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Spie Press Book

Aberration Theory Made Simple
Author(s): Virendra N. Mahajan
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Book Description

Out of print 10/12/2011. Replaced by TT93 (second edition). This book provides a clear, concise, and consistent exposition of what aberrations are, how they arise in optical imaging systems, and how they affect the quality of images formed by them. The emphasis of the book is on physical insight, problem solving, and numerical results, and the text is intended for engineers and scientists who have a need and a desire for a deeper and better understanding of aberrations and their role in optical imaging and wave propagation. Some knowledge of Gaussian optics and an appreciation for aberrations would be useful but is not required.

Book Details

Date Published: 1 July 1991
Pages: 190
Volume: TT06

Table of Contents
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Preface xv
Symbols and Notation xviii

PART I. RAY GEOMETRICAL OPTICS

1. Optical Aberrations
1.1 Introduction 3
1.2 Optical Imaging 3
1.3 Wave and Ray Aberrations 5
1.4 Defocus Aberration 7
1.5 Wavefront Tilt 9
1.6 Aberration Function of a Rotationally Symmetric System 10
1.7 Effect of Change in Aperture Stop Position on the Aberration Function 12
1.8 Aberrations of a Spherical Refracting Surface 15
1.9 Aberration Function of a Multielement System 18
Appendix: Sign Convention 19
2. Aberrations of a Thin Lens
2.1 Introduction 21
2.2 Gaussian Imaging 21
2.3 Primary Aberrations 23
2.4 Spherical Aberration and Coma 23
2.5 Numerical Problems 27
3. Aberrations of a Plane-Parallel Plate
3.1 Introduction 30
3.2 Gaussian Imaging 30
3.3 Primary Aberrations 32
3.4 Numerical Problem 33
4. Aberrations of a Spherical Mirror
4.1 Introduction 35
4.2 Primary Aberration Function 35
4.3 Aperture Stop at the Mirror 37
4.4 Aperture Stop at the Center of Curvature of the Mirror 38
4.5 Numerical Problems 40
5. Schmidt Camera
5.1 Introduction 43
5.2 Schmidt Plate 43
5.3 Numerical Problems 49
6. Aberrations of a Conic Surface
6.1 Introduction 50
6.2 Conic Surface 50
6.3 Conic Refracting Surface 51
6.3.1 On-Axis Point Object 51
6.3.2 Off-Axis Point Object 52
6.4 General Aspherical Refracting Surface 54
6.5 Conic Reflecting Surface 54
6.6 Paraboloidal Mirror 55
6.7 Multi-Mirror Systems 55
7. Ray Spot Diagrams
7.1 Introduction 56
7.2 Wave and Ray Aberrations 56
7.3 Spherical Aberration 58
7.4 Coma 60
7.5 Astigmatism 61
7.6 Field Curvature 63
7.7 Astigmatism and Field Curvature 64
7.8 Distortion 65

PART 11. WAVE DIFFRACTION OPTICS

8. Optical Systems with Circular Pupils
8.1 Introduction 69
8.2. Point-Spread Function (PSF) 70
8.2.1 Aberrated PSF 70
8.2.2 Aberration-Free PSF 71
8.2.3 Rotationally Symmetric PSF 72
8.2.4 Defocused PSF 72
8.2.5 Axial Irradiance 74
8.3 Strehl Ratio 74
8.3.1 General Expressions 74
8.3.2 Primary Aberrations 76
8.3.3 Balanced Primary Aberrations 76
8.3.4 Comparison of Approximate and Exact Results 79
8.3.5 Strehl Ratio for Nonoptimally Balanced Aberrations 79
8.3.6 Rayleigh�s l/4 Rule 80
8.3.7 Balanced Aberrations and Zernike Circle Polynomials 81
8.4 PSFs for Primary Aberrations 82
8.4.1 Defocus 84
8.4.2 Spherical Aberration Combined with Defocus 84
8.4.3 Astigmatism Combined with Defocus 86
8.4.4 Coma 86
8.5 Optical Transfer Function (OTF) 92
8.6 Hopkins Ratio 95
8.7 OTFs for Primary Aberrations 98
References 110
9. Optical Systems with Annular and Gaussian Pupils
9.1 Introduction 111
9.2 Annular Pupils 111
9.2.1 Aberration-Free PSF 111
9.2.2 Axial Irradiance 113
9.2.3 Strehl Ratio 118
9.3. Gaussian Pupils 124
9.3.1 Aberration-Free PSF 124
9.3.2 Axial Irradiance 126
9.3.3 Strehl Ratio 126
9.3.4 Weakly Truncated Pupils 127
References 130
10. Line of Sight of an Aberrated Optical System
10.1 Introduction 131
10.2 Theory 131
10.3 Numerical Results 132
10.4 Comments 134
References 134
11. Random Aberrations
11.1 Introduction 135
11.2 Theory 135
11.3 Random Image Motion 136
11.4 Atmospheric Turbulence 138
11.5 Annular Pupils 143
11.6 Fabrication Errors 147
References 149
12. Observation of Aberrations
12.1 Introduction 150
12.2 Primary Aberrations 150
12.3 Interferograms 151
Bibliography 157
Additional References 158
Index 164
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