Accelerating convergence in automatic lens design

Abstract

We have developed an acceleration algorithm for use with the damped least squares automatic design procedure, which has sharply reduced the number of iterations required to reach a stationary point. The algorithm was developed from the realization that the damped-least-squares defect function requires that the optimization procedure reduce the optical figure of merit as far as possible while simultaneously requiring that the changes in the lens prescription tend to zero. These components of the defect function oppose one another, producing stagnation that is overcome only by repeated iterations. The use of the acceleration algorithm reduced the number of iterations in a typical case from 175 to 16 while converging on the same stationary point.