Introduction ho NONIMAGING OPTICS

Julio Chaves Light Prescriptions Innovators Madrid, Spain

(^oC) CRC Press V*^ / Taylor & Francis Group Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Croup, an Informa business Contents

Foreword xv Preface xvii Acknowledgments xix Author xxi List of Symbols xxiii List of Abbreviations and Terms xxv

Part I Nonimaging Optics 1

1 Fundamental Concepts 3 1.1 Introduction 3 1.2 Imaging and Nonimaging Optics 3 1.3 The Compound Parabolic Concentrator 8 1.4 Maximum Concentration 17 1.5 Examples 22 References 23

2 Design of Two-Dimensional Concentrators 25 2.1 Introduction 25 2.2 Concentrators for Sources at a Finite Distance 25 2.3 Concentrators for Tubular Receivers 27 2.4 Angle Transformers 29 2.5 The String Method 30 2.6 Optics with Dielectrics 35 2.7 Asymmetrical Optics 37 2.8 Examples 41 References 52

3 Etendue and the Winston-Welford Design Method 55 3.1 Introduction 55 3.2 Conservation of Etendue 57 3.3 Nonideal Optical Systems 63 3.4 Etendue as a Geometrical Quantity 65 3.5 Two-Dimensional Systems 68 3.6 Etendue as an Integral of the Optical Momentum 70 3.7 Etendue as a Volume in Phase Space 75 3.8 Etendue as a Difference in Optical Path Length 78 3.9 Flow Lines 83 3.10 The Winston-Welford Design Method 87 3.11 Caustics as Flow Lines 99

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3.12 Maximum Concentration 102 3.13 Etendue and the Shape Factor 106 3.14 Examples 110 References 115

Vector Flux 117 4.1 Introduction 117 4.2 Definition of Vector Flux 121 4.3 Vector Flux as a Bisector of the Edge Rays 126 4.4 Vector Flux and Etendue 127 4.5 Vector Flux for Disk-Shaped Lambertian Sources 129 4.6 Design of Concentrators Using the Vector Flux 134 4.7 Examples 136 References 138

Combination of Primaries with Flow-Line Secondaries 139 5.1 Introduction 139 5.2 Reshaping the Receiver 141 5.3 Compound Elliptical Concentrator Secondary 145 5.4 Truncated Trumpet Secondary 148 5.5 Trumpet Secondary for a Large Receiver 150 5.6 Secondaries with Multiple Entry Apertures 152 5.7 Tailored Edge Ray Concentrators Designed for Maximum Concentration 156 5.8 Tailored Edge Ray Concentrators Designed for Lower Concentration 165 5.9 Fresnel Primaries 168 5.10 Tailored Edge Ray Concentrators for Fresnel Primaries 171 5.11 Examples 178 References 191

Stepped Flow-Line Nonimaging Optics 193 6.1 Introduction 193 6.2 Compact Concentrators 193 6.3 Concentrators with Gaps 200 6.4 Examples 206 References 209

Luminaires 211 7.1 Introduction 211 7.2 Luminaires for Large Source and Flat Mirrors 212 7.3 The General Approach for Flat Sources 224 7.4 Far-Edge Diverging Luminaires for Flat Sources 227 7.5 Far-Edge Converging Luminaires for Flat Sources 230 7 6 Near-Edge Diverging Luminaires for Flat Sources 234 7.7 Near-Edge Converging Luminaires for Flat Sources 239 7.8 Luminaires for Circular Sources 241 Contents xi

7.9 Examples 255 7.10 Appendix A: Mirror Differential Equation for Linear Sources 266 7.11 Appendix B: Mirror Differential Equation for Circular Sources 268 References 270

8 Minano-Benitez Design Method (Simultaneous Multiple Surface) 271 8.1 Introduction 271 8.2 The RR Optic 273 8.3 The XR, RX, and XX Optics 291 8.4 The Minano-Benitez Design Method with Generalized Wave Fronts 300 8.5 The RXI Optic 306 8.6 Other Types of Simultaneous Multiple Surface Optics 313 8.7 Examples 313 References 324

9 The Mifiano Design Method Using Poisson Brackets 325 9.1 Introduction 325 9.2 Design of Two-Dimensional Concentrators for Inhomogeneous Media 325 9.3 Edge Rays as a Tubular Surface in Phase Space 329 9.4 Poisson Brackets 335 9.5 Curvilinear Coordinate System 338 9.6 Design of Two-Dimensional Concentrators 340 9.7 An Example of an Ideal Two-Dimensional Concentrator 342 9.8 Design of Three-Dimensional Concentrators 349 9.9 An Example of an Ideal Three-Dimensional Concentrator 355 References 358

Part II Geometrical Optics 361

10 Lagrangian and Hamiltonian Geometrical Optics 363 10.1 Fermat's Principle 363 10.2 Lagrangian and Hamiltonian Formulations 370 10.3 Optical Lagrangian and Hamiltonian 374 10.4 Another Form for the Hamiltonian Formulation 378 10.5 Change of Coordinate System in the Hamilton Equations 382 References 388

11 Rays and Wave Fronts 389 11.1 Optical Momentum 389 11.2 The Eikonal Equation 394 11.3 The Ray Equation 395 Xll Contents

11.4 Optical Path Length between Two Wave Fronts 397 References 401

12 Reflection and Refraction 403 12.1 Reflected and Refracted Rays 403 12.2 The Laws of Reflection and Refraction 409 References 413

13 Symmetry 415 13.1 Conservation of Momentum and Apparent Refractive Index 415 13.2 Linear Symmetry 418 13.3 Circular Symmetry and Skew Invariant 420 References 429

14 Etendue in Phase Space 431 14.1 Etendue and the Point Characteristic Function 431 14.2 Etendue in Hamiltonian Optics 434 References 437

15 Classical Mechanics and Geometrical Optics 439 15.1 Fermat's Principle and Maupertuis' Principle 439 15.2 Skew Invariant and Conservation of Angular Momentum 443 15.3 Potential in Mechanics and Refractive Index in Optics 444 References 444

16 Radiometry, Photometry, and Radiation Heat Transfer 447 16.1 Definitions 447 16.2 Conservation of Radiance in Homogeneous Media 450 16.3 Conservation of Basic Radiance in (Specular) Reflections and Refractions 453 16.4 Etendue and Shape Factor 457 16.5 Two-Dimensional Systems 460 16.6 Illumination of a Plane 463 References 466

17 Plane Curves 467 17.1 General Considerations 467 17.2 Parabola 471 17.3 Ellipse 474 17.4 Hyperbola 475 17.5 Conies 477 17.6 Involute 478 17.7 Winding Macrofocal Parabola 480 17.8 Unwinding Macrofocal Parabola 483 17.9 Winding Macrofocal Ellipse 485 Contents xiii

17.10 Unwinding Macrofocal Ellipse 488 17.11 Cartesian Oval for Parallel Rays 490 17.12 Cartesian Oval for Converging or Diverging Rays 492 17.13 Cartesian Ovals Calculated Point by Point 500 17.14 Equiangular Spiral 502 17.15 Function Definitions 504 References 512

Index 513