Industrial Color Physics by Georg A. Klein

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Industrial Color Physics
By Georg A. Klein
Industrial Color Physics

Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Light Sources, Types of Colorants, Observer . . . . . . . . . . . . . 11
2.1 Optical Radiation Sources and Interactions of Light . . . . . . . . 11
2.1.1 Visible Spectrum and Colors . . . . . . . . . . . . . . . . 12
2.1.2 Types of Light Sources . . . . . . . . . . . . . . . . . . 14
2.1.3 Technical Light Sources . . . . . . . . . . . . . . . . . . 18
2.1.4 Illuminants . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.5 Geometric Optical Interactions . . . . . . . . . . . . . . 25
2.1.6 Interference of Light . . . . . . . . . . . . . . . . . . . . 34
2.1.7 Diffraction from Transmission and Reflection Gratings . . 38
2.2 Absorbing Colorants . . . . . . . . . . . . . . . . . . . . . . . . 43
2.2.1 Types and Attributes of Absorbing Colorants . . . . . . . 43
2.2.2 Pigment Mixtures and Light Transmittance . . . . . . . . 48
2.2.3 Description of Color Attributes . . . . . . . . . . . . . . 51
2.2.4 Color-Order Systems . . . . . . . . . . . . . . . . . . . 57
2.2.5 Surface Phenomenon . . . . . . . . . . . . . . . . . . . 59
2.3 Effect Pigments . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.3.1 Types of Metallic Pigments . . . . . . . . . . . . . . . . 65
2.3.2 Morphology of Metallic Particles . . . . . . . . . . . . . 69
2.3.3 Coloristic Properties of Metallic Pigments . . . . . . . . . 76
2.3.4 Sorts of Pearlescent and Interference Colorants . . . . . . 82
2.3.5 Interference Pigments Consisting of Multiple Layers . . . 85
2.3.6 Spectral Behavior of Pearlescent and Interference Colorants 91
2.3.7 Opaque Films Containing Absorbing and Effect Pigments . 101
2.3.8 Colors of Diffraction Pigments . . . . . . . . . . . . . . 104
2.4 Observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2.4.1 Color Perception and Color Theories . . . . . . . . . . . 110
2.4.2 Color Perception Phenomenon . . . . . . . . . . . . . . . 114
2.4.3 Subtractive and Additive Mixing of Colors . . . . . . . . 116
2.4.4 Tristimulus Color-Matching Experiments . . . . . . . . . 120
2.4.5 Determination of Tristimulus Values . . . . . . . . . . . . 123
2.4.6 CIE 1931 and CIE 1964 Standard Colorimetric Observers . 125
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3 Systems of Standardized Tristimulus Values, Color Qualities,
Chroma of Effect Pigments . . . . . . . . . . . . . . . . . . . . . . 133
3.1 Systems of Standardized Tristimulus Values . . . . . . . . . . . . 133
3.1.1 CIE 1931 Tristimulus Values . . . . . . . . . . . . . . . 134
3.1.2 Chromaticity Coordinates and Chromaticity Diagram . . . 137
3.1.3 CIE 1976 Color Spaces . . . . . . . . . . . . . . . . . . 141
3.1.4 DIN99o Color Space . . . . . . . . . . . . . . . . . . . . 148
3.2 Color Difference Metrics and Color Tolerances . . . . . . . . . . 152
3.2.1 CMC(l:c) Color Difference Formula . . . . . . . . . . . . 153
3.2.2 CIE94 Color Difference Expression . . . . . . . . . . . . 154
3.2.3 CIEDE2000 Color Difference Equation . . . . . . . . . . 157
3.2.4 Efficiency of Color Difference Formulas, CIE
Color Appearance Models . . . . . . . . . . . . . . . . . 159
3.2.5 Color Tolerances . . . . . . . . . . . . . . . . . . . . . . 161
3.3 Color Constancy and Metamerism . . . . . . . . . . . . . . . . . 164
3.3.1 Chromatic Adaptation and Color Constancy . . . . . . . . 164
3.3.2 Index of Color Inconstancy . . . . . . . . . . . . . . . . 166
3.3.3 Kinds of Metamerism . . . . . . . . . . . . . . . . . . . 169
3.3.4 Special Metamerism Indices . . . . . . . . . . . . . . . . 172
3.4 Specific Qualities of Colorants . . . . . . . . . . . . . . . . . . . 175
3.4.1 Build-up and Coloring Potential . . . . . . . . . . . . . . 176
3.4.2 Strength and Depth of Color . . . . . . . . . . . . . . . . 179
3.4.3 Covering Capacity . . . . . . . . . . . . . . . . . . . . . 185
3.4.4 Transparency and Coloring Power . . . . . . . . . . . . . 189
3.4.5 Color Fastness and Turbidity . . . . . . . . . . . . . . . . 192
3.4.6 Stability of Effect Pigments . . . . . . . . . . . . . . . . 197
3.5 Chroma of Effect Pigments . . . . . . . . . . . . . . . . . . . . 200
3.5.1 Coloristic Quantities of Effect Pigments . . . . . . . . . . 201
3.5.2 Color Difference Equation for Metallics . . . . . . . . . . 206
3.5.3 Chroma of Pearlesence and Interference Pigments . . . . . 209
3.5.4 Mixtures of Effect Pigments . . . . . . . . . . . . . . . . 214
3.5.5 Color Development of Diffraction Pigments . . . . . . . . 221
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
4 Measuring Colors . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
4.1 Measurement of Reflecting and Transmitting Materials . . . . . . 234
4.1.1 Measurement of Colors and Visual Judgment . . . . . . . 235
4.1.2 Measurement Geometries . . . . . . . . . . . . . . . . . 239
4.1.3 Sample Requirements . . . . . . . . . . . . . . . . . . . 248
4.1.4 Transparent, Translucent, Opaque Colors . . . . . . . . . 250
4.1.5 Color Matching . . . . . . . . . . . . . . . . . . . . . . 252
4.1.6 Acceptability and Tolerance Agreement . . . . . . . . . . 255
4.2 Measuring Methods . . . . . . . . . . . . . . . . . . . . . . . . 257
4.2.1 Tristimulus Colorimeter . . . . . . . . . . . . . . . . . . 257
4.2.2 Spectrophotometer . . . . . . . . . . . . . . . . . . . . . 259
4.2.3 Accuracy of Spectrophotometers . . . . . . . . . . . . . . 263
4.2.4 Reflectance and Transmittance of Layers . . . . . . . . . 266
4.2.5 Auxiliary Optical Methods for Effect Pigments . . . . . . 271
4.2.6 Fluorescent, Thermochromic, Photochromic Colors . . . . 274
4.3 Uncertainties of Spectral Color Measurement . . . . . . . . . . . 278
4.3.1 Qualitative Errors . . . . . . . . . . . . . . . . . . . . . 279
4.3.2 Quantitative Errors and Error Distribution . . . . . . . . . 280
4.3.3 Normal Distribution in Three and More Dimensions . . . . 284
4.3.4 Statistical Testing of Color Differences . . . . . . . . . . 287
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
5 Theories of Radiative Transfer . . . . . . . . . . . . . . . . . . . . 295
5.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
5.1.1 Basic Concepts and Definitions . . . . . . . . . . . . . . 296
5.1.2 Absorption and Scattering . . . . . . . . . . . . . . . . . 299
5.1.3 Single and Multiple Scattering . . . . . . . . . . . . . . . 302
5.1.4 Radiative Transfer Equation . . . . . . . . . . . . . . . . 306
5.1.5 Radiative Transfer in Plane Parallel Layers . . . . . . . . 308
5.1.6 Phase Function for Anisotropic Scattering . . . . . . . . . 313
5.2 Directional Two-Flux Approximation . . . . . . . . . . . . . . . 316
5.2.1 Reflection and Transmission . . . . . . . . . . . . . . . . 317
5.2.2 Optical Special Cases . . . . . . . . . . . . . . . . . . . 319
5.2.3 Optical Triangle . . . . . . . . . . . . . . . . . . . . . . 321
5.2.4 Determination of Optical Coefficients . . . . . . . . . . . 324
5.3 Theory of Kubelka and Munk . . . . . . . . . . . . . . . . . . . 326
5.3.1 Empirical Approach . . . . . . . . . . . . . . . . . . . . 327
5.3.2 Exceptional Optical Cases . . . . . . . . . . . . . . . . . 329
5.3.3 Determination of Optical Constants . . . . . . . . . . . . 331
5.3.4 Boundary Layer Correction . . . . . . . . . . . . . . . . 332
5.3.5 Limits of Kubelka–Munk Theory . . . . . . . . . . . . . 337
5.4 Three-Flux Approximation . . . . . . . . . . . . . . . . . . . . 340
5.4.1 Conception of Three-Flux Theory . . . . . . . . . . . . . 341
5.4.2 Reflection and Transmission . . . . . . . . . . . . . . . . 343
5.4.3 Optically Different Materials . . . . . . . . . . . . . . . 345
5.4.4 Correction of Surface Effects . . . . . . . . . . . . . . . 348
5.4.5 Special Cases of External Reflection and Transmission . . 352
5.5 Approximation of Radiative Transfer by Multi-Flux Theory . . . . 356
5.5.1 Exact Solutions for Internal Reflection and Transmission . 357
5.5.2 Surface Boundary Corrections . . . . . . . . . . . . . . . 363
5.5.3 Total Reflection and Optical Extreme Cases . . . . . . . . 368
5.5.4 Boundary Conditions, Matrices of Reflection
and Transmission . . . . . . . . . . . . . . . . . . . . . 370
5.5.5 Directional and Diffuse Reflection and Transmission . . . 372
5.5.6 Inclusion of Total Reflection . . . . . . . . . . . . . . . . 373
5.5.7 Corrected Optical Triangle . . . . . . . . . . . . . . . . . 377
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
6 Recipe Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
6.1 Classical Method . . . . . . . . . . . . . . . . . . . . . . . . . 382
6.1.1 Calibration Series with Absorbing Colorants . . . . . . . . 384
6.1.2 Calibration and Reference Colorations for Effect Pigments 390
6.1.3 Determination of Absorption and Scattering Coefficients . 393
6.1.4 Optical Path and Albedo . . . . . . . . . . . . . . . . . . 397
6.1.5 Coefficients of the Phase Function . . . . . . . . . . . . . 399
6.1.6 Accuracy of Predicted Recipes . . . . . . . . . . . . . . . 400
6.2 Strategies for Recipe Prediction . . . . . . . . . . . . . . . . . . 403
6.2.1 Numerical Methods . . . . . . . . . . . . . . . . . . . . 404
6.2.2 Spectrometric Strategy . . . . . . . . . . . . . . . . . . . 409
6.2.3 Colorimetric Method . . . . . . . . . . . . . . . . . . . 414
6.2.4 Balanced Color Differences . . . . . . . . . . . . . . . . 417
6.3 Realization of Recipes . . . . . . . . . . . . . . . . . . . . . . . 420
6.3.1 Selection of Suitable Recipes . . . . . . . . . . . . . . . 421
6.3.2 Sensitivity and Correctability of Color Recipes . . . . . . 424
6.3.3 Numerical Procedures for Recipe Correction . . . . . . . . 427
6.3.4 Databases . . . . . . . . . . . . . . . . . . . . . . . . . 431
6.3.5 Modified Expert Systems . . . . . . . . . . . . . . . . . 435
6.3.6 Neural Networks . . . . . . . . . . . . . . . . . . . . . . 441
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
A.1 Non-colored Applications of Effect Pigments . . . . . . . . . . . 447
A.1.1 Metallic Pigments . . . . . . . . . . . . . . . . . . . . . 447
A.1.2 Pearlescent Pigments . . . . . . . . . . . . . . . . . . . 448
A.2 Chromatic Adaption Transform CAT02 . . . . . . . . . . . . . . 448
A.2.1 Forward Mode . . . . . . . . . . . . . . . . . . . . . . . 448
A.2.2 Reverse Mode . . . . . . . . . . . . . . . . . . . . . . . 450
A.3 Two-Flux Approximations . . . . . . . . . . . . . . . . . . . . . 451
A.3.1 Directional Fluxes . . . . . . . . . . . . . . . . . . . . . 451
A.3.2 Diffuse Fluxes . . . . . . . . . . . . . . . . . . . . . . . 453
References in Alphabetic Order . . . . . . . . . . . . . . . . . . . . . 455
Name Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469

Preface
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.

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. PeterW. 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.


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