Bragg diffraction of spherical X-ray wave with allowance for two-dimensional curvature of wavefront

Abstract

Symmetrical Bragg diffraction of a spherical X-ray wave in a perfect semi-infinite crystal with a plane entrance surface is considered. As distinct from the standard theory, the two-dimensional curvature of the incident wavefront is taken into account. Using the corresponding Green function, a general expression for the amplitude of reflected wave on the entrance surface of the crystal is presented. Based on this expression, different cases of source-crystal distance are analyzed: the source is placed near the crystal and the crystal is in the Fresnel and Fraunhofer zones (large distance). The intensity distributions of the reflected wave are presented with allowance for two-dimensional curvature of the incident wavefront. Numerical calculations confirm the correctness of the used approximations.