Preface xi



1 Introduction 1

1.1 Overview of LED Lighting 1

1.2 Development Trends of LED Packaging and Applications 5

1.3 Three Key Issues of Optical Design of LED Lighting 7

1.3.1 System Luminous Efficiency 7

1.3.2 Controllable Light Pattern 7

1.3.3 Spatial Color Uniformity 8

1.4 Introduction of Freeform Optics 10

References 12



2 Review of Main Algorithms of Freeform Optics for LED Lighting 15

2.1 Introduction 15

2.2 Tailored Design Method 16

2.3 SMS Design Method 17

2.4 Light Energy Mapping Design Method 18

2.5 Generalized Functional Design Method 19

2.6 Design Method for Uniform Illumination with Multiple Sources 22

References 22



3 Basic Algorithms of Freeform Optics for LED Lighting 25

3.1 Introduction 25

3.2 Circularly Symmetrical Freeform Lens–Point Source 25

3.2.1 Freeform Lens for Large Emitting Angles 26

3.2.1.1 Step 1. Establish a Light Energy Mapping Relationship between the Light Source and Target 27

3.2.1.2 Step 2. Construct a Freeform Lens 31

3.2.1.3 Step 3. Validation and Optimization 33

3.2.2 TIR-Freeform Lens for Small Emitting Angle 33

3.2.3 Circularly Symmetrical Double Surfaces Freeform Lens 39

3.3 Circularly Symmetrical Freeform Lens – Extended Source 42

3.3.1 Step 1. Construction of a Point Source Freeform Lens 45

3.3.2 Step 2. Calculation of Feedback Optimization Ratios 45

3.3.3 Step 3. Grids Redivision of the Target Plane and Light Source 46

3.3.4 Step 4. Rebuild the Energy Relationship between the Light Source and Target Plane 46

3.3.5 Step 5. Construction of a Freeform Lens for an Extended Source 47

3.3.6 Step 6. Ray-Tracing Simulation and Feedback Reversing Optimization 47

3.4 Noncircularly Symmetrical Freeform Lens–Point Source 48

3.4.1 Discontinuous Freeform Lens Algorithm 49

3.4.1.1 Step 1. Establishment of a Light Energy Mapping Relationship 49

3.4.1.2 Step 2. Construction of the Lens 52

3.4.1.3 Step 3. Validation of Lens Design 55

3.4.2 Continuous Freeform Lens Algorithm 55

3.4.2.1 Radiate Grid Light Energy Mapping 57

3.4.2.2 Rectangular Grid Light Energy Mapping 58

3.5 Noncircularly Symmetrical Freeform Lens–Extended Source 60

3.5.1 Step 1. Establishment of the Light Energy Mapping Relationship 61

3.5.2 Step 2. Construction of a Freeform Lens 61

3.5.3 Step 3. Validation of Lens Design 62

3.6 Reversing the Design Method for Uniform Illumination of LED Arrays 63

3.6.1 Reversing the Design Method of LIDC for Uniform Illumination 64

3.6.2 Algorithm of a Freeform Lens for the Required LIDC 66

References 68



4 Application-Specific LED Package Integrated with a Freeform Lens 71

4.1 Application-Specific LED Package (ASLP) Design Concept 71

4.2 ASLP Single Module 72

4.2.1 Design Method of a Compact Freeform Lens 72

4.2.2 Design of the ASLP Module 73

4.2.2.1 Optical Modeling 73

4.2.2.2 Design of a Compact Freeform Lens 73

4.2.2.3 ASLP Module 74

4.2.3 Numerical Analyses and Tolerance Analyses 76

4.2.3.1 Numerical Simulation and Analyses 76

4.2.3.2 Tolerance Analyses 77

4.2.3.3 Experiments 81

4.3 ASLP Array Module 85

4.4 ASLP System Integrated with Multiple Functions 87

4.4.1 Optical Design 89

4.4.1.1 Problem Statement 89

4.4.1.2 Optical Modeling 89

4.4.1.3 Design of a Freeform Lens 90

4.4.1.4 Simulation of Lighting Performance 91

4.4.2 Thermal Management 91

4.4.3 ASLP Module 94

References 96



5 Freeform Optics for LED Indoor Lighting 99

5.1 Introduction 99

5.2 A Large-Emitting-Angle Freeform Lens with a Small LED Source 99

5.2.1 A Freeform Lens for a Philip Lumileds K2 LED 100

5.2.2 Freeform Lens for a CREE XLamp XR-E LED 103

5.3 A Large-Emitting-Angle Freeform Lens with an Extended Source 108

5.3.1 Target Plane Grids Optimization 108

5.3.2 Light Source Grids Optimization 108

5.3.3 Target Plane and Light Source Grids Coupling Optimization 109

5.4 A Small-Emitting-Angle Freeform Lens with a Small LED Source 110

5.5 A Double-Surface Freeform Lens for Uniform Illumination 113

5.5.1 Design Example 1 114

5.5.2 Design Example 2 115

5.5.3 Design Example 3 116

5.6 A Freeform Lens for Uniform Illumination of an LED High Bay Lamp Array 117

5.6.1 Design Concept 117

5.6.2 Design Case 118

5.6.2.1 Algorithms and Design Procedure 118

5.6.2.2 Optical Structures 119

5.6.2.3 Monte Carlo Optical Simulation 121

References 124



6 Freeform Optics for LED Road Lighting 125

6.1 Introduction 125

6.2 The Optical Design Concept of LED Road Lighting 126

6.2.1 Illuminance 127

6.2.2 Luminance 128

6.2.3 Glare RestrictionThreshold Increment 129

6.2.4 Surrounding Ratio 130

6.3 Discontinuous Freeform Lenses (DFLs) for LED Road Lighting 131

6.3.1 Design of DFLs for Rectangular Radiation Patterns 131

6.3.1.1 Step 1. Optical Modeling for an LED 131

6.3.1.2 Step 2. Freeform Lens Design 133

6.3.2 Simulation Illumination Performance and Tolerance Analyses 134

6.3.3 Experimental Analyses 139

6.3.4 Effects of Manufacturing Defects on the Lighting Performance 139

6.3.4.1 Surface Morphology 144

6.3.4.2 Optical Performance Testing 146

6.3.4.3 Analysis and Discussion 150

6.3.5 Case Study–LED Road Lamps Based on DFLs 152

6.4 Continuous Freeform Lens (CFL) for LED Road Lighting 154

6.4.1 CFL Based on the Radiate Grid MappingMethod 154

6.4.2 CFL Based on the Rectangular Grid MappingMethod 154

6.4.3 Spatial Color Uniformity Analyses of a Continuous Freeform Lens 158

6.5 Freeform Lens for an LED Road Lamp with Uniform Luminance 164

6.5.1 Problem Statement 164

6.5.2 Combined Design Method for Uniform Luminance in Road Lighting 166

6.5.3 Freeform Lens Design Method for Uniform-Luminance Road Lighting 171

6.6 Asymmetrical CFLs with a High Light Energy Utilization Ratio 174

6.7 Modularized LED Road Lamp Based on Freeform Optics 178

References 178



7 Freeform Optics for a Direct-Lit LED Backlighting Unit 181

7.1 Introduction 181

7.2 Optical Design Concept of a Direct-Lit LED BLU 183

7.3 Freeform Optics for Uniform Illumination with a Large DHR 186

7.4 Freeform Optics for Uniform Illumination with an Extended Source 191

7.4.1 Algorithm of a Freeform Lens for Uniform Illumination with an Extended Source 194

7.4.2 Design Method of a Freeform Lens for Extended Source Uniform Illumination 195

7.4.2.1 Step 1. Calculation of FORs 196

7.4.2.2 Step 2. Energy Grids Division for an Extended Source 197

7.4.2.3 Step 3. Construction of a Freeform Lens for an Extended Source 198

7.4.2.4 Step 4. Ray-Tracing Simulation and Circulation Feedback Optimization 198

7.4.3 Freeform Lenses for Direct-Lit BLUs with an Extended Source 198

7.5 Petal-Shaped Freeform Optics for High-System-Efficiency LED BLUs 203

7.5.1 Optical Co-design from the System Level of BLUs 203

7.5.2 Optimization of a High-Efficiency LIDC for BEFs 203

7.5.3 Petal-Shaped Freeform Lenses, and ASLPs for High-Efficiency BLUs 206

7.6 BEF-Adaptive Freeform Optics for High-System-Efficiency LED BLUs 210

7.6.1 Design Concept and Method 210

7.6.1.1 Step 1. Finding Out the Best Incident Angle Range 211

7.6.1.2 Step 2. Redistribution of Original Output LIDC 212

7.6.1.3 Step 3. Construction of a BEF-Adaptive Lens 213

7.6.2 BEF-Adaptive Lens Design Case 213

7.6.2.1 Basic Setup of a BLU 213

7.6.2.2 Design Results and Optical Validation 214

7.7 Freeform Optics for Uniform Illumination with Large DHR, Extended Source and Near Field 219

7.7.1 Design Method 220

7.7.1.1 IDF of Single Extended Source 220

7.7.1.2 IDF of Freeform Lens 221

7.7.1.3 Construction of Freeform Lens 222

7.7.1.4 Ray Tracing Simulation and Verification 223

7.7.2 Design Example 223

References 228



8 Freeform Optics for LED Automotive Headlamps 231

8.1 Introduction 231

8.2 Optical Regulations of Low-Beam and High-Beam Light 231

8.2.1 Low-Beam 231

8.2.2 High-Beam 232

8.2.3 Color Range 232

8.3 Application-Specific LED Packaging for Headlamps 234

8.3.1 Small étendue 234

8.3.2 High Luminance 235

8.3.3 Strip Shape Emitter with a Sharp Cutoff 236

8.3.4 Small Thermal Resistance of Packaging 236

8.3.5 ASLP Design Case 236

8.3.6 Types of LED Packaging Modules for Headlamps 238

8.4 Freeform Lens for High-Efficiency LED Headlamps 239

8.4.1 Introduction 239

8.4.2 Freeform Lens Design Methods 239

8.4.2.1 Design of Collection Optics 240

8.4.2.2 Design of Refraction Optics 241

8.4.3 Design Case of a Freeform Lens for Low-Beam and High-Beam 243

8.4.3.1 Design of a Low-Beam Lens 244

8.4.3.2 Design of a High-Beam Lens 246

8.4.4 Design Case of a Freeform Lens for a Low-Beam Headlamp Module 249

8.5 Freeform Optics Integrated PES for an LED Headlamp 250

8.6 Freeform Optics Integrated MR for an LED Headlamp 255

8.7 LED Headlamps Based on Both PES and MR Reflectors 260

8.8 LED Module Integrated with Low-Beam and High-Beam 263

References 266



9 Freeform Optics for Emerging LED Applications 269

9.1 Introduction 269

9.2 Total Internal Reflection (TIR)-Freeform Lens for an LED Pico-Projector 269

9.2.1 Introduction 269

9.2.2 Problem Statement 271

9.2.2.1 Defect of a Refracting Freeform Surface for Illumination with a Small Output Angle 271

9.2.2.2 Problem of an Extended Light Source 272

9.2.3 Integral Freeform Illumination Lens Design Based on an LED’s Light Source 273

9.2.3.1 Freeform TIR Lens Design 273

9.2.3.2 Top Surface Design of the TIR Lens 273

9.2.4 Optimization of the Integral Freeform Illumination Lens 279

9.2.5 Tolerance analysis 280

9.2.6 LED Pico-Projector Based on the Designed Freeform Lens 281

9.3 Freeform Lens Array Optical System for an LED Stage Light 283

9.3.1 Design of a One-Dimensional Beam Expander Based on a Freeform Lens Array 285

9.3.1.1 Part 1. Gridding of the One-Dimensional Target Plane 285

9.3.1.2 Part 2. Algorithm of a One-Dimensional Freeform Microstructure 285

9.3.1.3 Part 3. Optical Simulation Results of the Optical System 287

9.3.2 Design of a Rectangular Beam Expander Based on a Freeform Lens Array 287

9.3.2.1 Part 1. Algorithm of the Rectangular Freeform Structure 288

9.3.2.2 Part 2. Optical Simulation Results of the Optical System 291

9.4 Freeform Optics for a LED Airport Taxiway Light 291

9.4.1 Introduction 290

9.4.2 Requirement Statement 291

9.4.3 Design Method of an Optical System 291

9.4.4 Simulation and Optimization 293

9.4.5 Tolerance Analysis 294

9.4.6 Design of an LED Taxiway Centerline Lamp 295

9.5 Freeform Optics for LED Searchlights 297

9.5.1 Introduction 297

9.5.2 Freeform Lens Design of a Small Divergence Angle 298

9.5.3 Improving Methods and Tolerance Analysis 301

9.5.3.1 The Design of a Freeform Lens and Parabolic Reflector 301

9.5.3.2 Tolerance Analysis 304

References 305



10 Freeform Optics for LED Lighting with High Spatial Color Uniformity 307

10.1 Introduction 307

10.2 Optical Design Concept 308

10.3 Freeform Lens Integrated LED Module with a High SCU 309

10.3.1 Optical Design, Molding, and Simulation 309

10.3.2 Tolerance Analyses 312

10.3.3 Secondary Freeform Lens for a High SCU 313

10.3.4 Experimental Analyses 314

10.4 TIR-Freeform Lens Integrated LED Module with a High SCU 323

10.4.1 Introduction 323

10.4.2 Design Principle for a High SCU 325

10.4.3 Design Method of the Modified TIR-Freeform Lens 325

10.4.4 Optimization Results and Discussions 328

References 332



Appendix: Codes of Basic Algorithms of Freeform Optics for LED Lighting 335



Index 351