroma follows due to the defining equation (3.1.12) from ∗ ∗ ∗ = Cab,S − Cab,R . ΔCab

(3.1.19)

From a geometrical point of view, the chroma difference corresponds to the length difference of the cylinder radius between the color locus of the sample and the reference color as seen in Fig. 3.6. Similar to Equations (3.1.15), (3.1.16), and (3.1.17), the chroma difference can be interpreted using color attributes such as ∗ ΔCab =



> 0: more brillant, clearer . < 0: duller, less chromatic

(3.1.20)

b∗

S

b∗S ∗ ΔCab

∗ ΔHab

b∗R

R

Δhab

a∗R

O

a∗S

a∗

∗ , hue ΔH ∗ , and hue angle Δh of sample color S Fig. 3.6 Contributions of chroma ΔCab ab ab ___

___

∗ , OR = C∗ and reference color R: OS = Cab,S ab,R

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Systems of Standardized Tristimulus Values

147

With Equation (3.1.13), the change of hue angle follows as Δhab = hab,S − hab,R .

(3.1.21)

∗ , is shown The change of hue angle Δhab , along with the hue contribution ΔHab ∗ in Fig. 3.6. The quantity ΔHab is defined by

 ∗ ∗ C∗ ΔHab = 2 Cab,S ab,R · sin (Δhab /2)

(3.1.22a)

and is identical with expression ∗ = ΔHab



∗ )2 − (ΔL∗ )2 − (ΔC∗ )2 (ΔEab ab

(3.1.22b)

∗ corresponds to the arithmetic mean of [29]. Geometrically, the quantity ΔHab the chord lengths belonging to the chroma of the sample and reference color. ∗ leads to Solving Equation (3.1.22b) for ΔEab ∗ = ΔEab

 ∗ )2 + (ΔH ∗ )2 . (ΔL∗ )2 + (ΔCab ab

(3.1.23)

This is an additional relation for determining a color difference. Equations (3.1.18), (3.1.19), (3.1.20), (3.1.21), (3.1.22), and (3.1.23) give also the hue contribution by ∗ = ΔHab

 ∗ C∗ ∗ ∗ ∗ ∗ 2(Cab,S ab,R − aS aR − bR bS ).

(3.1.24)

∗ is positive, if the inequality a∗ b∗ − a∗ b∗ ≥ 0 holds; it is The sign of ΔHab R S S R ∗ follow directly otherwise negative [12]. Both the value and the sign of ΔHab from the equation ∗ = ΔHab

a∗R b∗S − a∗S b∗R ∗ C∗ ∗ ∗ ∗ ∗ 0.5 · (Cab,S ab,R + aS aR + bS bR )

,

(3.1.25)

∗ provided the sign of the root is positive. The contributions Δhab and ΔHab have the same sign. Therefore, Equation (3.1.25) can be used for the determination of the correct sign of Δhab , for example, if the color locus of the sample and reference color are located in adjoining quadrants of an a∗ , b∗ color plane. The CIELAB system does not define which of the equivalent color values L∗ , ∗ , h ∗ a , b∗ or respective L∗ , Cab ab are to be used. It is, at least, advisable to

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indicate the L∗ , a∗ , b∗ values from which the further ones immediately follow. It is, furthermore, not specified which of the Equations (3.1.18), (3.1.19), (3.1.20), (3.1.21), (3.1.22), and (3.1.23) is to be used to calculate the color ∗ [7,13]. In any case, it is useful to list the contributions difference ΔEab ∗ , ΔH ∗ , and Δh , which state the color difference ∗ ∗ ∗ ΔL , Δa , Δb , ΔCab ab ab precisely. Although this system does not represent the ideally desirable visually uniform color space, the progressive CIELAB formalism permits, however, to approximately answer further color physical questions which has been impossible in the past.

3.1.4 DIN99o Color Space After the introduction of the CIELAB system, since about the year 1976, international teams have, to a considerable degree, fallen back on the matching of absorption colors, which were selected and disposed of, to get closer to the desired uniform color space. The endeavors lead to the establishment of the DIN99 color space [14, 15], which is more extravagant than the CIELAB system, among other things. The color values of the DIN99 space are indicated by L99 , a99 , b99 or L99 , C99 , h99 and result from a transformation of the already known L∗ , a∗ , b∗ quantities. The revised and actually valid version of the DIN99 space is called DIN99o color space. This system delivers an improved metric, which is expressed by a more effective color difference formula. The color values of the DIN99o system L99o , a99o , b99o or C99o , h99o , likewise, follow from a nonlinear transformation of the L∗ , a∗ , b∗ quantities [14 –16]. The lightness L99o varies in logarithmic dependence on L∗ in the domain 0 ≤ L99o ≤ 100: L99o =

303.67 ln (1.0000 + 0.0039L∗ ). kE

(3.1.26)

The a99o , b99o color values are determined using the following four auxiliary functions: eo = a∗ cos (26◦ ) + b∗ sin (26◦ ),

(3.1.27)

fo = −0.83 · a∗ sin (26◦ ) + 0.83 · b∗ cos (26◦ ),

(3.1.28)

 heofo = arctan (fo eo),

(3.1.29)

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Systems of Standardized Tristimulus Values

149

 Go = + eo2 + fo2 .

(3.1.30)

For the variable heofo , the following value domains

heofo

⎧ 0 ⎪  ⎪ ⎪ ⎪ arctan (fo eo) ⎪ ⎪  ⎨ π 2  = π+ arctan (fo eo) ⎪ ⎪  ⎪ ⎪ ⎪ 3π 2  ⎪ ⎩ arctan (fo eo)

for for for for for for

eo = fo = 0 eo > 0 and fo ≥ 0 eo = 0 and fo > 0 eo < 0 eo = 0 and fo < 0 eo > 0 and fo ≤ 0

(3.1.31)

should be differentiated. The chroma C99o follows from formula

C99o =

ln (1.000 + 0.075 · Go) . 0.0435 · kCH kE

(3.1.32)

The correction factors kE and kCH in Equations (3.1.26) and (3.1.32) depend on the observation conditions of the color patterns. These are set to 1.0, provided that the CIE reference conditions are fulfilled (Section 3.2.2). The new values of the red to green and yellow to blue proportions follow from relations a99o = C99o cos (h99o ),

(3.1.33)

b99o = C99o sin (h99o ),

(3.1.34)

with the hue angle h99o given by h99o =

180◦ heofo + 26◦ π

(3.1.35)

using the condition in (3.1.31). The original color locus of constant chroma in a CIELAB color plane is, in the new a99o , b99o color plane, rotated and compressed to concentric “ellipses” nearly in the direction of the yellow-blue axis. This is similar to the transformation by the DIN99 system, cf. Figs. 3.7a, b and 3.8. With increasing chroma, the ellipses narrow. The transformed a99o , b99o quantities are smaller than the original values in the domains for a∗ ≥ 20 and b∗ ≥ 20, but larger than comparable a99 , b99 pairs. The up until now visually tolerated higher color differences with the CIELAB system for yellow, orange, and red colors of high chroma have been mostly reduced in the DIN99 and DIN99o color spaces. In the CIELAB as well as the DIN99o space, the metric relations are structured in an analog fashion. The color difference relation

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40

0

a)

–40

–80

–80

–40

0

40

80

a∗

b99 40

20

b)

0

–20

–40 –40

–20

0

20

40 a99

Fig. 3.7 Transformation of color locus of equal chroma from (a) a CIELAB a∗ , b∗ color plane into (b) the accompanying DIN99 color plane

ΔE99o =

 (ΔL99o )2 + (Δa99o )2 + (Δb99o )2

(3.1.36)

to apply in the case of DIN99o color values corresponds again to the threedimensional Pythagorean theorem, cf. formula (3.1.18).

3.1

Systems of Standardized Tristimulus Values

151

b99o

40

20

0

–20

–40

–60 –60

–40

–20

0

20

40

a99o

Fig. 3.8 Transformation of color locus of equal chroma from the CIELAB a∗ , b∗ color plane in Fig. 3.7a into the accompanying DIN99o color plane

The differences contained in Equation (3.1.36) between a sample and reference color of indices S and R of lightness ΔL99o , red to green Δa99o , and yellow to blue Δb99o are ΔL99o = L99o,S − L99o,R ,

(3.1.37)

Δa99o = a99o,S − a99o,R ,

(3.1.38)

Δb99o = b99o,S − b99o,R .

(3.1.39)

These are of the same coloristical meaning as in Equations (3.1.15), (3.1.16), and (3.1.17). The chroma difference ΔC99o and the change in hue angle follow from ΔC99o = C99o,S − C99o,R ,

(3.1.40)

Δh99o = h99o, S − h99o, R .

(3.1.41)

The total color difference ΔE99o can be alternatively calculated using the formula ΔE99o =



(ΔL99o )2 + (ΔC99o )2 + (ΔH99o )2 .

(3.1.42)

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The hue contribution ΔH99o and its sign are most simply determined, analogous to Equation (3.1.25), from the relation ΔH99o = 

a99o,R b99o,S − a99o,S b99o,R 0.5 · (C99o,S C99o,R + a99o,S a99o,R + b99o,S b99o,R )

,

(3.1.43)

provided that the positive sign of the square root is used as well. As already mentioned for the CIELAB space, Equations (3.1.36), (3.1.37), (3.1.38), (3.1.39), (3.1.40), (3.1.41), (3.1.42), and (3.1.43) are only applicable to small color differences ΔE99o ≤ 5. The new values of the color differences are mostly smaller than those corresponding values of the CIELAB system. The DIN99o color space actually shows a better metric than the CIELAB space, but it is, nevertheless, not visually equidistantly structured [17]. Similar to the CIELAB formalism, the DIN99o color space is also applicable to non-selfluminous colors of colorants, lacquers, plastics, textiles, printing inks, as well as colors of hygiene and cosmetic products. The question remains: Which color space should be applied in colorimetry? This question will be answered in Section 3.2.4. First of all, for simplicity in the following, we leave out the specifying indices and exponents of color values, color differences, and color difference contributions, provided that no confusion is introduced.

3.2 Color Difference Metrics and Color Tolerances The effort of empirically discovering a colorimetrical system, which matches the visually perceived color differences as closely as possible, has created more than 20 contrasting color difference formulas for absorption colorations. Only some of them have survived the constantly rising industrial requirements. In addition ∗ and ΔE to the ΔEab 99o relations, there are three key color difference equations. These are applied in different color fields: the so-termed CMC, CIE94, and CIEDE2000 color difference formulas. These three relations and also the ΔE99o equation are based on the CIELAB formula containing differently weighted color differences. Moreover, the color appearance model CIECAM02 delivers, in addition to new chromaticities, further Euclidian color spaces and color difference relations, in which the observing and surround field conditions are taken better into account than before. Independent of these, the color deviations of effect colorations need especially careful considerations and assessments. Among the color values given until now, because of the lack of suited effect models, few are appropriate for approximate colorimetrical characterization of some angle-dependent effect properties. This is also because the original color spaces were developed only for colored lights and absorption colors. The color differences of effect colors are more complex and are additionally not simply characterized by a

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Color Difference Metrics and Color Tolerances

153

numerical color difference value. Other properties such as the flop, brilliance, distinctiveness, or sparkle, for example, often also deviate. Such kinds of differences should be assessed rather with additional methods that are described in Section 3.5.

3.2.1 CMC(l:c) Color Difference Formula In 1963, the Society of Dyers and Colourists in Britain arranged the Colour Measurement Committee (CMC) for working out a color difference relation for absorption colorations that matches the visually perceived color differences better than the CIELAB formula. Investigations with different color collections confirmed the fundamental insight: perceived color tolerances are represented by ellipses of different axis instead of spheres of equal radii as is expected from color difference Equations (3.1.18), (3.1.23), and (3.1.42). The final results of the committee were published in 1984 and are condensed into the so-called CMC(l:c) color difference formula   ΔECMC(l:c) =

ΔL∗ lSL



2 +

∗ ΔCab cSC



2 +

∗ ΔHab SH )

2 ,

(3.2.1)

[18]. This corresponds to the equation of a three-dimensional ellipsoid with axes ∗ , ΔH ∗ . The tolin the direction of the color difference contributions ΔL∗ , ΔCab ab erance parameters l and c in (3.2.1) serve for weighting of the lightness and hue differences. For textile colorations, the values are normally set to l = 2 and c = 1. The corresponding color difference value is specified with the index CMC(2:1). For lacquers and plastic materials, the weighting factors l = 1.3 and c = 1 are used. The empirical functions SL , SC , SH are given by SL =

0.040975LS∗ for (1 + 0.01765LS∗ ) SC =

LS∗ ≥ 16,

∗ 0.0638 · Cab,S

∗ ) (1 + 0.0131 · Cab,S

else SL = 0.511,

(3.2.2)

+ 0.638,

(3.2.3)

SH = SC (f T + 1 − f ),

(3.2.4)

   f =

(3.2.5)

where f and T are given by ∗ )4 (Cab,S

∗ )4 + 1900 (Cab,S

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and T = 0.38 + |0.4 cos (35◦ + hab,S )|.

(3.2.6a)

In the hue angle domain 164◦ ≤ hab,S ≤ 345◦ , the equation T = 0.56 + |0.2 cos (168◦ + hab,S )|

(3.2.6b)

∗ , h is valid. The quantities LS∗ , Cab,S ab,S belong to the sample color. If the sample color is not known, then the arithmetic mean of both colors which are ∗ , ΔH ∗ of the color being compared should be used. The differences ΔL∗ , ΔCab ab contributions follow from Equations (3.1.15), (3.1.19), and (3.1.25). The length of each semi axis of the ellipsoid defined by the CMC(l:c) formula in (3.2.1) is given by the correction functions in (3.2.2), (3.2.3), and (3.2.4). In Color plate 6, the sizes and orientations of projected ellipsoids are shown in the range of ΔECMC(1:1) ≤ 2.0 in an a∗ , b∗ color plane for ΔL∗ = 0. The major axis of the ellipses grows with increasing chroma for all colors; the quantity of the minor axis, however, depends on the hue angle hab . The ellipses are smallest in the field of orange near hab = 55◦ and widest in the region of green at ∗ takes extreme values at each hab = 192◦ . The correction function SH for ΔHab ◦ ◦ ◦ ◦ of the hue angles 145 , 164 , 282 and 342 . Since its introduction, the CMC(l:c) formula has been paving the way for the discovery of improved color difference relations. This is underlined in the following three sections.

3.2.2 CIE94 Color Difference Expression Essentially, the CMC(l:c) formula has shown itself to be correct only for textile dyes and synthesized polymeric materials. The CIE, therefore, suggested matching of further absorbent colors in order to find an improved color difference equation. For that, previous data records were used. Those records were selected in view of statistical confidence limits as well as equal measurement and evaluation conditions. Consequently in 1994, a color difference equation was presented. It was termed the CIE94 color difference formula [17, 18]:      ∗ 2 ∗ 2 ΔCab ΔHab ΔL∗ 2 ∗ + + . (3.2.7) ΔE94 = kL SL kC SC kH SH With regard to the CMC(l:c) equation, this new relation shows modified correction functions SL , SC , SH . Now, these follow from more simply designed expressions: SL = 1,

(3.2.8)

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Color Difference Metrics and Color Tolerances

155

∗ SC = 1 + 0.045 · Cab ,

(3.2.9)

∗ , SH = 1 + 0.015 · Cab

(3.2.10)

kL = kC = kH = 1.0

for reference conditions, ∗ ∗ = Cab,R . Cab

(3.2.11) (3.2.12)

These are provided that the reference color is known, otherwise the geometrical  ∗ = ∗ C∗ mean Cab Cab,1 ab,2 of colors 1 and 2 to be compared should be used in Equations (3.2.9) and (3.2.10). The coefficients kL , kC , kH depend on the previously mentioned observation conditions, which were introduced at that time. These are set to 1.0 in Equation (3.2.7), as long as the so-called CIE reference conditions are fulfilled [19]. It is suitable to modify the mentioned three constants if one or more criteria deviate from the preset conditions. The CIE reference conditions, together with the experimental realizations, are listed in Table 3.3. These are to be regarded as minimum requirements and are primarily founded on the specific properties of the three factors determining color impression outlined in Sections 2.1 and 2.4. The conditions in Table 3.3 are intended to be used for the comparison and assessment of colors. They follow from these connections: 1. The standard illuminant D65 to simulate middle daylight shows a nearly constant spectral power distribution in the visible range (Fig. 2.4); colors are, to some degree, rendered neutral with this illuminant in comparison to other temperature or luminescence radiators. Change in illuminant possibly exposes nonlinear color changes such as color inconstancy, for example. Table 3.3 CIE reference conditions for assessment of absorption colors No.

Criterion

Realization of CIE reference condition

1 2 3 4 5 6 7

Illumination Illuminance Background field Viewing mode Viewing angle Sample separation Magnitude of color difference Sample structure

D65 simulator 1,000 lx Uniform, neutral gray of L ∗ = 50 Object mode > 4◦ Minimal, with direct edge contact ∗ ≤5 ΔEab

8

Homogeneous, without visible patterns or uniformities

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Standardized Tristimulus Values, Color Qualities, Chroma of Effect Pigments

2. The illuminance should be higher than 500 lx so that all cones of the retina are stimulated for color vision and the rods are switched off. This requirement is definitely achieved above an illuminance level of 1,000 lx; levels higher than 5,000 lx, however, cause blinding glare. 3. According to the color constancy investigations of Land and other groups, the surrounding color changes the color impression (cf. simultaneous contrast, Section 2.4.2). In order to avoid color shifts caused by peripheral colors, in the immediate surroundings of the color pattern (locating surface), a middle neutral gray of lightness L∗ = 50 should be used. It is known that differences between dark colors are resolved to a much lesser degree in a light surrounding than in a dark one. Therefore, a middle gray is a useful compromise. 4. In object modus, by definition, the reflected light of a free field non-selfluminous color is directly observed. In contrast, the assessment can also be carried out in illumination modus (direct light) or in aperture modus (observed field limited by an aperture), so that uncontrolled scattered light hardly contributes to the color impression. 5. The influence of the yellow pigment in the macula of the retina (Fig. 2.60) on color impression is nearly excluded for visual angles greater than 4◦ . Therefore, the need for the application of the 10◦ standard observer is clear. 6. Light or brilliant colors appear darker or duller with edge separation as in direct edge contact; conversely, dark and dull colors are perceived lighter or more brilliant with edge separation. Furthermore, the color assessment is increasingly influenced by the color of the gap between the color patterns; because of this “distraction effect,” higher color differences are tolerated as with perfect formation. These considerations follow directly from the third criterion above. 7. The color values of the color spaces discussed in Section 3.1 change in a nonlinear fashion with regard to color perception. Local changes, however, are assumed to be linear; this is generally valid for color differences ∗ ≤ 5. ΔEab 8. To avoid distorting the color impression from the beginning, only homogeneous, uniform, and optically defect-free color patterns should be employed. A structured surface increases the lightness and non-uniform colored samples distort the chromaticity values. All in all, the CIE reference conditions recommend that the mentioned observation criteria should be met for all sorts of color assessments and are independent of specially used color difference formulas as well. Deviations from the reference conditions or additional premises are to indicate for clarity. In a color appearance model outlined in Section 3.2.4, the color values are calculated directly considering observation criteria.

3.2

Color Difference Metrics and Color Tolerances

157

3.2.3 CIEDE2000 Color Difference Equation The color difference equation given in the previous section is only roughly appropriate for the varying expectations of different color technological industries. For this reason, the CIE recommended in 2001 an additional color difference formula which was worked out by several groups based on more than 3,600 color patterns [20–23]. This new color difference relation is denoted as CIEDE2000 and delivers the value ΔE00 :  ΔE00 =



ΔL kL SL

2

 +

ΔCab kC SC

2

 +

ΔHab kH SH

2

 + RT

ΔCab kC SC



 ΔHab . kH SH (3.2.13)

This expression is again founded on the CIELAB color values and has two innovations in comparison to the previous color difference formulas: and of hue ΔH are transformed by a∗ – the contributions of chroma ΔCab ab ∗ and Cab , instead of the unchanged lightness difference ΔL = ΔL∗ ; – there is a fourth summand which consists of the product of the chroma and hue contributions; the ellipsoid axes are, therefore, not oriented parallel to the , H . coordinates of Cab ab

The original CIELAB chroma and hue differences given in Section 3.1.3 are to modify in the manner that follows. The indices S and R stand for the sample and the reference color: L = L∗ ,

a = a∗ (1 + G),

b = b∗

(3.2.14)

with G=

  1  ∗ ∗ ∗ )7 /[(C∗ )7 + 257 ] , C∗ · 1 − (Cab,m ab,m = (Cab,S + Cab,R )/2, ab,m 2 (3.2.15) = Cab

h ab =



(a )2 + (b )2 ,

180◦ · arctan (b /a ), π

(3.2.16) (3.2.17)

ΔCab = Cab,S − Cab,R ,

(3.2.18)

Δh ab = h ab,S − h ab,R ,

(3.2.19)

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a R b∗S − a S b∗R ΔHab = . 0.5 · (Cab,S Cab,R + a S a R + b∗S b∗R )

(3.2.20)

Equations (3.2.14) and (3.2.15) change ellipses located near the lightness axes into circles of the a , b color plane. If the CIE reference conditions of the previous section are met, then the correction parameters in Equation (3.2.13) are kL = kC = kH = 1. The correction functions for lightness, chroma, and hue differences, SL , SC , SH , follow from the relations: − 50)2 1 + 0.15 · (Lm , SL =  − 50)2 20 + (Lm

Lm = (LS + LR )/2,

(3.2.21)

SC = 1 + 0.045 · Cm , Cm = (CS + CR )/2,

(3.2.22)

SH = 1 + 0.015 · Cm · T.

(3.2.23)

For the determination of the function values of T in Equation (3.2.23) and RT in Equation (3.2.13), the expressions T = 1 − 0.17 · cos (h m − 30◦ ) + 0.24 · cos (2h m ) + 0.32 · cos (3h m + 6◦ ) − 0.20 · cos (4h m − 63◦ ),

h m = 12 (h S + h R ) (3.2.24)

are used along with   RT = (2G − 1) · sin (ΔΘ), ΔΘ = 60 · exp −[(h m − 275◦ )/25◦ ]2 . (3.2.25) , C∗ , C , and h are the arithmetic mean of the correspondThe quantities Lm m m ab,m ing sample and reference values. Equation (3.2.22) is formally equivalent to that of the CIE94 formula in Equation (3.2.9). The function T in Equation (3.2.24) on the hue angle. The takes into account the additional dependence of ΔHab rotation function RT appears in a color difference equation for the first time. It corrects the direction of the major axis of the discrimination ellipses in the blue region of the color plane. To sum up, two different methods have been adopted until now to achieve a better match between numerical color differences and visually perceived color deviations:

3.2

Color Difference Metrics and Color Tolerances

159

– establishing Euclidian color spaces (CIELAB, DIN99o); the color difference expressions correspond to sphere equations; – creation of single color difference formulas which contain weighted and transformed contributions of CIELAB color differences (CMC(l:c), CIE94, CIEDE2000) and follow from assessment of color collections; the corresponding equations describe ellipsoids. Among these approaches, the Euclidian color space is generally preferred: every color locus of the space presents the same metric; furthermore, the color difference follows directly from uncorrected color contributions such as ΔL, Δa, Δb. These five color difference relations discussed here are standardized [24]. Out of these newest formulas at least two further questions show themselves. First, how effectively the individual color difference relations work? And second, are further improvements possible using other empirical methods? Both aspects are discussed in the next section.

3.2.4 Efficiency of Color Difference Formulas, CIE Color Appearance Models The determination of a suitable color difference formula for a special color application requires extensive coloristical experience. Ultimately, it is necessary to decide which of the discussed color difference expressions is at the most accurate. One principal reason for the lack of a generally applicable relation is the incomplete knowledge of the complicated neural sequences which cause the trichromatic color impression in the visual cortex. Furthermore it is not clear whether the postulated visually uniform color space is actually reproducible with mathematical elements. Already from the x, y chromaticity diagram or the CIELAB system, it follows that the visually accepted color difference depends on both the color locus and the direction of the color difference. As is known, the tolerated color deviations of light and brilliant colors are numerically higher than those of achromatic dark ∗ of brilliant coloration is as much colors. The tolerated chroma difference ΔCab ∗ . as four times higher than the corresponding hue difference ΔHab ∗ In comparison to the formulas for ΔEab and ΔE99o , the modified color difference relations such as CMC(l:c), CIE94, and CIEDE2000 result from the assessment of color collections of different chromatic colorant and binder sorts. Consequently, each of these relations is to be applied to the corresponding material as follows: – CMC(2:1) for textile fibers, – CMC(1.3:1) for lacquers and plastic materials, – CIE94 for textile fibers, lacquers, and plastics, ∗ , ΔE – ΔEab 99o , CIEDE2000 for every known base material.

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It goes without saying that the mentioned difference expressions cannot be compared with one another in a direct manner. The corresponding transformations are different, nonlinear, and, furthermore, based on different color collections. The workability or efficiency of such an expression can be estimated by testing additional color patterns followed by a strict statistical evaluation of the results. From this point of view, the five color difference formulas mentioned above were tested with more than 3,600 additional color samples of small color differences [16, 23]. Each spectrometrically determined color difference was divided into its contributions ΔL, Δa, Δb and assigned to an ellipsoid of volume ΔVex ; see Section 4.3.4. Afterward, the visually perceived color differences were evaluated and assigned to a separate ellipsoid of volume ΔVvis . From all of the experimental and visual color differences, a statistical dimension value PF/3 results. This characteristic is an approximate measure of the absolute difference between the ellipsoid volumes: PF/3 ≈ |ΔVex − ΔVvis |.

(3.2.26)

For complete correspondence of the visual and measured color differences, one should expect PF/3 = 0. A value of PF/3 = 30, for example, indicates a statistical deviation between both investigations of about 30%. The results of the above-mentioned five formulas for small differences ∗ ≤ 2.5 correspond to the PF/3 list in the upper half of Table 3.4. From ΔEab these, the advantage of the CIEDE2000 difference equation is clear. This result suggests that the CIEDE2000 or at best the DIN99o color difference formula should be applied for the assessment of small color differences. However, the statistic quantity PF/3 does not indicate if there are systematic deviations in one or more quadrants of the color plane or not. Table 3.4 Effectiveness of color differences from color spaces and color appearance models with regard to the absolute statistical dimension value PF/3 [16, 26] Color collections of small color differences

PF/3 value

Color collections of high color differences

PF/3 value

CIEDE2000 DIN99o CMC(1:1) CIE94 CIELAB

33 35 38 38 52

CIELAB

26

CAM02-SCD CAM02-UCS CAM02-LCD CIECAM02

34 35 47 47

CAM02-LCD CAM02-UCS CIECAM02 CAM02-SCD

23 25 25 27

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161

The other statistical dimension values PF/3 in Table 3.4 each follow from a so-called color appearance model (CAM). The corresponding color difference formula directly contains the surrounding and observation conditions, which are of significance in the color industry and also in image processing. Such a model delivers values of color difference as well as color impression and, additionally, specific color characteristics [25, 26]. The CIE recommends the special model CAM02 for specific applications [27]. As input values, the standard color values X, Y, Z are applied to the test illuminant. With this formalism, three attributes are introduced. These differ in relation to the chromatic content: chroma C, colorfulness M, and saturation s. These color attributes together with lightness J and hue angle h can create three different spaces of color coordinates (J, aC , bC ), (J, aM , bM ), and (J, aS , bS ). The derived color space of color values J, aM , bM shows the most uniform results when tested with the color collection with small color differences as mentioned ∗ ≤ 2.5 and ΔE ∗ ≈ above and a second collection with large differences (ΔEab ab 10). The color collection of small color differences results in a value PF/3 = 47, which is slightly smaller than the corresponding CIELAB value PF/3 = 52; see Table 3.4. Based on CIECAM02, three further systems (CAM02-SCD, -LCD, and UCS) for visually small (SCD), large (LCD), and combined small and large (UCS) differences have been derived [26]. These three formalisms produced the other PF/3 values listed in Table 3.4. Considering these, the CAM02-UCS is suitable for evaluation of both small and large color differences. Because improvements in CAMs are still in progress, we avoid describing the extensive formalisms of the four mentioned models in this text and simply refer to the literature [26, 27]. All in all, the CIECAM02 enables one to determine the above-mentioned parameters and further characteristics such as the color rendering index of light sources, color inconstancy index, or index of metamerism. This CAM is suited for the three major fields in colorimetry, namely color specification, color difference evaluation, and prediction of color appearance. It remains to be seen, whether the CAM02-UCS formalism is really a universal CAM or not.

3.2.5 Color Tolerances The immense effort put into the search for the visually uniform color space follows from the decades-long insight that, roughly speaking, the color differences between absorption colors are of greater significance in color technology than the sign and absolute values of the accompanying color values. Color differences almost inevitably result in production or recipe prediction, among other things. An accurate colorimetry is, however, an essential requirement for arranging an acceptable color tolerance agreement between manufacturer and customer. In

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most cases, the color tolerance agreement is supplemented by further restrictions. In order to obtain an acceptable color tolerance for non-self-luminous colors, we have, in particular, taken into account the different error influences introduced by the three outer factors – light source, color sample, and observer – producing color impression. From the term color difference, we should differentiate between the smallest visually resolvable off shade and the magnitude of the allowed numerical color tolerance [24, 29–33]. For comparison of colors, inevitably, one must consider the sort of binder, surface structures, parameters of manufacture, application, or processing, etc. In addition, it is important to realize that the smallest visually resolvable off shade is non-uniform and color locus dependent: the smallest color difference is about ∗ = 0.3 for achromatic dark absorption colors and about ΔE ∗ = 0.7 for ΔEab ab brilliant green, yellow to red colors; see Table 3.5. In comparison, the short-term ∗ | ≤ 0.02 repetition accuracy of modern spectrophotometers is at least |ΔEab and is, therefore, more than 10 times better than the visual capacity to resolve off shade differences. For series production of coatings with plain lacquers, higher tolerance values compared to the smallest visually discernable color shades are usually applied. In the case of plain colorations of automotive finishes, for example, ∗ ≤ 0.9. The corresponding color tolerances are allowed in the range 0.3 ≤ ΔEab dependence on color locus is standardized [29] and is indicated in the chromaticity diagram of Fig. 3.9. Because the tolerance areas in the diagram are discontinuously separated from each other, it is useful to meet further requirements for the vicinity of the thresholds. A continuous transition between adjoining sectors is realistic (cf. Section 3.5.2). The color tolerances for paint refinishing are twice as high as series coating of automotives; see Table 3.6. Color tolerances for absorption colorants are by no means transferable to metallic or other effect colorations; this is clear by simply considering the angle-dependent color impression. For effect colors, the color tolerances ΔE(μ) should rather be arranged as they depend on the angle of illumination β and of observation μ. As shown in Table 3.6, the tolerance value is ΔED (μ) ≤ 1.0 for delivery and first paint coating; for paint refinishing, a range Table 3.5 Smallest visually perceivable and measurable color differences Coloration, measuring equipment Absorption colorants

Spectrophotometer

Criterion

Minimal color difference value

Smallest visually perceivable color difference Achromatic dark colors Brilliant yellow until orange-red colors

∗ ∼ 0.3 ΔEab = ∗ ∼ 0.7 ΔEab =

Short-term repeatability

∗ ≤ 0.02 ΔEab

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Color Difference Metrics and Color Tolerances

163

y

0.6

0.7

0.9

0.4

0.5 0.3

0.2

0

0

0.2

0.4

0.6

x

Fig. 3.9 CIE diagram for the 10◦ standard observer showing arbitrary chosen color areas of ∗ for automotive solid paints [29] different color tolerances ΔEab

Table 3.6 Standardized tolerance ranges according to DIN 6175 [29, 30] Kind of paint

Processing

Standard tolerance range

Plain paint

First paint coating Paint refinishing, low-bake paint

∗ ≤ 0.9 0.3 ≤ ΔEab ∗ ≤ 1.8 0.6 ≤ ΔEab

Metallic paint

Delivery and first paint coating Paint refinishing, low-bake paint

ΔED (μ) ≤ 1.0 1.5 ≤ ΔEP (μ) ≤ 3.0

of 1.5 ≤ ΔEp (μ) ≤ 3.0 is permitted. Both tolerance intervals are based on a relatively small number of color samples and, therefore, need additional requirements. Apart from the necessity of color tolerance requirements, it is essential that those involved in the evaluations continuously undertake coloristical and colorimetrical training [34]. Subjective color differences, which have repeated results greater than numerical ones due to insufficient coloristical training, are unsuited for tolerance agreement. Further considerations with regard to color tolerances and their detection are discussed in Sections 4.1.5 and 4.1.6.

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3.3 Color Constancy and Metamerism Color inconstancy and metamerism are color phenomena which are mainly depending on the constituent absorption colorants. These phenomena appear exclusively by illuminant change. Both properties are rarely avoided during manufacturing or matching of colors, but the degree that these appear can be characterized numerically by colorimetrical methods. For this, each of the already mentioned color difference equations is suitable, provided that special restrictions are considered. The resulting color inconstancy value is a measure of the appearance, how much the color impression of one and the same coloration changes due to change in illumination. The fundamental color physical processes are, in fact, only vaguely understood. They can, however, be phenomenologically evaluated with a color difference formula. In contrast to color inconstancy, metamerism is related to a pair of color patterns. Such a pair of same hue at one illumination shows a color change occurring with change of illumination. Also, the extent of this special kind of metamerism is expressed by an additional color difference value. The use of colorimetric methods in this context fundamentally simplifies the manufacture of colors with required high color constancy or low metamerism.

3.3.1 Chromatic Adaptation and Color Constancy Already in Section 2.4.2, we have become familiar with some perplexing phenomena of color perception which should be considered with regard to the assessment of colors. Two further properties of human color sense also belong to this group. These are termed chromatic adaptation and color constancy. The description of both effects in this section can now provide a clearer understanding of color inconstant colorations. Apart from the capability for distinguishing as many as 10 million colors, the human color sense has another astonishing ability: the sense of vision accommodates itself, within certain limits, continuously a previous change of illumination. The corresponding adjustment is generally called adaptation. The accommodation to the altered lighting condition needs a certain time interval. This adaptation phase is nearly independent of the preceding change of light, but – like also of the most other criteria of color perception – depends on the individual constitution and other conditions of the observer. Before any conclusive visual assessment of colors, one should, therefore, wait for a relatively long-time adaptation phase of at least 30 min. This amount of time is generally sufficient to overcome differences in individual delays. We differentiate between four kinds of adaptation: those of absolute sensitivity, discrimination threshold, visual acuity, and chromatic adaptation.

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Color Constancy and Metamerism

165

The adaptation of absolute sensitivity occurs if the eye which had been sensitized to a constant illumination then registers a change of lightness. The transition from daylight vision to twilight vision is called dark adaptation; the opposite case is light adaptation. In the case of light adaptation, the visual sensitivity of the eye reduces with increasing luminance, whereas for dark adaptation, the sensitivity increases with lower illumination. Light adaptation takes place at photopic vision for luminance values higher than 10 cd/m2 , dark adaptation at scotopic vision for luminance lower than 0.01 cd/m2 . Both light and dark adaptation are caused exclusively by lightness changes of illumination and not by color differences of sources. Characteristic for adaptation of discrimination threshold is the fact that light adaptation needs shorter time than dark adaptation. Complete dark adaptation needs at least 30 min for the normal eye. In this case, the sensitivity is increased to 105 times that of the daylight sensitivity. The longer adaptation time for dark adaption comes down to the slower-acting rods in comparison to the cones. During light and dark adaptation, the diameter of the pupil changes; this is called adaptation of the visual acuity. The contraction of the pupil during light adaption increases the visual acuity and aberrations are simultaneously reduced. On the other hand, dark adaptation increases the diameter of the pupil and, therefore, the visual acuity worsens and aberrations become more noticeable. The chromatic adaptation is of special importance in our context of color assessment. This phenomenon takes place in photopic vision because the cones in the retina are capable of color vision only in this situation. It is a characteristic of this phenomenon that color sensation is kept nearly constant in spite of illumination change. The explanation for this is that in visual assessment also the illuminated surroundings are included which also change in the same way. The process of chromatic adaption can be divided into two steps: chromatic shift and adaptive shift. The chromatic shift occurs immediately, for example, by the change of a surrounding of daylight to that of a room with fluorescence lighting of illuminant FL 11. Immediately upon entering the room, all colors appear shifted somewhat reddish. This color shift is a consequence of the different spectral power distributions of natural daylight and artificial fluorescence light. During the “short” chromatic adaptation phase of some seconds, the perceived color shift disappears. This is partially a consequence of the effect that the most chromatic colored objects are in reality more or less color constant (see below). After chromatic adaption follows the adaptive shift. The exact process of this phase is not yet completely clear. It is, however, clear from observations that the perceived color impression is controlled by changes in the retina together with the color memory of the observer. In other words, the spectral differences of the sources are nearly balanced by a shift of the spectral sensitivity of the eye. Simultaneously, the perceived color is unconsciously compared to color

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impressions of similar color surroundings stored in the memory. The complete processes of chromatic adaptation needs, as mentioned above, a total time of about 30 min. The phenomenon of color constancy is closely associated with the chromatic shift. A color is considered color constant if it always produces the same color impression, independent of spectrally different illuminations. There is a comparable term, lightness constancy. This term characterizes the situation where the assessment of lightness is nearly independent of the energy level of the source. In reality, this judgment is based on a comparison of diffuse reflecting surfaces. A white sheet of paper is always perceived as white despite light changes, although the color stimulus caused by the sheet is different. It seems that the brain is trained to see colors as if they are always illuminated by white light. But color stimulus is – as discussed in Section 2.4.3 – dependent on the spectral power distribution of the light source. Color constancy is, therefore, an essential reason to characterize colors, color differences, and color appearances by applicable dimensional values rather than simply leaving it entirely up to individual visual judgment. In addition to color constant colorations, there exist a whole host of chromatic absorption colors which change considerably their color under varying illuminants (except monochromatic light sources). Such colors are called color inconstant. A quite unsettling example is a color of reddish hue in daylight which appears greenish under fluorescent illumination. Colors in applications which are subject to frequent illumination changes, therefore, should be generally of low color inconstancy. Dependent on the application field, new colors should be tested with regard to this property. The necessary approach for such tests is described in the next section.

3.3.2 Index of Color Inconstancy A high color constancy is by no means an unusual quality criterion. Safety colors, for example, must always be recognizable as such in daylight, twilight, and night light. Colors of consumer items should also certainly not change under an illumination change. The determination of color inconstancy under a test illuminant is carried out with regard to a reference illuminant, normally D65. The degree of color change, which a single color shows for both illuminants, is given by the index of color inconstancy CIC . Initially, it seems self-evident that the color inconstancy index should be identified as the color difference which appears between both illuminants. Detailed studies show, however, that the change of the corresponding color values is not suitable for an adequate description of color inconstancy. It is particularly important to know the relationship between the color values for colors which look precisely the same to an observer when they are adapted

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Color Constancy and Metamerism

167

to different illuminants. Such kinds of colors are called corresponding colors. Given color values R, G, B of a color sample under one illuminant, the color values RC , GC , BC for the corresponding color under another illuminant can be determined by calculation. The second illuminant is the so-called corresponding illuminant. The calculation of the corresponding color values is achieved by a chromatic adaptation transform (CAT). The numerical color difference ΔE between the color values of the corresponding color and the color under the original illuminant is an adequate measure for the degree of color inconstancy CCI (ΔE) = ΔE. For determination of the color values of the corresponding color, von Kries assumed that the three color receptors in the retina are differently affected by chromatic adaptation [35]. Accordingly, chromatic adaptation causes a reduction in sensitivity by constant factors for each of the three cones. The magnitude of each of the corresponding coefficients α, β, γ depends on the stimulus to which the observer is adapted. The von Kries coefficient law can be written as Rc = α · R, Gc = β · G, Bc = γ · B.

(3.3.1)

This law describes the transformation of the cone responses due to chromatic adaptation. Most of the various CATs developed have been founded on the von Kries law (3.3.1). The specific CAT to be used for absorption colors is CAT02. It was improved with a recent color collection of representative absorption colorations in 2002 and forms the basis of the sketched color appearance model CIECAM02 [36, 37]. The relevant transformation equations are given in Appendix A.2. The calculation of the color inconstancy index of a given color using CAT02 is performed in several steps. The input data are the standard color values of the sample, X, Y, Z, in the test illuminant and, XR , YR , ZR , in the reference illuminant. From these, the standard color values Xc , Yc , Zc of the corresponding illuminant are determined. The numerical degree of adaptation of the observer is also included in the process. Finally, the color difference ΔE is calculated with the triplets Xc , Yc , Zc and XR , YR , ZR . From the differences of the three color value pairs, the amount and the direction of the color shift can be seen. A value of CIC (ΔE) = 0 represents a completely color constant coloration for the chosen reference and test illuminant. The application of CAT02 is only for absorption colorants because the corresponding parameters and transformation relations were derived from the above-mentioned color collection. It is advantageous that the value CIC (ΔE) can be calculated in advance for every illuminant change without actually implementing the corresponding lighting. For clearness and comparability, along with the value of the color inconstancy index, the reference and test illuminants, the

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standard observer, the degree of adaption, the observation conditions, and the used color difference equation should also be indicated. As an example, we consider the color values of the reference colors given in Table 3.7. The standard color values X, Y, Z and L∗ , a∗ , b∗ belong to the illuminant/observer combinations D65/10◦ and A/10◦ . In the calculation, the field of the reference and sample is assumed to have a luminance of LA = 200 cd/m2 and presuppose normal observation conditions. In Table 3.8, the corresponding standard color values for the corresponding test illuminant Ac using CAT02 are listed. In the last column, the resulting quantities of the index of color inconstancy for three different color difference formulas are given. The first color sample has values between 6.27 and 6.72 and the second between 2.11 and 2.61. The second color is, therefore, much more color constant than the first. From the difference between the color values, one can estimate the direction and the amount of the color shift. In the special case of the chosen examples, the color inconstancy index is nearly independent of the used color difference formula – which is not typical for other absorption colors.

Table 3.7 Examples of starting values for determination of color inconstancy index in Table 3.8; 10◦ standard observer Sample number

Illuminants 10◦ observer

X

Y

Z

L∗

a∗

b∗

1

D65 A

20.51 24.08

24.09 22.91

26.14 8.99

56.18 54.98

–10.96 –5.64

–0.45 –4.51

2

D65 A

20.29 22.48

23.91 22.74

25.47 8.54

56.00 54.80

–11.26 –11.69

0.30 –2.66

Table 3.8 Color inconstancy index for combinations of reference/test illuminants of Table 3.7 [37] Reference/test illuminant corresponding Sample color; 10◦ observer 1 2

D65/Ac D65/Ac

Normal observation conditions

Color inconstancy index CIC (ΔE)

X

Y

Z

∗ ΔEab

ΔE(CMC1:1) ΔE00(1:1:1)

20.51 20.88

24.09 23.20

26.14 27.30

6.72

6.27

6.56

20.29 19.35

23.91 23.13

25.47 25.95

2.61

2.48

2.11

3.3

Color Constancy and Metamerism

169

3.3.3 Kinds of Metamerism The color property called metamerism is rather undesirable in many areas of color technology; it is, however, in many cases unavoidable. According to Ostwald [38], two colors are called metameric to each other (conditional equal), if they match for one illuminant but show a color difference under a change of illuminant. The metameric behavior is a consequence of additive color mixture of human color sense. It should be pointed out that color inconstancy is a property of one color, whereas metamerism is a property of the comparison of two colors. This effect is of particular importance, for example, in the production of colors in different charges, substitution of one or more colorants in recipes, or recipe prediction of a given color of unknown colorant composition. The degree of metamerism is – apart from color inconstancy and further properties – often the decisive factor for the choice of a desired coloration or suited color recipes among several alternative formulations. As an example, Fig. 3.10 shows the spectral reflectance of a pair of metameric colors which are perceived as nearly equal at midday light. The curve with a relative low maximum at λ = 510 nm for the sample color repeatedly intersects the curve of the reference color. Metameric pairs show generally one further characteristic: the spectral curves have at least three intersection points at different wavelengths in the visible range [20, 39, 40]. If there were fewer intersection points, either the lightness or the hue of the colors under reference illumination do not match. R(λ) R1(λ) 0.3 R2(λ) 0.2

0.1

0

400

500

600

Fig. 3.10 Spectral reflectance R1 (λ), R2 (λ) of a pair of metameric colors

700

λ nm

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Standardized Tristimulus Values, Color Qualities, Chroma of Effect Pigments

The occurrence of at least three intersections touches the heart of the methods of color recipe prediction. More than a hundred years of collective experience shows that to match a color of unknown composition requires at least three different colorants. In the simplest case, the accompanying colorant concentrations follow from the condition that the spectral curves of the recipe and reference color intersect for exactly three different wavelengths. Nearly equal spectral curves can only be achieved with greater number of colorations. A completely congruent pair of curves is only obtained with identical colorants and concentrations (Sections 6.3.3, 6.3.4, and 6.3.5). The spectral values of the color pair are only one factor for producing metamerism. The second is the spectral power distribution of the illuminant used. Both are combined in the color stimulus function Φ(λi ) which is interpreted as the original cause of the appearance of metamerism. The combination of this function and the chosen standard observer can lead – despite different spectral values – to equal standard color values X1 = X2 , Y1 = Y2 , Z1 = Z2 for the metameric color pair. For example, with the spectral reflectance R1 (λi ) and R2 (λi ) of each color, the spectral power distribution S(λi ) of the reference illuminant and, for simplified notation, the 2◦ standard observer follows from Equation (3.1.1): X1 = k

N 

S(λi )¯x(λi )R1 (λi )Δλ

(3.3.2)

S(λi )¯x(λi )R2 (λi )Δλ.

(3.3.3)

i=1

and X2 = k

N  i=1

Although the reflectance values of both colors are unequal at most wavelengths and the individual summands in Equations (3.3.2) and (3.3.3) to the same wavelength are mostly different: for metameric color pairs, equal totals always result and, therefore, identical standard color values X1 = X2 for the reference illuminant. The same holds for the remaining two color values. The existence of equal standard color values, here X1 = X2 , Y1 = Y2 , Z1 = Z2 , signifies always equal color sensation. Because of this, both colors produce the same color impression. The same holds for additional color values, especially of CIELAB or DIN99o color spaces. If the reference illuminant is substituted by another one of new spectral power distribution S0 (λi ), then the individual summands and totals of Equations (3.3.2) and (3.3.3) are different. The summands show now other weighting factors in comparison to those in the reference illuminant. Even all three color values differ, therefore, from one another, the change of illuminant results in two different color impressions.

3.3

Color Constancy and Metamerism

171

The individual contributions of different power distributions S(λ) in dependence of wavelength have already been seen, for example, from Fig. 2.4 for standard illuminants D65 and A. In the range of blue wavelengths, the distribution of D65 is essentially higher than A. In contrast, in the red range, the radiation intensity of A dominates compared to that of D65. Because unequal color values mean different color sensations, metameric pairs typically produce a color difference for a change of illuminant. Although the concept of metamerism was originally introduced by Ostwald for illuminant changes, it has also been extended to include states without illuminant changes. These are more accurately denoted as “conditional equal prerequisites”. Five metamerism kinds are known to this day. In the following survey, the first and second metamerism kinds are directly influenced by the different summand contributions. The last three are caused by the individual conditions of the observer and the measuring equipment used: 1. Illumination metamerism occurs under change of illuminant as described above; this is the most important sort of metamerism. 2. Observer geometry metamerism results from change between the 2◦ and 10◦ standard observers on the basis of the different CMFs x¯ (λi ), y¯ (λi ), z¯(λi ) and x¯ 10 (λi ), y¯ 10 (λi ), z¯10 (λi ), respectively. The consequences are by no means negligible, as is shown in the next section. 3. Observer metamerism is caused by the subjective color sense of different observers and the individual deviations from the underlying standard observer. Such deviations should be clarified between the involved partners in advance of the color tolerance agreement. 4. Geometry metamerism can occur under otherwise equal conditions and equal visual angle by a change in the line of sight. For effect pigments, for example, the color match by change of the angle of illumination or observation can be lost. A special case of geometry metamerism is the so-called silking effect. This effect means that the reflectance changes simply by rotation of an individual sample around an axis perpendicular to its surface. This phenomenon is caused by the nearly parallel needle-, flake-, or rod-shaped pigment particles. 5. Equipment metamerism can be considered due to the general lack of consistency among color measuring instruments of the same or different manufacturers. The variations in measured values are primarily caused by small but largely unavoidable production differences of the component parts or the equipment design. Illumination metamerism is, as already mentioned, practically unavoidable. It occurs during reproduction of a reference color of unknown composition by applying colorants of different batches, other colorants, binders, additives, and a different number of colored components. The chemical analysis is much

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too complex and priority is generally given to the use of available colorants. There should also be sufficient experience related to color inconstancy, color strength, color fastness, compatibility – only to list some of relevant criteria for reproduction of absorption colors. From each sketched type of metamerism above, an indication for its reduction is at the same time revealed. For lowering illumination metamerism, one can carry out a careful selection and tuning of the colorants during visual or recipe prediction. For a recipe with absorption colors, at minimum three and at best six different colorants should be used. This optimum comes because with increasing number, the risk of an “overshoot” instead of an approach of the spectral values is greater. Because of the substantially lower concentrations of the additional colorants relative to the already dominant ones, a minor admixture is often difficult to meter out or to homogenize. A reproduced color often shows an increased metamerism if for the dominant colorant the coloristical “most natural” one is chosen. To achieve recipes with minimal metamerism, each step of the spectral curve trace should be approached with a separate colorant (cf. Figs. 6.15 and 6.16). This aim in most cases, however, is not achieved with the “first best” colorant. The curve trace of the maximum as well as the rise and slope at the start or end of a curve step should be approximated as well as possible. This goes especially for violet, yellow, orange, or red and brown colors which show increased spectral values at wavelengths longer than 500 nm. For blue and green hues, however, the position of the maximum and the slope are well approximated by only few colorant components. One strategy of recipe prediction is based on the criteria that the color difference between the reproducing color and the target color is minimal for a given reference illuminant. This color difference can be calculated in advance without the necessity of implementing the corresponding recipe. A similar consideration holds for the color inconstancy index. It can be determined in advance for every change of illumination without the need of actually performing the lighting change. As a reference illuminant in both cases, D65 is mostly used, although other illuminants are possible. This strategy allows for the possibility of changing the types and numbers of colorants for a recipe in order to pursue the desired effect on the degree of metamerism. The amount of illumination or geometry observer metamerism is characterized by the index of metamerism. This is discussed in the next section.

3.3.4 Special Metamerism Indices The degree of metamerism of a color pair is indicated by the so-called special metamerism index for change of illumination. This index corresponds to the color difference which results from the change between reference and test illuminant for the given color pair [40]. The choice of the color difference formula

3.3

Color Constancy and Metamerism

173

is an option. In the cases of the CIELAB expressions (3.1.18) or (3.1.23), the color contributions are determined from equations ΔL∗ = LT∗ − LR∗ ,

Δa∗ = a∗T − a∗R ,

Δb∗ = b∗T − b∗R

(3.3.4)

or additionally from ∗ ∗ ∗ ΔCab = Cab,T − Cab,R ,

(3.3.5)

a∗R b∗T − a∗T b∗R ∗ . ΔHab = ∗ C∗ ∗ ∗ ∗ ∗ 0.5(Cab,T ab,R + aT aR + bT bR )

(3.3.6)

The indices T and R belong to the test and reference illuminant, respectively. In most cases, D65 is arranged as the reference illuminant and the test illuminant should greatly differ from the reference. The index of metamerism MXilm needs to be determined for approximate illuminants in which the color pairs are subjected to during application. The degree of metamerism remains unchanged under the exchange of the reference and test illuminants, which is a consequence of the squared color contributions (3.3.4), (3.3.5), and (3.3.6) in a color difference equation. The visually perceived and the numeric color differences can definitely be different because, as already explained, the stored values of the spectral power distribution of the illuminants and the standard observers are not identical with those of the sources used or the individual observer. For a clear interpretation and comparability of the metamerism index for illumination change MXilm , in addition to the numerical value, the following must also be specified in the result: the test and reference illuminants, the standard observer, and the color difference formula used. According to a recommendation of the CIE, the special metamerism index for change of observer can also be calculated under the same illuminant [41]. This is the analog of determining the color contributions (3.3.4), (3.3.5), and (3.3.6) of the CMFs of a test person with regard to one standard observer under the same illuminant. Also in this case, the calculated numerical value of the index MX 0 obs can deviate from that for another observer. For correct determination of the special index of metamerism, a peculiarity needs to be considered. In a number of cases, the standard color values of the color pair are not exactly the same as for the reference illuminant, that is, X1 = X2 , Y1 = Y2 , Z1 = Z2 . In such cases, the standard color values X2,T , Y2,T , Z2,T of the sample in the test illuminant need to be corrected using the respective factors:    fX = X1 X2 , fY = Y1 Y2 , fZ = Z1 Z2 .

(3.3.7)

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Otherwise, incorrect metamerism values result. The color difference is, therefore, determined between the color values X1 , Y1 , Z1 of the reference illuminant and  Y2 = fY Y2,T ,  Z2 = fZ Z2,T X2 = fX X2,T , 

(3.3.8)

for test illuminant. As an example, in order to determine the special indices for change in illuminant and observer geometry, we use the color pair of reflectance shown in Fig. 3.10. The accompanying standard and CIELAB color values for the combinations D65/10◦ and FL 2/10◦ as well as D65/2◦ and FL 2/2◦ are listed in Table 3.9. The standard color values of the test illuminant are to be corrected using Equation (3.3.8) because the X, Y, Z or L∗ , a∗ , b∗ values already differ for reference illuminant. The resulting special indices of metamerism for change of illuminant MXilm ∗ , are given in Table 3.10. In and MX 0 obs , each based on color difference ΔEab the second row of this table, the respectively used combinations which follow from Table 3.9 are indicated. The description 6 (1/5), for example, means that the color values of number 6 are multiplied by the ratio of the corresponding color values in lines 1 and 5. The results in the last two rows in Table 3.10 show that the index of metamerism for illuminant change is typically higher than that for the change of observer geometry. From comparison of the CIELAB values for reference and test illuminants for the same observer in Table 3.9, it should be clear that metamerism is here mainly caused by differing red to green amounts Δa∗ between both colors. The combinations 1, 6 with 2, 5 as well as 3, 8 with 4, 7 in Table 3.9 are equivalent because test and reference illuminants are exchanged with each other. The same holds for the change of standard observer with regard to the combinations 1, 7 with 3, 5 as well as 2, 8 with 4, 6. The slight deviations of the corresponding index values are caused by measuring and rounding errors. Table 3.9 CIE 1931 and 1976 standardized values of the metameric color pair in Fig. 3.10

No.

Illuminant/standard observer

X

Y

Z

L∗

a∗

b∗

1 2 3 4

Reference

D65/10◦ FL 2/10◦ D65/2◦ FL 2/2◦

16.862 19.096 17.444 18.753

13.577 15.210 14.068 15.491

7.356 4.735 7.473 4.637

43.62 45.92 44.33 46.30

24.20 17.95 24.10 18.44

20.94 24.89 22.13 25.46

5 6 7 8

Test

D65/10◦ FL 2/10◦ D65/2◦ FL 2/2◦

16.573 17.390 17.305 17.232

13.536 13.680 13.894 13.804

7.140 4.543 7.345 4.486

43.56 43.77 44.08 43.95

22.84 18.47 24.42 20.59

21.63 22.30 22.17 22.31

3.4

Specific Qualities of Colorants

175

Table 3.10 Indices of illumination and observer-geometry metamerism following from color values in Table 3.9 Kind of metamerism Illumination metamerism

Observergeometry metamerism

Number in Color Table 3.9 pattern

Illuminant/ standard observer

1 6 (1/5) 3 8 (3/7) 2 5 (2/6) 4 7 (4/8)

Reference Test Reference Test Reference Test Reference Test

D65/10◦ FL 2/10◦ D65/2◦ FL 2/2◦ FL 2/10◦ D65/10◦ FL 2/2◦ D65/2◦

1 7 (1/5) 2 8 (2/6) 3 5 (3/7) 4 6 (4/8)

Reference Test Reference Test Reference Test Reference Test

D65/10◦ D65/2◦ FL 2/10◦ FL 2/2◦ D65/2◦ D65/10◦ FL 2/2◦ FL 2/10◦

Special metamerism index ∗ MXilm = ΔEab

∗ MX 0 obs = ΔEab

4.65 3.84 4.57 3.94 1.77 2.19 1.75 2.18

In this section, it has been shown that two essential properties of absorption colors can be approximately described and numerically compared by colorimetrical methods using color difference formulas. The following sections deal with further colorimetrical procedures, which have been developed especially for numerically characterizing other qualities of absorption colors.

3.4 Specific Qualities of Colorants The color spaces CIE 1976 and DIN99o described as well as the color difference formulas – which were, in particular, intended for the assessment of collections with absorption colors – are designed for application to additional color properties. In the following, quantities such as color strength, spreading rate, covering capacity, transparency, or color fastness of formulations with regard to colorimetric characterization are discussed. Such properties are united under the term color qualities. With these accounts, the fact that the whole of colorimetric methods are only valid for small color differences needs to be considered. In order to have reasonable comparability of results, the same color space and chosen color difference formula should be maintained throughout.

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3.4.1 Build-up and Coloring Potential All colorants can be dispersed in different concentrations in a dye or binder dependent on the desired color. The change of the color values of a single colorant in dependence on concentration is called build-up. This behavior needs to be differentiated with regard to a dye in the same solvent and a colored absorption pigment in white mixtures for constant total pigment loading in the same binder. In the case of a chromatic absorption pigment in white/black mixtures, the dependence of lightness and chroma on the concentration of all three colorants is given by the so-called coloring potential. The build-up is graphically represented by a three-dimensional curve section in a color space. In comparison, the coloring potential is represented by a three-dimensional area in color space. Its shape depends on the concentration of the chromatic pigment in white/black mixtures. From the geometrical representation of the build-up and coloring potential, characteristic features of the corresponding colorants can be obtained. These are discussed in the following. Figure 3.11 shows the projection of the build-up of different dyes in solution in an a∗ , b∗ color plane. The simultaneous change in lightness here is of secondary importance. From this simplified representation, the color development in dependence of dye content directly follows. Each curve starts for b∗ 1 2

80 60

3 40 20

4

0 7 –20 –40

–40

5

6 –20

0

20

40

a∗

Fig. 3.11 Typical build-up of different dyes: 1 light-yellow, 2 yellow, 3 orange, 4 red, 5 blue, 6 dark-blue, 7 blue-green

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Specific Qualities of Colorants

177

minor dye concentration in the immediate vicinity of the achromatic locus. It ends with the coordinates of the mass tone, which is the natural color of the absorption colorant. At first, the chroma changes directly proportional to the dye content. But at certain high dye concentrations, a particularly noticeable change in hue occurs and the chroma lowers. The build-up describes, dependent on color locus, a left-hand or right-hand turn. The amount of the hue angle |hab | changes as shown between about 20◦ and 60◦ . Chromatic pigments in white mixtures show similar shaped projected buildups such as dyes in solution. However, it has not been clarified as to why a build-up describes systematically a right or left-hand curve in dependence on the quadrant of a color plane. For visualization of a coloring potential, Fig. 3.12 shows the change in ∗ of an organic colored pigment. The lightness L∗ dependent on chroma Cab parameters P/W and P/B indicate the blending ratio of pigment to white and black colorants, respectively, at constant pigment loading. On the envelope curve, three points P, W, and B are plotted. These represent the mass tone of the colored, white, and black pigments, respectively. The intermediately located curve sections have the following meaning: – The section from point W to point P represents the build-up of the colored ∗ plane. It extends from the pigment in white mixtures projected in the L∗ , Cab L∗ W 10P/90W 75 50P/50W

1B/99W 50 3B/97W

P

25 B

99P/1B 95P/3B

0 0

25

50

75

C ∗ab

Fig. 3.12 Coloring potential of an organic absorption pigment in white and black mixtures of constant pigmentation

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mass tone of white to the mass tone of the colored pigment. The downward curved slope of this section shows the decrease in lightness with increasing chromatic pigment content, as well as the simultaneous reduction of chroma. This is an analogous behavior to dyes, Fig. 3.11. – The curve element from P to B represents the color loci for mixtures of the colored pigment and the achromatic black pigment. – The last section of the envelope curve WB is a part of the lightness axis L∗ , representing achromatic mixtures between the mass tone of the white and black colorants without a colored pigment. The area enclosed by these three curve sections represents the coloring potential of an absorption pigment. In other words, the coloring potential forms a curved three-dimensional area in color space similar to a blade of a marine propeller. This area is flat in the surroundings of the lightness axes. The coloring potential includes, therefore, all color loci which can be entirely generated with a given chromatic pigment and white/black mixtures for fixed total pigment loading. The coloring potential is an additional fingerprint of a colored pigment. As can be seen in Fig. 3.12, the distances between the plotted points on curve sections WP, PB, and BW change non-uniformly with regard to the indicated mixing ratio values. This behavior signifies that the lightness, chroma, and hue of the colorant change nonlinearly in dependence on concentration. This nonlinearity is typical for all absorption colorants but, moreover, it develops differently. Altogether, this characteristic complicates the entire color physical and coloristical handling of all colorant sorts. It forces, for example, one to carry out the dosing or weighing of colorants with the upmost care and accuracy and to perform all manufacturing steps with greatest possible reproducibility. Recipe prediction needs, therefore, nonlinear approximation methods. Generally, the chroma, hue, and lightness respond considerably more sensibly to a fraction of black than white of same amount. This behavior can already be inferred for merely 1 part black from Fig. 3.12. The combination 99P/1B ∗ = 75 by about reduces the chroma of the color-intensive mass tone in P of Cab ∗ ∗ ΔCab = −34. The ratio 1B/99W decreases the lightness L = 92 in W for the mass tone of white, however, by about ΔL∗ = –25. Dark chromatic colorants such as violet or blue behave in a similar manner. This most striking nonlinearity turns out to have a particularly detrimental effect on the assessment, manufacture, and reproduction of colors. The strong change of color for a small fraction of a dark colorant is related to the sensitivity and correctability of color recipes. In comparison to organic colorants, inorganic pigments typically show a less developed coloring potential. This is a result of the characteristically higher scattering and lower chroma of the mass tone of these sort of colorants. For inorganic pigments, the arched curve sections in Fig. 3.12 turn into nearly rectilinear line segments of only slight curvature. The nonlinearity of inorganic pigments,

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179

in dependence on concentration, is in general similarly strongly developed as for organic pigments. The term coloring potential – in its original meaning – does not apply to effect pigments. This is because for these colorants, the angle-dependent color impression is of primary interest. Slight amounts of carbon black in formulations with effect pigments serve principally to absorb the complementary color of interference pigments, reduce chroma, and occasionally for correction of lightness flop. The natural interference colors of interference pigments emerge more clearly with only a minimal amount of carbon black. A borderline case is represented by mixtures of interference and colored pigments. With such mixtures, a new type of build-up in comparison to that of absorption colorants is combined (Section 3.5.4).

3.4.2 Strength and Depth of Color The concepts strength of color and depth of color are closely linked and are of coloristical as well as economic significance. Both distinguishing features were already established at the beginning of the 20th century for assessment of dyes and in 1930 began to be applied to absorption pigments. Whereas the coloration potential and build-up describe the development of a color in dependence on colorant concentration, the strength and depth of color characterize the coloring efficiency of a colorant. Color strength is defined as that property of a colorant, which acts by coloring upon other materials [42]. In contrast, color depth describes that feature of a colorant, which produces a more intense coloration or rather higher chroma with increasing concentration. It increases, therefore, up to the saturation of the colorant but decreases with rising lightness. The color depth correlates consequently with the color build-up. It is important to point out that color strength is a relative quantity. The color strength of an absorption colorant is a quantity in relation to another (similar) absorption colorant. In Fig. 3.13, the depth of color D for a pair of similar colorants in dependence on concentration c is plotted. For small and moderate values of c, the depth of color D changes linearly for the reference and sample colorant. At higher concentrations, the so-called saturation depth of the reference DS,R and sample colorant DS,S is attained. These depths are not necessary at the same level. The two straight lines through the origin have different slopes. The slope, however, is directly proportional to color strength. From this plot, it can be inferred that the color strength of the sample is related to the same level of color depth DSD as that of the reference color. Apart from a constant k, the slope of the straight line through the origin for moderate concentrations is a direct measure for the color strength P of a colorant. Using the notation in Fig. 3.13, the general equation of a straight line through the origin is

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Reference

DS,R DS,S Depth of color D

Sample

DSD = const.

0 0

cR

cS

Concentration c

Fig. 3.13 Schematic representation of color depth D in dependence on concentration c of a pair of similar absorption colorants

D = k · P · c,

(3.4.1)

where P is the absolute color strength. However, it should be noted that it is the relative color strength rather than the absolute that is relevant in practice. Under the condition of equal color depth level DSD for the sample and reference colorants, the relations DSD = kPS cS ,

(3.4.2)

DSD = kPR cR ,

(3.4.3)

follow. If the ratio of PS and PR is defined as the degree of relative color strength Prp of an absorption pigment, it follows that Prp =

PS cR = . PR cS

(3.4.4)

The relative color strength of an absorption pigment follows consequently from the quotient of the concentration cR of the reference pigment to the concentration cS of the sample pigment at equal color depth level DSD . The quantities Prp and D are dimensionless. In the case shown in Fig. 3.13, the initial slope of the reference colorant is twice that of the slope of the sample colorant. Following the definition in Equation (3.4.4), the sample pigment has a color strength of 1/2 related to the reference pigment, and consequently half that of the reference. On the other hand, both pigments are only at equal color depth if the condition cS = 2cR is met. Procedures for determining equal level DSD are described below.

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Specific Qualities of Colorants

181

For dyes in solution, the same considerations hold, but with the difference that the relative color strength Prd is then determined from the quotient of the extinction coefficients εS and εR at the absorption maximums of the reference and sample dyes Prd =

εS εR

(3.4.5)

at equal level of DSD [43]. The determination of relative color strength for pigments follows from brightening mixtures with a white pigment [42]. Instead of the concentration ratio, the mass ratio mR /mS of the reference and sample pigments is now inserted into Equation (3.4.4). First of all, the weighed portion mR is chosen so that the previously fixed color strength level DSD is achieved. At this step, it is necessary to pay attention to insure that the weight fraction of the white pigment mW is the same in the mixture of reference and sample pigments. Afterward the mass mS of the sample pigment is altered as long as both mixtures show nearly no difference with regard to the previously chosen adjustment criterion FAC , so ΔFAC ∼ = 0 (see below). If these conditions are fulfilled, the relative color strength Prp of the sample pigment follows from relation Prp =

mR mS

(3.4.6)

for secondary conditions: DSD = const., mW = const., and ΔFAC ∼ = 0. In addition to the value of relative color strength Prp , it is always necessary to indicate the reference colorant, the level SD of color depth, the sort of white pigment, respectively solvent, as well as the accompanying fraction, and the chosen matching criterion FAC . For comparability of the resulting relative color strength values with those of other colorants, the so-called standard color depth (SD) first for dyes and later geared to pigments was established. The standardized SDs for textile dyes are denoted as 1/25 SD, 1/12 SD, 1/6 SD, 1/3 SD, 1/1 SD, and 2/1 SD. For pigments, there are four standard depths: 1/25 SD, 1/9 SD, 1/3 SD, and 1/1 SD [44]. The production and testing of standard deep colors are described in [45]. Above and beyond the mentioned parameters DSD = const., mW = const., and ΔFAC ∼ = 0, it needs to be considered that the color strength of pigments additionally depends on the chosen reference pigment, the mean particle size, the sort and concentration of the white pigment, and a possible added black pigment. For dyes, the relations are simpler because only the reference dye, the solvent, and the concentration need to be indicated in addition to the chosen standard color depth and matching criteria. For absorption colorants, various effective matching criteria FAC exist. The perhaps obvious idea of using the visual assessment for determination of color

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Standardized Tristimulus Values, Color Qualities, Chroma of Effect Pigments

strength certainly must be ruled out. In particular, this approach is overtaxed if similar reflection or transmission spectra are present. The color matching needs to be carried out exclusively with measuring methods. Some widespread criteria founded on either spectral or colorimetrical quantities follow. The spectral-matching criteria are based on the term Kubelka–Munk function F(λ) = K(λ)/S(λ). It corresponds to the ratio of the absorption and scattering coefficient K(λ) and S(λ), respectively, in dependence on the wavelength λ, cf. Equation (5.3.14). Both coefficients have to be known with regard to the sample and reference colorants at the same wavelength. This quotient is, however, useless if the scattering coefficient tends to zero – especially for highly transparent or dark colorants. In such cases, it is necessary to switch to other criteria. The four most commonly used spectral-matching criteria are as follows: 1. The difference of the Kubelka–Munk functions between the sample and the reference colorant FS , FR , respectively, each at the accompanying wavelength λmax,R of the function maximum of the reference colorant: ΔFmax, R = FS (λmax, R ) − FR (λmax, R ) ∼ = 0.

(3.4.7)

2. The difference of the reflectance between the sample and the reference colorant, each at the accompanying wavelength λmin,R of the reflection minimum of the reference colorant: ΔRmin, R = RS (λmin, R ) − RR (λmin, R ) ∼ = 0;

(3.4.8)

this criterion is equivalent to the previous one. 3. The minimum of the sum, which results from the weighted differences of the Kubelka–Munk function values between sample and reference colorant, each determined at i = 1, 2, . . . , N measured wavelengths λi : N  i=1

ΔFi =

N 

αi [FS (λi ) − FR (λi )] ≡ minimum;

(3.4.9)

i=1

the weighting factors α i correspond to the sum of the CMFs αi = x¯ (λi ) + y¯ (λi ) + z¯(λi )

(3.4.10)

for the chosen 2◦ or 10◦ standard observer; this criterion leads to unsatisfactory results if the summands in Equation (3.4.9) are simultaneously of high and low values. In this case, it is opportune to apply the next criterion. 4. The minimum of the sum which follows from the squared deviation of the Kubelka–Munk function of the sample and reference colorant at N measured wavelengths λi

3.4

Specific Qualities of Colorants N  i=1

(ΔFi ) = 2

N 

183

[FS (λi ) − FR (λi )]2 ≡ minimum,

(3.4.11)

i=1

probably with other weighting factors as in the third criterion. The spectrophotometric matching of the sample to the reference colorant should certainly be performed with the same illuminant, standard observer, and spectrophotometer for each. These conditions need to be indicated along with the value of the relative color strength in addition to the employed reference colorant. Relative color strengths are only to be compared with each other if the same reference colorant and the mentioned three conditions had been used. For colorimetrical-matching criteria, one should alternatively take into consideration: 1. One of the differences ΔX = XS – XR , or ΔY = YS – YR , or ΔZ = ZS – ZR between the standard color values of the sample XS , YS , ZS and reference XR , YR , ZR , which contains the smallest value min (XR , YR , ZR ) of the reference colorant: ⎧ ⎫ ⎨ ΔX if XR = min(XR , YR , ZR ) ⎬ ΔY if YR = min(XR , YR , ZR ) ∼ (3.4.12) = 0. ⎩ ⎭ ΔZ if ZR = min(XR , YR , ZR ) 2. The difference of the standard color values YS , YR or lightness values LS , LR of the sample and reference colorant ΔY = |YS − YR | ∼ =0

(3.4.13)

ΔL = |LS − LR | ∼ = 0.

(3.4.14)

or

3. The smallest color difference ΔE with regard to the sample and reference colorant ΔE ≡ minimum;

(3.4.15)

the color difference formula is optional. 4. The depth of color Di at standard color depth SD; this matching method should be applied to dyes as well as pigments.

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Standardized Tristimulus Values, Color Qualities, Chroma of Effect Pigments

There exist empirical formulas, especially for matching of color strength with pigments. We restrict ourselves to these in the following discussion. Historically, these have been found in a similar manner as for dyes. A relation in widespread use is given by ΔDi =

√ Y[s · ai (ϕ) − 10] + bi ∼ = 0.

(3.4.16)

The quantities in this expression are as follows: ΔDi : difference in depth of color for standard color depth level i; i: level of standard color depth, one of 1/1 SD to 1/25 SD as mentioned above; Y: standard color value of the CIE 1931 system, a measure for lightness; s: measure of saturation, it corresponds to 10 times the distance in the CIE chromaticity diagram between color locus of the sample pigment (x, y) and the achromatic locus (xn , yn ) s = 10 ·



(x − xn )2 + (y − yn )2

(3.4.17)

for the chosen illuminant and standard observer, cf. Table 3.2 and Color plate 2; ai (ϕ): empirical function for weighing of s; it depends on hue angle ϕ = arctan [(y − yn )/(x − xn )] and the chosen level i of standard depth SD; empirically determined constant corresponding to the level i; it takes bi : values of b1/3 = 29, b1/9 = 41, b1/25 = 56. The added mass of the sample pigment mk+1 on the kth iteration step, k = 1, 2, 3, . . . , follows from the additional empirical relation mk+1 = mk · 0.9ΔDi ,

(3.4.18)

the exponent ΔDi following from Equation (3.4.16). Often the numerical value of the relative color strength Prp is emphasized alone for the argument for colorant substitution in color reproduction or color recipe prediction. But it needs to be taken into consideration that the replacement usually brings in changes in hue or lightness or other coloristic features with consequences for color constancy, metamerism, among other things. Provided that the new pigments are transparent or translucent, also the light transmission or the covering potential can change. In any case, such consequences must be thoroughly checked before the colorant exchange. Also, as normal in material sciences, it must be ensured that the replacement of one component has no negative effect on other components or system properties.

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Specific Qualities of Colorants

185

In summary, we point out that both spectrometric and colorimetric procedures are quite efficiently applied to determine and characterize the relative color strength of absorption colorants. The productive potential of colorimetry up until now is used, in the following, for a quantitative description of further color properties of absorbing colorants.

3.4.3 Covering Capacity Whereas the color strength, in some sense, indicates the coloristical effectiveness of an absorbing colorant, the covering capacity is a measure of the capability of a coating to hide a colored background [46]. This property is called hiding power in ASTM standards [47– 49]. For constant pigment loading, there exists a minimum coating thickness dC for which the color of a substrate can no longer be visually discerned. On the other hand, given a layer thickness d, there is a minimal colorant concentration cmin for which the background color is also not visible. In both cases, the inverse of the minimal covering thickness dC is a measure for the covering capacity of a scattering and absorbing coating, as in  D = 1 dC .

(3.4.19)

The quantity D is called the covering capacity value and is in units of reciprocal length. This dimension can be modified in such a way that it has an economical meaning. If the unit of film thickness dC is given in mm and multiplied by the ratio m2 /m2 , then for covering capacity value D, the quotient m2 /l follows; 1 l ≡ 103 cm3 is the volume unit liter. More precise, the quantity Dv = D relates to the volume. The corresponding numerical value of Dv indicates the area in square meters, which 1 l of color can totally cover at film thickness dC . On the other hand, if the mass density ρ m is given in dimensions g/cm3 , then the unit liter l can be substituted by the expression ρm−1 kg. If the numerical value D is given in the units mm–1 or m2 /l, then the multiplication with the value of mass density ρ m in unit g/cm3 results in dimension m2 /kg for Dm = ρm · Dv . The quantity Dm now relates to the mass, it indicates the area in square meters, which one kg of color can totally hide at film thickness dC . Therefore, the value of Dv or Dm is a realistic measure for the covering spreading rate of a formulation with absorption pigments. The quantity of the covering capacity can be simply verified from the dry film thickness. Now, the question needs to be answered as to which method can be used to find out the minimal covering film thickness dC . Just as for the color strength, the covering capacity value of absorption colorations is experimentally determined with the help of a colorimetrically defined criterion. For this purpose, there exist two methods of operation [46 – 50]. The first of them is based on the so-called

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3

Standardized Tristimulus Values, Color Qualities, Chroma of Effect Pigments

contrast ratio; it follows from the standard color values Yw and Yb which result from the measured reflectance of the film over white and black backgrounds (contrast substrate). According to this criterion, a minimal covering layer is achieved if the condition Yb ≥ 0.98 Yw

(3.4.20)

is fulfilled, for example, for the standard illuminant/observer combination D65/10◦ . The contrast ratio should, accordingly, attain a minimum value of 98% to indicate a covering film thickness. The second procedure uses the color difference ΔEbw which results also from the spectrophotometric measurement of the film over black and white backgrounds of known reflectance. A covering coating satisfies the condition

ΔEbw =

 (ΔLbw )2 + (ΔCbw )2 + (ΔH bw )2 ≤ 1,

(3.4.21)

where ΔLbw , ΔCbw , ΔHbw are the difference in lightness, chroma, and hue, respectively, each over both backgrounds. For opaque colors, the values are (Yb /Yw ) = 1 or ΔEbw = 0. Due to the color locus-dependent visual discrimination of color differences, it may be necessary to fix, in dependence of hue, a color difference in the value domain 0.3 ≤ |ΔEbw | ≤ 0.9. In the case of achromatic or nearly achromatic colors, Equation (3.4.21) reduces to |ΔLbw | ≤ 1 because the distribution of chroma and hue is now of secondary importance. In all cases, the spectral reflectance of the black and white backgrounds Rbg,b (λ) and Rbg,w (λ), respectively, should be constant and meet the conditions Rbg,b (λ) ≤ 0.2 and Rbg,w (λ) ≥ 0.8. The actual determination of the volume- or mass-related covering capacity value D from the color difference method can be achieved either graphically or numerically (for simplicity, in the following we leave out the corresponding indices v and m of D). The graphic method requires at least three colorations of different film thicknesses d, each over the black and white substrate. The layer thickness should be known to an uncertainty of ±1%. From the graph of ΔEbw in dependence of 1/d, the value D follows by extrapolation. It is represented by the slope point of coordinates (ΔEbw , 1/dC ) to which the color difference ΔEbw = 1 belongs; see Fig. 3.14. In contrast, the numerical procedure is based on the calculation of the reflectance spectra over both backgrounds. It has the advantage that only one control coloration needs to be manufactured. On the other hand, this method requires various known spectral quantities as input data: the optical constants of the pigments, binder, perhaps additives, and the reflectance of both backgrounds; in addition, the pigment loading and the single concentration ratio of

3.4

Specific Qualities of Colorants

187

ΔEbw

3.0

2.0

1.0 D ≈ 18 m2/l D 0 0

10

20

1/d/mm–1

Fig. 3.14 Determination of covering capacity value D of a pigmented coloration by extrapolation

the inserted colorants have to be known. This set of quantities is used to calculate the spectral reflectance over both backgrounds with the aid of a suitable radiative transfer approximation (see Chapter 5). Afterward, the covering capacity value D follows from iteration as given in Fig. 3.15. The process starts with an estimate for a non-covering film thickness dk = 1/Dk , which leads to the color difference value ΔEk (for simplicity, the exponent ws is left out in the following). In the next step, a suited value Dk+1 < Dk of corresponding color difference ΔEk+1 is determined. If for the sought after covering capacity value (3.4.19), the given color difference obeys ΔEC ≤ 1, then an improved value Dk+2 follows from equation Dk+2 = Dk+1 −

Dk+1 − Dk (ΔEk+1 − ΔEC ). ΔEk+1 − ΔEk

(3.4.22)

This relation results from the method regula falsi. According to this, at each iteration step, a curve section is approximated by a secant line. After a few iteration steps the covering capacity value D = 1/dC is obtained. The graphical and numerical methods do not necessarily result in same values. Covering capacity values can, consequently, only be compared with each other if they are determined using the same method. The determination of the value D runs, however, more elegantly, if this procedure is directly included in color recipe prediction. This is because the optical

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3

Standardized Tristimulus Values, Color Qualities, Chroma of Effect Pigments ΔE bw k=0

6.0

4.0

k=1 2.0

k=2 k=3 D ≈ 22.9 m2/l

0 10

20

30

40

1/d/mm–1

Fig. 3.15 Iterative determination of the covering capacity value D

constants of the inserted colorants and the concentration ratios are already known as well as the calculated spectral reflectance values (Section 6.2.3). The color recipe prediction even allows for the possibility of fixing a covering film thickness dC = 1/D and determining the corresponding colorant fractions. In fact, this method needs intensive computation, but it requires only one coloration in order to check the calculated covering thickness dC . If another covering thickness dC, x = 1/Dx is required, and this thickness differs not more than about ±10% of dC , then the new pigment loading cx follows from the previous one by the simple approximation cx = c ·

dC Dx . =c· dC, x D

(3.4.23)

For use of the maximal pigment loading cmax (in so-called high solids), the even covering and minimal thickness dC, min = 1/Dmax is determined from dC, min = dC ·

c cmax

;

(3.4.24)

the accompanying quantity Dmax follows from formula

Dmax = D ·

cmax . c

(3.4.25)

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Specific Qualities of Colorants

189

To complete the picture, we point out that the change of film thickness or pigment loading can additionally influence the volume or surface properties, for example, gloss, microhardness, abrasive resistance, color fastness, or weathering resistance. Such features, consequently, should also be checked. Moreover, we mention that the discussed methods will produce incorrect results if measured input quantities are inaccurate (“garbage in, garbage out”). On the basis of this fact, the quantities that we are interested in D, dC , or c should be determined in view of a load factor lf > 1 in order to compensate the consequences of unavoidable production fluctuations.

3.4.4 Transparency and Coloring Power According to the previous section, the transition from translucent to opaque of a colored layer is unambiguously characterized by either the covering capacity value, contrast ratio, or color difference over black and white contrast backgrounds. However, reverse has not yet been clarified as to which characteristic value describes the changeover between nearly transparent and slightly translucent materials. Before we discuss this question, we first have to characterize the real state of nearly transparent colorations. Ideal transparency is characterized by pure absorption and completely absent scattering. The greater the transparency of a real layer, the less the light is absorbed or scattered. In addition, transparency of a real material depends on refractive index, the layer thickness, contained colorants, binder, superstructure, as well as aging processes. Clearly, the spectral absorption influences both the light transmittance and color of the material; normally, color differences as small ∗ ≈ 0.02 are just provable. The color shift of nearly colorless transparas ΔEab ent materials is called the tinting power. This color shade is perceptible over a white background, the scattering component, on the other hand, over a black background. A measure for light transmittance is, apart from spectral transmission, the so-called transparency index. It characterizes the scattering component of a transparent medium. It is consequently determined from the color difference ΔEb which follows from reflectance measurements of the layer over a black background and the background itself. Because transparency depends non-linearly on layer thickness d, samples of various thicknesses are to be manufactured for determining the transparency index. In order to attain a transparency index independent of geometrical influence, the color difference value ΔEb for zero thickness d→0 by extrapolation should be determined. The plot of the difference ΔEb in dependence on d results in a nearly positive parabolic curve through the origin, as shown in Fig. 3.16. The transparency index TN is now defined by the reciprocal curve gradient at infinitesimal thickness difference Δd→0:

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3

Standardized Tristimulus Values, Color Qualities, Chroma of Effect Pigments ΔE b

ΔE2b

ΔE1b

0 0

d1

d2

d

Fig. 3.16 Determination of transparency index from the slope at the origin

1/TN = lim

Δd→0

Δ(ΔEb ) . Δd

(3.4.26)

The quantity of TN has the unit of d. The greater the transparency of a layer, the smaller the gradient at the origin. Consequently, the transparency index is a quantity which is a real characteristic of an optical material [51, 52]. The slope at the origin can be approximately determined by curve fitting. If we assign the measured value pairs di , ΔEib for i = 1, 2, 3. . . to a polynomial of second order through the origin ΔEb = a1 d + a2 d2

(3.4.27)

with coefficients a1 , a2 , then the transparency index follows from TN = 1/a1 .

(3.4.28)

Also for polynomials of higher order, the transparency index results from the inverse of the coefficient at d. For a rough estimate, two layers of thicknesses d1 and d2 > 1.5 d1 are sufficient. With the accompanying color differences ΔE1b , ΔE2b and using Equations (3.4.27) and (3.4.28), the relation TN =

q · (d2 − d1 ) q2 ΔE1b − ΔE2b

, q = d2 /d1 ,

(3.4.29)

can be derived. The quantity TN is quite sensitive to inaccuracies in the values of d1 and d2 . On the other hand, the relative uncertainty of the transparency index can be estimated by summing up and doubling the relative errors of color

3.4

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191

difference and thickness measurement. The computation of adjustment naturally delivers an enhanced error estimate for TN . The coloring power value CP of a layer is determined in a similar way, but using a white background rather than a black one. The quantity represents a dimensional value for the color of a nearly colorless transparent material. For the determination of the coloring power value, the color difference ΔEw between the layer separately over white background and the background is used, this again in dependence of layer thickness d. The color difference ΔEw behaves similar to ΔEb in dependence on d. Therefore, the formalism for TN can be nearly applied to derive a formula for determination of CP . From similar considerations as above, the quantity of CP follows directly from the slope in the origin CP = lim

Δd→0

Δ(ΔEw ) = a1 , Δd

(3.4.30)

provided that Equation (3.4.27) is applied with ΔEw instead of ΔEb . The unit of CP is the same as of d. The smaller the slope at the origin, the lower the value of CP and the less perceptible the natural color of the transparent material. Both quantities CP and TN can even be simultaneously determined from the same layer thicknesses if the transparent films are each measured over a black/white contrast substrate. With the thickness values d1 , d2 , and the accompanying color differences ΔE1w and ΔE2w ,

CP =

q2 ΔE1w − ΔE2w , q · (d2 − d1 )

q = d2 /d1 ,

(3.4.31)

follows from Equations (3.4.27) and (3.4.30). The error estimates of CP and TN are nearly the same, provided that in both cases the same measuring equipment, layer thicknesses, and contrast substrate are used. For more than three thicknesses, the values are to determine by computation of adjustment. The multiplication of transparency index and coloring power value of the same material leads to the dimensionless varnish power value Γ = TN · CP .

(3.4.32)

As stated at the beginning of this section, with the covering power criteria, it is necessary to differentiate between an opaque and a translucent coating. There does not, however, exist a colorimetrical method for distinguishing a nearly ideal transparent medium from a slightly translucent one. This problem is solved at the end of the next section after the discussion of aging stability.

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3.4.5 Color Fastness and Turbidity Despite experience indicating otherwise, until now we have disregarded the fact that components – especially colorants, binders, and additives – are subject to aging effects. The term color fastness is to be considered the resistance of a given coloration to physical or chemical influences during manufacturing, processing, storing, application, or aging [53, 54]. Color changes during such periods, however, are of prime importance for acceptance, quality, profitability, and conventional working life of a colored product. A high color fastness is necessary during manufacturing or processing because of the presence of the prevailing temperatures, IR radiation, pressures, shear rates, and processing auxiliaries [55]. Consequently, the short- or long-term aging stability of colorants and formulations should be known or at least approximated from results of simulation experiments. Aging processes depend on the inner and outer conditions of a material. The inner conditions consist of thermodynamic instable molecular states, which lead (especially in plastic materials) to after effects such as secondary crystallization, embrittlement, diffusion of colorants, plasticizers, or colorant auxiliaries by relief of residual stresses. Aging from the surface is primarily caused by radiation energy, from cosmic and radioactive radiation to radiation in the near-UV and far-IR range (cf. Fig. 2.1). The effects of humidity, liquids like brine solutions, acids, leaches, organic solvents, detergents, and also gases such as oxygen, ozone, carbon dioxide, and exhaust pollutants should not be underestimated. The inner and outer effects can damage both the individual colorants and the net color effect. The examinations for color aging can be divided into practice equivalent and time-lapsed methods. Of special interest among them is the long-term fastness to light under different climates. Economic reasons allow only in rare cases a long continual outdoor weathering in a temperate climate (Central Europe), warm dry (Arizona), or warm humid (Bombay) with solar energy influx between 127 and 150 W/m2 (about 10% of the solar constant). From material science, timelapsed simulation experiments are known and widely applied, from which the real aging stability should follow in a shorter exposure time. During an artificial weathering, the color samples are exposed to a continuous radiant flux and additionally loaded with thermal energy or agents [56]. For radiation sources are used independently of each other or combined: xenon radiators, luminescence and mercury vapor lamps, as well as carbon-arc lamps [57, 58]. The emitted spectra are irradiated directly without or with selective filters. In single cases, a spectral power distribution which corresponds to the standardized middle daylight D65 simulator is generally sought after. Because the higher radiant energy densities also cause an accelerated self-aging of the sources, the artificial radiators and the inserted UV filters should be exchanged no later than after 1,500 operating hours, and for multiple instrumentation this

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is in cyclic order. The overall influence of the radiant power is a measure of the radiation-invoked aging process of the relevant material. The artificially induced degradation should approximately correspond to that which will probably occur during working life of the colored product. During natural or artificial aging of colorants or color formulations, the corresponding color values change constantly. Periodically time-dependent color alterations are quite rare in practice. Only in some cases, the aging caused chalking or efflorescence of colorants and additives are pursued with colorimetrical methods. Also changes of wood substrates coated with varnishes need to be interpreted with some restriction and are at best judged qualitatively. Changes of gloss, microhardness, abrasion resistance, blistering, cracking or crazing as well as edge peeling, etc., are difficult or even impossible to characterize with colorimetrical methods; such kinds of damage are often judged subjectively according to standardized guidelines. Among the multitude of damage influences, we only describe the effects that are addressable colorimetrically, such as turbidity and yellowing of transparent and translucent materials. The color changes compared with the original condition can be established, for example, by the color difference contributions ΔL, ΔC, ΔH. Because the majority of the damage mechanisms proceed in an exponential time-dependent fashion, the color difference measurements need, at first, to be carried out in shorter, logarithmic time intervals. If the aged specimen field is larger than the aperture of the color measuring equipment, then the changes should be taken each time at the same marked measuring area and in the same orientation. In cases of fogging, striations, or grains present in the measuring field, at least three representative spots should be chosen and the arithmetic mean of the measured variables taken. Each measurement should be carried out with the same color measuring instrument and evaluated with the same method, the same color differences, and the same illuminant/observer combination. All of the aging and evaluation conditions need to be documented with the results. For performance evaluation with regard to color changes were developed, apart from color difference quantities, further empirical characteristics especially to use for different colorations or materials. Among them are the gray scale rating (principally of textiles), whiteness index (white pigments, paper), yellowness index (paper, foils), and turbidity or haze (foils, inorganic or organic glasses). The mentioned quantities are now discussed. The gray scale rating GS can be determined for achromatic and chromatic colorations. This quantity follows after the time-dependent degradation action with the special color difference formula ΔEC =



(ΔL∗ )2 + (ΔCC )2 + (ΔHC )2 .

(3.4.33)

The special chroma and hue differences ΔCC and ΔHC are empirical functions ∗ , Δh , ΔH ∗ , which are given by a standard [59]. of CIELAB differences ΔCab ab ab

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The value ΔEC corresponds to a gray scale rating value GS , which is a natural number in the range 1 ≤ GS ≤ 5. The GS value ranking in dependence on ΔEC is somewhat arbitrary and not clearly defined for intermediate ΔEC values outside given tolerance intervals; see Table 3.11. For example, a color difference in the value domain 12.6 ≤ ΔEC ≤ 14.6 corresponds to the lowest possible value GS = 1, the highest GS = 5 corresponds to the color difference interval ΔEC ≤ +0.2, a value in the domain 10.3 ≤ ΔEC ≤ 12.6, on the other hand, cannot be clearly assigned a concrete gray scale rating value. The whiteness index and whitening index were introduced for evaluation of nearly achromatic light colorations and accompanying color changes. The determination of the whiteness index W is founded on the x, y, Y system and follows from relation  W=

for D65/2◦ Yn + 800(xn − x) + 1700(yn − y) . (3.4.34) Yn + 800(xn, 10 − x10 ) + 1700(yn, 10 − y10 ) for D65/10◦

It comes from extensive color matching [60, 61]. In Equation (3.4.34), xn , yn and xn,10 , yn,10 denote the coordinates of the achromatic point in the chromatic diagram to the 2◦ and 10◦ standard observers, respectively (see Table 3.2). According to Equation (3.4.34), ideal white has a value W = Yn = 100.000 for each of the standard observers. Colorations containing fluorescent brighteners can exceed this value and need a suitable corrected formula or an entirely different one. For description of near-white shades of paper or textiles, on the other hand, the so-called whitening index Tw is used [62]. In comparison to W, its determination follows from a similar relation:  Tw =

1000(xn − x) − 700(yn − y) for D65/2◦ , 900(xn, 10 − x10 ) − 800(yn, 10 − y10 ) for D65/10◦

(3.4.35)

Table 3.11 Gray scale value, corresponding color difference, and color-difference tolerance of gray scale rating Gray-scale value GS

Color difference ΔEC

Tolerance ±δ(ΔEC )

1 1–2 2 2–3 3 3–4 4 4–5 5

13.6 9.6 6.8 4.8 3.4 2.5 1.7 0.8 0

1.0 0.7 0.6 0.5 0.4 0.35 0.3 0.2 +0.2

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where the indexed chromaticity coordinates have the same meaning as in Equation (3.4.34). The test color appears greenish for Tw > 0 and reddish in the case of Tw < 0. Ideal white is represented by the value Tw = 0 for both standard observers. For equal color coordinate values of x, y, Equations (3.4.34) and (3.4.35) show numerically different results. Clearly, the whiteness index is a measure for the lightness including the weighed relative red and green fractions of the sample. In contrast, the whitening index represents the difference between the relative red and green fractions. Both quantities, consequently, cannot be compared with one another, neither colorimetrically nor numerically. Greater color changes of white or brightened materials are characterized by the yellowness index Yness or yellowing index Ying . The yellowing is caused by energy absorption at wavelengths < 490 nm. The determination of the yellowness index Yness is based on a relative equation of type Yness = (α · X − β · Z)/Y,

(3.4.36)

this again comes from extensive color pattern matching. The empirical weighting factors α and β depend on the chosen illuminant and standard observer [61, 62]. The yellowness index is to calculate from  Yness =

(1.298 · X − 1.133 · Z)/Y for D65/2◦ . (1.301 · X10 − 1.149 · Z10 )/Y10 for D65/10◦

(3.4.37)

Each of the expressions in Equation (3.4.37) corresponds to the difference of the weighted red and blue fractions relative to the lightness value of the yellowish material. The yellowing index Ying is simply defined as the difference in a o : and at the original condition Yness yellowness index after aging Yness a o − Yness . Ying = Yness

(3.4.38)

Yellowing is accompanied by changes of chroma ΔC and hue ΔH, which characterize the color shift more closely. The yellowing of transparent organic materials like coatings, foils, inorganic or organic glasses is also often accompanied by increasing turbidity or haze. The turbidity of transparent finishes or haze of plastic materials transforms a directional light intensity into an attenuated directed and a diffuse component, as shown in Fig. 3.17. A measure for the diffuse scattering effect in the volume of the layer is the haze index HI [63]. This quantity is defined as the ratio of the diffuse transmissivity Td to the entire transmissivity Te of a layer multiplied by hundred HI = (Td /Te ) · 100.

(3.4.39)

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Fig. 3.17 Directional and diffuse intensities determine the haze index of a transparent turbid material

Id Io Ie

jdTe

The entire transmissivity equals the transmission of the material. The diffuse component Td is given by the ratio of the transmitted diffuse intensity Id to the irradiated intensity I0 : Td = Id /I0 .

(3.4.40)

The entire transmission Te follows from an analog consideration by the ratio Te = Ie /I0 ,

(3.4.41)

where Ie stands for the entire transmitted intensity. The value of Id is normally determined with angle dependence. For simplicity, the scattered radiation Jd is determined integrally at an axial angle of ±80◦ with respect to the direction of the incident intensity I0 . The diffuse flux Jd is composed of the transmitted component Id and the scattering jd Te caused by the physical elements of the measurement setup: Jd = Id + jd Te .

(3.4.42)

The diffuse flux jd is determined from an empty measurement in normal operating conditions. The haze index HI is consequently calculated from the relation   Jd jd − · 100. (3.4.43) HI = Ie I0

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This measuring principle responds quite sensitively to defects at the surfaces such as dust or scratches. In order to observe the haze coming from scattering centers in the volume, the samples need to be handled quite carefully. Transparent materials with structured surfaces are, therefore, also unusable for this measuring method. This is because turbidity depends on discontinuity of refractive index at the interface only to a small extent. The haze index of transparent real materials is in the domain HI ≤ 0.05 and of translucent mediums in the interval 0.05 ≤ HI ≤ 0.30. The haze index value HI ≤ 0.05 is a suitable criterion for discerning transparent layers from translucent ones. The haze index HI is, according to definition equation (3.4.39), a dimensionless quantity, whereas the transparency index TN , from Equation (3.4.29), has the units of length. Also this comparison shows clearly that both quantities represent different optical properties. The discussed evaluation relations in this chapter have been outlined generally for the representation of typical properties of colorations with absorption colorants. Certainly, colors containing flake-shaped effect pigments need separate considerations with regard to color fastness because some color properties of this pigment sort cannot be characterized by colorimetrical methods. More detailed information about this is given in the next section for colorations especially with metallic pigments.

3.4.6 Stability of Effect Pigments Similar to that which was discussed for absorption colors, colorations with effect pigments lose their initial color physical properties due to physical or chemical influences. Because of the composition, morphology, and greater size of such particles compared with absorption pigments, the effect flakes present – in a real and figurative sense – a bigger target. The effect pigments should have high resistance against shear load, light or heat load and to a large degree against aggressive chemical environments. Formulations with effect colorants generally require more extensive fastness tests than for absorption colorants. From the catalog of possibilities for metallic and interference pigments, we restrict the discussion to some fundamental degradation mechanisms. The mechanical loads which flake-shaped effect pigments undergo during manufacturing or processing should, by no means, be underestimated. The mechanical ring pumps of painting plants or fluid plastic melts through narrow nozzles and spiral channels cause enormous pressure gradients – shear rates up to 105 s–1 . Incorporated effect particles should survive a process with a maximal shear stress of 102 MN/m2 undamaged. Because of shear stress load, preferential thin metal particles are uncontrollably deformed and scratched, outer sections of the flakes fold down or fracture: the metallic brilliance grays. In a similar way, the brilliance of pearl luster and interference pigments is also reduced.

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The degree of shear stability of effect particles is characterized either by the gray scale rating GS or colorimetrical lightness L. For determination of the decrease in lightness, test effect pigments are agitated in a cooled mixer machine of a suited agitator at a speed of 20,000 rpm for 15 min. Afterward a coating with such shear-loaded particles is manufactured in a clear binder and the CIELAB lightness difference ΔL∗ is determined between the damaged flakes LS∗ and the lightness of the reference coloration LR∗ . The measurements are each performed at an illumination angle of 45◦ and fixed aspecular measuring angle of μas = 20◦ . In dependence of the amount of lightness difference value ΔL∗ (20◦as ) = |LS∗ (20◦as ) − LR∗ (20◦as )|,

(3.4.44)

three empirically defined groups can be differentiated. These are listed in Table 3.12: shear stable, low shear stable, and non-shear stable platelets. In order to further characterize the degradation, a higher measuring angle is used to determine the difference of flop index (Section 3.5.1), or the damage time is to increase. The highest shear stability show clearly thick glitter particles, the lowest metallic corn flakes. The stability of pearlescent and interference pigments can be increased by coating with suited interface-active substances. Although metallic pigments show a higher light resistance in comparison to absorption pigments, high-energy radiation, thermal energy, or an unfavorable polymer surrounding can lead to immediate degradation of the flakes. The metallic character is further lowered by such influences. Particles of copper/zinc alloys (brass) turn out to be particularly susceptible. Because of the lower melting point, the flakes become thermally unstable at temperatures higher than about 200◦ C; the flakes are, therefore, suitably stabilized for application in baking finishes or plastic materials of high melting and glass transition temperature, respectively. Water-borne systems or hygroscopic polymers are able to activate decomposing effective zinc and copper ions from brass particles. These can cause considerable color shift and luster decrease. Both ions lead to accelerated disintegration of PVC molecules; already a thermal load at a temperature as low as 80◦ C leads to separation of hydrogen chloride. The combined coloristical variTable 3.12 Connection between change of lightness and shear stability of metallic pigments Lightness difference ΔL∗ (20◦as )

Degree of shear stability

<5

Shear stable

5–10 > 10

Low shear stable Non-shear stable

Examples of metallic pigments Glitter particles of metal foils Silver dollar flakes Cornflakes

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199

ations can be quantified by the previously discussed colorimetrical methods for determination of yellowing. The damaging effects of the copper and zinc ions can be reduced, however, by appropriate polymer coatings of the flakes. In such a way, stabilized particles can have elevated processing temperatures of up to 260◦ C. An additional property of effect pigments, which especially need to be considered for aluminum flakes, is the leafing stability. This particle formation can be unintentionally reduced or altogether time-dependent decay by false additives. The standardized testing value for leafing stability indicates the time during which a leafing pigment is flooded and finally shows visible wetting [64]. Leafing stability can also be determined relative to a reference formulation. It is possible to additionally pursue the leafing decay with the colorimetrical lightness L. The chemically caused influences can induce particularly enormous degradations of the metal particles. For example, the brilliance of aluminum flakes is reduced in the presence of water as in water-based paint systems or in the form of water vapor. The particles are oxidized with the release of hydrogen and lose, therefore, their initial brilliance. The dehydration of polymeric materials with comparably high humidity content such as polyamides, polycarbonates, or polyethylene terephthalates should be performed separately and actually directly before incorporation of the aluminum pigments. Otherwise the particles become partially oxidized from the surface by released water vapor under the formation of Al2 O3 (Appendix A.1.1). This unwanted influence causes a distinct reduction of lightness. Moreover, the surface-oxidized aluminum platelets tend to conglomerate during incorporation in binders or melts of high polymeric materials. The conglomerations in paints lead to local restricted mottlings, which are caused by turbulent solvent evaporation. Such heterogeneities are detected as local lightness fluctuations with a small aperture color measuring instrument and applying the method described above in connection with Equation (3.4.44). Coatings with effect and absorption pigments, which are exposed to high humidity, are indispensable for the examination of the so-called condensation water resistance. This test is performed with colorations containing single or various combined pigment types. For this, effect pigments can be coated with various covering organic substances. In such a way, modified particles are subjected to a saturated water vapor atmosphere of 40◦ C for 240 h [65, 66]. The colorimetrical changes to detect are again followed in logarithmic time steps. In general, these actions produce stronger damages as the standardized salt spray testing [67]. This was originally introduced to control recipes for absorption pigments. With this method, conventional effect paints and water-based systems are controlled with regard to swelling, blistering, adhesion, reduction of brilliance, and distinctiveness of image DOI. For outdoor use, metallic, pearl luster, and interference pigments have to meet the greatest demands concerning color constancy or weather stability. In

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addition to the testing procedures mentioned until now, the exterior weathering is also assessed with the non-standardized Florida test. This test is regarded as passed, if after a 2-year natural weathering – under daytime-dependant strong fluctuations of air humidity and temperature – the color difference of a chromatic color regarding the undamaged reference coloration is less than unity: ∗ <1. This color difference holds also for effect colorations for illumination ΔEab and measuring angle of β = 45◦ and μas = 15◦ , respectively. For control, it is sensible to perform a standardized outdoor exposure [68]. The weather durability of effect pigments can be greatly enhanced by coating the flakes with a clear colorless UV-absorbing paint, for example, with a silane. Also inorganic layers can improve the climate resistance of effect pigments. If, for example, the mica substrate of a pearl luster pigment is first coated with SnO2 , then the light fastness is improved. A topcoat of the muscovite consisting of TiO2 nanoparticles causes an enhanced UV stability. This is due to the reduced photo activity of the TiO2 layer by UV absorption. Combination pigments with Fe2 O3 or Cr2 O3 layers show – compared to those with only TiO2 -evaporated pearlescent pigments – a refined adhesion between the particle surface and the binder of the formulation. To summarize, the consequences of a natural or artificial degradation of effect colorations can be partially pursued with specially geared colorimetric evaluation methods. In some cases, these procedures are even overtaken from tests for absorption colorants. Since we discussed essential spectrometric properties of effect pigments already in Section 2.3, it is absolutely consistent to represent the primary angle-dependent color physical properties of such pigments with colorimetrical elements in the following.

3.5 Chroma of Effect Pigments Because, until present, for effect colors there is no specific color space, therefore, conventional standard color values are of limited use for characterizing properties of such colorations. As a few examples, we already discussed the changes in brilliance and lightness difference of metallic pigment coatings in connection with the assessment of shear and weathering resistance. In this section, we first become acquainted with specific characteristics of metal effect colorations which are partly based on colorimetric determination procedures including metal effect value, lightness-flop index, distinctiveness of image grade DOI, sparkle degree, graininess, as well as an angle-dependent color difference formula. Afterward, the projection method of color build-up into a color area, already known from absorption colorants in dependence of colorant concentration, is transferred to effect pigments. These curve elements, now taken in dependence of illumination or measuring angle at constant colorant concentration, are denoted as chroma curves for differentiation. From such

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201

kinds of curves, the color changes of pearl luster and interference pigments in dependence of the evaporated overlay thickness on the particle’s substrate are immediately observed, for example. Moreover, chroma curves of different interference pigments show common characteristics for similar thicknesses and dependences of the illumination and measuring angle. Chroma curves of interference pigments mixed with absorption and additional effect pigments are particularly instructive. Even more impressive forms show angle-dependent chroma curves of diffraction pigments with different grating constants or for those with ferromagnetic substrates. Consequently, chroma curves enable a direct overview of almost the entire angle-dependent color development of effect pigments.

3.5.1 Coloristic Quantities of Effect Pigments As already seen in Section 2.3, the platelet-shaped geometry of effect pigments needs an almost completely different color physical characterization as that for absorption pigments. For the moment, it is most suitable to consider properties of effect pigments which are quantified with as simple methods as possible. Although these efforts are by no means complete, some optical characteristics can be addressed, for example: – metallic value MV, this quantity is a measure of metallic brilliance; – flop index FI, this can quantify the lightness flop; – distinctiveness of image DOI, this property characterizes the covering capacity; – sparkle effect (microbrightness, glints, diamonds) describes the lightness impression caused by dominant reflecting particles; – graininess (coarseness, texture, structure, “salt and pepper”) is a quantity which is independent of sparkling. The degree of reflection caused by metallic particles in formulations is described by the so-called metallic value MV. This characteristic is determined by reflection measurements at two different angles: a plane sample, consisting of metallic pigments in a clear coat, is directionally illuminated at angle β = 45◦ with white light and reflectance R is measured at aspecular angles μas = 7◦ and μas = 45◦ [69].3 The illuminant type is actually unimportant; however, an LED is suitable with regard to emission constancy and long lifetime. The metallic value is calculated with the formula MV = 3 For angle

R(μas = 7◦ ) · 100. R(μas = 45◦ )

counting, see Section 4.1.2, Figs. 4.5 and 4.6.

(3.5.1)

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Because the specular reflectance is usually high for small aspecular angles μas , the quantity MV generally has values higher than 100. Experience shows that pigments of low metallic effect have metallic values of about MV = 150. The reasonable range extends to roughly MV = 5,000 for especially distinct metallic reflection behavior. The second property to characterize is the lightness flop. The reflection of metallic pigments typically decreases with increasing aspecular measuring angle μas , as already shown in Fig. 2.39, and correlating with CIELAB lightness L∗ . This behavior can be taken from Fig. 3.18. Accordingly, the lightness difference ΔL∗ between two extreme aspecular measuring angles can be regarded as a measure for the amount of lightness flop. For determination of the so-called flop index FI, the coating containing metallic pigments is illuminated under β = 45◦ and the lightness L∗ (μas ) is measured at three aspecular angles μas = 15◦ , 45◦ , and 110◦ . The value of the flop index follows from the empirical expression

FI = 2.69 ·

[L∗ (μas = 15◦ ) − L∗ (μas = 110◦ )] 1.11 [L∗ (μas = 45◦ )] 0.85

(3.5.2)

[70]. The flop index corresponds to the lightness difference at small and large aspecular angles L∗ (15◦as ) and L∗ (110◦as ), respectively, related to the lightness L∗ (45◦as ) at observation perpendicular to the surface of the coating. The numerator and denominator in Equation (3.5.2) are weighted with different exponents. Because the measured reflectance values are related to an absorbing and scattering white standard with reflectance of almost R = 1.0, metallics can show reflectance values of R > 1.0 not only at near specular angles; this also leads to lightness values higher than 100. By definition, a dark lightness flop corresponds to a high lightness difference between small and large aspecular observation direction angles. A light lightness flop is, however, characterized by a small lightness difference (Section 2.3.2). Standard metallic flakes of middle light flop show FI values in the domain 10 ≤ FI ≤ 20, high-quality brilliant formulations with metallic pigments of dark flop attain, however, FI values up to 60. As can be taken from the values listed in Fig. 3.18, in comparison to the change of lightness curves, the FI value is directly proportional to the lightness difference between small and large aspecular measuring angles. This corresponds to the numerator in Equation (3.5.2). From Fig. 3.18, it is to infer that the lightness value L∗ (25◦as ) at angle μas = 25◦ plays a central role – it shows values in the range 95 ≤ L∗ (25◦as ) ≤ 110. The curves seem to be slightly rotated at a point with rough coordinates (μas ≈ 25◦ , L∗ ≈ 100). The steeper the lightness curve in the vicinity of this point, the higher the corresponding FI value and the darker the lightness flop. Metallic pigments of high lightness flop index reach lightness values of L∗ (15◦as ) > 300 at small aspecular angles.

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203

103

L∗

β = 45°

Flop index 11.7 15.5 19.8 37.5 55.4

102

101 0

20

40

60

80

100

μas / o

Fig. 3.18 Lightness L∗ in dependence of aspecular measuring angle μas of metallic pigments with different flop indices

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It seems obvious to use similar considerations for characterization of the color flop index. For that, however, it is necessary to verify if there is a suitable additional formula structured like Equation (3.5.2) with chroma instead of lightness, but at the same aspecular angles and other weighting parameters. Additionally, we need to know if it is necessary to vary the angle of illumination. In each case, both extreme flop colors should be indicated together with the color flop index value(s). An additional property of metallic pigments which can be expressed numerically is the distinctiveness of image DOI, cf. Section 2.3.2. The DOI value more or less represents the uniformity of the visually perceived metallic effect and is correlated with the covering capacity of the metallic formulation. The determination of the DOI value is again carried out under an illumination angle β = 45◦ , the reflection measurement at an aspecular angle μas = 15.0◦ , and slightly varied angles μas = (15.0 ± 0.3)◦ . The source used is normally white light, but illuminations of other spectral composition in the visible range are also possible. The DOI value is given by one of the following relations: ! R(μas = 14.7◦ ) · 100, R(μas = 15.0◦ )

(3.5.3a)

! R(μas = 15.3◦ ) DOI = 1 − · 100 R(μas = 15.0◦ )

(3.5.3b)

DOI = 1 −

[71, 72]. For uniformly parallelized flakes, each of the reflection values in the numerator of both equations should be approximately the same. Both formulas (3.5.3a) and (3.5.3b) limit the DOI value domain to the interval 0 < DOI < 100. The higher the distinctiveness of image, the smaller the reflectance value in the numerator compared to the relative value R(μas = 15.0◦ ) in the denominator. Large-sized flakes show low DOI values, on the other hand, fine particles have high DOI values. These higher values indicate that minimal contrast differences are better reproduced. This property comes down to the smaller edge circumference and the smaller surface area of these flakes. Also high-contrast objects are better imaged against the surroundings by the reflections from the small-sized particles. Moreover, this method can also be applied for DOI determination of pearlescent and interference pigments. The DOI value is related to the covering capacity of a formulation with metallic and interference pigments. Both the sparkle effect and graininess of effect colorations are determined using directional light. Actually, sparkling depends on illumination and measuring angle, but in order to reduce the effort of measuring, three illumination angles of β v = 15◦ , – 45◦ , and –75◦ with respect to the normal to the surface are generally sufficient (the negative sign means that the angle is, as regards the normal, opposite to positive ones). Each of the measurements is performed at an

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205

angle μv = 0◦ with a digital CCD camera.4 The registered gray levels are processed as lightness values of the relevant effect coloration. For evaluation of the sparkle effect, two quantities are used: sparkling area Ask and sparkling intensity Isk . The sparkling area corresponds to the total area, which follows from the summation of each registered particle. But for agreement of the result with visual impression, the only reflecting particles taken into consideration are those lighter than the middle basic lightness of the actual coloration. On the other hand, the sparkling intensity Isk follows from the summation of all individually registered intensities. The sparkle effect is determined separately for each of the three measuring angles. For characterization of this phenomenon, the sparkle grade SG and sparkling intensity Isk are used. The sparkle grade is defined as the geometric mean of Isk and sparkling area Ask :  (3.5.4) SG = Isk · Ask . For an effect coating without any sparkle particles with Ask = 0, a sparkle grade of SG = 0 follows. Normal sparkling effect colorations of size 34 μm ≤ d50 ≤ 54 μm show illumination angle-dependent values in the interval 0 ≤ SG ≤ 10. In extreme cases, values up to SG = 30 at β v = 15◦ are attained. On the other hand, for a constant sparkle degree, if Isk is plotted against Ask , then variations in manufacturing or processing with empirical tolerance ellipses follow, those have limits of permissible variations ΔIsk and ΔAsk (for tolerance specifications, see Section 4.3.3). The sparkle grade of a fine and coarse gray effect coating at three illumination angles is listed in Table 3.13. Both colorations are visually perceived as identical. As expected, the sparkle grade decreases with higher value of illumination angle for both colors. This is because smaller particles reflect light in the direction of the sensor at more flat angles. On the other hand, the lower sparkle grade of the fine coloration continues to higher illumination angles. This behavior comes from the orientation distribution of the flakes, although the majority of the particles are orientated parallel to the coating surface. Because the appearance of graininess of a coating can be recognized only at a small distance from the coating’s surface, this property is independent of observation angle. The quantitative determination of this phenomenon is performed by measurement with diffuse illumination. Graininess is mainly seen out of direct daylight. In order to ascertain the graininess, the non-uniformity of the light/dark fields is evaluated. These fields are registered by the CCD chip as gray scales. The more non-uniform the fields appear, the higher the value of graininess Gr ≥ 0. A value Gr = 0 represents a coated area without discernible graininess. The value domain of real colorations extends to about Gr = 30. The 4 CCD: charge

coupled device

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Table 3.13 Sparkle grade and graininess value of fine and coarse, dark gray visual and colorimetric equal effect colorations [73] Sparkle grade SG at illumination angle β v Grain quality

15◦

– 45◦

–75◦

Graininess Gr

Fine Coarse

1.3 6.9

1.2 2.9

0.8 1.6

6.0 9.5

graininess values of the above fine and coarse effect colors are also indicated in Table 3.13. Altogether, it is important to emphasize that only recently introduced experimental methods of sparkle grade and graininess enable the accurate description of additional optical properties of effect colorations. The results are consistent and agree well with visual impressions. On the other hand, the entirety of measuring methods discussed in this section is only to be regarded as complementary to the usual angle-dependent color measurements of effect pigments.

3.5.2 Color Difference Equation for Metallics As already pointed out, the color difference formulas given in Sections 3.1.3, 3.1.4, 3.2.1, 3.2.2, 3.2.3, and 3.2.4 are only applicable to absorption colorants. For formulations with metallic or other flake-shaped pigments, it is necessary to additionally consider the angle-dependent, anisotropic reflection of such coatings. A color difference formula only for use in automotive coatings which contain metallic pigments is subject to a standard [30]. This standard is principally designed for refinishing paintwork and low-bake paints. Comprehensive color difference relations for other effect pigments have not been developed up until now. The need of such relations really depends on further use of those colorants. On the other hand, the change of the unusual color physical properties of such effect pigments can generally not be simply reduced to a color difference expression. For determination of color differences occurring with totally covering metallic colorations, the customary illumination angle of β = 45◦ and aspecular measuring angles μas = 15◦ , 25◦ , 45◦ , 75◦ , 110◦ are normally used. For simplicity, the index of the measuring angle is left out below. The measuring results should only be compared with each other if the sample and reference colors are of similar surface gloss and other colorimetrical requirements are the same for both. The reflectance measurement of a metallic coating is performed at about five different points of the plane patterns of the sample and reference coloration. From each of the resulting CIELAB color values of the sample color

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Chroma of Effect Pigments

207

LS∗ (μ), a∗S (μ), b∗S (μ) and the reference color LR∗ (μ), a∗R (μ), b∗R (μ), the arithmetic mean for each of the five measuring angles is taken. The calculated color difference contributions ΔL∗ (μ), Δa∗ (μ), Δb∗ (μ), ΔC∗ (μ), ΔH∗ (μ) lead to five angle-dependent color differences, denoted by ΔEeff (μ). If the coloration consists of both metallic and absorption pigments, then the color flop can be represented by two color loci which are possibly positioned in different areas of a color plane. In such cases, the local color differences are calculated with different formulas. In the mentioned standard, two extended color difference expressions for uncolored and colored colorations are given: ∗ (μ) < 10 as well as pas1. For achromatic colors with chroma values 0 ≤ Cab ∗ < 18 and lightness tel colors (of high “silver” or white content) of 0 ≤ Cab L∗ (μ) > 27, relation

(μ) ΔEab

 =

ΔL∗ (μ) gL SL (μ)



2 +

Δa∗ (μ) ga Sa



2 +

Δb∗ (μ) gb Sb

2 (3.5.5)

is applied. ∗ (μ) ≥ 10, but not including pastel colors, the 2. For chromatic colors with Cab formula (μ) ΔECH

 =

ΔL∗ (μ) gL SL (μ)



2 +

ΔC∗ (μ) gC SC (μ)



2 +

ΔH ∗ (μ) gH SH (μ)

2 (3.5.6)

is valid. The visually tolerated color difference for chromatic metallic formulations is non-uniform as well. This is already known for absorption colors or colored lights. This conclusion is particularly clear for dark and pastel shades. The values of the empirical weighting factors gL , ga , . . . , gH in Equation (3.5.6) are given in Table 3.14 for different manufacturing steps. The correction functions SL , Sa , . . . , SH in Equations (3.5.5) and (3.5.6) follow also from the assessment of color collections:   (3.5.7) SL (μ) = 0.15 L(μ) + (31.5◦ μ), Sa = Sb = 0.7,    SC (μ) = max [0.7; 0.48 C(μ) − 0.35 L(μ) + (42◦ μ)],    SH (μ) = max [0.7; 0.14 C(μ) − 0.2 L(μ) + (21◦ μ) + 0.7],

(3.5.8) (3.5.9) (3.5.10)

where L(μ) is the geometric mean of the lightness values of the sample color LS∗ (μ) and reference color LR∗ (μ), each at the same measuring angle μ:

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Table 3.14 Empirical weighting factors for color differences in Equations (3.5.5) and (3.5.6) Empirical weighting factors Condition

gL

ga

gb

gC

gH

Delivery First paint coating, refinishing paint, low-bake paint

1.0 2.0

1.0 1.2

1.0 1.2

1.0 1.8

1.0 1.2

L(μ) =



LS∗ (μ) · LR∗ (μ).

(3.5.11)

Also the function C(μ) is given by a geometric average, now of the chroma of the sample CS∗ (μ) and the reference color CR∗ (μ): C(μ) =

 CS∗ (μ) · CR∗ (μ).

(3.5.12)

Concerning the correction functions (3.5.9) and (3.5.10), it is important to point out that, at first, the calculation is based on the algebraic expression. If the calculated value is less than 0.7, then it is set to 0.7, otherwise the relevant value ≥ 0.7 is inserted into Equation (3.5.6). At the switchover between the above-mentioned color areas, discontinuous color differences follow from Equations (3.5.5) to (3.5.6). This discontinuity issue is rectified using the Fermi function σ (μ). It is based on Equation (6.3.21) and given as σ (μ) =

1 1 + e[C(μ)−C0 (μ)]

,

(3.5.13)

where C0 (γ ) = 10 +

8 27−L(γ )] [ 1+e

(3.5.14)

is another angle-dependent correction function. The value domain of σ (γ ) is limited to the interval [0,1], cf. Fig. 6.18. The single valuedness of σ (μ) depends ∗ (μ) on the chroma value Cab  σ (μ) =

∗ (μ) >> 10 0 for Cab ∗ (μ) << 10 . 1 for Cab

(3.5.15)

The finite color difference ΔEeff (μ) for each measuring angle μ is calculated using Equations (3.5.4) and (3.5.5) from the function

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Chroma of Effect Pigments

209

ΔEeff (μ) = σ (μ) · ΔEab (μ) + [1 − σ (μ)] · ΔECH (μ).

(3.5.16)

With this adjustment, the color difference ΔEeff (μ) changes continuously between quantities ΔEab (μ) and ΔECH (μ). This follows immediately from Equation (3.5.16), given the relation  ΔEeff (μ) =

(μ) for σ (μ) = 1 ΔEab . ΔECH (μ) for σ (μ) = 0

(3.5.17)

Delivered and also first paint effect coatings should have a color difference of ΔED (μ) ≤ 1.0 in comparison to a reference coating, cf. Table 3.6. For paint refinishing or low-bake paints, the color difference between adjoining body panels should not exceed the value of ΔEP (μ) = 1.5. In cases of body shell apertures separated by body flanges, slats, or gaps, the standard permits a color difference of ΔEP (μ) ≤ 3.0, but this tolerance is generally much too high and it should be kept to ≤ 2.0 and for dark metallic paints down to ≤ 1.0. The angle-dependent color difference of matched metallic colors is, however, still not a comprehensive criterion for the quality of the matching. The color difference value of ΔE(μ) is rather an evaluation measure for a discernable color difference. It leaves additional specific metallic properties unaddressed, which are often the most characteristic for the actual coloration. The working out of effect colorations succeeds, as experience shows, with coloristical feeling; see Section 6.3.5, among other things. The optical behavior of pearlescent, interference, and diffraction pigments results in a host of novel color appearances. These can still be increased and improved by mixtures with absorption colorants. The change of the chroma of natural effect pigments and of different mixtures in dependence on layer thickness, illumination, and observation angle are topics of the next sections.

3.5.3 Chroma of Pearlesence and Interference Pigments Whereas some typical properties of metallic pigments can be described by the colorimetrical lightness, this quality is of minor importance for the description of the color appearance of pearl luster, interference, or diffraction pigments. The dominant color properties of such effect colorants are rather described by the colorimetrical quantities of chroma, hue, or hue angle. As already discussed in Sections 2.1 and 2.3, interference and diffraction colors depend on the refractive index, especially of each single layer thickness, as well as the illumination and observation angle. The dependence of interference colors on layer thickness is simply demonstrated with pearlescent pigments of muscovite substrate evaporated with TiO2

210

3

Standardized Tristimulus Values, Color Qualities, Chroma of Effect Pigments

or Fe2 O3 . The similar color physical behavior of both pearl luster types follow not only from Figs. 2.46 and 2.48 but also from corresponding curves in an a∗ , b∗ color plane. The meaning of such, generally called chroma curves, is explained in the following. Figure 3.19 represents the chroma curves for different layer thickness of the above-mentioned pearl luster pigments determined by diffuse illumination and directional measurement. The layer thickness increases in the clockwise direction. In the case of TiO2 layers, this corresponds to the given quantities and colors in Table 2.15. The chroma curve of the TiO2 pigment sweeps almost over all four quadrants, whereas the chroma curve of flakes with hematite layers nearly remains in the first quadrant. This second curve represents colors which change from yellow to “golden” to rust colored. To manufacture a needed intermediate color, the accompanying thickness of the metal-oxide layer can be estimated from the corresponding chroma curve. Each of the chroma curves represents a special color build-up. This build-up describes the interference colors in dependence on the evaporated layer thickness. For further increases in the layer thickness, each curve extends as a spiral which ends, due to increasing absorption, in the vicinity of the achromatic point. For constant layer thickness, directional illumination, and directional measuring, however, two sorts of chroma curves result. Those are due to a change of illumination or measuring angle β and μ, respectively [74, 75]. The measuring conditions are characterized by the standardized angle direction as indicated b∗ 40 TiO2

Fe2O3

20

0

–20

–40

–40

–20

0

20

∗ 40 a

Fig. 3.19 Chroma curves of mica pigments coated with rutile TiO2 or α-Fe2 O3 ; the layer thickness increases in the clockwise direction; the color values a∗ , b∗ are determined from spectral values shown in Figs. 2.46 and 2.48; measuring geometry de:8, standard illuminant D65, 10◦ standard observer

3.5

Chroma of Effect Pigments

211

in Fig. 4.4: the illumination angle β v is counted from the vertical to the illuminated surface and the measuring angle μas from the direction of the specular reflected beam. Measuring angles are positive signed in direction of the source – the aspecular direction – negative otherwise. According to the nomenclature in Section 4.1.2, this corresponds to the measuring geometry indicated by β v /μas . Both of the above-mentioned types of chroma curves are determined by the following measuring conditions: 1. β v is a variable and μas is kept constant; the interference colors change in dependence on β v along a so-called interference line; 2. β v is kept constant and μas is varied; the accompanying interference colors vary in dependence on measuring μas along a so-called effect line or aspecular line. The following chroma curves result from reflectance measurements over a black background using standard illuminant D65 and 10◦ standard observer. The first example in Fig. 3.20, this one for a blue pearlescent pigment, shows one interference line for constant measuring angle μas = 15◦ and two aspecular lines at constant illumination angles β v = 45◦ and β v = 65◦ , respectively. The starting points of the effect lines are located on the interference line, the respective end points for β v = 45◦ /μas = 65◦ and β v = 65◦ /μas = 70◦ are in the vicinity of the achromatic point. The effect line corresponding to β v = 65◦ represents a change ∗ ≈ 100. The interference line represents a color change in chroma of about ΔCab from violet blue at 65◦ /15◦ to turquoise at 20◦ /15◦ . The configuration of the three chroma curves in Fig. 3.20 is reminiscent of the projection from the side of a surfboard (interference line) with a stretched sail (restricted by both effect lines); the head seems to “hang in” in the neighborhood of the achromatic point. The greatest possible surface patch of the color area enclosed by the interference and aspecular lines can be interpreted as a kind of chroma potential of the corresponding interference colorant. The chroma curves in Fig. 3.20 are limited only by special construction of the illumination and measuring unit. Similarly shaped interference and aspecular lines are shown in Fig. 3.21 for an interference pigment consisting of a SiO2 substrate coated with TiO2 . A typical cross section of such particles is shown in the SEM picture in Fig. 2.44b. For the aspecular line at constant measuring angle μas = 15◦ , the color of this pigment changes from purple to weak red to green. In the end, the interference line traverses three quadrants of a color plane. Each effect line begins for small illumination angle at the interference line and ends again in the vicinity of the achromatic point. Compared to that of Fig. 3.20, the entire graphical plot seems rotated around the achromatic axis and simultaneously reduced in size. The situation is the same for transparent liquid crystal pigments as depicted in Fig. 3.22: the interference line is simply more curved and the “surfboard” stands on sail top.

212

3

Standardized Tristimulus Values, Color Qualities, Chroma of Effect Pigments b∗

45°/65°

65°/70°

Effect line 45° = const. –40

Effect line 65° = const.

45°/20° 20°/15° 45°/15°

65°/20°

–80

Interference line 15° = const. 65°/15° –120 –40

0

a∗

40

Fig. 3.20 Interference line with β v = 15◦ and two effect lines with μas = 45◦ , 65◦ of the blue pearl luster pigment in Fig. 2.46, curve (e) b∗ 40

20

65°/15°

0

45°/65° 45°/15° 65°/70°

–20

–40

20°/15° –40

–20

0

20

40 a∗

Fig. 3.21 Interference line and two effect lines of a combination pigment with titaniumdioxide/silicon-dioxide/mica layers; see Fig. 2.40

The mutual configuration of the chroma curves is maintained for opaque multi-layered pigments as can be seen in the next two plots. The interference line for the Al pigment coated with SiO2 and Fe2 O3 with β v = 15◦ in Fig. 3.23

3.5

Chroma of Effect Pigments

213

b∗ 100

80

45°/15°

60 40

20°/15° 20

65°/15° 65°/70° 45°/65°

0 –20 –80

–60

–40

–20

0

20

40

a∗

Fig. 3.22 Interference line and two effect lines of a liquid crystalline interference pigment b∗ 80

65°/15°

60

40

45°/15°

65°/70°

20

45°/65° 0

20°/15°

–20 –40 –40

–20

0

20

40

60

80

a∗

Fig. 3.23 Interference line and two effect lines of an iron-III-oxide/silicon dioxide multilayered interference pigment

actually covers only two quadrants, the interference color changes from deep red to light yellow. As seen in Fig. 3.24, the interference line produced from the Al pigment – now evaporated with MgF2 and Cr – takes a big swing and travels

214

3

Standardized Tristimulus Values, Color Qualities, Chroma of Effect Pigments

b∗ 80 65°/15° 40 20°/15°

45°/65°

65°/70°

0

–40

45°/15°

–80

–120 –120

–80

–40

0

40

80

a∗

Fig. 3.24 Interference line and two effect lines of an optical variable green/purple multilayered interference pigment; see Fig. 2.41 and Color plate 9

through all four quadrants! It represents a color travel from green over blue and red to orange (cf. the corresponding light microscopic pictures in Color plate 9). The layer thicknesses of such multi-layer particles, which vary merely some ∗ ≈ 115 combined nanometers, produce a remarkably high chroma of about Cab with an extreme color flop. In summary, it should be emphasized that, from topological point of view, equal chroma curves are produced from pearl luster and different sorts of interference pigments. The interference and effect lines are rotated in a characteristic manner around the achromatic axis and contracted or stretched. Clearly, the color travel of such interference pigments includes the more colors, the greater the number of quadrants which are traversed by the interference line. Altogether, it is to conclude that not only absorption pigments can be described by chroma curves but also the impressive color travel of chromatic effect pigments. The chroma results are in agreement with visual perception.

3.5.4 Mixtures of Effect Pigments From mixtures of effect colorants with other effect colorants or with absorption pigments, it is possible to obtain additional new color shades. For two colorants, this results in hues somewhere between those of the natural colors of the involved colorants. The types of the resulting color mixing of some pigment combinations are listed in Table 2.17. If pearlescent or interference pigments of complementary natural colors are mixed, then – at perpendicular observation –

3.5

Chroma of Effect Pigments

215

no white is produced. Instead, a gray results; this is caused by edge scattering of the particles. This achromatic color depends on the d50 value and the particle size distribution. The smaller the particles and broader the size distribution the darker the gray. To begin with, we discuss homologous multi-layered interference pigments of aluminum substrate and layer composition Cr/MgF2 /Al/ . . . /Cr, which differ only with regard to the magnesium fluoride layer thickness. Consequently, each pigment of this series shows a color travel with systematically altered extreme colors. Such a type of interference particles is shown in Color plate 9. The colored flop of this pigment travels between the extreme colors of green to purple. In bright-field illumination, the pigments aligned parallel to the image plane appear green or nearly turquoise, the purple ones are tilted. The same image detail shows only the purple flop color at higher observation angles in darkfield illumination. This color then dominates, because the particles are laterally illuminated but observed perpendicularly. For dark-field illumination, the morphology and the edges of the particles are much easier to distinguish than in bright-field observation. The colorimetric measurements for seven natural interference pigments of the above-mentioned layer composition were performed over a black background with diffuse geometry de:8. The evaluation was performed as described in the previous section. The color locus of each of the seven pigments is represented in Fig. 3.25 with an open circle. The indicated color pairs correspond to the extreme flop colors of the respective pigment. Starting at the color locus of the silver/green in direction of the green/purple pigment, the thickness of the MgF2 layer evaporated on the Al substrate increases in the clockwise direction through all other points. This curve again traces out a clockwise spiral and seems to be the contour of a nautilus swimming to the right. On the basis of only slight thickness fluctuations of the relevant evaporated layer thickness, the chroma values of the present interference pigments in Fig. 3.25 are always higher than those of pearlescent pigments with mica substrate, cf. Fig. 3.19. The color locus of mixtures produced by two neighboring natural pigments always traces out a straight line between both initial points as seen in Fig. 3.26 [77]. This indicates additive color mixture. The spiral shown in Fig. 3.25 is, for better overview, not included in Fig. 3.26. It is not surprising that mixtures of homologue pearl luster pigments show an analogous behavior under the same measuring conditions, as we will see below. On the other hand, mixtures of the cyan/purple interference and a red absorption pigment produce under directional illumination and measuring conditions the results represented in Fig. 3.27. The original interference line, already known from Fig. 3.24, decreases with increasing red pigment content and converges to the color locus of the absorption pigment (subtractive color mixture). Similarly mixtures of pearlescent and absorption pigments behave as discussed below.

216

3

Standardized Tristimulus Values, Color Qualities, Chroma of Effect Pigments b∗ 80

Gold/Silver

40 Silver/Green

Green/Purple 0

Red/ Gold –40

Cyan/ Purple Purple/ Orange

Blue/ Red –80

–40

–20

0

40 a∗

20

Fig. 3.25 Color locus of seven interference pigments composed of Cr/MgF2 /Al/MgF2 /Cr with different MgF2 -layer thicknesses; the thickness increases in the clockwise direction b∗ 80 Gold/Silver 40 Silver/Green Red/ Gold

0 Green/ Purple Cyan/ Purple –40 Blue/ Red

Magenta/ Gold Purple/ Orange

–80

–40

–20

0

20

40 a∗

Fig. 3.26 Color locus of mixtures with eight interference pigments composed of Cr/MgF2 /Al/MgF2 /Cr layer of different MgF2 -layer thicknesses

Although the interference and effect lines are suitable for the visualization of the angle-dependent color development of effect pigments, the measurements are actually quite extravagant to perform. For a relevant and colorimetric

3.5

Chroma of Effect Pigments

217

b∗

80

100/0

Interference/ Absorption Pigment

90/10 40 70/30 0

–40

–80

–120 –120

–80

–40

0

40

80

a∗

Fig. 3.27 Interference lines of the optical variable multi-layered interference pigment of Fig. 3.24 with three different amounts of a red quinacridone pigment

identification of such colorants in mixtures, it is not advisable to determine the total slope of the relevant interference line and effect lines. It is more reasonable to simply apply an abbreviated measuring procedure. From extensive investigations, it follows that the eight measuring geometries listed in Table 3.15 are sufficient for this. The angle combinations are already subject to standards [78–81]. As an example of the reduced measuring method, we discuss now mixtures of the blue pearlescent pigment characterized in Fig. 3.20, a blue absorption

Table 3.15 Standardized measuring geometries for characterization of interference pigments or mixtures with other sorts of colorants [78–81] Illumination angle β v /degree

Aspecular measuring angle μas /degree

Interference line

15 15 45

15 –15 –15

Effect line

45

15 25 45 75 110

Chroma curve

218

3

Standardized Tristimulus Values, Color Qualities, Chroma of Effect Pigments

pigment, and a silver dollar aluminum pigment. The content of the blue absorption pigment is kept constant at a fraction of 60% in three of the four following mixtures. The shortened interference and effect line forms a so-called anchor curve [82].

3.5.4.1 Pearl Luster with Absorption Pigment In Fig. 3.28, five anchor curves are plotted. The curve parameters indicate the mixing ratio of pearl luster/absorption pigment for constant pigment loading. For simplicity, the measurement for μas = –15◦ has been left out. One endpoint of each effect line tends to the color point of the blue absorption pigment. At these coordinates, the effect and the interference lines vanish. On the other hand, both line lengths increase with increasing content of the pearl pigment. The interference line section of the natural pearl luster pigment (100/0) falls out from the family of the parallel interference lines. This is caused by the measurement of the transparent natural pearlescent pigment over a black background (cf. Fig. 3.20). The endpoint of the accompanying effect line at an angle μas = 110◦ , therefore, does not agree with the color point of the natural colored pigment. Already for a slight fraction of absorption pigment, the coloration becomes opaque. This is the reason why the anchor curves then change systematically. From such mixtures of pearl and absorption pigments, these are the following colorimetric properties:

b∗

–20

0/100

–40 100/0 20/80

–60

40/60 –80

60/40 80/20

–100 –80

–60

–40

–20

0

a∗

Fig. 3.28 Anchor curves of mixtures with a blue pearl luster and blue absorption pigment; the ratio of pearlescent to absorption pigment content is indicated

3.5

Chroma of Effect Pigments

219

a. the sections of the interference line behave nearly parallel to one another in dependence on concentration of the chromatic pigment; b. for low concentration of the absorption colorant, the effect line of β = 45◦ tends to reach the color locus of the absorption colorant; c. the lengths of the interference and effect lines decrease simultaneously with increasing colored pigment content; both lines vanish in the color point of this pigment; d. the endpoints of the effect lines for a measuring angle of μas = 110◦ are located on a spiral segment between the color points of both natural pigments. 3.5.4.2 Aluminum Flakes with Absorption Pigment Colorant mixtures of a silver dollar aluminum pigment with the same blue absorption pigment as above result in an altered colorimetrical behavior. The results in Fig. 3.29 essentially come down to the presence of the stacked metallic flakes. The anchor curves can be characterized as follows: a. the sections of the reduced interference lines have almost the same slope as the adjacent effect line; b. the distance between effect lines increases with increasing content of aluminum pigment; c. in addition, for both lines the conclusions in Section 3.5.4.1 (b) – (d) hold. b∗

100/0

–20

0/100 80/20

–40

60/40 –60

20/80

40/60

–80

–100 –80

–60

–40

–20

0

a∗

Fig. 3.29 Anchor curves of mixtures with a silver dollar blue pearl luster and blue absorption pigment; the ratio of metallic to chromatic pigment content is indicated

220

3

Standardized Tristimulus Values, Color Qualities, Chroma of Effect Pigments

Such distinguishing colorimetrical features enable one to discern mixtures of aluminum with colored pigments from mixtures with other effect pigments. 3.5.4.3 Interference with Metallic Pigment Some of the previously mentioned colorimetric features become more clearly evident from mixtures of the blue pearlescent and the silver dollar aluminum pigment. From the family of anchor curves in Fig. 3.30, which are now characterized by the fractions of the pearl and metallic pigment, it is possible to list the following characteristics: a. the mean slope of the interference lines changes in dependence on the metallic pigment concentration; b. independent of the concentration of the metallic pigment, the initial slope of the effect lines remains constant; c. for both lines, the properties mentioned in Section 3.5.4.1 (c), (d) remain valid, but where the term colored pigment is substituted by metallic pigment. b∗

0/100

20/80 40/60

–20

60/40 80/20 –40

100/0 –60

–80

–100 –80

–60

–40

–20

0

a∗

Fig. 3.30 Anchor curves of mixtures with a blue interference and an aluminum pigment; the ratio of interference to aluminum pigment content is indicated

3.5.4.4 Interference, Metallic, and Absorption Pigments Each of the measured mixtures now contains 60 proportions of the blue absorption pigment. As seen from the form of the anchor curves in Fig. 3.31 and from comparison with the results of the previous three mixtures, the colorimetrical

3.5

Chroma of Effect Pigments

221

b∗

–20

–40 0/40 20/20

–60

30/10 38/2

40/0

–80

–100 –80

–60

–40

–20

0

a∗

Fig. 3.31 Anchor curves of mixtures with three colorants: blue pearl luster, aluminum cornflake, and blue absorption pigment; the ratio of pearlescent to effect pigment content is given; each mixture contains 60 parts of the same blue absorption pigment

behavior of the mixtures is predominantly controlled by the aluminum and blue absorption pigments. On the one hand, again the endpoints of the effect lines for μas = 110◦ tend toward the color point of the colored pigment; on the other hand, the interference lines turn with increasing aluminum content into that direction, which corresponds to the initial slope of the adjacent effect line for μas = 15◦ , cf. Fig. 3.29. In addition, one can observe in Fig. 3.31 that the anchor hooks come close to this initial slope with increasing concentration of the pearlescent pigment. From investigations with other effect and absorption pigments, similar shaped chroma curves follow [82]. To summarize, the abbreviated method of anchor curves produces new insight into the colorimetrical behavior of various pigment mixtures. This procedure is not, however, suitable for quantitative or qualitative analysis of real mixtures with different pigment sorts as demanded. The light microscopic procedure as part of expert system remains more practical for this purpose (Section 6.3.5).

3.5.5 Color Development of Diffraction Pigments Diffraction pigments based on grating structures and groove geometries are the most complex to produce effect pigments (Section 2.3.8). The grating geometry establishes the number of observable diffraction orders and the degree of

222

3

Standardized Tristimulus Values, Color Qualities, Chroma of Effect Pigments

optical efficiency or brilliance. Now, we consider the angle-dependent chroma of diffraction pigments with a linear sine-shaped groove cross section and grating constants of 1,000 and 1,400 l/mm (l/mm meaning lines/mm) [82, 83]. As we will see, the chroma curves of diffraction pigments differ considerably from those of interference pigments regarding the effect line. The angle-dependent chroma curves in the following are determined with a special gonio spectrophotometer. This device allows for an illumination angle of β = 45◦ and adjustment of the measuring aspecular angle in steps as small as Δμ = 1◦ in the interval –35◦ ≤ μas ≤ 78◦ . Each of the samples is in optical contact with the same black background. The resulting CIELAB color values a∗ and b∗ belong to standard illuminant D65 and 10◦ standard observer. The change of lightness in this case – similar to interference pigments – is not being considered here, but rather the color development. First, we follow the chroma change of simple structured particles with symmetrical permutation of layers of MgF2 /Al/MgF2 and grating constant of 1,000 l/mm. The corresponding angle-dependent effect line is shown in Fig. 3.32. It runs clockwise from μas = –35◦ in the vicinity of the achromatic point to μas = +78◦ the diffraction orders z = 0, 1, 2. Between angles μas = –35◦ and μas = +15◦ , the chroma has a kind of hairpin bend; the sharply shaped chroma maximum corresponds to a specular angle μas = 0◦ . The angle range 15◦ ≤ μas ≤ 50◦ belongs to the diffraction order z = 1. The accompanying section of the chroma curve traces out a kind of ellipse centered near the achromatic point. A following “ellipse” corresponds to the second diffraction order z = 2; it ends for a measuring angle μas = 78◦ in the neighborhood of the achromatic point. Higher orders, z > 2, are of quite low luminosity and, due to the technically limited angle adjustment, are not measured. The curve shape in Fig. 3.32 looks altogether like an “unfinished treble clef.” Each diffraction order contains all wavelengths emitted by the applied source, which for a reflecting grating are given by Equation (2.1.24) in dependence of diffraction angle. Correspondingly, in the case of the xenon discharge lamp used, the chroma curve section of each diffraction order z > 0 extends over all four quadrants of the color plane. Because the intensity of the higher diffraction orders decreases quickly (Fig. 2.21), the accompanying chroma becomes also smaller. The spectra of higher orders tend, therefore, to achromatic colors. With increased diffraction order, the chroma curve always traces out smaller “ellipses” until these vanish in the achromatic point. If the illumination angle is increased with respect to the normal of the sample, then the chroma maximum at the specular angle shifts nearer to the start of the curve for μas = –35◦ . The corresponding height of the chroma maximum reduces due to increasing scattering at the grooves and the edges of the particles. However, the chroma curve in Fig. 3.32 includes the majority of the second diffraction order. This indicates that the grating geometry is not optimized because the intensities of the first two orders are each lowered by the higher orders.

3.5

Chroma of Effect Pigments

223

∗ b

0°

40 10° –10° 20

40°

– 20°

78°

60°

0 30°

– 35°

20°

50° –20 –20

–10

0

10

a

∗

Fig. 3.32 Chroma curve respective effect line representing diffraction orders z = 0, 1, 2 of a two-layered pigment; illumination angle β = 45◦ ; parameter is the measuring angle with regard to the specular angle; grating constant 1,000 l/mm

However, in the range until the limiting measuring angle μas = 78◦ , the optimized diffraction particles with linear grating constant of 1,400 l/mm and sine-shaped groove cross section produce a chroma curve, which does not contain the order z = 2, cf. Fig. 3.33. This conclusion is also true for extrapolation to higher measuring angles on account of the curve sections always being smaller for higher angle decades to a maximum of μas = 135◦ . In comparison to the pigment with 1,000 l/mm, the curve section for z = 1 in Fig. 3.33 shows a chroma about double: the intensities of the order z = 0 and z ≥ 2 are mostly transferred to the diffraction spectrum for z = 1. This is achieved by the realized blaze technique for the present diffraction particles (Section 2.1.7). Particles consisting of right-angled crossed groove structure, each of 1,400 l/mm with sine-shaped groove cross section, produce the chroma curve shown in Fig. 3.34. The undeflected (zeroth) order and first diffracted order have lower chroma values than the linear grating of same grating constant compared to Fig. 3.33. This behavior is caused by mutually perpendicular crossed √ grooves, with which an additional grating constant of g˜ = (1,400/ 2) l/mm = 990 l/mm is introduced. Whereas the chroma of diffraction order z = 0 is nearly

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b∗ Linear

40

0°

50°

–10°

10°

60°

20 –20°

0

–35° 20°

–20

70°

40° 78°

30°

–40

–20

–10

0

10

20

a∗

Fig. 3.33 Chroma curve of an optimized linear sine-shaped diffraction pigment; grating constant 1,400 l/mm

the same as in Fig. 3.33, the new grating constant reduces the chroma of the higher orders in magnitude comparable to Fig. 3.32 for grating constant of 1,000 l/mm. Moreover, the combined perpendicular and diagonal grating structures produce an azimuthal anisotropy of chroma, which shows a periodicity of 45◦ for rotation of the sample vertical to its surface [83]. An increased linear grating constant of 3,000 l/mm leads, however, to a reduced chroma; in the chroma curves (not shown), the different diffraction orders are barely distinguishable. The reason for this is the more closely crowded grooves: at the edges and corners the light is increasingly scattered so that the remaining light intensity for diffraction is weakened. In addition, small-sized grating particles reduce the chroma caused by increased light scattering at the particle edges. Though it is inappropriate to arbitrarily extend the dimensions for the given pigments of d50 = 20 ± 2 μm, because the smaller groove distances lead to a stronger notch effect of the brittle particles. Such pigments are, depending on application method or processing, subject to increased mechanical degradation. Mixtures of diffraction pigments with other effect or absorption colorants have not been described in literature until now. On the basis of the correspond-

3.5

Chroma of Effect Pigments

225

b∗ Crossed 40

0° 10°

–10°

20 –20°

50° 20° –35° 0 70°

78° 40°

–20

30°

–40

–20

–10

0

10

20

a∗

Fig. 3.34 Chroma curve of a linear diffraction pigment with perpendicular crossed grooves; grating constant in both directions 1,400 l/mm

ing insight with interference pigments it is, however, sufficient to regard only the first-order diffraction and to estimate the chroma changes in dependence on the further added colorant fractions. With increased content of the additional pigment, the “diffraction ellipse” decreases and is pulled back into the color locus of the contained absorption or metallic pigment. As already discussed in Section 2.3.5, the optical anisotropy of diffraction pigments is additionally influenced by a substrate consisting of a ferromagnetic material such as nickel, for example. In a magnetic field, the grooves of elongated grating particles orient parallel to the lines of the field. If the particles are simultaneously subject to a shear gradient parallel to the direction of the magnetic field, then this alignment is preferentially fixed during crosslinking time of the binder. The particles are orientated similar to a smectic texture (Fig. 2.42). Ferromagnetic diffraction pigments of symmetrical permutation of layers MgF2 /Al/Ni/Al/MgF2 with a 400 nm thick coating of magnesium fluoride and linear grating constant of 1,400 l/mm appear brilliant metallic under diffuse illumination. With directional illumination however, these particles develop an

226

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impressive chroma. This chroma depends on the orientation of the grooves perpendicular or parallel to the optical measuring plane. The optical measuring plane is built from the illuminating and measuring beam. In the case of grooves preferentially oriented normal to the measuring plane, ∗ ≈ the first diffraction order shows an increased maximal chroma of about Cab 85 at an orange color of high brilliance; see outer curve in Fig. 3.35. In this alignment, the particles enhance the diffraction effect. This conclusion is clear by comparing Fig. 3.33: for the ferromagnetic pigment, the chroma values of the first diffraction order are in the domain 30◦ ≤ μas ≤ 78◦ . This is more than two times greater than that of the previously optimized non-ferromagnetic pigment. The chroma scale between both pigment orientations can be influenced by magnet field strength and exposure time. However, if the grooves are aligned parallel to the measuring plane, then the previous brilliant chroma development is almost lost. This is represented by the inner curve in Fig. 3.35. This chroma curve is shrunk. Only the specular color can be identified and the chroma of the first diffraction order degenerates to achromatic. Because the influx is oriented parallel to the grooves and not in the normal direction, nearly no real diffraction develops. In this case, the b∗ Measuring plane normal parallel

80

60°

0° 40

10° 50°

–10° –20°

20°

–35°

0

70°

30° –40 78°

–80 40°

–120 –60

–40

–20

0

20

40

a∗

Fig. 3.35 Chroma curves of a three-layered ferromagnetic diffraction pigment; grating grooves perpendicular and parallel to the measuring plane; grating constant 1,400 l/mm

3.5

Chroma of Effect Pigments

227

incident light is attenuated by the covering MgF2 and essentially reflected off the aluminum layer. For diffuse illumination and right angle observation, ferromagnetic diffraction pigments with an additional cover layer of chromium Cr/MgF2 /Al/Ni/. . ./. . ./Cr produce a yellow-golden color impression. For directional illumination and measuring, however, the accompanying chroma curve changes dramatically, if the grooves are normal to the measuring plane, as can be seen in Fig. 3.36. Both particle alignments produce no “ellipses” around the achromatic point; furthermore, the chroma curves travel through at least two adjacent quadrants. This means that the zero and first diffraction orders are missing corresponding colors such as yellow-green, green, or blue. In the case where the grooves are normal to the measuring plane, the color impression oscillates with increased measuring angle only between yellow to orange-red to red-violet with increasing chroma. This particle alignment acts as an interference filter for blue to yellow-green wavelengths caused by the reflecting chromium and aluminum layers spaced by dielectric MgF2 , cf. Fig. 2.18. With the alignment parallel to the measuring plane, the first diffraction order is degenerated again near the achromatic point. This particle orientation behaves b∗

Measuring plane normal parallel

60

0° 60°

0° –10°

40

10°

–20°

–30° 20

–35°

50° 20°

–35°

70° 30°

78°

0

30°

78°

–20 40° –20

0

20

40

60

a∗

Fig. 3.36 Chroma curves of a four-layered ferromagnetic diffraction pigment; grating grooves perpendicular and parallel to the measuring plane; grating constant 1,400 l/mm

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like a dielectric mirror with a specular color of orange red. The brilliance and the diffraction colors as well as the filtered or reflected wavelengths are influenced by the thickness of the nonmetallic layer and the grating structure. To complete this picture, diffraction and interference are superimposed for these pigments and this gives rise to the extreme chroma curves restricted to the first quadrant of the color plane in Fig. 3.36. With the above description of ferromagnetic diffraction pigments, we finish the colorimetrical characterization of some special color physical properties of both absorption and effect colorants. The fact that the color development of effect colorants, which changes with illumination and observation angle, is mainly reproduced by different chroma curves is actually quite astonishing. However, the necessarily large extent of measuring brings a degree of impracticality. On the other hand, the methods for detailed coloristical description of colorations with flake-shaped effect pigments are by no means completed.

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19. CIE No 101: “Parametric Effects in Colour-Difference Evaluation”, CIE, Bureau Central de la CIE, Wien (1993) 20. Luo, MR, Cui, G, Rigg, B: “The development of the CIE 2000 colour difference formula: CIEDE2000”, Col Res Appl 26 (2001) 340 21. Chou, W, Lin, H, Luo, MR, Westland, S, Rigg, B, Nobbs, J: “Performance of lightness difference formulae”, Coloration Techn 117 (2001) 19 22. CIE No 142: “Improvement to Industrial Colour-Difference Evaluation”, Commission Internationale de L’Éclairage (CIE), Bureau Central de la CIE, Wien (2001) 23. Witt, K: “CIE color difference metrics”, in: Schanda, J, ed.: “Colorimetry: Understanding the CIE System”, Wiley, Hoboken, NJ (2007) 24. ASTM D 2244: “Standard Practice for Calculation of Color Tolerances and Color Differences from Instrumentally Measured Color Coordinates”, American Society for Testing and Materials, West Conshohocken, PA (2005) 25. Fairchild, MD: “Colour Appearance Models”, 2nd ed., repr, Wiley, Chichester (2006) 26. Luo, MR, Li, CJ: “CIE Colour Appearance Models and associated Colour Spaces”, in: Schanda, J, ed.: “Colorimetry: Understandig the CIE System”, Wiley, Hoboken, NJ (2007) 27. CIE No 159: “A colour appearance model for colour management systems: CIECAM02”, Commission Internationale de L’Éclairage (CIE), Bureau Central de la CIE, Wien (2004) 28. Luo, MR, Cui, GH, Li, CJ, Rigg, B: “Uniform color spaces based on CIECAM02 colour appearance model”, Col Res Appl 31 (2006) 320 29. DIN 6175-1: “Farbtoleranzen fuer Automobillackierungen”, part 1: “Toleranzen fuer Unilackierungen”, Deutsches Institut fuer Normung eV, Berlin (1986) 30. DIN 6175-2: “Farbtoleranzen fuer Automobillackierungen”, part 2: “Toleranzen fuer Effektlackierungen”, Deutsches Institut fuer Normung eV, Berlin (2001) 31. McDonald, R: “A Review of the Relationship between Visual and Instrumental Assessments of Colour Difference, Part I, II”, J Oil Col Chem Assoc 65 (1982) 43–53, 93–106 32. DIN Fachbericht 49: “Verfahren zur Vereinbarung von Farbtoleranzen”, Deutsches Institut fuer Normung eV, Berlin (1995) 33. ASTM D 3134–97(2008)e1: “Standard Practice for Establishing Color and Gloss Tolerances”, American Society for Testing and Materials, West Conshohocken, PA (2008) 34. ASTM E 1499–97(2003): “Standard Guide for Selection, Evaluation, and Training of Observers”, American Society for Testing and Materials, West Conshohocken, PA (2003) 35. von Kries, J: “Chromatische Adaption”, Festschrift der Albrecht-Ludwigs-Universitaet, Freiburg (1902) 145–158; reprint in: “Sources of Color Science”, MIT Press, Cambridge MA (1970) 109 36. CIE No 159: “A color appearance model for color management systems: CIECAM02”, CIE, Commission Internationale de L’Éclairage, Bureau Central de la CIE, Wien (2004) 37. Luo, MR, Li, CJ, “CIE Color Appearance Models and associated Color Spaces”, in: Shanda, J, ed.: “Colorimetry”, Wiley-Interscience, New York (2007) 38. Ostwald, W: “Farbenlehre”: Vol 1: “Mathematische Farbenlehre”, 2nd ed., Unesma, Leipzig (1930); Vol 2: “Physikalische Farbenlehre”, Unesma, Leipzig (1923) 39. Kang, HR: “Computational color technology”, SPIE Press, Bellingham (2006) 40. DIN 6172: “Metamerie-Index von Probenpaaren bei Lichtartwechsel”, Deutsches Institut fuer Normung eV, Berlin (1993) 41. CIE No 80: “Special Metamerism Index: Change in Observer”, Commission Internationale de L’Éclairage (CIE), Bureau Central de la CIE, Wien (1989) 42. DIN 55978: “Bestimmung der relativen Farbstaerke in Loesungen, Spektralphotometrisches Verfahren”, Deutsches Institut fuer Normung eV, Berlin (1981) 43. DIN 55603: “Pruefung von Pigmenten – Bestimmung der relativen Farbstaerke und des Restfarbenabstandes von anorganischen Pigmenten in Weissaufhellungen nach dem Helligkeitsverfahren”, Deutsches Institut fuer Normung eV, Berlin (2003)

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44. DIN 53235-1: “Pruefung von Pigmenten – Pruefungen an standardfarbtiefen Proben – Part 1: Standardfarbtiefen”, “Pruefung von Pigmenten – Pruefungen an standardfarbtiefen Proben – Part 2: Einstellen von Proben auf Standardfarbtiefe”, (2005); Deutsches Institut fuer Normung eV, Berlin 45. DIN 53235-2: “Pruefung von Pigmenten – Pruefungen an standardfarbtiefen Proben – Part 2: Einstellen von Proben auf Standardfarbtiefe”, (2005); Deutsches Institut fuer Normung eV, Berlin 46. DIN 55987: “Bestimmung des Deckvermoegenswertes pigmentierter Medien”, Deutsches Institut fuer Normung eV, Berlin (1981) 47. ASTM D 2805 – 96a(2003): “Standard Test Method for Hiding Power of Paints by Reflectometry”, American Society for Testing and Materials, West Conshohocken, PA (2003) 48. ASTM D 6441–05: “Standard Test Methods for Measuring Hiding Power of Powder Coatings”, American Society for Testing and Materials, West Conshohocken, PA (2005) 49. ISO 6504-3:2006: “Paints and varnishes – Determination of hiding-Power – Part 3: Determination of contrast ratio of light-coloured paints at a fixed spreading rate”, International Organization of Standardization, Genf (2006) 50. DIN 55984: “Bestimmung des Deckvermoegenswertes von weissen und hellgrauen Medien”, Deutsches Institut fuer Normung eV, Berlin (1986) 51. DIN 55988: “Bestimmung der Transparenzzahl (Lasur) von pigmentierten und unpigmentierten Systemen”, Deutsches Institut fuer Normung eV, Berlin (1989) 52. ASTM D 1746–03: “Standard Test Method of Transparency of Plastic Sheeting”, American Society for Testing and Materials, West Conshohocken, PA (2003) 53. DIN EN ISO 105 – A01: “Textilien – Farbechtheitspruefungen – Part A01: Allgemeine Pruefgrundlagen (ISO 105-A01:2008)”, Deutsches Institut fuer Normung eV, Berlin (2008) 54. DIN EN ISO 105, A06: “Textilien – Farbechtheitspruefungen – Part A06: Farbmetrische Bestimmung der 1/1 Richttype (ISO 105-A06:1995)”, Deutsches Institut fuer Normung eV, Berlin (1997) 55. Graystone, J: “Journeys into Colorspace”, Surf Coat Int, Part B Coat Trans, 87 (B3) (2004) 221 56. ISO 4582:2007: “Plastics – Determination of changes in colour and variation in properties after exposure to daylight under glass, natural weathering and laboratory sources”, International Organization of Standardization, Genf (2007) 57. ISO 11507:2007: “Paints and varnishes – Exposure of coatings to artificial weathering – Exposure to fluorescent UV lamps and water”, International Organization of Standardization, Genf (2007) 58. ISO 4892-1/4: “Plastics – Methods of exposure to laboratory sources; Part 1: General Guidance; Part 2: Xenon-arclamps; Part 3: Fluorescent and UV-lamps; Part 4: Open-flame carbon-arc lamps”, International Organization of Standardization, Genf (1999–2006); identical with: DIN EN ISO 4892-1/4: “Kunststoffe – Kuenstliches Bestrahlen oder Bewittern in Geraeten”, Deutsches Institut fuer Normung eV, Berlin (2000–2001) 59. ISO 105-J05: “Textiles – Test for colour fastness – Part J05: Instrumental assessment of change in colour for determination of grey scale rating”, International Organization of Standardization, Genf (1997); identical with: DIN EN ISO 105-J05: “Textilien – Farbechtheitspruefungen – Part J05: Instrumentelle Bewertung der Aenderung der Farbe zur Bestimmung der Graumassstabszahl”, Deutsches Institut fuer Normung eV, Berlin (1997) 60. ISO 105-J02: “Textiles – Test for colour fastness – Part J02: Instrumental assessment of whiteness”, International Organization of Standardization, Genf (1998) 61. ASTM E 313–05: “Standard Practice for Calculating Yellowness and Whiteness-Indices from instrumentally measured Color Coordinates”, American Society for Testing and Materials, West Conshohocken, PA (2005)

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62. DIN 6167: “Beschreibung der Vergilbung von nahezu weissen oder nahezu farblosen Materialien”, Deutsches Institut fuer Normung eV, Berlin (1980) 63. ASTM D 1003 – 07e1: “Standard Test Method for Haze and Luminous Transmittance of Transparent Plastics”, American Society for Testing and Materials, West Conshohocken, PA (2007) 64. DIN 55923: “Pigmente: Aluminiumpigmente und Aluminiumpigmentpasten fuer Anstrichfarben”, Deutsches Institut fuer Normung eV, Berlin (1983) 65. DIN 50017: “Kondenswasser-Pruefklimate”, Deutsches Institut fuer Normung eV, Berlin (1982) 66. DIN EN ISO 6270-1/4: “Beschichtungsstoffe – Bestimmung der Bestaendigkeit gegen Feuchtigkeit (ISO 6270)”, Deutsches Institut fuer Normung eV; Part 1–4 (2002 – 2007) 67. DIN EN ISO 9227: “Korrosionspruefung in kuenstlichen Atmosphaeren – Salzspruehnebelpruefungen (ISO 9227:2006)”, Deutsches Institut fuer Normung eV, Berlin (2006) 68. DIN EN ISO 2810: “Beschichtungsstoffe – Freibewitterung von Beschichtungen – Bewitterung und Bewertung (ISO 2810:2004)”, Deutsches Institut fuer Normung eV, Berlin (2004) 69. Wissling, P et al.: “Metallic Pigments”, Vincentz, Hannover (2007) 70. Kelly, RJ: “Process for matching color of paint to a colored surface”, US Patent No 4692481, DuPont Nemours and Company, Wilmington, Del (1987) 71. ASTM D 5767 – 95(2004): “Standard Test Methods for Instrumental Measurement of Distinctness-of-Image Gloss of Coating Surfaces”, American Society for Testing and Materials, West Conshohocken, PA (2004) 72. ASTM E 430 – 05: “Standard Test Methods for measurement of Gloss of High Gloss Surfaces by Abridged Goniophotometry”, American Society for Testing and Materials, West Conshohocken, PA (2005) 73. Kigl-Boeckler, G: “Total Color Measurement of Effect Finishes”, ECS Nuernberg, Nuernberg (2007) 74. Gabel, PW, Hofmeister, F, Pieper, H: “Interference Pigments as Focal Point of Color Measurement”, Kontakte (Darmstadt) 2 (1992) 25 75. Cramer, WR, Gabel, PW: “Effektvolles Messen”, Farbe Lack 107(1) (2001) 42 76. Nadal, ME, Early, EA: “Color measurements for pearlescent coatings”, Col Res Appl 29 (2004) 38 77. Droll, FJ: “Stunning Views”, PPCJ 191(4441) (2001) 78. ASTM E 2194–03: “Standard Practice for Multiangle Color Measurement of Metal Flake Pigmented Materials”, American Society for Testing and Materials, West Conshohocken, PA (2003) 79. ASTM WK 1164: “New Standard Practice for Multiangle Color Measurement of Interference Pigmented Materials”, American Society for Testing and Materials, West Conshohocken, PA (2006) 80. ASTM E 2539–08: “Standard Practice for Multiangle Color Measurement of Interference Pigments”, American Society for Testing and Materials, West Conshohocken, PA (2008) 81. DIN 6175-3: “Farbtoleranzen fuer Automobillackierungen”, Part 3: “Messgeometrien fuer Interferenzpigmente”, draft, Deutsches Institut fuer Normung eV, Berlin (2006) 82. Cramer, WR, Gabel, PW: “Dreiecksbeziehungen aus Bunt-, Aluminium- und Interferenz-Pigmenten”, Farbe u Lack 109(10) (2003) 78 83. Argoitia, A, Witzman, M: “Pigments exhibiting diffractive effects”, Soc Vacuum Coaters, 45th Ann Techn Conf Proc (2002) 84. Argoitia, A, Chu, S: “The concept of printable holograms through the alignment of diffraction pigments”, Flex Prods Inc, Santa Rosa, CA (2002)

Yellow

Hue

Green

Red

Blue Color plate 4. A color plane of CIELAB space (source: Konica-Minolta, Langenhagen/ Hannover, Germany)

Color plate 7. Light microscopic images of pearlescent pigments with mica substrate in bright-field illumination: top: coated with titanium-dioxide (rutile), the particles appear yellow from the top view; bottom: coated with iron-III-oxide (α-hematite), the particles appear deep red from the top view (source: Clariant Produkte GmbH, Frankfurt am Main, Germany)

Color plate 8. Light microscopic images of a red pearl luster pigment with mica substrate coated with titanium-dioxide (rutile) of greater thickness than those in color plate 7; top: in bright-field, bottom: in dark-field illumination of the same frame (source: Clariant Produkte GmbH, Frankfurt am Main, Germany)

Color plate 9. Light microscopic images of an optically variable green/purple interference pigment of aluminum substrate coated with chromium and magnesium-fluoride; top: brightfield, bottom: dark-field of the same frame (source: Clariant Produkte GmbH, Frankfurt am Main, Germany)

Color plate 10. Light microscopic images of a blue liquid crystalline interference pigment of polysiloxane, both over black background; top: bright-field, bottom: dark-field of the same frame (source: Clariant Produkte GmbH, Frankfurt am Main, Germany)

Color plate 11. Light microscopic bright- and dark-field image of an effect coloration of yellow-gold color impression from the top view; the images show mixed metallic, pearlescent and absorption colorants; top: bright-field, bottom: dark-field of the same frame (source: Clariant Produkte GmbH, Frankfurt am Main, Germany)

Color plate 12. Light microscopic bright- and dark-field image of a brown effect color coating from the top view; the images show mixed pearl luster and absorption pigments; top: bright-field, bottom: dark-field of the same frame (source: Clariant Produkte GmbH, Frankfurt am Main, Germany)

Chapter 4

Measuring Colors

At the beginning of the previous chapter, empirical color value systems suitable for numerical quantification of color impressions were described. A fundamental requirement for such systems is an accurate and precise measurement of the spectral reflectance or transmittance of the relevant color patterns. This necessity comes down to the fact that the retinal color stimulus is caused by the spectral reflection or transmission of the colored object, among other things. Accordingly, the measuring result should agree with the visual impression as well as possible. Color measuring instruments have been established and used since about 1960. Today, they are indispensable pieces of equipment for industrial color physics. Color measuring and especially the clear interpretation of the results require extensive knowledge and experience with regard to the underlying visual, color physical, and metrological interrelations. The measurement quantities are of importance for answering questions in research and development, quality control, and process control or application techniques. Moreover, the measurement results offer an objective base for realistic color tolerance agreements. For such agreements, the people involved should be familiarized with the measuring conditions, performance features of the instruments used, the meaningfulness, and trustworthiness of the measuring quantities. The technological progress attained with regard to color measuring instruments has, however, often been overrated, especially concerning the measuring uncertainty. Undoubtedly, the improvement of component parts has contributed to an increased reliability of the measured quantities and extent of information. Such components include high-resolution reflection gratings or photodiodes with half-width of about 5 nm, cleverly designed interconnect elements for optical wave guides, high-speed microprocessors, and storage mediums of several terabytes at the time of this writing. On the other hand, for measurement of colors, one must take into consideration three fundamental points. These are perhaps self-evident, but nevertheless pointed out explicitly at this stage:

G.A. Klein, Industrial Color Physics, Springer Series in Optical Sciences 154, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-1197-1_4, 

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1. The measured values obtained from a color pattern represent the actual physical state at the moment of measurement; even if the measurement is of the highest quality, it is useless, if the color sample does not maintain the required color physical state. 2. The sensitivity of color measuring instruments is already about an order of magnitude better than the visual color sensitivity of even a practiced colorist! Further reductions in measurement uncertainty below this level are, therefore, unnecessary for color industry. 3. Although the result of a color measurement is at present accurate to at least three digits, the final human visual impression determines if the actually measured color pattern is acceptable or not. Experience shows that the combination of subjective visual judgment and objectively obtained color characteristics can be quite successful. These considerations are the subject to a more detailed discussion in the following. At first, we clarify the double meaning of the term color measurement and describe useful requirements for visual and metrological execution of color measurement. Moreover, the measurement geometries proposed by the CIE and the most important color measuring procedures are discussed [1–8]. In addition, we give suggestions for preparation and conditioning of color patterns. With regard to effect pigments, additional measurement methods are given. Finally, we discuss in detail the assessment of measurement uncertainty and statistics of chromaticities. These are indispensable for visual color matching, tolerance agreement, and quality control, among other things.

4.1 Measurement of Reflecting and Transmitting Materials Among the three factors contributing to the color impression of non-selfluminous colors, the final decision maker, as mentioned previously, is undoubtedly the observer. Simply put, in color measuring techniques, the observer is substituted by the color measuring instrument and computer. This substitution follows, e.g., also by comparison of Figs. 2.29a and 4.1, for example. More precisely, the optical image formation by the eye and the trichromatic elements of the retina are simulated by the optical components and photodiodes of the measuring instrument. The transfer of the trichromatic stimulus to the visual cortex and its assessment by the brain are simulated by analog–digital converters interfaced with a computer using suitable software. These days, this software includes the majority of the colorimetrical relations given in Chapter 3 as well as right designed graphic diagrams. Furthermore, it is important to stress that the characteristics and quantities which result from color measurements are also merely representatives of the special spectral or colorimetric properties of the relevant color pattern. The

4.1

Measurement of Reflecting and Transmitting Materials

Fig. 4.1 Principle sketch of a color measuring equipment; the observer is substituted by the measuring instrument and computer, cf. Fig. 2.29a

235 Computer X, Y, Z, L, a, b

Monochromator, Analog-digital converter Light source

Sample

interpretation and judgment of the numerical or graphical results should be carried out by experienced colorists. Often, the subjective color sensation is the decisive factor, because the colorimetrical formalisms only approximately imitate the nonlinear peculiarities of human color sense.

4.1.1 Measurement of Colors and Visual Judgment To measure means to compare. In the context of colors, to compare has a double meaning, namely metrological and visual. In the first case, a property which we are interested in is compared quantitatively with a suitably chosen reference color or standard; in the second case, the comparison is performed using the subjective color sense. First, we consider the fundamental aspects of quantitative measuring of color characteristics. Then, we go into the peculiarities which need to be taken into account for visual comparisons. Already from the law of energy conservation, it is known that light interactions in optical materials can cause effects such as reflection and transmission. The reflection of a layer is comprised of at least two superimposed principle components: backscattering from the volume and reflection from the interfaces. Reflection can be not only directional or partly directional but also diffuse or mixed such as partly diffuse, depending on the main directed or diffuse component (cf. Fig. 2.28). In some cases, the angle-dependent diffuse reflection of a matt surface obeys the Lambert law I(ϑ) = A · B · cos ϑ,

(4.1.1)

where I(ϑ) is the luminous intensity which is reflected into angle ϑ with respect to the face normal of a completely diffuse reflecting surface of size A and luminance B. A diffuse reflecting field satisfying this law is called Lambert radiator.

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On the other hand, even the specular reflection of a highly glossy color pattern or one with metallic pigments is superimposed with a quite small, but detectable diffuse component. Reflectance measurements are performed with regard to two so-called standards which serve as fixed points on the photometer scale. With the blackbody at absolute zero, the theoretical zero point of the photometer scale is established. At this temperature, the blackbody radiator emits no light but absorbs all entering light (Section 2.1.2). In practice, however, a hollow body of napped black interior called blackbody trap is used. The second fixed point of the photometer scale is given by a white standard, which – ideally – reflects, respectively scatters, the incident light completely. The spectral values obtained from the white and black standards are corrected in a suited manner and interpreted as 0.00 and 100.00% reflectance, respectively. The scale between both points is linearly subdivided and called photometer scale. This scale is applied to all sorts of colorants, the reason why colorations containing effect or fluorescence colorants attain apparent reflectance values of R > 100% or lightness values of L > 100. However, to this day, an ideal white standard does not exist. Such a standard is only realized approximately, e.g., by a freshly pressed layer of powdered BaSO4 or polytetrafluorethylene (PTFE). Both materials show a wavelength-dependent reflectance of about 98.5% in the visible range. This value is determined from the ratio of the reflected spectral energy of the white standard to the emitted spectral energy of the illuminating source. Other materials of high spectral reflectance such as MgO or ZnO are, on account of process reasons, very rarely used as white standards these days [1]. Altogether, there exist three different sorts of standards for measuring colors. The relevant quality levels arise from the following rank order: 1. Primary standard is manufactured and certified by a Bureau of Standards.1 The remarkable features of such a primary standard are the highest possible technical precision and greatest dependability. 2. Transfer standard is calibrated using a primary standard; it is preferentially employed by instrument manufacturers for calibration of reference (master) instruments. 3. Secondary standard is calibrated in turn on the basis of a transfer standard; this type of standard is enclosed within the measuring instrument; its photometric scale is previously calibrated with such black and white standards. Secondary standards are only really designed to use for scaling of the accompanying instrument during operation.

1 For

example: National Institute of Standards and Technology (NIST), Gaithersburg, MD, USA; Community Reference Bureau (CRB) of the European Union, Bruxelles, Belgium; Physikalisch-Technische Bundesanstalt (PTB), Braunschweig, Germany.

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Measurement of Reflecting and Transmitting Materials

237

In the case of transparent materials, the determination of transmission seems to turn out easier. Transmission is a measure for transparency of a material; it is reduced by interface reflection, absorption, and scattering. Clearly, the transmission can occur not only directionally or partly directionally but also diffusely or mixed such as partly diffusely. There does not exist a specific standard for the determination of the transmittance of a material. Rather the spectral intensity of the light source – without any sample – receiving the detector for closed and opened aperture diaphragm is simply interpreted as 0.00 and 100.00% transmittance, respectively. However, the measurement of transmittance is often influenced by heterogeneities at the interfaces of the relevant material. For non-self-luminous colors, there also does not exist unambiguously defined color standards. Certainly it is useful within itself to check the linearity of the gray scale of color measuring instruments with regard to the reflective factors in the domain 0 ≤ R(λ) ≤ 1.0 with tiles of so-called BCRA II ceramic.2 This consists of an entire set of 12 colored and hueless tiles which, for years ahead, have turned out to be almost color constant in appropriate storage conditions. Actually, the reflection of these patterns depends slightly on azimuthal angle. This influence can be excluded by repeated measurements in which the same measuring spot at the same orientation is always used. Otherwise gonio spectrophotometers can fake a falsely calibrated angle scale. Known and reproducible wavelengths of illuminant sources are used for calibration of the wavelength scale of a color measuring equipment. Such sources are also used to characterize light colors of sources, LEDs, screens, or panels. In order to cover the range of interest, devices such as the gas discharge of helium, mercury, and sodium vapor lamps are used. These sources emit different numbers of sharp spectral lines of known wavelengths in the visible range: He emits 18 lines in the interval 365.0 nm ≤ λHe ≤ 690.7 nm, Hg shows 12 lines in the domain 370.5 nm ≤ λHg ≤ 728.1 nm, and Na merely the pair of lines 589.0 and 589.6 nm. For inspection of the angle scale of gonio spectrophotometers, there exist no obligatory standards until now. As experience shows, each scaling depends on temperature and humidity of the surroundings, the instrument construction, and the standards used. The calibration should, therefore, be performed in operating conditions. Furthermore, the instrumentation and the secondary standards should not be exposed to higher fluctuations of temperature and humidity than specified by the manufacturer. Generally, the best situation is an installation of the instrument and secondary standards in a constant standard climate at temperature ϑ = 20◦ C and atmospheric humidity of 50%.

2 BCRA Series II Ceramic Standards: previously manufactured by British Ceramic Research Association, nowadays by Ceram Research, Penkhull, UK.

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The visual assessment of colors turns out to be the something more problematic; this can by no means be ignored. After all, the entire coloring efforts are oriented toward the human color sense. Clearly, only people with normally developed color perception should be involved in the assessment of colors. The capability of the individual color perception should be checked at regular intervals, and the test should be passed with the Ishihara color panels [9], even better with the Nagel anomaloscope [10], or with another standard [11]. In addition, also the ability to distinguish colors can be selectively reduced or unequally developed (color amblyopy). This also needs to be checked with a visual color test. Moreover, possibly the CMFs of joined observers differ from each other and deviate from those of both CIE standard observers. This observer metamerism needs to be considered by the involved people. The visual judgment is performed not only between similar colorations but can also include a great variety of special colorations. The systematic comparison of sample colors (sample, test, pattern) with reference colors (reference, standard, target) is called equality method. A sample color can be compared with special own standards of the manufacturer, reference colors, a systematic color collection, a pattern collection selected from manufacturing, or with patterns of a color-order system, among other things. A disadvantage of the equality method is the subjective judgment of the colorist – this often turns out to be too strict. For more objective methods, however, the tristimulus and the spectral measuring methods are available (Sections 4.2.1 and 4.2.2). In case of routine examinations under daylight conditions, it is sufficient to expose the colors to diffuse north skylight in the northern hemisphere and to diffuse south skylight in the southern hemisphere. In each of these cases, the skylight should be incident through windows which are as high as possible. During the visual comparison under artificial illumination, of course, it is necessary to meet at least the CIE reference conditions. In a light booth for color judgment, the illuminants that correspond to the colorations to which the color will presumably be exposed in future are to be activated. The basic equipment of a standardized booth includes simulators of illuminants D65, A, FL 2, FL 11 as well as two UV sources of defined bandwidth for stimulation of fluorescence emission [12, 13]. Due to a general lack of time in practice, often the sources are switched in fractions of a second among the various illuminants which means within the short-termed chromatic adaption phase. This procedure is certainly left for only experienced colorists; otherwise, it is better to wait for the longer adaption phase. Special diligence and experience are necessary, if equal colorations are to be compared with each other in different binders or of different surface structures. Further critical color aspects may arise with colorations containing effect and absorption pigments. In most cases, problems emerge by comparing the angledependent lightness or color flop, brilliance, or covering capacity. These require intensive training in color perception in unusual domains of a color space as well

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Measurement of Reflecting and Transmitting Materials

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as a sensitive interpretation of spectral reflectance and transmittance or rather of the relevant color values.

4.1.2