Sparse recovery of undersampled intensity patterns for coherent diffraction imaging at high X-ray energies

TL;DR

This paper introduces a sparsity-based method to recover fine fringe details in high-energy coherent X-ray diffraction data, enabling 3D imaging of crystalline materials despite undersampling issues.

Contribution

The authors propose a novel two-step approach combining in-plane detector motion and sparse numerical solving to enhance fringe resolution in high-energy BCDI data.

Findings

Successful recovery of fringe detail in simulated data

Reduced number of detector translations needed for signal recovery

Potential for improved imaging of bulk crystalline materials at high energies

Abstract

Coherent X-ray photons with energies higher than 50 keV offer new possibilities for imaging nanoscale lattice distortions in bulk crystalline materials using Bragg peak phase retrieval methods. However, the compression of reciprocal space at high energies typically results in poorly resolved fringes on an area detector, rendering the diffraction data unsuitable for the three-dimensional reconstruction of compact crystals. To address this problem, we propose a method by which to recover fine fringe detail in the scattered intensity. This recovery is achieved in two steps: multiple undersampled measurements are made by in-plane sub-pixel motion of the area detector, then this data set is passed to a sparsity-based numerical solver that recovers fringe detail suitable for standard Bragg coherent diffraction imaging (BCDI) reconstruction methods of compact single crystals. The key insight of this paper is that sparsity in a BCDI data set can be enforced by recognising that the signal in the detector, though poorly resolved, is band-limited. This requires fewer in-plane detector translations for complete signal recovery, while adhering to information theory limits. We use simulated BCDI data sets to demonstrate the approach, outline our sparse recovery strategy, and comment on future opportunities.