Optical Imaging and Aberrations: Part I. Ray Geometrical Optics / Edition 1

Optical Imaging and Aberrations: Part I. Ray Geometrical Optics / Edition 1

by Virendra N. Mahajan

This book examines how aberrations arise in optical systems and how they affect optical wave propagation and imaging based on geometrical and physical optics. It focuses on concepts, physical insight, and mathematical simplicity, intended for students and professionals. Figures and drawings illustrate concepts and enhance readability. This book is useful as a textbook… See more details below


This book examines how aberrations arise in optical systems and how they affect optical wave propagation and imaging based on geometrical and physical optics. It focuses on concepts, physical insight, and mathematical simplicity, intended for students and professionals. Figures and drawings illustrate concepts and enhance readability. This book is useful as a textbook, reference, or tutorial.

Product Details

SPIE Press
Publication date:
Press Monographs
Edition description:
New Edition
Product dimensions:
7.10(w) x 10.00(h) x 1.20(d)

Table of Contents

Part I.Ray Geometrical Optics
Symbols and notationxv
Chapter 1Gaussian Optics
1.2Foundations of Geometrical Optics4
1.2.1Fermat's Principle5
1.2.2Laws of Geometrical Optics6
1.2.3Optical Path Lengths of Neighboring Rays9
1.2.4Malus-Dupin Theorem11
1.2.5Hamilton's Point Characteristic Function12
1.3Gaussian Imaging13
1.3.2Sign Convention14
1.3.3Spherical Reflecting Surface (Spherical Mirror)15 Imaging Equation15 Power and Focal Lengths17 and Lagrange Invariant18 Imaging21 Imaging Equation21
1.3.4Thin Lens22 Imaging Equation22 Power and Focal Length23 Ray25 and Lagrange Invariant27 Imaging Equation29
1.3.5Refracting Systems29 Points and Planes30 Imaging32 Points35 Imaging Equation36
1.3.6Afocal System37
1.3.7Spherical Reflecting Surface (Spherical Mirror)41 Imaging Equation41 Power and Equivalent Focal Length42 and Lagrange Invariant45 Imaging47 Imaging Equation47
1.4Paraxial Ray Tracing49
1.4.1Refracting Surface50
1.4.2Thin Lens53
1.4.3Two Thin Lenses55
1.4.4Thick Lens57
1.4.5Reflecting Surface (Mirror)61
1.4.6Two-Mirror System61
1.4.7Catadioptric System: Thin Lens-Mirror Combination64
Chapter 2Radiometry of Imaging
2.2Stops, Pupils, and Vignetting76
2.2.2Aperture Stop, and Entrance and Exit Pupils76
2.2.3Chief and Marginal Rays79
2.2.5Size of an Imaging Element82
2.2.6Telecentric Aperture Stop82
2.2.7Field Stop, and Entrance and Exit Windows82
2.3Radiometry of Point Sources84
2.3.1Irradiance of a Surface84
2.3.2Flux Incident on a Circular Aperture87
2.4Radiometry of Extended Sources88
2.4.1Lambertian Surface89
2.4.2Exitance of a Lambertian Surface89
2.4.3Radiance of a Tube of Rays91
2.4.4Irradiance by a Lambertian Surface Element92
2.4.5Irradiance by a Lambertian Disc92
2.5Radiometry of Point Object Imaging96
2.6Radiometry of Extended Object Imaging98
2.6.1Image Radiance98
2.6.2Pupil Distortion101
2.6.3Image Irradiance: Aperture Stop in Front of the System102
2.6.4Image Irradiance: Aperture Stop in Back of the System104
2.6.5Telecentric Systems105
2.6.7Condition for Uniform Image Irradiance106
2.6.8Concentric Systems108
2.7.1Photometric Quantities and Spectral Response of Human Eye109
2.7.2Imaging by a Human Eye110
2.7.3Brightness of a Lambertian Surface111
2.7.4Observing Stars in the Daytime113
Appendix AA Radiance Theorem117
Appendix BGeneralized Lagrange Invariant121
Chapter 3Optical Aberrations
3.2Wave and Ray Aberrations131
2.2.2Relationship Between Wave and Ray Aberrations134
3.3Defocus Aberration137
3.4Wavefront Tilt139
3.5Aberration Function of a Rotationally Symmetric System141
3.5.1Rotational Invariants141
3.5.2Power-Series Expansion145 Dependence on Object Coordinates145 Explicit Dependence on Object Coordinates148
3.5.3Zernike Circle-Polynomial Expansion153
3.5.4Relationships Between Coefficients of Power-Series and Zernike-Polynomial Expansions158
3.6Observation of Aberrations159
3.6.1Primary Aberrations160
3.7Conditions for Perfect Imaging167
3.7.1Imaging of a 3-D Object167
3.7.2Imaging of a 2-D Transverse Object170
3.7.3Imaging of a 1-D Axial Object172
3.7.4Linear Coma and the Sine Condition174
3.7.5Optical Sine Theorem175
3.7.6Linear Coma and Offense Against the Sine Condition178
Appendix ADegree of Approximation in Eq. (3-11)182
Appendix BWave and Ray Aberrations: Alternative Definition and Derivation184
Chapter 4Geometrical Point-Spread Function
4.3Application to Primary Aberrations199
4.3.1Spherical Aberration200
4.3.3Astigmatism and Field Curvature212
4.4Balanced Aberrations for Minimum RMS Spot Radius222
4.5Spot Diagrams224
4.6Summary of Results226
4.6.1Spherical Aberration226
4.6.3Astigmatism and Field Curvature228
Chapter 5Calculation of Primary Aberrations: Refracting Systems
5.2Spherical Refracting Surface with Aperture Stop at the Surface237
5.2.1On-Axis Point Object237
5.2.2Off-Axis Point Object240 with Respect to Petzval Image Point240 with Respect to Gaussian Image Point246
5.3Spherical Refracting Surface with Aperture Stop249
5.3.1On-Axis Point Object249
5.3.2Off-Axis Point Object251
5.4Aplanatic Points of a Spherical Refracting Surface253
5.5Conic Refracting Surface258
5.5.1Sag of a Conic Surface258
5.5.2On-Axis Point Object262
5.5.3Off-Axis Point Object263
5.6General Aspherical Refracting Surface267
5.7Series of Coaxial Refracting (and Reflecting) Surfaces268
5.7.1General Imaging System268
5.7.2Petzval Curvature and Corresponding Field Curvature Wave Aberration269
5.7.3Relationship between Petzval Curvature and Field Curvature Astigmatism Wave Aberration Coefficients273
5.8Aberation Function in Terms of Seidel Sums or Seidel Coefficients274
5.9Effect of Change in Aperture Stop Position on the Aberration Function193
5.9.1Change of Peak Aberration Coefficients277
5.9.2Illustration of the Effect of Aperture-Stop Shift on Coma and Distortion281
5.9.3Aberrations of a Spherical Refracting Surface with Aperture Stop Not at the Surface Obtained from those with Stop at the Surface282
5.10Thin Lens284
5.10.1Imaging Relations285
5.10.2Aberration Function of a Thin Lens with Spherical Surfaces and Aperture Stop at the Lens287
5.10.3Petzval Surface292
5.10.4Spherical Aberration and Coma293
5.10.5Aplantic Lens295
5.10.6Aberration Function of a Thin Lens with Conic Surfaces298
5.10.7Aberration Function of a Thin Lens with Aperture Stop Not at the Lens299
5.11Field Flattener300
5.11.1Imaging Relations300
5.11.2Aberration Function301
5.12Plane-Parallel Plate304
5.12.2Imaging Relations304
5.12.2Aberration Function307
5.13Chromatic Aberrations308
5.13.2Single Refracting Surface309
5.13.3Thin Lens312
5.13.4General System: Surface-by-Surface Approach315
5.13.5General System: Use of Principal and Focal Points320
Chapter 6Calculation of Primary Aberrations: Reflecting and Catadioptric Systems
6.2Conic Reflecting Surface339
6.2.1Conic Surface339
6.2.2Imaging Relations342
6.2.3Aberration Function342
6.3Petzval Surface346
6.4Spherical Mirror349
6.4.1Aberration Function and Aplantic Points262
6.4.2Aperture Stop at the Mirror Surface263
6.4.3Aperture Stop at the Center of Curvature of Mirror265
6.5Paraboloidal Mirror267
6.6Catadioptric Systems356
6.6.1Schmidt Camera356
6.6.2Bouwers-Maksutov Camera366
6.7Beam Expander370
6.7.2Gaussian Parameters370
6.7.3Aberration Contributed by Primary Mirror372
6.7.4Aberration Contributed by Secondary Mirror373
6.7.5System Aberration373
6.8Two-Mirror Astronomical Telescopes374
6.8.2Gaussian Parameters375
6.8.3Petzval Surface290
6.8.4Aberration Contributed by Primary Mirror280
6.8.5Aberration Contributed by Secondary Mirror382
6.8.6System Aberration383
6.8.7Classical Cassegrain and Gregorian Telescopes384
6.8.8Aplanatic Cassegrain and Gregorian Telescopes387
6.8.9Afocal Telescope388
6.8.10Couder Anastigmatic Telescopes389
6.8.11Schwarzschild Telescope390
6.8.12Dall-Kirkham Telescope393
6.9Astronomical Telescopes Using Aspheric Plates394
6.9.2Aspheric Plate in a Diverging Object Beam394
6.9.3Aspheric Plate in a Converging Image Beam396
6.9.4Aspheric Plate and a Conic Mirror398
Chapter 7Calculation of Primary Aberrations: Perturbed Optical Systems
7.2Aberrations of a Misaligned Surface408
7.2.1Decentered Surface408
7.2.2Tilted Surface412
7.2.3Despaced Surface414
7.3Aberrations of Perturbed Two-Mirror Telescopes414
7.3.1Decentered Secondary Mirror415
7.3.2Tilted Secondary Mirror415
7.3.3Decentered and Tilted Secondary Mirror417
7.3.4Despaced Secondary Mirror419
7.4Fabrication Errors419
7.4.1Refracting Surface420
7.4.2Reflecting Surface422

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