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

Abstract

This two-part article series provides a generalized description of the scattering geometry of Bragg coherent diffraction imaging (BCDI) experiments, the shear distortion effects inherent in the 3D image obtained from presently used methods and strategies to mitigate this distortion. Part I starts from fundamental considerations to present the general real-space coordinate transformation required to correct this shear, in a compact operator formulation that easily lends itself to implementation with available software packages. Such a transformation, applied as a final post-processing step following phase retrieval, is crucial for arriving at an undistorted, correctly oriented and physically meaningful image of the 3D crystalline scatterer. As the relevance of BCDI grows in the field of materials characterization, the available sparse literature that addresses the geometric theory of BCDI and the subsequent analysis methods are generalized here. This geometrical aspect, specific to coherent Bragg diffraction and absent in 2D transmission CDI experiments, gains particular importance when it comes to spatially resolved characterization of 3D crystalline materials in a reliable nondestructive manner. This series of articles describes this theory, from the diffraction in Bragg geometry to the corrections needed to obtain a properly rendered digital image of the 3D scatterer. Part I of this seriesmore » provides the experimental BCDI community with the general form of the 3D real-space distortions in the phase-retrieved object, along with the necessary post-retrieval correction method. Part II builds upon the geometric theory developed in Part I with the formalism to correct the shear distortions directly on an orthogonal grid within the phase-retrieval algorithm itself, allowing more physically realistic constraints to be applied. Taken together, Parts I and II provide the X-ray science community with a set of generalized BCDI shear-correction techniques crucial to the final rendering of a 3D crystalline scatterer and for the development of new BCDI methods and experiments.« less

Authors:
 [1];  [2];  [3];  [4];  [1];  [4];  [4];  [1];  [1];  [1];  [5];  [5];  [2];  [2];  [1]
  1. Argonne National Lab. (ANL), Lemont, IL (United States)
  2. Aix-Marseille Univ., Marseille (France)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  4. Univ. of Chicago, IL (United States)
  5. Argonne National Lab. (ANL), Lemont, IL (United States); Univ. of Chicago, IL (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; European Union (EU)
OSTI Identifier:
1630854
Alternate Identifier(s):
OSTI ID: 1726109
Report Number(s):
LA-UR-19-27049
Journal ID: ISSN 1600-5767; JACGAR
Grant/Contract Number:  
89233218CNA000001; 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; Bragg coherent diffraction imaging; Bragg ptychography; conjugate spaces; coordinate transformation; phase retrieval; scattering geometry; shear correction

Citation Formats

Maddali, S., Li, P., Pateras, A., Timbie, D., Delegan, N., Crook, A. L., Lee, H., Calvo-Almazan, I., Sheyfer, D., Cha, W., Heremans, F. J., Awschalom, D. D., Chamard, V., Allain, M., and Hruszkewycz, S. O. General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part I. United States: N. p., 2020. Web. https://doi.org/10.1107/S1600576720001363.
Maddali, S., Li, P., Pateras, A., Timbie, D., Delegan, N., Crook, A. L., Lee, H., Calvo-Almazan, I., Sheyfer, D., Cha, W., Heremans, F. J., Awschalom, D. D., Chamard, V., Allain, M., & Hruszkewycz, S. O. General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part I. United States. https://doi.org/10.1107/S1600576720001363
Maddali, S., Li, P., Pateras, A., Timbie, D., Delegan, N., Crook, A. L., Lee, H., Calvo-Almazan, I., Sheyfer, D., Cha, W., Heremans, F. J., Awschalom, D. D., Chamard, V., Allain, M., and Hruszkewycz, S. O. Fri . "General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part I". United States. https://doi.org/10.1107/S1600576720001363. https://www.osti.gov/servlets/purl/1630854.
@article{osti_1630854,
title = {General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part I},
author = {Maddali, S. and Li, P. and Pateras, A. and Timbie, D. and Delegan, N. and Crook, A. L. and Lee, H. and Calvo-Almazan, I. and Sheyfer, D. and Cha, W. and Heremans, F. J. and Awschalom, D. D. and Chamard, V. and Allain, M. and Hruszkewycz, S. O.},
abstractNote = {This two-part article series provides a generalized description of the scattering geometry of Bragg coherent diffraction imaging (BCDI) experiments, the shear distortion effects inherent in the 3D image obtained from presently used methods and strategies to mitigate this distortion. Part I starts from fundamental considerations to present the general real-space coordinate transformation required to correct this shear, in a compact operator formulation that easily lends itself to implementation with available software packages. Such a transformation, applied as a final post-processing step following phase retrieval, is crucial for arriving at an undistorted, correctly oriented and physically meaningful image of the 3D crystalline scatterer. As the relevance of BCDI grows in the field of materials characterization, the available sparse literature that addresses the geometric theory of BCDI and the subsequent analysis methods are generalized here. This geometrical aspect, specific to coherent Bragg diffraction and absent in 2D transmission CDI experiments, gains particular importance when it comes to spatially resolved characterization of 3D crystalline materials in a reliable nondestructive manner. This series of articles describes this theory, from the diffraction in Bragg geometry to the corrections needed to obtain a properly rendered digital image of the 3D scatterer. Part I of this series provides the experimental BCDI community with the general form of the 3D real-space distortions in the phase-retrieved object, along with the necessary post-retrieval correction method. Part II builds upon the geometric theory developed in Part I with the formalism to correct the shear distortions directly on an orthogonal grid within the phase-retrieval algorithm itself, allowing more physically realistic constraints to be applied. Taken together, Parts I and II provide the X-ray science community with a set of generalized BCDI shear-correction techniques crucial to the final rendering of a 3D crystalline scatterer and for the development of new BCDI methods and experiments.},
doi = {10.1107/S1600576720001363},
journal = {Journal of Applied Crystallography (Online)},
number = 2,
volume = 53,
place = {United States},
year = {2020},
month = {3}
}

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