Aberration Theory - A Spectrum Of Design Techniques For The Perplexed

Abstract

The early medieval scholar Maimonides wrote a famous book called "Guide for the Perplexed", which explained various thorny philosophical and religious questions for the benefit of the puzzled novice. I wish I had had such a person to guide me when I first started a career in lens design. There the novice is often struck by how much of an "art" this endeavor is. The best bet, for a beginner with no experience, should be to turn to optical aberration theory - which, in principle, should explain much of what goes into designing an optical system. Unfortunately, this subject is usually presented in the form of proofs and derivations, with little time spent on the practical implications of aberration theory. Furthermore, a new generation of lens designers, who grew up with the computer, often consider aberration theory as an unnecessary relic from the past. My career, by contrast, is based on the conviction that using the results of aberration theory is the only intelligent way to design optical systems. Computers are an invaluable aide, but we must, ultimately, bite the bullet and think. Along these lines, I have given several papers over the last few years which deal directly with the philosophy of lens design; the kind of guides for the perplexed that I wished I had had from the start. These papers include: "Lens design on a desert island - A simple method of optical design", "A modular method of optical design", "Optical design with air lenses", "Optical design with 'phantom' aspherics", "Optical design methods: your head as a personal computer", "Aberration theory and the meaning of life", and a paper at Innsbruck - "Some interesting correspondences in aberration theory". In all cases, the emphasis is on using your head to think, and the computer to help you out with the numerical work and the "fine-tuning" of a design. To hope that the computer will do the thinking for you is folly. Solutions gained by this route rarely equal the results of an experienced and/or intelligent human thinker. Other writers who have emphasized this same theme before me, and whom I highly recommend, are Bob Hopkins, Jan Hoogland, and Erhard Glatzel. This paper will not attempt to review the many different design methods set forth in the papers just listed. It will, however, "walk through" the thinking behind just one optical design in a way which will show the enormous power and versatility of aberration theory as a design tool. It is my strong conviction that just about everything worth saying about the results and implications of aberration theory (which is highly mathematical) can be stated in ordinary English, so there will be no mathematics in this paper.