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دانلود کتاب Introduction to NONIMAGING OPTICS

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Introduction to NONIMAGING OPTICS

Julio Chaves
Light Prescriptions Innovators,Madrid, Spain

CRC Press
Taylor & Francis Group
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Library of Congress Cataloging-in-Publication Data
Chaves, Julio C.
Introduction to nonimaging optics / Julio C. Chaves.
p. cm. -- (Optical science and engineering series ; 134)
Includes bibliographical references and index.
ISBN-13: 978-1-4200-5429-3 (hardcover : alk. paper)
ISBN-10: 1-4200-5429-5 (hardcover : alk. paper)
1. Solar collectors. 2. Optics. 3. Reflectors, Lighting. I. Title. II. Series.
TJ812.C427 2008
621.36--dc22 2007047468
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com

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 Étendue and the Winston–Welford Design Method .................... 55
3.1 Introduction .........................................................................................55
3.2 Conservation of Étendue ...................................................................57
3.3 Nonideal Optical Systems .................................................................63
3.4 Étendue as a Geometrical Quantity .................................................65
3.5 Two-Dimensional Systems ................................................................68
3.6 Étendue as an Integral of the Optical Momentum ........................ 70
3.7 Étendue as a Volume in Phase Space ...............................................75
3.8 Étendue 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
x Contents
3.12 Maximum Concentration ................................................................ 102
3.13 Étendue and the Shape Factor ......................................................... 106
3.14 Examples ............................................................................................ 110
References ................................................................................................... 115
4 Vector Flux ....................................................................................... 117
4.1 Introduction ....................................................................................... 117
4.2 Defi nition of Vector Flux ................................................................. 121
4.3 Vector Flux as a Bisector of the Edge Rays.................................... 126
4.4 Vector Flux and Étendue.................................................................. 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
5 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
6 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
7 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 Miñano–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 Miñano–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 Miñano 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
xii Contents
11.4 Optical Path Length between Two Wave Fronts ........................ 397
References ................................................................................................... 401
12 Reflection and Refraction ............................................................. 403
12.1 Refl ected and Refracted Rays ........................................................403
12.2 The Laws of Refl ection 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 Étendue in Phase Space ................................................................. 431
14.1 Étendue and the Point Characteristic Function .......................... 431
14.2 Étendue 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 Defi nitions ........................................................................................447
16.2 Conservation of Radiance in Homogeneous Media ..................450
16.3 Conservation of Basic Radiance in (Specular)
Refl ections and Refractions ...........................................................453
16.4 Étendue 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 Conics................................................................................................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 Defi nitions .....................................................................504
References .................................................................................................. 512
Index .......................................................................................................... 513

 

 

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