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

Abstract

Coherent diffractive imaging (CDI), using both x-rays and electrons, has made extremely rapid progress over the past two decades. The associated reconstruction algorithms are typically iterative, and seeded with a crude first estimate. A deterministic method for Bragg Coherent Diffraction Imaging (Pavlov et al 2017 Sci. Rep. 7 1132) is used as a more refined starting point for a shrink-wrap iterative reconstruction procedure. The appropriate comparison with the autocorrelation function as a starting point is performed. Real-space and Fourier-space error metrics are used to analyse the convergence of the reconstruction procedure for noisy and noise-free simulated data. Our results suggest that the use of deterministic-CDI reconstructions, as a seed for subsequent iterative-CDI refinement, may boost the speed and degree of convergence compared to the cruder seeds that are currently commonly used. We also highlight the utility of monitoring multiple error metrics in the context of iterative refinement.

X-ray multi-modal intrinsic-speckle-tracking

“…Finally, we mention a third contribution to the effective diffusion coefficient in the Fokker-Planck formalism, namely that which is due to the effective point-spread function associated with the imaging system [1,2]. This third contribution is listed for completeness, but is otherwise of marginal relevance here, since its contribution will be negligible in 9 Compare with the use of such an edge wave in the different phase-retrieval context of a deterministic approach to coherent diffractive imaging [59][60][61]. This may also be analogous to the different type of behaviour observed for diffuse scattering from dislocation ensembles having shorter and longer correlation lengths.…”

Simulation of X-ray diffraction in a cylindrical crystal

“…At present, triple-crystal diffractometry (Iida & Kohra, 1979;Punegov, 2015) and Bragg coherent diffraction imaging (Robinson et al, 2001;Pavlov et al, 2017Pavlov et al, , 2018Shabalin et al, 2017) are widely applied to the study of crystalline structures. Calculations of rocking curves and reciprocal space maps RSMs) for lateral crystals of rectangular cross section have been performed using the Takagi equations (Kolosov & Punegov, 2005) and two-dimensional recurrence relations (Punegov et al, 2014(Punegov et al, , 2016.…”

“…Calculations of rocking curves and reciprocal space maps RSMs) for lateral crystals of rectangular cross section have been performed using the Takagi equations (Kolosov & Punegov, 2005) and two-dimensional recurrence relations (Punegov et al, 2014(Punegov et al, , 2016. For a lateral imperfect crystal, a deterministic version of Bragg coherent diffraction imaging in the kinematical approximation has been considered (Pavlov et al, , 2018. The effects of dynamical diffraction in Bragg coherent diffraction imaging were shown by Shabalin et al (2017) using the Takagi-Taupin equations (Takagi, 1962;Taupin, 1964).…”