Total Hessian in Least Squares Optimization of Lens Design

Abstract

In least squares optimization of lens design the contribution of second order aberration derivatives in the Hessian matrix are excluded in comparison with the same from the first order aberration derivatives. Except for some cursory remarks on the relative maginitudes of the two contributions, no formal basis justifying this exclusion has been reported in the literature. In spite of the practical success in optimization with truncated Hessian matrix, it is generally felt that optimization with total Hessian matrix is likely to produce better results. With the phenomenal rise in computational speed in the recent past, the primary difficulty in undertaking systematic investigations on this problem is gradually petering out. This paper presents some results of our investigations on least squares optimization of lens design using total Hessian matrix.