A role of second-order derivatives of amplitudes in X-ray beam dynamical diffraction equations

Dynamical diffraction equations for X-ray beams are considered with retaining the second-order derivatives of amplitudes in the direction perpendicular to the diffraction plane. For the dynamical diffraction problem, the retarded Green function is determined in case of a perfect crystal. Amplitudes of transmitted and diffracted waves in the crystal are represented as convolution over the crystal surface with use of determined Green function. Such representation can be used for solving diffraction problems in Laue and Bragg geometries in perfect crystals with both plane and not plane entrance and exit surfaces.