Automatic computation of optical aberration coefficients

Abstract

A method based on ray tracing equations is presented facilitating the computation of polynomial functions that predict the x and y intercepts, direction tangents, and optical path length of an arbitrary skew ray on a defocused image surface. The optical systems considered may contain surfaces of general nonrotationally symmetric figure and orientation, refracting as well as reflecting, including plane diffraction gratings. The classical aberration coefficient equations are a subset of these polynomials. The method can, without hard programming work, be extended to arbitrarily high orders.