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An abundance of knowledge about the optical transfer function (OTF) has been published in many excellent articles during the past 35 years or so, but somehow a niche for this knowledge has never been found in the engineering and scientific structure. As a result, OTF publications are scattered throughout the archival literature of scientific and technical journals. Our book aims to bring together into one source much of this wealth of information.
Those concerned with grounding engineers and scientists in the procedures of optical evaluation have found that spacial frequency, wave-front distortion, and optical transfer function, though not particularly difficult concepts to understand, do not as easily become part of one's thinking, and therefore practice, as the concepts of rays, ray tracing, and ray aberrations. The word ray (geometrical optics), for example , in contrast with spatial frequency (physical optics) is used so commonly in our language that it is no longer an esoteric term reserved for optics. Actually, there are advantages peculiar to each of the two viewpoints, and an optical analyst is handicapped by a lack of facility with either. We hope that our book is articulate enough in the art to bring practitioners up to speed in the realm of spatial frequency and the OTF.
Specifically, our text dwells on such fundamental concepts as spatial frequency, spread function, wave aberration, and transfer function - how these are related in an optical system, how they are measured and calculated, and how they may be useful. In the early chapters we review the historical background for the OTF, the related concepts, and the necessary nomenclature and coordinate systems. We dicuss in some detail the wave aberration function, which is a measure of an optical system's ability to produce an image that is a "reasonable facsimile" of the object and which, therefore, is a fundamental characterization of the system's excellence of performance. We derive the optical transfer function and related concepts mathematically, and we discuss some ways that the OTF can be used for assessing the quality of an optical system both during its design and during testing of the manufactured system.
We show how the OTF can be used; when specifications for the optical system are being drawn up, when the OTF is part of a merit function while the system is being designed by computer, and when the optical system is being tested to verify adherence to specifications. Finally, we show how the OTF can be calculated mathematically, both by analytical procedures and by numerical methods of integration.
In the appendixes some pertinent mathematical basics are reviewed, and we document a number of OTF calculations that other workers have made.
Our book makes liberal use of illustrations. For the reader who wishes to pursue studies beyond the scope of our text, we provide a full complement of references at the end of each chapter.
The reader of our mathematical chapters should have had courses in calculus; a course in transform theory would be helpful but not necessary because the mathematics in the appendixes provide a review of all the Fourier transform theory that the reader will need. Besides the professional nonexpert in physical optics, the level of our text is intended to suit undergraduates with limited exposure to optics, such as juniors and seniors in science, mathematics, and engineering.
We have purposely avoided certain OTF topics: We do not treat the geometrical approximation fo the OTF, the OTF of sampled images, or the polychromatic OTF, because we feel that the state of the art concerning each of these topics is not quite ready to be included in a tutorial book on the optical transfer function.
We make no pretense that the ideas in this book are original with us. Our information has come through various paths and from many sources, and we have tried to give credit at the appropriate places in the text to the many whose work we have used.
Charles S. Williams
Orville A. Becklund
Dallas, Texas
May 1988
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