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Title: General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part II

Abstract

X-ray Bragg coherent diffraction imaging (BCDI) has been demonstrated as a powerful 3D microscopy approach for the investigation of sub-micrometre-scale crystalline particles. The approach is based on the measurement of a series of coherent Bragg diffraction intensity patterns that are numerically inverted to retrieve an image of the spatial distribution of the relative phase and amplitude of the Bragg structure factor of the diffracting sample. This 3D information, which is collected through an angular rotation of the sample, is necessarily obtained in a non-orthogonal frame in Fourier space that must be eventually reconciled. To deal with this, the approach currently favored by practitioners (detailed in Part I) is to perform the entire inversion in conjugate non-orthogonal real- and Fourier-space frames, and to transform the 3D sample image into an orthogonal frame as a post-processing step for result analysis. In this article, which is a direct follow-up of Part I, two different transformation strategies are demonstrated, which enable the entire inversion procedure of the measured data set to be performed in an orthogonal frame. The new approaches described here build mathematical and numerical frameworks that apply to the cases of evenly and non-evenly sampled data along the direction of sample rotationmore » (i.e.the rocking curve). The value of these methods is that they rely on the experimental geometry, and they incorporate significantly more information about that geometry into the design of the phase-retrieval Fourier transformation than the strategy presented in Part I. Finally, two important outcomes are (1) that the resulting sample image is correctly interpreted in a shear-free frame and (2) physically realistic constraints of BCDI phase retrieval that are difficult to implement with current methods are easily incorporated. Computing scripts are also given to aid readers in the implementation of the proposed formalisms.« less

Authors:
 [1];  [2]; ORCiD logo [3];  [2];  [2];  [1];  [1];  [4]
  1. Aix-Marseille Univ., Marseille (France)
  2. Argonne National Lab. (ANL), Argonne, IL (United States). Materials Science Division
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  4. Argonne National Lab. (ANL), Argonne, IL (United States). X-ray Science Division
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; European Research Council (ERC)
OSTI Identifier:
1630890
Report Number(s):
LA-UR-20-21519
Journal ID: ISSN 1600-5767; JACGAR
Grant/Contract Number:  
89233218CNA000001; 724881; AC02-06CH11357
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Applied Crystallography (Online)
Additional Journal Information:
Journal Name: Journal of Applied Crystallography (Online); Journal Volume: 53; Journal Issue: 2; Journal ID: ISSN 1600-5767
Publisher:
International Union of Crystallography
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; material science; Bragg coherent diffraction imaging; Fourier synthesis; non-orthogonal Fourier sampling; coordinate transformation; shear correction; Bragg ptychography

Citation Formats

Li, Peng, Maddali, Siddarth, Pateras, Anastasios, Calvo-Almazan, Irene, Hruszkewycz, Stephan O., Chamard, Virginie, Allain, Marc, and Cha, W. General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part II. United States: N. p., 2020. Web. https://doi.org/10.1107/S1600576720001375.
Li, Peng, Maddali, Siddarth, Pateras, Anastasios, Calvo-Almazan, Irene, Hruszkewycz, Stephan O., Chamard, Virginie, Allain, Marc, & Cha, W. General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part II. United States. https://doi.org/10.1107/S1600576720001375
Li, Peng, Maddali, Siddarth, Pateras, Anastasios, Calvo-Almazan, Irene, Hruszkewycz, Stephan O., Chamard, Virginie, Allain, Marc, and Cha, W. Fri . "General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part II". United States. https://doi.org/10.1107/S1600576720001375. https://www.osti.gov/servlets/purl/1630890.
@article{osti_1630890,
title = {General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part II},
author = {Li, Peng and Maddali, Siddarth and Pateras, Anastasios and Calvo-Almazan, Irene and Hruszkewycz, Stephan O. and Chamard, Virginie and Allain, Marc and Cha, W.},
abstractNote = {X-ray Bragg coherent diffraction imaging (BCDI) has been demonstrated as a powerful 3D microscopy approach for the investigation of sub-micrometre-scale crystalline particles. The approach is based on the measurement of a series of coherent Bragg diffraction intensity patterns that are numerically inverted to retrieve an image of the spatial distribution of the relative phase and amplitude of the Bragg structure factor of the diffracting sample. This 3D information, which is collected through an angular rotation of the sample, is necessarily obtained in a non-orthogonal frame in Fourier space that must be eventually reconciled. To deal with this, the approach currently favored by practitioners (detailed in Part I) is to perform the entire inversion in conjugate non-orthogonal real- and Fourier-space frames, and to transform the 3D sample image into an orthogonal frame as a post-processing step for result analysis. In this article, which is a direct follow-up of Part I, two different transformation strategies are demonstrated, which enable the entire inversion procedure of the measured data set to be performed in an orthogonal frame. The new approaches described here build mathematical and numerical frameworks that apply to the cases of evenly and non-evenly sampled data along the direction of sample rotation (i.e.the rocking curve). The value of these methods is that they rely on the experimental geometry, and they incorporate significantly more information about that geometry into the design of the phase-retrieval Fourier transformation than the strategy presented in Part I. Finally, two important outcomes are (1) that the resulting sample image is correctly interpreted in a shear-free frame and (2) physically realistic constraints of BCDI phase retrieval that are difficult to implement with current methods are easily incorporated. Computing scripts are also given to aid readers in the implementation of the proposed formalisms.},
doi = {10.1107/S1600576720001375},
journal = {Journal of Applied Crystallography (Online)},
number = 2,
volume = 53,
place = {United States},
year = {2020},
month = {3}
}

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