Integral representation of high-frequency electromagnetic fields contains the surface integrals of the following form

* (1)

with k >> 1. If the surface S is an open one (for example, in case of diffraction by a finite-size screen or radiation of an aperture antenna), one can expect the asymptotic of (1) to contain the contributions of the stationary-phase points and of the edge contour Г. The case of S being a flat surface, and Ф and Г being smooth enough functions, has been considered earlier in [1, 2], The method used there enabled the authors to extract out only the contribution of a stationary point of elliptic type.

In the present paper,

a)   an integral over an arbitrary non-flat surface is considered, and an asymptotic of (1) is obtained as a sum of contributions from Г and from stationary-phase point of arbitrary type.

b)   the edge-contour contribution is evaluated for an amplitude function of the form

*

that is important in engineering problem of diffraction and radiation. Here, F₀ is a continuous function, and δ is the distance to Г. The method of the paper (1] based on integral theorems of vector analysis, is not applicable in such a case.