Near-to-Far Zone Transition in the Problem of Wave Backscattering by a Statistically Rough Surface

Abstract

For a case of wave backscattering by a statistically rough surface the asymptotics of twofold integrals of rapidly oscillating functions which determine temporary correlation function of the scattered field are found. At grazing angles much greater than the characteristic angle of the Fresnel zone in calculi, the method of a stationary phase will be utilized. The solution obtained enables passages to the limit to values of physical parameters adequate to “large” and “small” surface elements. For a grazing angle much less than the Fresnel angle the combined solution is the method of a stationary phase on a variable azimuth and approximation of Fraunhofer diffraction on a radial variable. The calculations allow the relationship with solutions based on heuristic simplifying hypotheses.