Illumination Engineering
Design with Nonimaging Optics
Herausgegeben von Koshel, R. John
Illumination Engineering
Design with Nonimaging Optics
Herausgegeben von Koshel, R. John
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This book brings together experts in the field who present material on a number of important and growing topics including lighting, displays, solar concentrators. The first chapter provides an overview of the field of nonimagin and illumination optics. Included in this chapter are terminology, units, definitions, and descriptions of the optical components used in illumination systems. The next two chapters provide material within the theoretical domain, including etendue, etendue squeezing, and the skew invariant. The remaining chapters focus on growing applications.
This entire field of…mehr
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This book brings together experts in the field who present material on a number of important and growing topics including lighting, displays, solar concentrators. The first chapter provides an overview of the field of nonimagin and illumination optics. Included in this chapter are terminology, units, definitions, and descriptions of the optical components used in illumination systems. The next two chapters provide material within the theoretical domain, including etendue, etendue squeezing, and the skew invariant. The remaining chapters focus on growing applications.
This entire field of nonimaging optics is an evolving field, and the editor plans to update the technological progress every two to three years. The editor, John Koshel, is one of the most prominent leading experts in this field, and he is the right expert to perform the task.
This entire field of nonimaging optics is an evolving field, and the editor plans to update the technological progress every two to three years. The editor, John Koshel, is one of the most prominent leading experts in this field, and he is the right expert to perform the task.
Produktdetails
- Produktdetails
- Verlag: IEEE Press / Wiley & Sons
- 1. Auflage
- Seitenzahl: 336
- Erscheinungstermin: 29. Januar 2013
- Englisch
- Abmessung: 240mm x 161mm x 22mm
- Gewicht: 684g
- ISBN-13: 9780470911402
- ISBN-10: 0470911409
- Artikelnr.: 30977135
- Verlag: IEEE Press / Wiley & Sons
- 1. Auflage
- Seitenzahl: 336
- Erscheinungstermin: 29. Januar 2013
- Englisch
- Abmessung: 240mm x 161mm x 22mm
- Gewicht: 684g
- ISBN-13: 9780470911402
- ISBN-10: 0470911409
- Artikelnr.: 30977135
John Koshel (Tucson, AZ), obtained Ph.D in Optics from University of Rochester in 1996. He is currently an adjunct assistant professor at University of Arizona, Optical Sciences Center. He also works as a vice president of optical engineering consulting firm, Photon Engineering, LLC. He frequently chairs at SPIE conferences and provides tutorial on the subject (nonimaging optics). He is a well respected figure in the International optical engineering community publishing numerous peer reviewed papers.
PREFACE xiii CONTRIBUTORS xvii GLOSSARY xix CHAPTER 1 INTRODUCTION AND
TERMINOLOGY 1 1.1 What Is Illumination? 1 1.2 A Brief History of
Illumination Optics 2 1.3 Units 4 1.3.1 Radiometric Quantities 4 1.3.2
Photometric Quantities 6 1.4 Intensity 9 1.5 Illuminance and Irradiance 10
1.6 Luminance and Radiance 11 1.6.1 Lambertian 13 1.6.2 Isotropic 14 1.7
Important Factors in Illumination Design 15 1.7.1 Transfer Effi ciency 15
1.7.2 Uniformity of Illumination Distribution 16 1.8 Standard Optics Used
in Illumination Engineering 17 1.8.1 Refractive Optics 18 1.8.2 Refl ective
Optics 20 1.8.3 TIR Optics 22 1.8.4 Scattering Optics 24 1.8.5 Hybrid
Optics 24 1.9 The Process of Illumination System Design 25 1.10 Is
Illumination Engineering Hard? 28 1.11 Format for Succeeding Chapters 29
References 30 CHAPTER 2 ÉTENDUE 31 2.1 Étendue 32 2.2 Conservation of
Étendue 33 2.2.1 Proof of Conservation of Radiance and Étendue 34 2.2.2
Proof of Conservation of Generalized Étendue 36 2.2.3 Conservation of
Étendue from the Laws of Thermodynamics 40 2.3 Other Expressions for
Étendue 41 2.3.1 Radiance, Luminance, and Brightness 41 2.3.2 Throughput 42
2.3.3 Extent 43 2.3.4 Lagrange Invariant 43 2.3.5 Abbe Sine Condition 43
2.3.6 Confi guration or Shape Factor 44 2.4 Design Examples Using Étendue
45 2.4.1 Lambertian, Spatially Uniform Disk Emitter 45 2.4.2 Isotropic,
Spatially Uniform Disk Emitter 48 2.4.3 Isotropic, Spatially Nonuniform
Disk Emitter 50 2.4.4 Tubular Emitter 52 2.5 Concentration Ratio 59 2.6
Rotational Skew Invariant 61 2.6.1 Proof of Skew Invariance 61 2.6.2 Refi
ned Tubular Emitter Example 63 2.7 Étendue Discussion 67 References 68
CHAPTER 3 SQUEEZING THE ÉTENDUE 71 3.1 Introduction 71 3.2 Étendue
Squeezers versus Étendue Rotators 71 3.2.1 Étendue Rotating Mappings 74
3.2.2 Étendue Squeezing Mappings 77 3.3 Introductory Example of Étendue
Squeezer 79 3.3.1 Increasing the Number of Lenticular Elements 80 3.4
Canonical Étendue-Squeezing with Afocal Lenslet Arrays 82 3.4.1 Squeezing a
Collimated Beam 82 3.4.2 Other Afocal Designs 83 3.4.3 Étendue-Squeezing
Lenslet Arrays with Other Squeeze-Factors 85 3.5 Application to a Two
Freeform Mirror Condenser 88 3.6 Étendue Squeezing in Optical Manifolds 95
3.7 Conclusions 95 Appendix 3.A Galilean Afocal System 96 Appendix 3.B
Keplerian Afocal System 98 References 99 CHAPTER 4 SMS 3D DESIGN METHOD 101
4.1 Introduction 101 4.2 State of the Art of Freeform Optical Design
Methods 101 4.3. SMS 3D Statement of the Optical Problem 103 4.4 SMS Chains
104 4.4.1 SMS Chain Generation 105 4.4.2 Conditions 106 4.5 SMS Surfaces
106 4.5.1 SMS Ribs 107 4.5.2 SMS Skinning 108 4.5.3 Choosing the Seed Rib
109 4.6 Design Examples 109 4.6.1 SMS Design with a Prescribed Seed Rib 110
4.6.2 SMS Design with an SMS Spine as Seed Rib 111 4.6.3 Design of a Lens
(RR) with Thin Edge 115 4.6.4 Design of an XX Condenser for a Cylindrical
Source 117 4.6.5 Freeform XR for Photovoltaics Applications 129 4.6.5.1 The
XR Design Procedure 131 4.6.5.2 Results of Ray Tracing Analysis 135 4.7
Conclusions 140 References 144 CHAPTER 5 SOLAR CONCENTRATORS 147 5.1
Concentrated Solar Radiation 147 5.2 Acceptance Angle 148 5.3 Imaging and
Nonimaging Concentrators 156 5.4 Limit Case of Infi nitesimal Étendue:
Aplanatic Optics 164 5.5 3D Miñano-Benitez Design Method Applied to High
Solar Concentration 171 5.6 Köhler Integration in One Direction 180 5.7
Köhler Integration in Two Directions 195 5.8 Appendix 5.A Acceptance Angle
of Square Concentrators 201 5.9 Appendix 5.B Polychromatic Effi ciency 204
Acknowledgments 207 References 207 CHAPTER 6 LIGHTPIPE DESIGN 209 6.1
Background and Terminology 209 6.1.1 What is a Lightpipe 209 6.1.2
Lightpipe History 210 6.2 Lightpipe System Elements 211 6.2.1
Source/Coupling 211 6.2.2 Distribution/Transport 211 6.2.3 Delivery/Output
212 6.3 Lightpipe Ray Tracing 212 6.3.1 TIR 212 6.3.2 Ray Propagation 212
6.4 Charting 213 6.5 Bends 214 6.5.1 Bent Lightpipe: Circular Bend 214
6.5.1.1 Setup and Background 214 6.5.2 Bend Index for No Leakage 215 6.5.3
Refl ection at the Output Face 216 6.5.4 Refl ected Flux for a Specifi c
Bend 217 6.5.5 Loss Because of an Increase in NA 218 6.5.6 Other Bends 219
6.6 Mixing Rods 220 6.6.1 Overview 220 6.6.2 Why Some Shapes Provide
Uniformity 221 6.6.3 Design Factors Infl uencing Uniformity 223 6.6.3.1
Length 223 6.6.3.2 Solid versus Hollow 223 6.6.3.3 Periodic Distributions
224 6.6.3.4 Coherence 224 6.6.3.5 Angular Uniformity 224 6.6.3.6 Circular
Mixer with Ripples 225 6.6.4 RGB LEDs 226 6.6.4.1 RGB LEDs with Square
Mixers 226 6.6.4.2 RGB LEDs with Circular Mixers 227 6.6.5 Tapered Mixers
228 6.6.5.1 Length 229 6.6.5.2 Straight Taper Plus Lens 229 6.6.5.3 Angular
Uniformity 231 6.6.5.4 Straight + Diffuser + Taper 232 6.7 Backlights 233
6.7.1 Introduction 233 6.7.2 Backlight Overview 234 6.7.3 Optimization 235
6.7.4 Parameterization 235 6.7.4.1 Vary Number 236 6.7.4.2 Vary Size 236
6.7.5 Peak Density 237 6.7.6 Merit Function 237 6.7.7 Algorithm 238 6.7.8
Examples 239 6.7.8.1 Peaked Target Distribution 239 6.7.8.2 Border
Extractors 240 6.7.8.3 Input Surface Texturing 241 6.7.8.4 Variable Depth
Extractors 242 6.7.8.5 Inverted 3D Texture Structure 242 6.7.8.6 Key Pads
244 6.8 Nonuniform Lightpipe Shapes 245 6.9 Rod Luminaire 246
Acknowledgments 247 References 247 CHAPTER 7 SAMPLING, OPTIMIZATION, AND
TOLERANCING 251 7.1 Introduction 251 7.2 Design Tricks 253 7.2.1 Monte
Carlo Processes 254 7.2.1.1 Monte Carlo Sources 254 7.2.1.2 Monte Carlo Ray
Tracing 255 7.2.2 Reverse Ray Tracing 257 7.2.3 Importance Sampling 260
7.2.4 Far-Field Irradiance 263 7.3 Ray Sampling Theory 266 7.3.1 Transfer
Effi ciency Determination 266 7.3.2 Distribution Determination: Rose Model
268 7.4 Optimization 272 7.4.1 Geometrical Complexity 273 7.4.1.1 CAD
Geometry 274 7.4.1.2 Variables and Parameterization 275 7.4.1.3 Object
Overlap, Interference, Linking, and Mapping 277 7.4.2 Merit Function
Designation and Calculation 280 7.4.3 Optimization Methods 281 7.4.4
Fractional Optimization with Example: LED Collimator 282 7.5 Tolerancing
289 7.5.1 Types of Errors 290 7.5.2 System Error Sensitivity Analysis: LED
Die Position Offset 290 7.5.3 Process Error Case Study: Injection Molding
291 References 297 INDEX 299
TERMINOLOGY 1 1.1 What Is Illumination? 1 1.2 A Brief History of
Illumination Optics 2 1.3 Units 4 1.3.1 Radiometric Quantities 4 1.3.2
Photometric Quantities 6 1.4 Intensity 9 1.5 Illuminance and Irradiance 10
1.6 Luminance and Radiance 11 1.6.1 Lambertian 13 1.6.2 Isotropic 14 1.7
Important Factors in Illumination Design 15 1.7.1 Transfer Effi ciency 15
1.7.2 Uniformity of Illumination Distribution 16 1.8 Standard Optics Used
in Illumination Engineering 17 1.8.1 Refractive Optics 18 1.8.2 Refl ective
Optics 20 1.8.3 TIR Optics 22 1.8.4 Scattering Optics 24 1.8.5 Hybrid
Optics 24 1.9 The Process of Illumination System Design 25 1.10 Is
Illumination Engineering Hard? 28 1.11 Format for Succeeding Chapters 29
References 30 CHAPTER 2 ÉTENDUE 31 2.1 Étendue 32 2.2 Conservation of
Étendue 33 2.2.1 Proof of Conservation of Radiance and Étendue 34 2.2.2
Proof of Conservation of Generalized Étendue 36 2.2.3 Conservation of
Étendue from the Laws of Thermodynamics 40 2.3 Other Expressions for
Étendue 41 2.3.1 Radiance, Luminance, and Brightness 41 2.3.2 Throughput 42
2.3.3 Extent 43 2.3.4 Lagrange Invariant 43 2.3.5 Abbe Sine Condition 43
2.3.6 Confi guration or Shape Factor 44 2.4 Design Examples Using Étendue
45 2.4.1 Lambertian, Spatially Uniform Disk Emitter 45 2.4.2 Isotropic,
Spatially Uniform Disk Emitter 48 2.4.3 Isotropic, Spatially Nonuniform
Disk Emitter 50 2.4.4 Tubular Emitter 52 2.5 Concentration Ratio 59 2.6
Rotational Skew Invariant 61 2.6.1 Proof of Skew Invariance 61 2.6.2 Refi
ned Tubular Emitter Example 63 2.7 Étendue Discussion 67 References 68
CHAPTER 3 SQUEEZING THE ÉTENDUE 71 3.1 Introduction 71 3.2 Étendue
Squeezers versus Étendue Rotators 71 3.2.1 Étendue Rotating Mappings 74
3.2.2 Étendue Squeezing Mappings 77 3.3 Introductory Example of Étendue
Squeezer 79 3.3.1 Increasing the Number of Lenticular Elements 80 3.4
Canonical Étendue-Squeezing with Afocal Lenslet Arrays 82 3.4.1 Squeezing a
Collimated Beam 82 3.4.2 Other Afocal Designs 83 3.4.3 Étendue-Squeezing
Lenslet Arrays with Other Squeeze-Factors 85 3.5 Application to a Two
Freeform Mirror Condenser 88 3.6 Étendue Squeezing in Optical Manifolds 95
3.7 Conclusions 95 Appendix 3.A Galilean Afocal System 96 Appendix 3.B
Keplerian Afocal System 98 References 99 CHAPTER 4 SMS 3D DESIGN METHOD 101
4.1 Introduction 101 4.2 State of the Art of Freeform Optical Design
Methods 101 4.3. SMS 3D Statement of the Optical Problem 103 4.4 SMS Chains
104 4.4.1 SMS Chain Generation 105 4.4.2 Conditions 106 4.5 SMS Surfaces
106 4.5.1 SMS Ribs 107 4.5.2 SMS Skinning 108 4.5.3 Choosing the Seed Rib
109 4.6 Design Examples 109 4.6.1 SMS Design with a Prescribed Seed Rib 110
4.6.2 SMS Design with an SMS Spine as Seed Rib 111 4.6.3 Design of a Lens
(RR) with Thin Edge 115 4.6.4 Design of an XX Condenser for a Cylindrical
Source 117 4.6.5 Freeform XR for Photovoltaics Applications 129 4.6.5.1 The
XR Design Procedure 131 4.6.5.2 Results of Ray Tracing Analysis 135 4.7
Conclusions 140 References 144 CHAPTER 5 SOLAR CONCENTRATORS 147 5.1
Concentrated Solar Radiation 147 5.2 Acceptance Angle 148 5.3 Imaging and
Nonimaging Concentrators 156 5.4 Limit Case of Infi nitesimal Étendue:
Aplanatic Optics 164 5.5 3D Miñano-Benitez Design Method Applied to High
Solar Concentration 171 5.6 Köhler Integration in One Direction 180 5.7
Köhler Integration in Two Directions 195 5.8 Appendix 5.A Acceptance Angle
of Square Concentrators 201 5.9 Appendix 5.B Polychromatic Effi ciency 204
Acknowledgments 207 References 207 CHAPTER 6 LIGHTPIPE DESIGN 209 6.1
Background and Terminology 209 6.1.1 What is a Lightpipe 209 6.1.2
Lightpipe History 210 6.2 Lightpipe System Elements 211 6.2.1
Source/Coupling 211 6.2.2 Distribution/Transport 211 6.2.3 Delivery/Output
212 6.3 Lightpipe Ray Tracing 212 6.3.1 TIR 212 6.3.2 Ray Propagation 212
6.4 Charting 213 6.5 Bends 214 6.5.1 Bent Lightpipe: Circular Bend 214
6.5.1.1 Setup and Background 214 6.5.2 Bend Index for No Leakage 215 6.5.3
Refl ection at the Output Face 216 6.5.4 Refl ected Flux for a Specifi c
Bend 217 6.5.5 Loss Because of an Increase in NA 218 6.5.6 Other Bends 219
6.6 Mixing Rods 220 6.6.1 Overview 220 6.6.2 Why Some Shapes Provide
Uniformity 221 6.6.3 Design Factors Infl uencing Uniformity 223 6.6.3.1
Length 223 6.6.3.2 Solid versus Hollow 223 6.6.3.3 Periodic Distributions
224 6.6.3.4 Coherence 224 6.6.3.5 Angular Uniformity 224 6.6.3.6 Circular
Mixer with Ripples 225 6.6.4 RGB LEDs 226 6.6.4.1 RGB LEDs with Square
Mixers 226 6.6.4.2 RGB LEDs with Circular Mixers 227 6.6.5 Tapered Mixers
228 6.6.5.1 Length 229 6.6.5.2 Straight Taper Plus Lens 229 6.6.5.3 Angular
Uniformity 231 6.6.5.4 Straight + Diffuser + Taper 232 6.7 Backlights 233
6.7.1 Introduction 233 6.7.2 Backlight Overview 234 6.7.3 Optimization 235
6.7.4 Parameterization 235 6.7.4.1 Vary Number 236 6.7.4.2 Vary Size 236
6.7.5 Peak Density 237 6.7.6 Merit Function 237 6.7.7 Algorithm 238 6.7.8
Examples 239 6.7.8.1 Peaked Target Distribution 239 6.7.8.2 Border
Extractors 240 6.7.8.3 Input Surface Texturing 241 6.7.8.4 Variable Depth
Extractors 242 6.7.8.5 Inverted 3D Texture Structure 242 6.7.8.6 Key Pads
244 6.8 Nonuniform Lightpipe Shapes 245 6.9 Rod Luminaire 246
Acknowledgments 247 References 247 CHAPTER 7 SAMPLING, OPTIMIZATION, AND
TOLERANCING 251 7.1 Introduction 251 7.2 Design Tricks 253 7.2.1 Monte
Carlo Processes 254 7.2.1.1 Monte Carlo Sources 254 7.2.1.2 Monte Carlo Ray
Tracing 255 7.2.2 Reverse Ray Tracing 257 7.2.3 Importance Sampling 260
7.2.4 Far-Field Irradiance 263 7.3 Ray Sampling Theory 266 7.3.1 Transfer
Effi ciency Determination 266 7.3.2 Distribution Determination: Rose Model
268 7.4 Optimization 272 7.4.1 Geometrical Complexity 273 7.4.1.1 CAD
Geometry 274 7.4.1.2 Variables and Parameterization 275 7.4.1.3 Object
Overlap, Interference, Linking, and Mapping 277 7.4.2 Merit Function
Designation and Calculation 280 7.4.3 Optimization Methods 281 7.4.4
Fractional Optimization with Example: LED Collimator 282 7.5 Tolerancing
289 7.5.1 Types of Errors 290 7.5.2 System Error Sensitivity Analysis: LED
Die Position Offset 290 7.5.3 Process Error Case Study: Injection Molding
291 References 297 INDEX 299
PREFACE xiii CONTRIBUTORS xvii GLOSSARY xix CHAPTER 1 INTRODUCTION AND
TERMINOLOGY 1 1.1 What Is Illumination? 1 1.2 A Brief History of
Illumination Optics 2 1.3 Units 4 1.3.1 Radiometric Quantities 4 1.3.2
Photometric Quantities 6 1.4 Intensity 9 1.5 Illuminance and Irradiance 10
1.6 Luminance and Radiance 11 1.6.1 Lambertian 13 1.6.2 Isotropic 14 1.7
Important Factors in Illumination Design 15 1.7.1 Transfer Effi ciency 15
1.7.2 Uniformity of Illumination Distribution 16 1.8 Standard Optics Used
in Illumination Engineering 17 1.8.1 Refractive Optics 18 1.8.2 Refl ective
Optics 20 1.8.3 TIR Optics 22 1.8.4 Scattering Optics 24 1.8.5 Hybrid
Optics 24 1.9 The Process of Illumination System Design 25 1.10 Is
Illumination Engineering Hard? 28 1.11 Format for Succeeding Chapters 29
References 30 CHAPTER 2 ÉTENDUE 31 2.1 Étendue 32 2.2 Conservation of
Étendue 33 2.2.1 Proof of Conservation of Radiance and Étendue 34 2.2.2
Proof of Conservation of Generalized Étendue 36 2.2.3 Conservation of
Étendue from the Laws of Thermodynamics 40 2.3 Other Expressions for
Étendue 41 2.3.1 Radiance, Luminance, and Brightness 41 2.3.2 Throughput 42
2.3.3 Extent 43 2.3.4 Lagrange Invariant 43 2.3.5 Abbe Sine Condition 43
2.3.6 Confi guration or Shape Factor 44 2.4 Design Examples Using Étendue
45 2.4.1 Lambertian, Spatially Uniform Disk Emitter 45 2.4.2 Isotropic,
Spatially Uniform Disk Emitter 48 2.4.3 Isotropic, Spatially Nonuniform
Disk Emitter 50 2.4.4 Tubular Emitter 52 2.5 Concentration Ratio 59 2.6
Rotational Skew Invariant 61 2.6.1 Proof of Skew Invariance 61 2.6.2 Refi
ned Tubular Emitter Example 63 2.7 Étendue Discussion 67 References 68
CHAPTER 3 SQUEEZING THE ÉTENDUE 71 3.1 Introduction 71 3.2 Étendue
Squeezers versus Étendue Rotators 71 3.2.1 Étendue Rotating Mappings 74
3.2.2 Étendue Squeezing Mappings 77 3.3 Introductory Example of Étendue
Squeezer 79 3.3.1 Increasing the Number of Lenticular Elements 80 3.4
Canonical Étendue-Squeezing with Afocal Lenslet Arrays 82 3.4.1 Squeezing a
Collimated Beam 82 3.4.2 Other Afocal Designs 83 3.4.3 Étendue-Squeezing
Lenslet Arrays with Other Squeeze-Factors 85 3.5 Application to a Two
Freeform Mirror Condenser 88 3.6 Étendue Squeezing in Optical Manifolds 95
3.7 Conclusions 95 Appendix 3.A Galilean Afocal System 96 Appendix 3.B
Keplerian Afocal System 98 References 99 CHAPTER 4 SMS 3D DESIGN METHOD 101
4.1 Introduction 101 4.2 State of the Art of Freeform Optical Design
Methods 101 4.3. SMS 3D Statement of the Optical Problem 103 4.4 SMS Chains
104 4.4.1 SMS Chain Generation 105 4.4.2 Conditions 106 4.5 SMS Surfaces
106 4.5.1 SMS Ribs 107 4.5.2 SMS Skinning 108 4.5.3 Choosing the Seed Rib
109 4.6 Design Examples 109 4.6.1 SMS Design with a Prescribed Seed Rib 110
4.6.2 SMS Design with an SMS Spine as Seed Rib 111 4.6.3 Design of a Lens
(RR) with Thin Edge 115 4.6.4 Design of an XX Condenser for a Cylindrical
Source 117 4.6.5 Freeform XR for Photovoltaics Applications 129 4.6.5.1 The
XR Design Procedure 131 4.6.5.2 Results of Ray Tracing Analysis 135 4.7
Conclusions 140 References 144 CHAPTER 5 SOLAR CONCENTRATORS 147 5.1
Concentrated Solar Radiation 147 5.2 Acceptance Angle 148 5.3 Imaging and
Nonimaging Concentrators 156 5.4 Limit Case of Infi nitesimal Étendue:
Aplanatic Optics 164 5.5 3D Miñano-Benitez Design Method Applied to High
Solar Concentration 171 5.6 Köhler Integration in One Direction 180 5.7
Köhler Integration in Two Directions 195 5.8 Appendix 5.A Acceptance Angle
of Square Concentrators 201 5.9 Appendix 5.B Polychromatic Effi ciency 204
Acknowledgments 207 References 207 CHAPTER 6 LIGHTPIPE DESIGN 209 6.1
Background and Terminology 209 6.1.1 What is a Lightpipe 209 6.1.2
Lightpipe History 210 6.2 Lightpipe System Elements 211 6.2.1
Source/Coupling 211 6.2.2 Distribution/Transport 211 6.2.3 Delivery/Output
212 6.3 Lightpipe Ray Tracing 212 6.3.1 TIR 212 6.3.2 Ray Propagation 212
6.4 Charting 213 6.5 Bends 214 6.5.1 Bent Lightpipe: Circular Bend 214
6.5.1.1 Setup and Background 214 6.5.2 Bend Index for No Leakage 215 6.5.3
Refl ection at the Output Face 216 6.5.4 Refl ected Flux for a Specifi c
Bend 217 6.5.5 Loss Because of an Increase in NA 218 6.5.6 Other Bends 219
6.6 Mixing Rods 220 6.6.1 Overview 220 6.6.2 Why Some Shapes Provide
Uniformity 221 6.6.3 Design Factors Infl uencing Uniformity 223 6.6.3.1
Length 223 6.6.3.2 Solid versus Hollow 223 6.6.3.3 Periodic Distributions
224 6.6.3.4 Coherence 224 6.6.3.5 Angular Uniformity 224 6.6.3.6 Circular
Mixer with Ripples 225 6.6.4 RGB LEDs 226 6.6.4.1 RGB LEDs with Square
Mixers 226 6.6.4.2 RGB LEDs with Circular Mixers 227 6.6.5 Tapered Mixers
228 6.6.5.1 Length 229 6.6.5.2 Straight Taper Plus Lens 229 6.6.5.3 Angular
Uniformity 231 6.6.5.4 Straight + Diffuser + Taper 232 6.7 Backlights 233
6.7.1 Introduction 233 6.7.2 Backlight Overview 234 6.7.3 Optimization 235
6.7.4 Parameterization 235 6.7.4.1 Vary Number 236 6.7.4.2 Vary Size 236
6.7.5 Peak Density 237 6.7.6 Merit Function 237 6.7.7 Algorithm 238 6.7.8
Examples 239 6.7.8.1 Peaked Target Distribution 239 6.7.8.2 Border
Extractors 240 6.7.8.3 Input Surface Texturing 241 6.7.8.4 Variable Depth
Extractors 242 6.7.8.5 Inverted 3D Texture Structure 242 6.7.8.6 Key Pads
244 6.8 Nonuniform Lightpipe Shapes 245 6.9 Rod Luminaire 246
Acknowledgments 247 References 247 CHAPTER 7 SAMPLING, OPTIMIZATION, AND
TOLERANCING 251 7.1 Introduction 251 7.2 Design Tricks 253 7.2.1 Monte
Carlo Processes 254 7.2.1.1 Monte Carlo Sources 254 7.2.1.2 Monte Carlo Ray
Tracing 255 7.2.2 Reverse Ray Tracing 257 7.2.3 Importance Sampling 260
7.2.4 Far-Field Irradiance 263 7.3 Ray Sampling Theory 266 7.3.1 Transfer
Effi ciency Determination 266 7.3.2 Distribution Determination: Rose Model
268 7.4 Optimization 272 7.4.1 Geometrical Complexity 273 7.4.1.1 CAD
Geometry 274 7.4.1.2 Variables and Parameterization 275 7.4.1.3 Object
Overlap, Interference, Linking, and Mapping 277 7.4.2 Merit Function
Designation and Calculation 280 7.4.3 Optimization Methods 281 7.4.4
Fractional Optimization with Example: LED Collimator 282 7.5 Tolerancing
289 7.5.1 Types of Errors 290 7.5.2 System Error Sensitivity Analysis: LED
Die Position Offset 290 7.5.3 Process Error Case Study: Injection Molding
291 References 297 INDEX 299
TERMINOLOGY 1 1.1 What Is Illumination? 1 1.2 A Brief History of
Illumination Optics 2 1.3 Units 4 1.3.1 Radiometric Quantities 4 1.3.2
Photometric Quantities 6 1.4 Intensity 9 1.5 Illuminance and Irradiance 10
1.6 Luminance and Radiance 11 1.6.1 Lambertian 13 1.6.2 Isotropic 14 1.7
Important Factors in Illumination Design 15 1.7.1 Transfer Effi ciency 15
1.7.2 Uniformity of Illumination Distribution 16 1.8 Standard Optics Used
in Illumination Engineering 17 1.8.1 Refractive Optics 18 1.8.2 Refl ective
Optics 20 1.8.3 TIR Optics 22 1.8.4 Scattering Optics 24 1.8.5 Hybrid
Optics 24 1.9 The Process of Illumination System Design 25 1.10 Is
Illumination Engineering Hard? 28 1.11 Format for Succeeding Chapters 29
References 30 CHAPTER 2 ÉTENDUE 31 2.1 Étendue 32 2.2 Conservation of
Étendue 33 2.2.1 Proof of Conservation of Radiance and Étendue 34 2.2.2
Proof of Conservation of Generalized Étendue 36 2.2.3 Conservation of
Étendue from the Laws of Thermodynamics 40 2.3 Other Expressions for
Étendue 41 2.3.1 Radiance, Luminance, and Brightness 41 2.3.2 Throughput 42
2.3.3 Extent 43 2.3.4 Lagrange Invariant 43 2.3.5 Abbe Sine Condition 43
2.3.6 Confi guration or Shape Factor 44 2.4 Design Examples Using Étendue
45 2.4.1 Lambertian, Spatially Uniform Disk Emitter 45 2.4.2 Isotropic,
Spatially Uniform Disk Emitter 48 2.4.3 Isotropic, Spatially Nonuniform
Disk Emitter 50 2.4.4 Tubular Emitter 52 2.5 Concentration Ratio 59 2.6
Rotational Skew Invariant 61 2.6.1 Proof of Skew Invariance 61 2.6.2 Refi
ned Tubular Emitter Example 63 2.7 Étendue Discussion 67 References 68
CHAPTER 3 SQUEEZING THE ÉTENDUE 71 3.1 Introduction 71 3.2 Étendue
Squeezers versus Étendue Rotators 71 3.2.1 Étendue Rotating Mappings 74
3.2.2 Étendue Squeezing Mappings 77 3.3 Introductory Example of Étendue
Squeezer 79 3.3.1 Increasing the Number of Lenticular Elements 80 3.4
Canonical Étendue-Squeezing with Afocal Lenslet Arrays 82 3.4.1 Squeezing a
Collimated Beam 82 3.4.2 Other Afocal Designs 83 3.4.3 Étendue-Squeezing
Lenslet Arrays with Other Squeeze-Factors 85 3.5 Application to a Two
Freeform Mirror Condenser 88 3.6 Étendue Squeezing in Optical Manifolds 95
3.7 Conclusions 95 Appendix 3.A Galilean Afocal System 96 Appendix 3.B
Keplerian Afocal System 98 References 99 CHAPTER 4 SMS 3D DESIGN METHOD 101
4.1 Introduction 101 4.2 State of the Art of Freeform Optical Design
Methods 101 4.3. SMS 3D Statement of the Optical Problem 103 4.4 SMS Chains
104 4.4.1 SMS Chain Generation 105 4.4.2 Conditions 106 4.5 SMS Surfaces
106 4.5.1 SMS Ribs 107 4.5.2 SMS Skinning 108 4.5.3 Choosing the Seed Rib
109 4.6 Design Examples 109 4.6.1 SMS Design with a Prescribed Seed Rib 110
4.6.2 SMS Design with an SMS Spine as Seed Rib 111 4.6.3 Design of a Lens
(RR) with Thin Edge 115 4.6.4 Design of an XX Condenser for a Cylindrical
Source 117 4.6.5 Freeform XR for Photovoltaics Applications 129 4.6.5.1 The
XR Design Procedure 131 4.6.5.2 Results of Ray Tracing Analysis 135 4.7
Conclusions 140 References 144 CHAPTER 5 SOLAR CONCENTRATORS 147 5.1
Concentrated Solar Radiation 147 5.2 Acceptance Angle 148 5.3 Imaging and
Nonimaging Concentrators 156 5.4 Limit Case of Infi nitesimal Étendue:
Aplanatic Optics 164 5.5 3D Miñano-Benitez Design Method Applied to High
Solar Concentration 171 5.6 Köhler Integration in One Direction 180 5.7
Köhler Integration in Two Directions 195 5.8 Appendix 5.A Acceptance Angle
of Square Concentrators 201 5.9 Appendix 5.B Polychromatic Effi ciency 204
Acknowledgments 207 References 207 CHAPTER 6 LIGHTPIPE DESIGN 209 6.1
Background and Terminology 209 6.1.1 What is a Lightpipe 209 6.1.2
Lightpipe History 210 6.2 Lightpipe System Elements 211 6.2.1
Source/Coupling 211 6.2.2 Distribution/Transport 211 6.2.3 Delivery/Output
212 6.3 Lightpipe Ray Tracing 212 6.3.1 TIR 212 6.3.2 Ray Propagation 212
6.4 Charting 213 6.5 Bends 214 6.5.1 Bent Lightpipe: Circular Bend 214
6.5.1.1 Setup and Background 214 6.5.2 Bend Index for No Leakage 215 6.5.3
Refl ection at the Output Face 216 6.5.4 Refl ected Flux for a Specifi c
Bend 217 6.5.5 Loss Because of an Increase in NA 218 6.5.6 Other Bends 219
6.6 Mixing Rods 220 6.6.1 Overview 220 6.6.2 Why Some Shapes Provide
Uniformity 221 6.6.3 Design Factors Infl uencing Uniformity 223 6.6.3.1
Length 223 6.6.3.2 Solid versus Hollow 223 6.6.3.3 Periodic Distributions
224 6.6.3.4 Coherence 224 6.6.3.5 Angular Uniformity 224 6.6.3.6 Circular
Mixer with Ripples 225 6.6.4 RGB LEDs 226 6.6.4.1 RGB LEDs with Square
Mixers 226 6.6.4.2 RGB LEDs with Circular Mixers 227 6.6.5 Tapered Mixers
228 6.6.5.1 Length 229 6.6.5.2 Straight Taper Plus Lens 229 6.6.5.3 Angular
Uniformity 231 6.6.5.4 Straight + Diffuser + Taper 232 6.7 Backlights 233
6.7.1 Introduction 233 6.7.2 Backlight Overview 234 6.7.3 Optimization 235
6.7.4 Parameterization 235 6.7.4.1 Vary Number 236 6.7.4.2 Vary Size 236
6.7.5 Peak Density 237 6.7.6 Merit Function 237 6.7.7 Algorithm 238 6.7.8
Examples 239 6.7.8.1 Peaked Target Distribution 239 6.7.8.2 Border
Extractors 240 6.7.8.3 Input Surface Texturing 241 6.7.8.4 Variable Depth
Extractors 242 6.7.8.5 Inverted 3D Texture Structure 242 6.7.8.6 Key Pads
244 6.8 Nonuniform Lightpipe Shapes 245 6.9 Rod Luminaire 246
Acknowledgments 247 References 247 CHAPTER 7 SAMPLING, OPTIMIZATION, AND
TOLERANCING 251 7.1 Introduction 251 7.2 Design Tricks 253 7.2.1 Monte
Carlo Processes 254 7.2.1.1 Monte Carlo Sources 254 7.2.1.2 Monte Carlo Ray
Tracing 255 7.2.2 Reverse Ray Tracing 257 7.2.3 Importance Sampling 260
7.2.4 Far-Field Irradiance 263 7.3 Ray Sampling Theory 266 7.3.1 Transfer
Effi ciency Determination 266 7.3.2 Distribution Determination: Rose Model
268 7.4 Optimization 272 7.4.1 Geometrical Complexity 273 7.4.1.1 CAD
Geometry 274 7.4.1.2 Variables and Parameterization 275 7.4.1.3 Object
Overlap, Interference, Linking, and Mapping 277 7.4.2 Merit Function
Designation and Calculation 280 7.4.3 Optimization Methods 281 7.4.4
Fractional Optimization with Example: LED Collimator 282 7.5 Tolerancing
289 7.5.1 Types of Errors 290 7.5.2 System Error Sensitivity Analysis: LED
Die Position Offset 290 7.5.3 Process Error Case Study: Injection Molding
291 References 297 INDEX 299