The method of phase retrieval of complex wavefield from two intensity measurements applicable to hard X-rays

A novel algorithm for a reconstruction of the phase shift profile produced by a transparent object in a coherent wave, from a set of two recorded intensity distributions is presented. Contrary to well known algorithms of in-line holography, the method works under the near-held condition where the size of the first Fresnel zone is much less than the characteristic size of the object's details. Such a condition is typical for an in-line holography experimental setup with the use of coherent high energy X-rays (E > 20 keV) produced by synchrotron radiation sources of the third generation like ESRF. The novel algorithm is fast and insensitive to a partial loss of coherence or weak detector resolution. The method can be applied to X-ray refraction tomography.