Spherical aberration correction using aspheric surfaces with an analytic-numerical method

Abstract

This method is a discrete case of the E. Wolf method for the design of an aspheric surface. Using the proposed method, the designer can select how many points $(x,y)$ there will be on the entrance pupil at which the spherical aberration will be zero, by using the aspheric coefficients as degrees of freedom. For fitting the coordinates that correct the spherical aberration to an aspheric surface we solve a system of equations of the first degree. An optimisation procedure is not required because we use equations without approximations and with exact ray tracing. We obtained diffraction limited optical systems faster than the commercial programs.