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Many problems in eikonal function theory can be formulated as an optimization problem in one or more sets of two variables. We show that such problems can be attacked quite successfully by purely numerical methods instead of the usual series developments. As an example, we determine the angle eikonal of a lens designed to form a perfect one-to-one image of a curved object plane onto a flat image plane and then calculate the aberrations when the lens is used backward.
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A. Walther (1988) studied this question.
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