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E. Nakamura, S. Yonezawa, A. Asano, H. Suzuki, and S. Yokozeki,
Optimization Method on Ill-Condition in Automatic Lens Design
Kogaku(Japanese Journal of Optics), 23, 7, 424-430 (1994) [in Japanese].


The solution sets of the optimization problem in automatic lens design may have extremely large values when the valance of parameters and aberrations is ill-conditioned. This situation prevents the process of the optimization. The ill-condition occurs when there exist correlations among the column vectors in the matrix of the partial differential coefficients. We propose a novel optimization method for the automatic lens design. Our method distinguishes the set of independent vectors from that of the dependent ones using Schmidt orthogonalization method. the method derives a relationship between the set of the independent solutions and that of the dependent ones. We propose a method to get reasonable solutions from the relationship using Lagrangian undetewrmined multipliers method. Simulational experiments are carried out to show the efficiency of our method.