Synthesis of Bifocal Mirror–Lens Cylindrical System with Minimum Aberrations

Abstract

A method for the synthesis and optimization of bifocal mirror–lens cylindrical systems is developed using sequential finding of fragments of the first surface of the dielectric lens and mirror adjacent to second surface of the lens. The starting fragment of the first surface of the lens is represented as a quadratic polynomial the parameters of which are found from the solution to an original equation that generally provides continuity of the second derivatives of functions describing the surfaces of the lens and mirror. The starting fragment of the mirror is found from the solution to the problem of synthesis of a plane front for the central position of the source. Optimization parameters are determined to minimize the rms aberration at fixed thickness and refractive index of the lens and the angle of view of the bifocal system. The boundaries of the domain of existence are found for the solution to the synthesis problem on the plane of the parameters for angles of view of 50, 70, and 105 degrees, and the dependences of the rms aberration on the optimization parameters and a set of parameters providing the minimum aberration are determined.