Abstract

The extrapolated least-squares (ELS) optimization method is a new approach to improving the optimization efficiency of the least-squares techniques used in lens-design computer programs. The ELS method retains information between iterative optimization cycles for the development of second-order extrapolation factors that include up to second-derivative terms. The extrapolation factors are used to update the first-derivative matrix of the residual vector to reflect optimization progress more accurately without requiring the recomputation of the residual vector’s first derivatives. For optical-design problems in which the first-derivative matrix is costly and time-consuming to compute, the ELS method may provide great benefit. The performance of the ELS optimization method and several conventional least-squares optimization methods are compared for a variety of test problems. Several problems include specific test functions that display a specific feature or limitation of the ELS method. Also, lens-design problems are used to provide a comparison of the ELS and conventional least-squares approaches to different types of optical-design optimization situations. The selected test problems demonstrate the predicted limitations of the ELS method as well as the expected improvement in efficiency of the ELS method when compared with conventional least-squares methods.

© 1985 Optical Society of America

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