Detector Tilt Considerations in Bragg Coherent Diffraction Imaging: A Simulation Study

Siddharth Maddali,Peng Li,Marc Allain,Virginie Chamard,Stephan O Hruszkewycz

doi:10.3390/cryst10121150

Abstract

This paper addresses the three-dimensional signal distortion and image reconstruction issues in X-ray Bragg coherent diffraction imaging (BCDI) in the event of a general non-orthogonal orientation of the area detector with respect to the diffracted beam. Growing interest in novel BCDI adaptations at fourth-generation synchrotron light sources has necessitated improvisations in the experimental configuration and the subsequent data analysis. One such possibly unavoidable improvisation that is envisioned in this paper is a photon-counting area detector whose face is tilted away from the perpendicular to the Bragg-diffracted beam during the acquisition of the coherent diffraction signal. We describe a likely circumstance in which one would require such a detector configuration, along with the experimental precedent at third-generation synchrotrons. Using physically accurate diffraction simulations from synthetic scatterers in the presence of such tilted detectors, we analyze the general nature of the observed signal distortion qualitatively and quantitatively and provide a prescription to correct for it during image reconstruction. Our simulations and reconstructions are based on an adaptation of the known theory of BCDI sampling geometry, as well as the recently developed projection-based methods of wavefield propagation. Such configurational modifications and their numerical remedies are potentially valuable in realizing unconventional coherent diffraction measurement geometries, eventually paving the way for the integration of BCDI into new material characterization experiments at next-generation light sources.

Highlights

Bragg coherent X-ray diffraction imaging (BCDI) is a synchrotron-based lensless imaging technique for the spatial resolution of lattice distortions on the scale of a few tens of nanometers [1,2,3,4,5,6,7].BCDI is a valuable means of material characterization owing to its ability to spatially resolve specific components of the 3D lattice strain tensor in deformed crystals, in a nondestructive manner.This is done by reconstructing three-dimensional (3D) real-space images via phase retrieval inversion algorithms [8,9,10,11]
The shear-correcting coordinate inversion method summarized in Section 1 generalizes to any BCDI configuration provided the sampling basis matrix Brecip is properly parameterized according to the experimental degrees of freedom
Such a modification would greatly simplify the design of a BCDI measurement, with the burden of correcting for the tilt-induced signal distortion being placed on numerical methods

Summary

Introduction

Bragg coherent X-ray diffraction imaging (BCDI) is a synchrotron-based lensless imaging technique for the spatial resolution of lattice distortions on the scale of a few tens of nanometers [1,2,3,4,5,6,7]. BCDI is a valuable means of material characterization owing to its ability to spatially resolve specific components of the 3D lattice strain tensor in deformed crystals, in a nondestructive manner This is done by reconstructing three-dimensional (3D) real-space images via phase retrieval inversion algorithms [8,9,10,11]. The structural response of such a material encodes subtle variations in the local polarization (via ion displacement) when viewed on the scale of tens of nanometers, the typical spatial resolution of BCDI To resolve these variations, one requires the enhanced strain sensitivity of a BCDI measurement at a higher-order Bragg reflection that may well be outside the accessible rotation range of a conventional detector arm. The method to directly compute gradients on a grid of such sheared sample points (required to convert the scatterer’s complex phase to a spatially resolved lattice strain field) is provided in the Appendix of [23]

A Tilted Detector

Simulation Results

Conclusions