Studies of the focal region of a spherical reflector: Stationary phase evaluation

Abstract

The geometric optics and polarization properties of a spherical reflector are used to develop an integral representation of its focal region fields. These integrals are evaluated by the extended method of stationary phase for field points off the caustics, on the axial caustic, on the caustic surface, and at the paraxial focus. The contributions to the field at a field point are shown to arise respectively from three ordinary stationary points: a stationary ring and a stationary point at the vertex; an ordinary stationary point and a caustic type stationary point; and a fourth-order stationary point. The resulting formulas are used to compute the value of the focal region fields. The computed results are then compared to measured data.