Identifying Defects in Bragg Coherent Diffractive Imaging with ArrayFire

John MelonakosArrayFire, Case Studies Leave a Comment

Researchers from the Materials Science Division of Argonne National Laboratory published a scientific report using ArrayFire to identify defects in Bragg coherent diffractive imaging (BCDI). From the article in Nature, the following abstract summarizes the research:

Crystallographic defects such as dislocations can significantly alter material properties and functionality. However, imaging these imperfections during operation remains challenging due to the short length scales involved and the reactive environments of interest. BCDI has emerged as a powerful tool capable of identifying dislocations, twin domains, and other defects in 3D detail with nanometer spatial resolution within nanocrystals and grains in reactive environments. However, BCDI relies on phase retrieval algorithms that can fail to accurately reconstruct the defect network. Here, numerical simulations are used to explore different guided phase retrieval algorithms for imaging defective crystals using BCDI. Different defect types, defect densities, Bragg peaks, and guided algorithm fitness metrics are explored as a function of signal-to-noise ratio. Based on these results, a general prescription for the phasing of defective crystals is offered with no a priori knowledge.

Some of the descriptive figures from the paper provide more detail about the algorithm and its applications, such as this depiction of the algorithm developed with ArrayFire and GPUs in order to achieve fast enough results to be tractable.

figure 1
Flow diagram for the guided phase retrieval algorithm. (a) 2D view of the crystal with a perfect screw dislocation. (b) 3D view of the dislocation showing the Burgers vector (1/2 [1–1 0]). (c) The (2–20) diffraction pattern computed from the atomic arrangement in (a,b) with Poisson noise added to simulate experimental data. (d) The noisy data is used to generate three individual real space random starts by using different random phases and the inverse Fourier transform. (e) 515 total iterations alternating between ER and HIO with Shrinkwrap are performed for each individual to recover the real space image shown in (f)(g) The best image from the first generation of individuals is selected according to a fitness metric. It is then bred into the other individuals. The total number of individuals is always fixed at three. (h) The bred individuals are fed back into (e–g) for a number of generations. The final answer (modulus shown) (i) is compared against the noise-free diffraction data (j) to compute the final modulus error. (k) The sequence (c–j) is repeated 100x to estimate the variance and success rate for a given fitness metric. We keep all algorithm parameters fixed except for the metric used to select the fittest individual from a generation. 3D reconstructions were performed although 2D cross-sections are shown.

The authors state that the data reported in this paper are available upon request. All code, including the reconstruction algorithm, is also available upon request.

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