EXTRAPOLATED LEAST SQUARES OPTIMIZATION APPLIED TO LENS DESIGN

Abstract

A new approach to least squares optimization has been developed which uses extrapolation factors to introduce variable metric techniques into the least squares optimization methods used in optical design. This new approach retains derivative information between successive optimization iterative steps to form approximate second derivatives in order to develop extrapolation factors. These extrapolation factors are used to update and refine important system parameters including the merit function, the first derivative matrix and the system metric without requiring the reevaluation of the system derivatives. This extrapolated least squares (ELS) optimization method does not simply add damping terms to the diagonal elements of the system metric to control optimization step lengths as is done in the various damped least squares (DLS) optimization methods; but the total system metric is updated to reflect the current optimization progress made to within the limit of the extrapolated quadratic approximation to the problem. The ELS and conventional least squares optimization methods are compared in numerous optimization problem examples including several test functions as well as typical optical design problems. The extrapolated least squares (ELS) optimization method is shown to reduce computational overhead and to accelerate convergence of least squares types of optimization problems.