Synthesis and analysis of an aplanatic mirror-lens system with axial symmetry

The problems of synthesis and analysis of an axisymmetric aplanatic mirror-lens system that transforms the spherical front of a source into a flat one are considered. Two methods have been developed for solving the problem of synthesizing the system’s generatrices: using a numerical procedure and the Kelleher formula, and also by reducing it to a differential equation with a retarded argument. Formulas are obtained for the eikonal in the aperture of the system when the source is displaced from the focus. The dependence of the mean square aberration of the eikonal on the system parameters has been studied and their optimal values have been found.