Feature

Global Optimization In Lens Design

Greg Forbes and Andrew Jones

The goal of any design task is to find the best system. For most problems, however, it is generally infeasible to guarantee that the globally best system has been located. The traditional fall-back position has been to find a system that is locally best—that is, small changes in the resulting design are assuredly detrimental. Unfortunately, most locally-optimal systems are inadequate so the designer is put upon to provide an appropriate, rough configuration that is then incrementally modified until a locally-best (hopefully adequate) form is found. Local optimization algorithms carry out this task and typically proceed by monitoring derivatives to advance to a local extremum. This is straightforward: it is as simple as rolling down a hillside until there's no more rolling to be had. The quality of the final form, however, is critically dependent on the start point and it is evident that conventional computer-aided design serves primarily but to polish the designer's original system.