On the integral representation of wave fields and its applications

Abstract

This paper deals with an integral representation which has been suggested by the author of wave fields as a superposition of only homogeneous plane waves (IRHW) and with its application. In literature there was an assertion that the fields outside sources which occupy a finite region of space cannot strictly be represented by a superposition of only homogeneous plane waves: the so-called angular spectrum must contain both homogeneous and inhomogeneous plane waves. The integral representation suggested by P. Debae [see Ann. der Phys. bf 30, No. 14, p.755, 1909] containing only homogeneous plane waves and used to analyze the field in the neighbourhood of the lens focus is an approximate one.