Deterministic Bragg Coherent Diffraction Imaging

Abstract

A deterministic variant of Bragg Coherent Diffraction Imaging is introduced in its kinematical approximation, for X-ray scattering from an imperfect crystal whose imperfections span no more than half of the volume of the crystal. This approach provides a unique analytical reconstruction of the object’s structure factor and displacement fields from the 3D diffracted intensity distribution centred around any particular reciprocal lattice vector. The simple closed-form reconstruction algorithm, which requires only one multiplication and one Fourier transformation, is not restricted by assumptions of smallness of the displacement field. The algorithm performs well in simulations incorporating a variety of conditions, including both realistic levels of noise and departures from ideality in the reference (i.e. imperfection-free) part of the crystal.

Deterministic X-ray Bragg coherent diffraction imaging as a seed for subsequent iterative reconstruction

“…This builds upon a deterministic 2D reconstruction approach [30], which may be considered as a form of Fourier holography [16,17], and which was later extended and further developed by several groups (see the recent review on deterministic CDI by Allen et al [25], together with references therein). Deviations from the specified crystalline shapes or quality produce errors in the obtained reconstructions as shown in Pavlov et al [36]. In the present paper we show via x-ray simulations that such artefacts in the deterministic Bragg-CDI reconstruction may be improved via subsequent iterative refinement.…”

“…To avoid any aliasing problems and allow a successful iterative reconstruction procedure we use 4×4×4=64 oversampling ratio as defined in Miao et al [37]. In our previous paper [36], we introduced a reconstruction method based on an assumption that at least half of the crystal is ideal, i.e., deformation and defect free. In this paper we assume that there are three spherical inclusions (structural defects) in the upper half of the crystal, as in Pavlov et al [36].…”

“…In our previous paper [36], we introduced a reconstruction method based on an assumption that at least half of the crystal is ideal, i.e., deformation and defect free. In this paper we assume that there are three spherical inclusions (structural defects) in the upper half of the crystal, as in Pavlov et al [36]. We also assume the existence of a curved deformation field in the entire crystal (see figure 2(a)) according to the following functional form [36]:…”

“…In this paper we assume that there are three spherical inclusions (structural defects) in the upper half of the crystal, as in Pavlov et al [36]. We also assume the existence of a curved deformation field in the entire crystal (see figure 2(a)) according to the following functional form [36]:…”

“…The particular technique we consider here is a new deterministic method for 3D Bragg-CDI, which allows a non-destructive reconstruction of chemical composition and strain in facetted crystalline materials [36]. This builds upon a deterministic 2D reconstruction approach [30], which may be considered as a form of Fourier holography [16,17], and which was later extended and further developed by several groups (see the recent review on deterministic CDI by Allen et al [25], together with references therein).…”