The displacement field in highly non uniformly strained crystals is obtained by addition of constraints to an iterative phase retrieval algorithm. These constraints include direct space density uniformity and also constraints to the sign and derivatives of the different components of the displacement field. This algorithm is applied to an experimental reciprocal space map measured using high resolution X-ray diffraction from an array of silicon lines and the obtained component of the displacement field is in very good agreement with the one calculated using a finite element model.

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The iterative phase retrieval algorithm and its applicability for the imaging of the deformation fields in crystals are investigated. For this reason the x-ray-diffracted data are simulated for the strained modeled crystal with different values of inhomogeneity of deformations. The influence of the constraints introduced by Minkevich et al. ͓Phys. Rev. B 76, 104106 ͑2007͔͒ to the iterative phase retrieval algorithm is shown for the reconstruction of highly inhomogeneous strain field.

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In this paper, we study the success rate of the reconstruction of objects of finite extent given the magnitude of its Fourier transform and its geometrical shape. We demonstrate that the commonly used combination of the hybrid input output and error reduction algorithm is significantly outperformed by an extension of this algorithm based on randomized overrelaxation. In most cases, this extension tremendously enhances the success rate of reconstructions for a fixed number of iterations as compared to reconstructions solely based on the traditional algorithm. The good scaling properties in terms of computational time and memory requirements of the original algorithm are not influenced by this extension.