Optical models for material appearance

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 MatteSurfaces: 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 Response of 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 PlatesSeparated 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 TransferMatrices for Layersand Interfaces............................. 119

5.3.2     Examples of Multilayers......................................................................... 120

5.3.3     Optical Characterization of Liquids.................................................... 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

ExtendedSaunderson 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 ProbabilityMatrices............................................................ 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