Inversion of the Diffraction Pattern from an Inhomogeneously Strained Crystal using an Iterative Algorithm

TL;DR

This paper presents an iterative algorithm that reconstructs the displacement field in inhomogeneously strained crystals from diffraction data, incorporating constraints to improve accuracy, validated against experimental measurements and finite element models.

Contribution

The paper introduces a novel iterative phase retrieval algorithm with specific constraints for accurately inverting diffraction patterns of strained crystals.

Findings

The algorithm successfully reconstructs displacement fields from experimental data.

Reconstructed displacement fields agree well with finite element calculations.

Constraints improve the stability and accuracy of phase retrieval in complex strain conditions.

Abstract

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.