Inversion of the Diffraction Pattern from an Inhomogeneously Strained   Crystal using an Iterative Algorithm
  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. 
A.A. Minkevich, M. Gailhanou, J.-S. Micha, B. Charlet, V. Chamard, O.   Thomas