Illumination Engineering Design with Nonimaging Optics

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

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