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Description
Bragg Coherent Diffraction X-ray Imaging (BCDI) is a non-invasive X-ray characterisation technique for probing in three-dimensions (3D) structures of single nano-objects. While traditional BCDI analysis yields 3D maps of electron density, displacement, and heterogeneous strain, this work introduces a methodology and a user-friendly open-source tool for resolving 3D d-spacing maps within the examined object.
In BCDI, the primary output of phase retrieval algorithms is a 3D map of phase with a spatial resolution of approximately 10 nm. However, analysing BCDI data goes beyond this, and essentially revolves around deriving this phase into more physics-related aspects such as atomic displacement and strain. To address potential ambiguities and differences in strain definitions across different scientific communities, we introduce the concepts of heterogeneous and homogeneous strains. Heterogeneous strain aligns with traditional BCDI strain analysis, while homogeneous strain corresponds to the shift of the Bragg peak in reciprocal space, a fundamental quantity in X-ray analysis under Bragg conditions. To combine both types of strain information, we present a methodology for computing 3D maps of local d-spacing, an absolute and more fundamental quantity than traditional heterogeneous strain maps. Expanding on this concept allows for the generation of 3D maps of global strain, a quantity analogous to d-spacing.
Cdiutils [1] is a python package designed to facilitate pre- and post-processing stages of BCDI data. It meticulously manages the cropping of the Fourier window prior to phasing, with a particular focus on handling the centre of mass of the 3D Bragg peak intensity relative to the cropped Fourier window. This feature enables the subsequent post-processing of the phase ramp, strain shift, and particularly, d-spacing maps. When coupled with PyNX software [2] for the phasing stage, cdiutils integrates all the steps of the entire data analysis process, including pre-processing, phasing and post-processing, all within a single user-friendly notebook. Multiple methods for heterogeneous strain computation are routinely employed and compared to ensure robust data analysis. Cdiutils runs on ESRF machine environment, transitions between CPUs and GPUs when required, can handle several data formats and beamline geometries and is easily adaptable to any other machine environments and beamline geometries.
[1] Atlan, C., Chatelier, C. & Olson, K. A python package to help Coherent Diffraction Imaging (CDI) practitioners in their analysis. (2023) doi:10.5281/zenodo.8013233.
[2] Favre-Nicolin, V. et al. PyNX: high performance computing toolkit for coherent X-ray imaging based on operators. J Appl Crystallogr 53, 1404–1413 (2020).
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