Imaging with four spherical mirrors.

We investigate unobstructed, plane-symmetric imaging systems of four spherical mirrors. Fifteen parameters are necessary to specify the configuration of such a system. Constraints are determined that ensure that any resultant system possesses a given set of first-order properties. These constraints remove four parameters as available degrees of freedom. To illustrate the efficacy of this design approach, we present two example studies: one for a class of systems with the object at infinity and another for finite-conjugate projection systems. For each study a global optimizer is used as the primary search tool. Example systems from these studies are presented.