Reducible complexity in lens design

Abstract

A major challenge in lens design is the presence of many local minima in the optimization landscape. However, unlike other global optimization problems, the lens design landscape has an additional structure, that can facilitate the design process: many local minima are closely related to minima of simpler problems. For discussing this property, in addition to local minima other critical points in the landscape must also be considered. Usually, in a global optimization problem with M variables one has to perform M-dimensional searches in order to find minima that are different from the known ones. We discuss here simple examples where, due to the special structure that is present, all types of local minima found by other methods can be obtained by a succession of one-dimensional searches. Replacing M-dimensional searches by a set of one-dimensional ones has very significant practical advantages. If the ability to reach solutions by decomposing the search in simple steps will survive generalization to more complex systems, new design tools using this property could have a significant impact on lens design.

One-dimensional searches for finding new lens design solutions efficiently

“…All lenses are in contact (i.e., all air spaces between lenses are zero). The thicknesses of all lenses in a minimum system are set equal, in order to avoid the multiple appearance of essentially the same minimums (with similar curvatures, but different lens thicknesses) that would unnecessarily complicate the study [19].…”