Numerical reconstruction of an object image using an X-ray dynamical diffraction Fraunhofer hologram

A numerical method of reconstruction of an object image using an X-ray dynamical diffraction Fraunhofer hologram is presented. Analytical approximation methods and numerical methods of iteration are discussed. An example of a reconstruction of an image of a cylindrical beryllium wire is considered. The results of analytical approximation and zero-order iteration coincide with exact values of the amplitude complex transmission coefficient of the object as predicted by the resolution limit of the scheme, except near the edges of the object. Calculations of the first- and second-order iterations improve the result at the edges of the object. This method can be applied for determination of the complex amplitude transmission coefficient of amplitude as well as phase objects. It can be used in X-ray microscopy.