Geometric Diffraction Theory Created by the Methods of Edge and Angle Catastrophes

摘要

A survey of the results is presented that form, within the framework of the geometric diffraction theory, a novel scientific direction--the theory of edge and angle catastrophes. A classification of standard dif fraction structures is Performed that is stable in the space of physical parameters of the problem and takes into account combined focusing of primary and secondary wave fields. Uniform asymptotics the describe fields in such domains are represented using a finite set of special functions of the wave catastrophes and their first deriv- atives. The methods for determining coefficients of asymptotic representations and calculating special functions are considered. In actual radiophysical problems, stable diffraction field structures are represented asymptoti- cally as a superposition of contributions of standard fields corresponding to principal, edge, and angle catastro- phes of different types.