The Author......................................................................................................................... III
Preface................................................................................................................................... V
Foreword........................................................................................................................... VII
CHAPTER 2 Spectral Radiometry of Surfaces.................................................................................... 29
2.1 Types of Reflecting Surfaces............................................................................... 30
2.1.1 Mirrors and Specular Reflectors............................................................... 30
2.1.2 Very Matte Surfaces: Lambertian Reflectors........................................ 30
2.1.3 Intermediate Cases.................................................................................... 31
2.2 Light Transmission Through Objects................................................................. 31
2.3 Angular Spectral Reflectance and Transmittance.............................................. 32
2.4 Bi-DirectionalReflectance/Transmittance Distribution Function (BRDF/BTDF) 33
2.4.1 Definition...................................................................................................... 33
2.4.2 BRDF of Some Typical Reflectors.......................................................... 34
2.4.3 Lambert’s Azimuthal Equal-Area Projection........................................ 35
2.4.4 BRDF Measurement Systems.................................................................. 36
2.5 Spectral Reflectance and Transmittance Factors............................................... 37
2.5.1 Reflectance, Transmittance...................................................................... 37
2.5.2 Spectral Reflectance/Transmittance Factor........................................... 38
2.5.3 Spectral Radiance Factor........................................................................... 39
2.6 Geometries and Devices for the Measurement of Reflectance Factors........... 39
2.6.1 Nicodemus’ Nomenclature for Nine Reflectance Factors.................... 40
2.6.2 Geometries Using Integrating Spheres..................................................... 41
2.6.3 Bidirectional and Annular Geometries.................................................. 43
2.6.4 Effective Measurement Geometry.............................................................. 43
2.7 Surface Distribution Functions............................................................................... 45
2.7.1 Bidirectional Scattering-Surface Reflectance Distribution Function (BSSRDF)..................................................... 45
2.7.2 Point Spread Function (PSF).................................................................... 46
CHAPTER 3 Visual Characterization of Surfaces............................................................................... 49
3.1 Color and Colorimetry........................................................................................... 51
3.1.1 A Relative Perception............................................................................... 51
3.1.2 Color Mixing and Early Color Representation Systems..................... 53
3.1.3 Trichromacy................................................................................................ 56
3.1.4 CIE 1931 RGB and XYZ ColorSpaces................................................ 57
3.1.5 CIE 1931 Chromaticity Diagram............................................................ 59
3.1.6 Color of Light Sourcesand Illuminants................................................. 61
3.1.7 CIE 1976 L*a*b*ColorSpace and Color Appearance Models......... 62
3.1.8 Von Kries Chromatic Adaptation............................................................ 66
3.2 Color Measurement and Color Imaging.............................................................. 67
3.2.1 Color Characterization of a Surfaceby Using a Spectrophotometer..................................... 67
3.2.2 Metamerism................................................................................................. 69
3.2.3 Color and Spectral Measurement by Imaging Techniques................. 70
3.2.4 Measuring the Spectral Responseof an RGB Camera........................ 73
3.2.5 Color Calibration of an RGB Imaging System..................................... 74
3.3 Gloss.......................................................................................................................... 77
3.3.1 Definition for Gloss.................................................................................... 77
3.3.2 Gloss Measurement................................................................................... 78
CHAPTER 4 Plane Optical Interfaces and Transparent Layers........................................................ 81
4.1 Radiance Reflection and Transmission at an Interface...................................... 82
4.2 Bi-Hemispherical Reflectance and Transmittance of an Interface.................. 84
4.3 Metals and Strongly Absorbing Media............................................................... 86
4.4 Angular Reflectance and Transmittance of a Clear Plate............................... 88
4.4.1 Angular Reflectance and Transmittance............................................... 88
4.4.2 Bi-Hemispherical Reflectance and Transmittance................................. 91
4.5 Spectral Transmittance of Absorbing Layers.................................................... 93
4.5.1 Bouguer’s Law and Beer’s Law............................................................... 93
4.5.2 Piles of Absorbing Layers and Mixing of Absorbing Media.............. 95
4.6 Spectral Reflectance and Transmittance of an Absorbing Plate................... 95
4.6.1 Angular Reflectance and Transmittance............................................... 96
4.6.2 Bi-Hemispherical Reflectance and Transmittance................................. 97
4.6.3 Obtaining the Intrinsic Parameters of an Absorbing Plate............... 98
4.7 Extensions and Applications.................................................................................. 99
CHAPTER 5 Transparent Multilayers: Two-Flux Models for Directional Light......................... 101
5.1 Piles of Transparent Plates Separated by Air................................................. 102
5.1.1 Angular Reflectance and Transmittance of Two Plates.................. 103
5.1.2 Generalization to Non-Symmetric Plates............................................ 105
5.1.3 Generalization to N Plates: Iterative Model...................................... 105
5.1.4 Generalization to N Plates: Flux Transfer Matrix Model............... 105
5.2 Piles of Identical Plates...................................................................................... 108
5.2.1 Angular Reflectance and Transmittance............................................. 108
5.2.2 Degree of Polarization............................................................................ 112
5.2.3 Bi-Hemispherical Reflectance and Transmittance.............................. 116
5.2.4 Generalization to Non-Symmetric Plates............................................ 117
5.2.5 Invariance of Parameter a...................................................................... 118
5.3 Layers of Different Refractive Indices in Optical Contact............................ 118
5.3.1 Flux Transfer Matrices for Layersand Interfaces............................. 119
5.3.2 Examples of Multilayers......................................................................... 120
5.3.3 Optical Characterization ofLiquids.................................................... 121
5.3.4 Total Reflections................................................................................... 122
5.3.5 Nonpolarity of Directional Transmittance......................................... 123
5.4 Examples.............................................................................................................. 124
5.4.1 Piles of Colored Films Separated by Air............................................. 124
5.4.2 Piles of Colored Films Separated by Different Media....................... 125
5.5 Piles of Films on Top of a Specular Background.......................................... 130
CHAPTER 6 Diffusing Layers and Multilayers: Two-Flux Models for Diffuse Light................. 133
6.1 The Kubelka–Munk Model................................................................................. 134
6.1.1 The Kubelka–Munk Differential Equations........................................ 134
6.1.2 Reflectance and Transmittance Formulae........................................... 135
6.2 Layers in Optical Contact with a Background............................................... 137
6.3 Light Transfersat the Interfaces Bordering the Layer.................................. 138
6.3.1 Saunderson Correction and Inverse Formulae...................................... 138
6.3.2 Saunderson Correction and Inverse Formulae for a Diffusing Plate............................................................ 141
6.4 Deducing K and S from Measurements........................................................... 143
6.4.1 Drawdown Card Method......................................................................... 143
6.4.2 Reflectance and Transmittance Method................................................. 145
6.4.3 Choosing the Appropriate Method....................................................... 145
6.5 Example.................................................................................................................. 146
6.6 Mixture of Scattering Materials......................................................................... 148
6.7 Validity of the Kubelka–Munk Model............................................................... 149
6.8 Diffusing Multilayers............................................................................................ 150
6.8.1 Kubelka’s Compositional Formulae and Flux Transfer Matrix Model.............................................. 151
6.8.2 Example: Piles of Identical Diffusing Sheets....................................... 152
6.8.3 Kubelka’s Formulae and Kubelka–Munk Model.................................. 153
6.8.4 Extended Saunderson Correction for Multilayers: The Matrix Method 154
CHAPTER 7 Nonscattering Layers on a Diffusing Background..................................................... 157
7.1 Uniform Layer on Top of a Diffusing Background......................................... 158
7.1.1 Williams–Clapper Model....................................................................... 158
7.1.2 Berns’ Model............................................................................................ 161
7.1.3 Insurface and Subsurface Reflections According to the Lighting Geometry................................... 162
7.2 Transparent Multilayers on Top of a Diffusing Background........................ 165
7.3 Generalized Two-Flux Model.............................................................................. 168
7.3.1 Configurations Where a Two-Flux Model Applies............................ 168
7.3.2 Multiple Reflection Processes and Homogeneous Discrete-Time Markov Chains.................... 170
7.3.3 Transition Probability Matrices............................................................ 172
7.3.4 Average Number of Transfers................................................................ 173
7.4 Spectral Reflectance of Printed Surfaces......................................................... 174
7.4.1 Halftone Colors......................................................................................... 174
7.4.2 Spectral Neugebauer Model..................................................................... 176
7.4.3 Yule–Nielsen Modified Spectral Neugebauer Model............................ 177
7.4.4 Clapper–Yule Model............................................................................... 179
7.5 Calibration of the Halftone Color Prediction Models.................................... 180
7.5.1 Obtaining Spectral Parameters............................................................. 181
7.5.2 Ink Spreading Assessment Methods........................................................ 182
7.5.3 Basic Ink Spreading (BIS) Method....................................................... 182
7.5.4 Superimposition-Dependent Ink Spreading (SDIS) Method............... 184
7.5.5 Predicting the Spectral Reflectance of Halftones............................... 184
7.5.6 Four-Ink Halftone Colors........................................................................ 186
CHAPTER 8 Angle-Dependent Light Scattering................................................................................ 187
8.1 Surface Scattering................................................................................................. 187
8.1.1 Surface Roughness Measurement............................................................. 188
8.1.2 Modelling a Randomly Rough Surface................................................ 188
8.1.3 BRDF and BTDF Optical Models........................................................ 189
8.1.4 Microfacet Model and Smith’s Shadowing-Masking Function........... 190
8.1.5 Spherical Surfaces................................................................................... 193
8.2 Volume Scattering................................................................................................. 195
8.2.1 Scattering Description Parameters.......................................................... 195
8.2.2 Types of Scattering.................................................................................. 198
8.2.3 The Radiative Transfer Equation......................................................... 199
8.2.4 Scattering in Lambertian Layers........................................................... 200
Exercises............................................................................................................................ 201
Corrections........................................................................................................................ 211
Acknowledgements.......................................................................................................... 229
References.......................................................................................................................... 231
Index................................................................................................................................... 243