Mapping data between sample and detector conjugated spaces in Bragg coherent diffraction imaging

Abstract

Bragg coherent X-ray diffraction imaging (BCDI) is a non-destructive, lensless method for 3D-resolved, nanoscale strain imaging in micro-crystals. A challenge, particularly for new users of the technique, is accurate mapping of experimental data, collected in the detector reciprocal space coordinate frame, to more convenient orthogonal coordinates, e.g. attached to the sample. This is particularly the case since different coordinate conventions are used at every BCDI beamline. The reconstruction algorithms and mapping scripts composed for individual beamlines are not readily interchangeable. To overcome this, a BCDI experiment simulation with a plugin script that converts all beamline angles to a universal, right-handed coordinate frame is introduced, making it possible to condense any beamline geometry into three rotation matrices. The simulation translates a user-specified 3D complex object to different BCDIrelated coordinate frames. It also allows the generation of synthetic coherent diffraction data that can be inserted into any BCDI reconstruction algorithm to reconstruct the original user-specified object. Scripts are provided to map from sample space to detector conjugated space, detector conjugated space to sample space and detector conjugated space to detector conjugated space for a different reflection. This provides the reader with the basis for a flexible simulation tool kit that is easily adapted to different geometries. It is anticipated that this will find use in the generation of tailor-made supports for phasing of challenging data and exploration of novel geometries or data collection modalities.

Nanoscale lattice strains in self-ion implanted tungsten

“…This minimises the effect of long timescale drift on the data quality. For a comprehensive description of the experimental geometry see [46]. Diffraction patterns were flat-field and dead-time corrected, and then aligned to minimise their Pearson correlation coefficients using a 3D version of the algorithm described by Guizar-Sicairos et al [47].…”

“…After applying the appropriate coordinate transform to the retrieved data [46], the projection of the crystal electron density is given by the ab-solute value of the recovered data whilst the phase is proportional to the lattice displacement u(r), along the direction of the Bragg vector q hkl , i.e. φ(r) = q hkl • u(r).…”

“…Firstly, phase offsets of ±π/2 (two are typically sufficient) are applied to the recovered phase for each reflection in the detector conjugated coordinate frame and the values constrained between 0 and 2π. Then the recovered phase and the two copies are transformed into an orthogonal sample space [46] common to all reflections in the MBCDI dataset. The spatial derivatives of φ(r) are then computed and the pixel-by-pixel gradient with the smallest magnitude used for computing the lattice strain tensor through the minimisation of the squared error of the displacement gradient and the gradient of the measured phase for each reflection,…”

Annealing of focused ion beam damage in gold microcrystals: an in situ Bragg coherent X-ray diffraction imaging study

“…If the CXDP is oversampled by at least twice the Nyquist frequency (Miao & Sayre, 2000), at least 4 pixels per fringe period, iterative phase retrieval algorithms that apply constraints in real and reciprocal space can be used to recover the phase (Fienup, 1982;Robinson et al, 2001). The amplitude and phase in reciprocal space are related to the real-space object via an inverse Fourier transform (Miao & Sayre, 2000;Robinson et al, 2001;Clark et al, 2012) followed by a space transformation from detector conjugated space to orthogonal lab or sample space (Yang et al, 2019;Li et al, 2019;Maddali et al, 2020). The resulting amplitude, (r), where r is the position vector, is proportional to the effective electron density of the crystalline volume associated with the particular crystal reflection.…”

On the use of the scattering amplitude in coherent X-ray Bragg diffraction imaging

“…The methodology inherent to coherent X-ray Bragg diffraction imaging has been the subject of intense work, for example about the coherence of the beam (Vartanyants & Robinson, 2001; Leake et al, 2009;Clark et al, 2012), the algorithms (Ulvestad et al, 2017;Pavlov et al, 2017;, the data acquisition parameters (Ö ztü rk et al, 2017;Carnis et al, 2019), and sampling and coordinate changes [particularly by Yang et al (2019) and P. ; see also Carnis et al (2019) and Lauraux et al (2020)]. Other subjects have been discussed, like the curvature of the Ewald sphere (Hruszkewycz et al, 2015), noise in the data set (Chamard et al, 2015), misalignment between the beam and the centre of the diffractometer (Pateras et al, 2015), the flatfield-illumination assumption (Chamard et al, 2010;Cha et al, 2010), and the projection approximation in Bragg projection ptychography (Hruszkewycz et al, 2016).…”