### Spie Press Book

Aberration Theory Made Simple, Second EditionFormat | Member Price | Non-Member Price |
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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.

The second edition of *Aberration Theory Made Simple* features an updated Cartesian sign convention, which is used in advanced books on geometrical optics and in optical design software. New topics include centroid and standard deviation of ray aberrations, spot diagrams for primary aberrations, the golden rule of optical design about relying on such diagrams, update of 2D PSFs for primary aberrations, aberration-free optical transfer function of systems with annular and Gaussian pupils, Zernike polynomials for circular, annular, and Gaussian pupils, effect of longitudinal image motion on an image, lucky imaging in ground-based astronomy, and adaptive optics.

- Symbols and Notation 9
- Preface to the Second Edition 11
- Preface to the First Edition 13
- CHAPTER 1: OPTICAL ABERRATIONS 1
- 1.1 Introduction 1
- 1.2 Optical Imaging 1
- 1.3 Wave and Ray Aberrations 3
- 1.4 Defocus Aberrations 5
- 1.5 Wavefront Tilt 7
- 1.6 Aberration Function of a Rotationally Symmetric System 8
- 1.7 Effect of Change in Aperture Stop Position on the Aberration Function 10
- 1.8 Aberrations of a Spherical Refracting Surface 13
- 1.9 Aberration Function of a Multielement system 16
- Appendix: Sign Convention 17
- CHAPTER 2: THIN LENS 19
- 2.1 Introduction 19
- 2.2 Gaussian Imaging 19
- 2.3 Primary Aberrations 20
- 2.4 Spherical Aberration and Coma 21
- 2.5 Numerical Problems 24
- 2.5.1 Thin Lens Focusing a Parallel Beam of Light 24
- 2.5.2 Aplanatic Doublet Focusing a Parallel Beam of Light 25
- CHAPTER 3: ABERRATIONS OF A PLANE-PARALLEL PLATE 27
- 3.1 Introduction 27
- 3.2 Gaussian Imaging 27
- 3.3 Primary Aberrations 29
- 3.4 Numerical Problem 30
- CHAPTER 4: ABERRATIONS OF A SPHERICAL MIRROR 33
- 4.1 Introduction 33
- 4.2 Primary Aberration Function 33
- 4.3 Aperture Stop at the Mirror 35
- 4.4 Aperture Stop at the Center of Curvature of the Mirror 36
- 4.5 Numerical Problems 38
- CHAPTER 5: SCHMIDT CAMERA 43
- 5.1 Introduction 43
- 5.2 Schmidt Plate 43
- 5.3 Numerical Problems 49
- CHAPTER 6: ABERRATIONS OF A CONIC SURFACE 51
- 6.1 Introduction 51
- 6.2 Conic Surface 51
- 6.3 Conic Refracting Surface 52
- 6.3.1 On-Axis Point Object 52
- 6.3.2 Off-Axis Point Object 53
- 6.4 General Aspherical Refracting Surface 55
- 6.5 Conic Refracting Surface 57
- 6.6 Paraboloidal Mirror 56
- 6.7 Multimirror Systems 56
- CHAPTER 7: RAY SPOT SIZES AND DIAGRAMS 57
- 7.1 Introduction 57
- 7.2 Wave and Ray Aberrations 57
- 7.3 Spherical Aberration 60
- 7.4 Coma 62
- 7.5 Astigmatism 64
- 7.6 Field Curvature 67
- 7.7 Astigmatism and Field Curvature 68
- 7.8 Distortion 68
- 7.9 Spot Diagrams 69
- 7.10 Aberration Tolerance and Golden Rule of Optical Design 70
- CHAPTER 8: SYSTEMS WITH CIRCULAR PUPILS 73
- 8.1 Introduction 73
- 8.2 Point-Spread Function 74
- 8.2.1 Aberrated PSF 74
- 8.2.2 Aberration-Free PSF 75
- 8.2.3 Rotationally Symmetric PSF 77
- 8.2.4 Defocused PSF 77
- 8.2.5 Axial Irradiance 78
- 8.3 Strehl Ratio 79
- 8.3.1 General Expressions 79
- 8.3.2 Primary Aberrations 81
- 8.3.3 Balanced Primary Aberrations 81
- 8.3.4 Comparison of Approximate and Exact Results 82
- 8.3.5 Strehl Ratio for Nonoptimally Balanced Aberrations 84
- 8.3.6 Rayleigh's Lambda/4 Rule 84
- 8.3.7 Balanced Aberrations and Zernike Circle Polynomials 85
- 8.4 2D PSFs 88
- 8.5 Optical Transfer Function (OTF) 97
- 8.5.1 OTF and Its Physical Significance 97
- 8.5.2 Aberration-Free OTF 98
- 8.5.3 Hopkins Ratio and Aberration Tolerance 100
- 8.5.4 Contrast Reversal 101
- CHAPTER 9: SYSTEMS WITH ANNULAR AND GAUSSIAN PUPILS 105
- 9.1 Introduction 105
- 9.2 Annular Pupils 105
- 9.2.1 Aberration-Free PSF 105
- 9.2.2 Aberration-Free OTF 110
- 9.2.3 Axial Irradiance 111
- 9.2.4 Strehl Ratio 113
- 9.2.5 Balanced Aberrations and Zernike Annular Polynomials 119
- 9.3 Gaussian Pupils 120
- 9.3.1 Aberration-Free PSF 120
- 9.3.2 Aberration-Free OTF 122
- 9.3.3 Axial Irradiance 125
- 9.3.4 Strehl Ratio 126
- 9.3.5 Balanced Aberrations and Zernike-Gauss Circle Polynomials 127
- 9.3.6 Weakly Truncated Pupils 129
- References 131
- CHAPTER 10: LINE OF SIGHT OF AN ABERRATED SYSTEM 133
- 10.1 Introduction 133
- 10.2 Theory 133
- 10.3 Numerical Results 134
- 10.4 Comments 134
- References 137
- CHAPTER 11: RANDOM ABERRATIONS 139
- 11.1 Introduction 139
- 11.2 Random Image Motion 139
- 11.2.1 Transverse Image Motion 139
- 11.2.2 Longitudinal Image Motion 141
- 11.3 Imaging through Atmospheric Turbulence 142
- 11.3.1 Introduction 142
- 11.3.2 Long-Exposure Image 143
- 11.3.3 Short-Exposure Image 147
- 11.3.4 Lucky Imaging and Adaptive Optics 150
- 11.4 Fabrication Errors and Tolerances 152
- References 153
- CHAPTER 12: OBSERVATION OF ABERRATIONS 155
- 12.1 Introduction 155
- 12.2 Primary Aberrations 155
- 12.3 Interferograms 156
- References 161
- Bibliography 163
- Additonal References 165
- Index 173

## Preface to the Second Edition

I wrote *Aberration Theory Made Simple* some 20 years ago to provide a clear, concise, and consistent exposition of what aberrations are, how they arise in optical imaging systems, and how they affect the quality of optical images formed by them, both in terms of geometrical and diffraction optics. Later, I expanded this Tutorial Text into a textbook under the title *Optical Imaging and Aberrations* in two parts, one on Ray Geometrical Optics and the other on Wave Diffraction Optics. Detailed mathematical derivations missing in the Tutorial Text are given in this textbook, along with problems at the end of each chapter.

In this second edition of *Aberration Theory Made Simple*, I have updated the sign convention for Gaussian optics to the Cartesian sign convention, as used in advanced books on geometrical optics and in the optical design software programs. The quantities such as object and image distances that are numerically negative are indicated in figures with a parenthetical negative sign (-). Thus a reader will find a change in the sign of some parameters in equations in the part on geometrical optics when compared with those in the first edition. In this new edition, I have deleted certain advanced details that are available in the long textbook. Deletions include the plots of the optical transfer function for primary aberrations. I have added some new material as wells such as the centroid and standard deviation of ray aberrations, spot diagrams for primary aberrations, golden rule of optical design about relying on such diagrams, update of 2D PSFs for primary aberrations, aberration-free optical transfer function of systems with annular and Gaussian pupils, Zernike polynomials for circular, annular, and Gaussian pupils, effect of
longitudinal image motion on an image, lucky imaging in ground-based astronomy, and adaptive optics. It is hoped that these additions will be helpful to the reader of this edition of *Aberration Theory Made Simple*.

Virendra N. Mahajan

June 2011

El Segundo, California

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