Fields in the neighborhood of a caustic

Starting with Picht's solution of the wave equation in the form of an integral of plane waves over a caustic, we derive expressions for the solution which depend entirely on the geometry of the problem. An asymptotic evaluation of Picht's integral for high frequencies gives the desired result which can have a number of different forms, depending on the precise region where the field is being observed. In particular, a change in the asymptotic field occurs in going from the regular ray field to the caustic or from a regular part of the caustic to a cusp.