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Tables of Contents for Optical Imaging and Aberrations
Chapter/Section Title
Page #
Page Count
PART I. RAY GEOMETRICAL OPTICS
Preface
xvii
4
Acknowledgments
xxi
2
Symbols and Notation
xxiii
CHAPTER 1: GAUSSIAN OPTICS
1
88
1.1 Introduction
3
2
1.2 Foundations of Geometrical Optics
5
9
1.2.1 Fermat's Principle
5
3
1.2.2 Laws of Geometrical Optics
8
2
1.2.3 Optical Path Lengths of Neighboring Rays
10
1
1.2.4 Malus-Dupin Theorem
11
2
1.2.5 Hamilton's Point Characteristic Function and Direction of a Ray
13
1
1.3 Gaussian Imaging
14
38
1.3.1 Introduction
14
1
1.3.2 Sign Convention
14
1
1.3.3 Spherical Refracting Surface
15
1
1.3.3.1 Gaussian Imaging Equation
15
3
1.3.3.2 Focal Lengths and Refracting Power
18
1
1.3.3.3 Magnifications and Lagrange Invariant
19
3
1.3.3.4 Graphical Imaging
22
2
1.3.3.5 Newtonian Imaging Equation
24
1
1.3.4 Thin Lens
24
1
1.3.4.1 Gaussian Imaging Equation
24
1
1.3.4.2 Focal Lengths and Refracting Power
25
1
1.3.4.3 Undeviated Ray
26
2
1.3.4.4 Magnifications and Lagrange Invariant
28
2
1.3.4.5 Newtonian Imaging Equation
30
1
1.3.5 Refracting Systems
31
1
1.3.5.1 Cardinal Points and Planes
31
2
1.3.5.2 Gaussian Imaging, Focal Lengths, and Magnifications
33
3
1.3.5.3 Nodal Points
36
2
1.3.5.4 Newtonian Imaging Equation
38
1
1.3.6 Afocal Systems
38
4
1.3.7 Spherical Reflecting Surface (Spherical Mirror)
42
1
1.3.7.1 Gaussian Imaging Equation
42
2
1.3.7.2 Focal Length and Reflecting Power
44
2
1.3.7.3 Magnifications and Lagrange Invariant
46
3
1.3.7.4 Graphical Imaging
49
3
1.3.7.5 Newtonian Imaging Equation
52
1
1.4 Paraxial Ray Tracing
52
17
1.4.1 Refracting Surface
52
2
1.4.2 Thin Lens
54
3
1.4.3 Two Thin Lenses
57
2
1.4.4 Thick Lens
59
3
1.4.5 Reflecting Surface (Mirror)
62
3
1.4.6 Two-Mirror System
65
2
1.4.7 Catadioptric System: Thin Lens-Mirror Combination
67
2
1.5 Two-Ray Lagrange Invariant
69
4
1.6 Matrix Approach to Paraxial Ray Tracing and Gaussian Optics
73
11
1.6.1 Introduction
73
1
1.6.2 System Matrix
73
4
1.6.3 Conjugate Matrix
77
4
1.6.4 System Matrix in Terms of Gaussian Parameters
81
1
1.6.5 Gaussian Imaging Equations
81
3
References
84
1
Problems
85
4
CHAPTER 2: RADIOMETRY OF IMAGING
89
50
2.1 Introduction
91
1
2.2 Stops, Pupils, and Vignetting
92
8
2.2.1 Introduction
92
1
2.2.2 Aperture Stop, and Entrance and Exit Pupils
92
2
2.2.3 Chief and Marginal Rays
94
1
2.2.4 Vignetting
95
3
2.2.5 Size of an Imaging Element
98
1
2.2.6 Telecentric Aperture Stop
98
1
2.2.7 Field Stop, and Entrance and Exit Windows
98
2
2.3 Radiometry of Point Sources
100
4
2.3.1 Irradiance of a Surface
100
3
2.3.2 Flux Incident on a Circular Aperture
103
1
2.4 Radiometry of Extended Sources
104
8
2.4.1 Lambertian Surface
104
1
2.4.2 Exitance of a Lambertian Surface
105
1
2.4.3 Radiance of a Tube of Rays
106
1
2.4.4 Irradiance by a Lambertian Surface Element
107
1
2.4.5 Irradiance by a Lambertian Disc
108
4
2.5 Radiometry of Point Object Imaging
112
2
2.6.1 Image Radiance
114
3
2.6.2 Pupil Distortion
117
1
2.6.3 Image Irradiance: Aperture Stop in Front of the System
118
3
2.6.4 Image Irradiance: Aperture Stop in Back of the System
121
2
2.6.5 Telecentric Systems
123
1
2.6.6 Throughput
123
1
2.6.7 Condition for Uniform Image Irradiance
123
2
2.6.8 Concentric Systems
125
1
2.7 Photometry
126
8
2.7.1 Photometric Quantities and Special Response of the Human Eye
126
1
2.7.2 Imaging by a Human Eye
127
2
2.7.3 Brightness of a Lambertian Surface
129
1
2.7.4 Observing Stars in the Daytime
130
4
Appendix: Radiance Theorem
134
2
References
136
1
Problems
137
2
CHAPTER 3: OPTICAL ABERRATIONS
139
64
3.1 Introduction
141
1
3.2 Wave and Ray Aberrations
142
6
3.2.1 Definitions
142
3
3.2.2 Relationship Between Wave and Ray Aberrations
145
3
3.3 Defocus Aberration
148
2
3.4 Wavefront Tilt
150
2
3.5 Aberration Function of a Rotationally Symmetric System
152
17
3.5.1 Rotational Invariants
152
3
3.5.2 Power-Series Expansion
155
1
3.5.2.1 Explicit Dependence on Object Coordinates
156
3
3.5.2.2 No Explicit Dependence on Object Coordinates
159
4
3.5.3 Zernike Circle-Polynomial Expansion
163
5
3.5.4 Relationships Between Coefficients of Power-Series and Zernike Polynomial Expansions
168
5
3.6 Observation of Aberrations
169
9
3.6.1 Primary Aberrations
172
1
3.6.2 Interferograms
173
5
3.7 Conditions for Perfect Imaging
178
14
3.7.1 Imaging of a 3-D Object
178
3
3.7.2 Imaging of a 2-D Transverse Object
181
2
3.7.3 Imaging of a 1-D Axial Object
183
1
3.7.4 Linear Coma and the Sine Condition
184
2
3.7.5 Optical Sine Theorem
186
2
3.7.6 Linear Coma and Offense Against the Sine Condition
188
4
Appendix A: Degree of Approximation in Eq. (3-11)
192
2
Appendix B: Wave and Ray Aberrations: Alternative Definition and Derivation
194
6
References
200
1
Problems
201
2
CHAPTER 4: GEOMETRICAL POINT-SPREAD FUNCTION
203
42
4.1 Introduction
205
1
4.2 Theory
205
4
4.3 Application to Primary Aberrations
209
26
4.3.1 Spherical Aberration
210
7
4.3.2 Coma
217
7
4.3.3 Astigmatism and Field Curvature
224
9
4.3.4 Distortion
233
2
4.4 Balanced Aberrations for Minimum RMS Spot Radius
235
1
4.5 Spot Diagrams
236
3
4.6 Summary of Results
239
4
4.6.1 Spherical Aberration
240
1
4.6.2 Coma
240
1
4.6.3 Astigmatism and Field Curvature
241
1
4.6.4 Distortion
242
1
4.6.5 Aberration Tolerance
242
1
References
243
1
Problems
244
1
CHAPTER 5: CALCULATION OF PRIMARY ABERRATIONS: REFRACTING SYSTEMS
245
120
5.1 Introduction
247
2
5.2 Spherical Refracting Surface with Aperture Stop at the Surface
249
12
5.2.1 On-Axis Point Object
249
3
5.2.2 Off-Axis Point Object
252
1
5.2.2.1 Aberrations with Respect to Petzval Image Point
253
6
5.2.2.2 Aberrations with Respect to Gaussian Image Point
259
2
5.3 Spherical Refracting Surface with Aperture Stop Not at the Surface
261
5
5.3.1 On-Axis Point Object
262
2
5.3.2 Off-Axis Point Object
264
2
5.4 Aplantic Points of a Spherical Refracting Surface
266
5
5.5 Conic Refracting Surface
271
10
5.5.1 Sag of a Conic Surface
271
4
5.5.2 On-Axis Point Object
275
3
5.5.3 Off-Axis Point Object
278
3
5.6 General Aspherical Refracting Surface
281
1
5.7 Series of Coaxial Refracting (and Reflecting) Surfaces
281
6
5.7.1 General Imaging System
282
1
5.7.2 Petzval Curvature and Corresponding Field Curvature Wave Aberration
282
5
5.7.3 Relationship Among Petzval Curvature, Field Curvature, and Astigmatism Wave Aberration Coefficients
287
1
5.8 Aberration Function in Terms of Seidel Sums or Seidel Coefficients
287
3
5.9 Effect of Change in Aperture Stop Position on the Aberration Function
290
9
5.9.1 Change of Peak Aberration Coefficients
291
4
5.9.2 Illustration of the Effect of Aperture-Stop Shift on Coma and Distortion
295
2
5.9.3 Aberrations of a Spherical Refracting Surface with Aperture Stop Not at the Surface Obtained from Those with Stop at the Surface
297
2
5.10 Thin Lens
299
15
5.10.1 Imaging Relations
300
1
5.10.2 Thin Lens with Spherical Surfaces and Aperture Stop at the Lens
301
5
5.10.3 Petzval Surface
306
1
5.10.4 Spherical Aberration and Coma
307
3
5.10.5 Aplanatic Lens
310
2
5.10.6 Thin Lens with Conic Surfaces
312
1
5.10.7 Thin Lens with Aperture Stop Not at the Lens
313
1
5.11 Field Flattener
314
4
5.11.1 Imaging Relations
315
1
5.11.2 Aberration Function
316
2
5.12 Plane-Parallel Plate
318
5
5.12.1 Introduction
318
1
5.12.2 Imaging Relations
318
3
5.12.3 Aberration Function
321
2
5.13 Chromatic Aberrations
323
25
5.13.1 Introduction
323
1
5.13.2 Single Refracting Surface
323
4
5.13.3 Thin Lens
327
4
5.13.4 General System: Surface-by-Surface Approach
331
5
5.13.5 General System: Use of Principal and Focal Points
336
11
5.13.6 Chromatic Aberrations as Wave Aberrations
347
1
5.14 Symmetrical Principle
348
1
5.15 Pupil Aberrations and Conjugate-Shift Equations
349
11
5.15.1 Introduction
349
1
5.15.2 Pupil Aberrations
350
5
5.15.3 Conjugate-Shift Equations
355
2
5.15.4 Invariance of Image Aberrations
357
1
5.15.5 Simultaneous Correction of Aberrations for Two or More Object Positions
358
2
References
360
1
Problems
361
4
CHAPTER 6: CALCULATION OF PRIMARY ABERRATIONS: REFLECTING AND CATADIOPTRIC SYSTEMS
365
70
6.1 Introduction
367
1
6.2 Conic Reflecting Surface
367
8
6.2.1 Conic Surface
367
3
6.2.2 Imaging Relations
370
1
6.2.3 Aberration Function
370
5
6.3 Petzval Surface
375
2
6.4 Spherical Mirror
377
7
6.4.1 Aberration Function and Aplanatic Points for Arbitrary Location of Aperture Stop
377
2
6.4.2 Aperture Stop at the Mirror Surface
379
2
6.4.3 Aperture Stop at the Center of Curvature of Mirror
381
3
6.5 Paraboloidal Mirror
384
1
6.6 Catadioptric Systems
385
13
6.6.1 Introduction
385
1
6.6.2 Schmidit Camera
385
9
6.6.3 Bouwers-Maksutov Camera
394
4
6.7 Beam Expander
398
4
6.7.1 Introduction
398
1
6.7.2 Gaussian Parameters
398
2
6.7.3 Aberration Contributed by Primary Mirror
400
1
6.7.4 Aberration Contributed by Secondary Mirror
401
1
6.7.5 System Aberration
402
1
6.8 Two-Mirror Astronomical Telescopes
402
20
6.8.1 Introduction
402
1
6.8.2 Gaussian Parameters
403
5
6.8.3 Petzval Surface
408
1
6.8.4 Aberration Contributed by Primary Mirror
408
2
6.8.5 Aberration Contributed by Secondary Mirror
410
2
6.8.6 System Aberration
412
1
6.8.7 Classical Cassegrain and Gregorian Telescopes
413
3
6.8.8 Aplantic Cassegrain and Gregorian Telescopes
416
1
6.8.9 Afocal Telescope
416
1
6.8.10 Couder Anastigmatic Telescopes
417
1
6.8.11 Schwarzschild Telescope
418
2
6.8.12 Dall-Kirkham Telescope
420
2
6.9 Astronomical Telescopes Using Aspheric Plates
422
9
6.9.1 Introduction
422
1
6.9.2 Aspheric Plate in a Diverging Object Beam
422
3
6.9.3 Aspheric Plate in a Converging Image Beam
425
1
6.9.4 Aspheric Plate and a Conic Mirror
426
2
6.9.5 Aspheric Plate and a Two-Mirror Telescope
428
3
References
431
1
Problems
432
3
CHAPTER 7: CALCULATION OF PRIMARY ABERRATIONS: PERTURBED OPTICAL SYSTEMS
435
26
7.1 Introduction
437
1
7.2 Aberrations of a Misaligned Surface
438
7
7.2.1 Decentered Surface
438
4
7.2.2 Titled Surface
442
2
7.2.3 Despaced Surface
444
1
7.3 Aberrations of Perturbed Two-Mirror Telescopes
445
9
7.3.1 Decentered Secondary Mirror
445
2
7.3.2 Titled Secondary Mirror
447
1
7.3.3 Decentered and Tilted Secondary Mirror
448
3
7.3.4 Despaced Secondary Mirror
451
3
7.4 Fabrication Errors
454
4
7.4.1 Refracting Surface
454
2
7.4.2 Reflecting Surface
456
2
References
458
1
Problems
459
2
Bibliography
461
2
Index
463