Dynamical theory of X-ray diffraction in crystals with defects

Sets of integral equations are obtained that describe the X-ray diffraction in defective crystals. A simple description of defects is suggested both for weakly and strongly distorted regions. In the case of ideal crystals, the solution for the wave fields with arbitrary incident beam distribution is given for crystals of arbitrary thickness. For distorted crystals, the integral equations give the universal method of treatment of both weakly and strongly distorted regions. The problem of image determination from strongly distorted regions is reduced to the solution of a simple one-dimensional integral equation. The first iteration approximation of initial integral equations is shown to give results similar to those of a Fourier analysis method with the defect being treated as a small perturbation.