Optimization

Abstract

For the first 40 years of the twentieth century, optical design was done using a mixture of Seidel theory, a little ray tracing, and a great deal of experimental work. All of the computations were done using log tables. The usual method was to design a prototype lens using Seidel theory, then to manufacture this prototype and measure its aberrations. The designer would then modify the target values for the Seidel aberrations and produce a new design. Ray tracing was relatively little used; in most companies skew rays were almost never traced until about 1940. This seems strange to us nowadays, but it must have been sensible at the time; ray tracing, after all, is only a simulation technique, and if it is cheaper and quicker to do the real experiment, there is little point in carrying out a simulation. Mechanical calculators were little used until about 1940. Again, this is now difficult to comprehend, but the reason appears to be that techniques for the use of log tables were developed to the point that an experienced “computer,” usually a young lady, could actually trace rays faster than with calculators. Computers were first used in the UK for optical design in 1949, when C.G. Wynne had some ray tracing done at Manchester University. Unfortunately, this pioneering work took so long that the lens was made and delivered to the customer before the ray tracing results were ready! The use of computers for ray tracing did not really become practical until about 1957, when Taylor Hobson acquired an Elliott computer for this purpose, but for several years it was the only British company with a computer dedicated to optical design. However, rapid ray tracing, in itself, was not in most cases sufficient to enable the design of more advanced lenses, except where lens manufacturers were building very complex systems. For example, the author was fortunate to be employed in the early 1960s by Rank Taylor Hobson, where G.H. Cook and RA. Merigold were designing complex zoom lenses. For these systems, the use of a computer for ray tracing did enable the design of lenses that would have been impractical otherwise, but this was an exceptional situation. For most lens designers, the major impact of computers came when optimization techniques began to be used in lens design. While early workers in this field suggested various methods, the dominant method has become that of damped least squares (DLS), proposed by Wynne in the UK and Girard in France, and now known to computer scientists as the Levenberg-Marquardt method. Many optical designers have developed variations on this basic technique. Some designers have also used other methods with success, such as the adaptive method of Glatzel and Rayces.