Abstract
Bragg coherent X-ray diffraction imaging (BCDI) has emerged as a powerful technique to image the local displacement field and strain in nanocrystals, in three dimensions with nanometric spatial resolution. However, BCDI relies on both dataset collection and phase retrieval algorithms that can induce artefacts in the reconstruction. Phase retrieval algorithms are based on the fast Fourier transform (FFT). We demonstrate how to calculate the displacement field inside a nanocrystal from its reconstructed phase depending on the mathematical convention used for the FFT. We use numerical simulations to quantify the influence of experimentally unavoidable detector deficiencies such as blind areas or limited dynamic range as well as post-processing filtering on the reconstruction. We also propose a criterion for the isosurface determination of the object, based on the histogram of the reconstructed modulus. Finally, we study the capability of the phasing algorithm to quantitatively retrieve the surface strain (i.e., the strain of the surface voxels). This work emphasizes many aspects that have been neglected so far in BCDI, which need to be understood for a quantitative analysis of displacement and strain based on this technique. It concludes with the optimization of experimental parameters to improve throughput and to establish BCDI as a reliable 3D nano-imaging technique.
Highlights
Bragg coherent X-ray diffraction imaging (BCDI) has emerged as a powerful technique to image the local displacement field and strain in nanocrystals, in three dimensions with nanometric spatial resolution
We study the capability of the phasing algorithm to retrieve quantitatively the strain of the surface voxels, which is an important parameter in surface physics and chemistry of materials
Labat et al mentioned briefly that the retrieved phase and the retrieved displacement are of opposite sign as a result of the fast Fourier transform (FFT) convention used by their Python-based phasing algorithms[20]
Summary
Bragg coherent X-ray diffraction imaging (BCDI) has emerged as a powerful technique to image the local displacement field and strain in nanocrystals, in three dimensions with nanometric spatial resolution. Methodical investigation of the performance and capability of phase retrieval has been approached with numerical simulations[11,12,13,14,15,16,17,18,19] It has been demonstrated[11] that a minimum dynamic range of 106 is needed for the intensity measurement to reach ultimate reconstruction performance and that the best resolution can be achieved with an overall oversampling ratio beyond 30. There is no tool to understand and distinguish the phase components caused by the real lattice displacement from the phase fluctuations that are statistical uncertainties introduced by the phase retrieval process itself These artefacts affect the accuracy and reliability of the recovered modulus and phase and cannot be associated to physical phenomena in the measured crystal. The study proposes optimum experimental conditions and tools to achieve optimum BCDI
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