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Aberration Theory Made Simple

Aberration Theory Made Simple
Author(s):    Virendra N Mahajan
Published:   1991
DOI:             10.1117/3.43000
eISBN: 9780819478788  |  Print ISBN13: 9780819405364  |  Print ISBN10: 0819405361
Description:

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.

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Aberration theory is a subject that is as old and fascinating as the field of optics. It is, however, a cumbersome subject that many students of optics do not appreciate fully. The purpose of this tutorial book is 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 images formed by them. Its emphasis is on physical insight, problem solving, and numerical results. It is intended for engineers and scientists who have a need and/or a desire for a deeper and better understanding of aberrations and their role in optical imaging and wave propagation. Although some knowledge of Gaussian optics and an appreciation for aberrations would be useful, they are not prerequisites. What is needed is dedication and perseverance. A novice trying to learn this subject without investing much time will probably be disappointed in spite of the title of the book. The book is not intended for teaching lens design or optical testing. However, it is hoped that those working in these fields will benefit from it. It should be useful to students who may want to learn aberration theory without having to go through any lengthy derivations. These derivations are omitted out of necessity for brevity and in keeping with the spirit of these tutorials.

These tutorials have been adapted from my lectures for a graduate course entitled “Advanced Geometrical Optics,” which I have been teaching in the Electrical Engineering-Electrophysics Department of the University of Southern California since 1984. They were originally developed for a short course on optical imaging and aberrations, which I taught at The Aerospace Corporation to Aerospace and Air Force personnel. They were then expanded for a short course I have been teaching at the Optical Society of America and SPIE meetings. Generally speaking, only the primary aberrations of optical systems are discussed here; they provide the first and a significant step beyond Gaussian imaging. Although a knowledge of these aberrations is very useful, they may not sufficiently describe the imaging properties of a high-quality optical system. Higher-order aberrations in such systems are often determined by ray tracing them.

This book is organized in two parts: Part I is on ray geometrical optics and Part II is on wave diffraction optics. The first chapter introduces the concepts of aperture stop and entrance and exit pupils of an optical imaging system. The wave and ray aberrations are defined and wavefront defocus and tilt aberrations are discussed. Various forms of the primary aberration function of a rotationally symmetric system are given, and how this function changes as the aperture stop of the system is moved from one position to another is discussed. The aberration function for the simplest imaging system, namely, a single spherical refracting surface, is given. Finally, a procedure by which the aberration function of a multielement system may be calculated is described. This chapter provides a foundation for the next six chapters.

Chapters 2–6 give the primary aberrations of simple systems, such as a thin lens, plane-parallel plate, spherical mirror, Schmidt camera, and a conic mirror. Numerical problems are discussed here and there to illustrate how to apply the formulas given in these chapters. Part I of the book ends with chapter 7, where the aberrated images of a point object based on geometrical optics are discussed. Thus the ray spot diagrams and, in particular, the spot sizes for primary aberrations are discussed. The concept of aberration balancing, based on geometrical optics to reduce the size of an image spot, is introduced.

In Part II, chapters 8–11 discuss the effects of aberrations on the image of a point object based on wave diffraction optics. Chapter 8 considers systems with circular exit pupils. The aberration-free characteristics of such systems are discussed in terms of their point-spread and optical transfer functions. How the aberrations affect these functions is discussed and aberration tolerances are obtained for a given Strehl or a Hopkins ratio. The concept of aberration balancing, based on wave diffraction optics, to maximize Strehl or Hopkins ratios is discussed. Systems with annular and Gaussian pupils are considered in chapter 9. The effect of obscuration on the point-spread function and on aberration tolerance is discussed. Similarly, the effect of Gaussian amplitude at the exit pupil is discussed. The content of this chapter provides a basis for assessing the effects of aberrations on the optical performance of reflecting telescopes, such as Cassegrain and Ritchey-Chrétien, and on the propagation of laser beams.

The line of sight of an aberrated system is discussed in chapter 10 in terms of the centroid of its point-spread function. It is pointed out that only coma type aberrations change the centroid. Random aberrations are considered in chapter 11, where the average point-spread and optical transfer functions for random image motion and aberrations introduced by atmospheric turbulence are discussed. Part II of the book ends with chapter 12, where a brief discussion is given on how the aberrations of a system may be observed and recognized interferometrically.

Each chapter is written to be as independent of the others as possible, although some are more so than others. For example, chapter 7 may be followed by chapter 1. Except for the first few sections of chapter 1, it is not necessary to understand Part I in order to understand Part II. However, reading Part II without Part I would be like knowing half of a story. Chapter 12 may be read at any time; however, the reason for using certain specific values of defocus, for example, in the case of spherical aberration, may not be understood unless the concepts of aberration balancing discussed in chapters 7 and 8 are understood.

On the matter of references to the literature on aberration theory, I have listed under bibliography those books that treat this subject to some or a large extent. These are the ones I have had the opportunity to read and benefit from. On the wave diffraction optics, I have given references in the text either for historical reasons (such as the papers by Airy and Lord Rayleigh) or because the work is relatively recent and has not appeared in books. Additional references are given after the bibliography for further study on part of the reader.

Finally, I would like to thank those who have helped me with the preparation of this book. I have had many discussions with Dr. Bill Swantner on geometrical optics and Dr. Richard Boucher on diffraction optics. Dr. Boucher also did computer simulations of the point-spread functions and interferograms and prepared the photographs for this book. Prof. Don O'Shea provided critical and valuable comments when he reviewed this book. Helpful comments were also provided by Prof. R. Shannon. The Sanskrit verse and its translation on p. xx were provided by Dr. S. Sutherland, University of California at Berkeley. The manuscript and its many revisions were typed by Iva Moore. The final version was produced by Betty Wenker and Candy Worshum. I thank The Aerospace Corporation for providing help and facilities to prepare this book. I also thank Dr. Roy Potter and Eric Pepper of the SPIE staff for suggesting and facilitating the preparation of this book, which was carefully edited by Rick Hermann. I cannot thank my wife and children enough for their patience during the course of this work and so I dedicate this book to them.

Virendra N. Mahajan

Los Angeles

1991

© 1991 Society of Photo-Optical Instrumentation Engineers

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