The method of stationary phase and the method of Fresnel zones

Abstract

The method of stationary phase is discussed and reasons are given why it is often preferable to the method of steepest descent, in spite of the mathematicians' partiality to the latter. The method of Fresnel zones is compared with the method of stationary phase and is shown to be a primitive version of it. The purpose of the zones is to reduce the double integral to a single integral; this same artifice underlies the various attempts to prove the method of stationary phase for double integrals.