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We investigate unobstructed, plane-symmetric systems of two spherical mirrors that are intended for imaging a single point. Low-order imaging constraints are determined that eliminate all but two of the seven parameters that specify the configuration of such a system. It is found that when these constraints are applied, the object point, the center of curvature of each mirror, and the image point necessarily lie along a single line. The associated merit function space is mapped as a function of the two independent parameters. Selected systems from various regions of the configuration space are illustrated.
Howard et al. (Tue,) studied this question.