On the equations of diffracted geodesics

Abstract

An explicit form for the geodesic equations that would describe diffracted light rays is obtained and the Levi-Civita connection that enters into it is shown to be a sum of contributions from the metric of the ambient space, the index of refraction of the optical medium, and diffraction effects. The nature of the problem of obtaining explicit forms for the diffraction correction in various problems of interest to optics is discussed briefly.