Astigmatic foci along a skew ray

Abstract

A method for astigmatism calculations along any skew ray is presented. This is useful in the case of extremely wide angle optical systems (and not only imaging systems), where skew ray aberrations are most dominant, but it is essential in the case of systems which are not rotationally symmetric, where all the rays may be skew. Equations relating the position of the astigmatic foci before and after refraction or reflection are derived from the analysis of infinitesimal wave fronts in the immediate neighbourhood of the point of incidence of any ray, but particularly the central ray of any pencil on an optical surface. The method is then illustrated and checked with representative numerical examples.