Near-to-far zone transition in the problem of plane wave scattering by statistically rough surface

Abstract

For a case of plane wave scattering by a statistically rough surface, the asymptotics of twofold integrals of oscillating functions which determine the time correlation function of the scattered field are found. At grazing angles much greater than the characteristic angle of the Fresnel zone, the method of stationary phase has been used for calculations. For grazing scattering, the combined method has been applied, namely, the method of stationary phase for the transverse (with respect to the scattering plane) variable and the Fraunhofer approximation for the longitudinal variable. The correlation with the results known from literature has been established.