Eikonal approximation of dynamical diffraction equations for X-ray beams with two-dimensional curvature of the wave front. I. Basic formulas

Abstract

Taking into account the second derivatives of amplitudes with respect to the coordinate perpendicular to the diffraction plane, the eikonal approximation of dynamical diffraction equations for X-ray beams with two-dimensional curvature is presented. The diffracted field outside the crystal, in vacuum is described by the corresponding eikonal approximation of the parabolic equation of diffraction. The corresponding eikonal equations and complete integrals are obtained in case of a perfect crystal. A method is described, by which the eikonals and trajectories inside the crystal as well as in vacuum, outside the crystal, satisfying the given boundary conditions, can be obtained. This method allows to describe diffraction using sufficiently general assumptions on the incident wave front and for the non-plane entrance and exit surfaces of the crystal.