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Optical models for material appearance

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Presentation

Material appearance has emerged as a scientific topic in its own right rather recently and an increasing number of professionals concerned by this topic, belonging to various application areas, are entering this vast field. Thanks to the rise of imaging systems and visual rendering software, and the rapid development of accessible devices for color and gloss analysis, non-expert people can now check, for example, the compliance of a product with an appearance standard, or create a realistic virtual prototype. Most of these tools are based on optical concepts which are generally not in the forefront at an elementary level usage, but which are necessary for a consistent analysis of the specific cases studied. The objective of this book is precisely to introduce the fundamental notions of optics allowing the readers to understand the radiometric quantities measured with common devices, to learn how to analyze them, and to review some classical optics-based predictive models for various types of materials and structures. We have chosen to illustrate the theoretical notions with numerous examples and corrected exercises, easily transposable to a variety of materials: glass plates, polymer films, pigment layers, metals, papers and printed surfaces, coatings, etc. The book targets an audience of students, engineers and researchers who have a scientific background but not necessarily versed in optics, who are seeking sound bases in order to characterize the appearance of products and better comprehend the more advanced research currently being conducted in this area.

Resume

  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     Lamberts 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     Bouguers Law and Beers 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 KubelkaMunk Model................................................................................. 134


6.1.1     The KubelkaMunk 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 KubelkaMunk Model............................................................... 149


6.8        Diffusing Multilayers............................................................................................ 150


6.8.1     Kubelkas Compositional Formulae and Flux Transfer Matrix Model.............................................. 151

6.8.2     Example: Piles of Identical Diffusing Sheets....................................... 152

6.8.3     Kubelkas Formulae and KubelkaMunk 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     WilliamsClapper 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     YuleNielsen Modified Spectral Neugebauer Model............................ 177

7.4.4     ClapperYule 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 Smiths 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


 

 

Compléments

Characteristics

Language(s): English

Audience(s): Students, Research, Professionals

Publisher: EDP Sciences & Science Press

Collection: IOGS - Institut d'Optique Graduate School Textbook

Published: 25 august 2022

EAN13 (hardcopy): 9782987526476

Reference Paper book: L26476

EAN13 Paper book: 9782759826476

EAN13 eBook [PDF]: 9782759826483

Interior: Colour

Format (in mm) Paper book: 160 x 240

Pages count Paper book: 260

Size: 13 Mo (PDF)

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