Imaging a point with two spherical mirrors

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.