Nonimaging Optics

Front Cover......Page 1
Copyright......Page 5
Contents......Page 6
Preface......Page 12
1.1 Nonimaging Collectors......Page 13
1.2 Definition of the Concentration Ratio; The Theoretical Maximum......Page 15
1.3 Uses of Concentrators......Page 17
References 1......Page 18
2.1 The Concepts of Geometrical Optics......Page 19
2.2 Formulation of the Ray-Tracing Procedure......Page 20
2.3 Elementary Properties of Image-Forming Optical Systems......Page 23
2.4 Aberrations in Image-Forming Optical Systems......Page 25
2.5 The Effect of Aberrations in an Image-Forming System on the Concentration Ratio......Page 26
2.6 The Optical Path Length and Fermat’s Principle......Page 28
2.7 The Generalized Étendue or Lagrange Invariant and the Phase Space Concept......Page 30
2.8 The Skew Invariant......Page 34
Reference 2......Page 35
3.2 Some General Properties of Ideal Image-Forming Concentrators......Page 37
3.3 Can an Ideal Image-Forming Concentrator Be Designed?......Page 43
3.4 Media with Continuously Varying Refractive Indices......Page 46
3.5 Another System of Spherical Symmetry......Page 49
3.6 Image-Forming Mirror Systems......Page 50
3.7 Conclusions on Classical Image-Forming Concentrators......Page 52
References 3......Page 53
4.1 Limits to Concentration......Page 55
4.2 Imaging Devices and Their Limitations......Page 56
4.3 Nonimaging Concentrators......Page 57
4.4 The Edge-Ray Principle or “String” Method......Page 59
4.5 Light Cones......Page 61
4.6 The Compound Parabolic Concentrator......Page 62
4.7 Properties of the Compound Parabolic Concentrator......Page 68
4.8 Cones and Paraboloids As Concentrators......Page 76
References 4......Page 79
5.2 The Dielectric-Filled CPC with Total Internal Reflection......Page 81
5.3 The CPC with Exit Angle Less Than p/2......Page 84
5.4 The Concentrator for A Source at A Finite Distance......Page 86
5.5 The Two-Stage CPC......Page 88
5.6 The CPC Designed for Skew Rays......Page 90
5.7 The Truncated CPC......Page 92
5.8 The Lens-Mirror CPC......Page 96
5.10 Extension of the Edge-Ray Principle......Page 97
5.11 Some Examples......Page 99
5.13 Mechanical Construction for 2D Concentrator Profiles......Page 101
5.14 A General Design Method for A 2D Concentrator with Lateral Reflectors......Page 104
5.15 Application of the Method: Tailored Designs......Page 107
5.16 A Constructive Design Principle for Optimal Concentrators......Page 108
References 5......Page 109
6.1 The Concept of the Flow Line......Page 111
6.2 Lines of Flow from Lambertian Radiators: 2D Examples......Page 112
6.3 3D Example......Page 114
6.4 A Simplified Method for Calculating Lines of Flow......Page 115
6.5 Properties of the Lines of Flow......Page 116
6.6 Application to Concentrator Design......Page 117
6.8 Elaborations of the Hyperboloid: the Truncated Hyperboloid......Page 118
6.9 The Hyperboloid Combined with A Lens......Page 119
6.11 Generalized Flow Line Concentrators with Refractive Components......Page 120
6.12 Hamiltonian Formulation......Page 121
6.13 Poisson Bracket Design Method......Page 127
6.14 Application of the Poisson Bracket Method......Page 140
6.15 Multifoliate-Reflector-Based Concentrators......Page 150
6.16 The Poisson Bracket Method in 2D Geometry......Page 154
6.17 Elliptic Bundles in Homogeneous Media......Page 156
6.18 Conclusion......Page 167
References 6......Page 169
7.1 Introduction......Page 171
7.2 Reflector Producing A Prescribed Functional Transformation......Page 172
7.3 Some Point Source Examples with Cylindrical and Rotational Optics......Page 173
7.4 The Finite Strip Source with Cylindrical Optics......Page 174
7.5 The Finite Disk Source with Rotational Optics......Page 178
7.6 The Finite Tubular Source with Cylindrical Optics......Page 184
7.7 Freeform Optical Designs for Point Sources in 3D......Page 185
References 7......Page 190
8.1 Introduction......Page 193
8.2 Definitions......Page 194
8.3 Design of A Nonimaging Lens: the RR Concentrator......Page 196
8.4 Three-Dimensional Ray Tracing of Rotational Symmetric RR Concentrators......Page 201
8.5 The XR Concentrator......Page 204
8.6 Three-Dimensional Ray Tracing of Some XR Concentrators......Page 206
8.7 The RX Concentrator......Page 207
8.8 Three-Dimensional Ray Tracing of Some RX Concentrators......Page 210
8.9 The XX Concentrator......Page 213
8.10 The RXI Concentrator......Page 214
8.11 Three-Dimensional Ray Tracing of Some RXI Concentrators......Page 219
8.12 Comparison of the SMS Concentrators with Other Nonimaging Concentrators and with Image Forming Systems......Page 221
8.13 Combination of the SMS and the Flow-Line Method......Page 223
8.14 An Example: the XRI F Concentrator......Page 224
References 8......Page 229
9.1 Introduction......Page 231
9.2 Imaging Properties of the Design Method......Page 232
9.3 Results......Page 237
9.4 Nonimaging Applications......Page 243
References 9......Page 245
10.1 Introduction......Page 247
10.2 Rotational Symmetry......Page 248
10.3 Translational Symmetry......Page 259
References 10......Page 275
11.1 Introduction......Page 277
11.2 Mathematical Properties of Mappings in Nonimaging Optics......Page 278
11.3 Factors Affecting Performance......Page 279
11.4 The Effect of Source and Target Inhomogeneities on the Performance Limits of Nonsymmetric Nonimaging Optical Systems......Page 280
11.5 The Inverse-Engineering Formalism......Page 286
11.6 Examples of Globally Optimized Concentrator Designs......Page 288
References 11......Page 315
12.1 Introduction......Page 317
12.3 Measuring Radiance......Page 318
12.4 Near-Field and Far-Field Limits......Page 321
12.5 A Wave Description of Measurement......Page 322
12.6 Focusing and the Instrument Operator......Page 323
12.8 Experimental Test of Focusing......Page 325
12.9 Conclusion......Page 327
References 12......Page 328
13.1 Requirements for Solar Concentrators......Page 329
13.2 Solar Thermal Versus Photovoltaic Concentrator Specifications......Page 330
13.3 Nonimaging Concentrators for Solar Thermal Applications......Page 339
13.4 SMS Concentrators for Photovoltaic Applications......Page 362
13.5 Demonstration and Measurement of Ultra-High Solar Fluxes (C g Up to 100,000)......Page 378
13.6 Applications Using Highly Concentrated Sunlight......Page 393
13.7 Solar Processing of Materials......Page 397
13.8 Solar Thermal Applications of High-Index Secondaries......Page 399
13.9 Solar Thermal Propulsion in Space......Page 401
References 13......Page 403
14.1 Introduction......Page 407
14.3 Contour Error Model......Page 408
14.4 The Concentrator Error Multiplier......Page 422
14.5 Sensitivity to Errors......Page 423
14.6 Conclusions......Page 424
References 14......Page 425
A.4 Conventional photometry and the étendue......Page 0
A.3 The mechanical analogies and liouville’s theorem......Page 431
References A......Page 432
B.2 The Continuous Case......Page 434
B.3 The Sequential Surface Case......Page 439
B.4 The Flow-Line Mirror Case......Page 440
B.5 Generation of Edge Rays at Slope Discontinuities......Page 442
B.6 Offence Against the Edge-Ray Theorem......Page 443
References B......Page 445
C.1 Skew Invariant......Page 446
C.2 Luneburg Treatment for Skew Rays......Page 447
C.4 Design of Concentrators for Nonmeridian Rays......Page 448
References C......Page 450
APPENDIX D: Conservation of Étendue for Two-Parameter Bundles of Rays......Page 452
D.1 Conditions for Achromatic Designs......Page 454
D.2 Conditions for Constant Focal Length in Linear Systems......Page 459
References D......Page 460
E.1 Introduction......Page 462
E.2 The 2D Case......Page 463
E.3 The 3D Case......Page 465
References E......Page 472
APPENDIX F: The Luneberg Lens......Page 474
APPENDIX G: The Geometry of the Basic Compound Parabolic Concentrator......Page 480
APPENDIX H: The ui/uo Concentrator......Page 484
APPENDIX I: The Truncated Compound Parabolic Concentrator......Page 486
APPENDIX J: The Differential Equation for the 2D Concentrator Profile with Nonplane Absorber......Page 490
Reference J......Page 492
APPENDIX K: Skew Rays in Hyperboloidal Concentrator......Page 494
APPENDIX L: Sine Relation for Hyperboloid/Lens Concentrator......Page 496
M.1 The Differential Equation......Page 498
M.2 The Ratio of Input to Output Areas for the Concentrator......Page 499
M.3 Proof That Extreme Rays Intersect at the Exit Aperture Rim......Page 501
M.4 Another Proof of the Sine Relation for Skew Rays......Page 502
M.5 The Frequency Distribution of h......Page 503
Index......Page 506