skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on May 23, 2020

Title: Phase retrieval for Bragg coherent diffraction imaging at high x-ray energies

Abstract

Coherent x-ray beams with energies ≥ 50 keV can potentially enable three-dimensional imaging of atomic lattice distortion fields within individual crystallites in bulk polycrystalline materials through Bragg coherent diffraction imaging (BCDI). However, the undersampling of the diffraction signal due to Fourier-space compression at high x-ray energies renders conventional phase-retrieval algorithms unsuitable for three-dimensional reconstruction. To address this problem, we utilize a phase-retrieval method with a Fourier constraint specifically tailored for undersampled diffraction data measured with coarse-pitched detector pixels that bin the underlying signal. With our approach, we show that it is possible to reconstruct three-dimensional strained crystallites from an undersampled Bragg diffraction data set subject to pixel-area integration without having to physically upsample the diffraction signal. Using simulations and experimental results, we demonstrate that explicit modeling of Fourier-space compression during phase retrieval provides a viable means by which to invert high-energy BCDI data, which is otherwise intractable.

Authors:
 [1];  [2];  [3];  [3];  [3];  [3];  [3];  [4];  [1]
  1. Argonne National Lab. (ANL), Argonne, IL (United States). Materials Science Division
  2. Aix-Marseille Univ., Marseille (France); National Centre for Scientific Research (CNRS), Paris (France)
  3. Argonne National Lab. (ANL), Argonne, IL (United States). X-ray Sciences Division
  4. Argonne National Lab. (ANL), Argonne, IL (United States). Mathematics and Computer Science Division
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1526256
Alternate Identifier(s):
OSTI ID: 1515573
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 99; Journal Issue: 5; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats

Maddali, S., Allain, M., Cha, W., Harder, R., Almer, J., Kenesei, P., Park, J. -S., Nashed, Y., and Hruszkewycz, S. O. Phase retrieval for Bragg coherent diffraction imaging at high x-ray energies. United States: N. p., 2019. Web. doi:10.1103/PhysRevA.99.053838.
Maddali, S., Allain, M., Cha, W., Harder, R., Almer, J., Kenesei, P., Park, J. -S., Nashed, Y., & Hruszkewycz, S. O. Phase retrieval for Bragg coherent diffraction imaging at high x-ray energies. United States. doi:10.1103/PhysRevA.99.053838.
Maddali, S., Allain, M., Cha, W., Harder, R., Almer, J., Kenesei, P., Park, J. -S., Nashed, Y., and Hruszkewycz, S. O. Thu . "Phase retrieval for Bragg coherent diffraction imaging at high x-ray energies". United States. doi:10.1103/PhysRevA.99.053838.
@article{osti_1526256,
title = {Phase retrieval for Bragg coherent diffraction imaging at high x-ray energies},
author = {Maddali, S. and Allain, M. and Cha, W. and Harder, R. and Almer, J. and Kenesei, P. and Park, J. -S. and Nashed, Y. and Hruszkewycz, S. O.},
abstractNote = {Coherent x-ray beams with energies ≥ 50 keV can potentially enable three-dimensional imaging of atomic lattice distortion fields within individual crystallites in bulk polycrystalline materials through Bragg coherent diffraction imaging (BCDI). However, the undersampling of the diffraction signal due to Fourier-space compression at high x-ray energies renders conventional phase-retrieval algorithms unsuitable for three-dimensional reconstruction. To address this problem, we utilize a phase-retrieval method with a Fourier constraint specifically tailored for undersampled diffraction data measured with coarse-pitched detector pixels that bin the underlying signal. With our approach, we show that it is possible to reconstruct three-dimensional strained crystallites from an undersampled Bragg diffraction data set subject to pixel-area integration without having to physically upsample the diffraction signal. Using simulations and experimental results, we demonstrate that explicit modeling of Fourier-space compression during phase retrieval provides a viable means by which to invert high-energy BCDI data, which is otherwise intractable.},
doi = {10.1103/PhysRevA.99.053838},
journal = {Physical Review A},
number = 5,
volume = 99,
place = {United States},
year = {2019},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on May 23, 2020
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Simultaneous sample and spatial coherence characterisation using diffractive imaging
journal, October 2011

  • Clark, Jesse N.; Peele, Andrew G.
  • Applied Physics Letters, Vol. 99, Issue 15
  • DOI: 10.1063/1.3650265

Diffraction-limited storage rings – a window to the science of tomorrow
journal, August 2014

  • Eriksson, Mikael; van der Veen, J. Friso; Quitmann, Christoph
  • Journal of Synchrotron Radiation, Vol. 21, Issue 5
  • DOI: 10.1107/S1600577514019286

Synchrotron beam coherence: a spatially resolved measurement
journal, January 2005


Upsampling speckle patterns for coherent X-ray diffraction imaging
journal, March 2013


Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography
journal, April 2014


Maximum-likelihood refinement for coherent diffractive imaging
journal, June 2012


Unconstrained Optimization of Real Functions in Complex Variables
journal, January 2012

  • Sorber, Laurent; Barel, Marc Van; Lathauwer, Lieven De
  • SIAM Journal on Optimization, Vol. 22, Issue 3
  • DOI: 10.1137/110832124

Coherent X-ray diffraction imaging of strain at the nanoscale
journal, April 2009

  • Robinson, Ian; Harder, Ross
  • Nature Materials, Vol. 8, Issue 4
  • DOI: 10.1038/nmat2400

Performance evaluation of Bragg coherent diffraction imaging
journal, October 2017


Bragg coherent diffractive imaging of single-grain defect dynamics in polycrystalline films
journal, May 2017


High-resolution three-dimensional partially coherent diffraction imaging
journal, January 2012

  • Clark, J. N.; Huang, X.; Harder, R.
  • Nature Communications, Vol. 3, Issue 1
  • DOI: 10.1038/ncomms1994

Quantitative Nanoscale Imaging of Lattice Distortions in Epitaxial Semiconductor Heterostructures Using Nanofocused X-ray Bragg Projection Ptychography
journal, September 2012

  • Hruszkewycz, S. O.; Holt, M. V.; Murray, C. E.
  • Nano Letters, Vol. 12, Issue 10
  • DOI: 10.1021/nl303201w

Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint
journal, January 1987


Far-field high-energy diffraction microscopy: a tool for intergranular orientation and strain analysis
journal, July 2011

  • Bernier, J. V.; Barton, N. R.; Lienert, U.
  • The Journal of Strain Analysis for Engineering Design, Vol. 46, Issue 7
  • DOI: 10.1177/0309324711405761

Sparse recovery of undersampled intensity patterns for coherent diffraction imaging at high X-ray energies
journal, March 2018


Noise models for low counting rate coherent diffraction imaging
journal, January 2012

  • Godard, Pierre; Allain, Marc; Chamard, Virginie
  • Optics Express, Vol. 20, Issue 23
  • DOI: 10.1364/OE.20.025914

Diffractive Imaging Using Partially Coherent X Rays
journal, December 2009


X-ray diffraction contrast tomography: a novel technique for three-dimensional grain mapping of polycrystals. I. Direct beam case
journal, March 2008

  • Ludwig, Wolfgang; Schmidt, Søeren; Lauridsen, Erik Mejdal
  • Journal of Applied Crystallography, Vol. 41, Issue 2
  • DOI: 10.1107/S0021889808001684

Identifying Defects with Guided Algorithms in Bragg Coherent Diffractive Imaging
journal, August 2017


Enhancing resolution in coherent x-ray diffraction imaging
journal, October 2016


Arbitrary-path fly-scan ptychography
journal, January 2018

  • Odstrčil, Michal; Holler, Mirko; Guizar-Sicairos, Manuel
  • Optics Express, Vol. 26, Issue 10
  • DOI: 10.1364/OE.26.012585

Biomolecular imaging and electronic damage using X-ray free-electron lasers
journal, December 2010

  • Quiney, Harry M.; Nugent, Keith A.
  • Nature Physics, Vol. 7, Issue 2
  • DOI: 10.1038/nphys1859

Invited Article: A unified evaluation of iterative projection algorithms for phase retrieval
journal, January 2007

  • Marchesini, S.
  • Review of Scientific Instruments, Vol. 78, Issue 1
  • DOI: 10.1063/1.2403783

Reconstruction of the Shapes of Gold Nanocrystals Using Coherent X-Ray Diffraction
journal, October 2001


Dynamic diffraction artefacts in Bragg coherent diffractive imaging
journal, February 2018


Numerical study of Bragg CDI on thick polycrystalline specimens
journal, January 2018

  • Pedersen, Anders Filsøe; Chamard, Virginie; Poulsen, Henning Friis
  • Optics Express, Vol. 26, Issue 18
  • DOI: 10.1364/OE.26.023411

Efficient concentration of high-energy x-rays for diffraction-limited imaging resolution
journal, January 2017


Probing Microstructure Dynamics With X-Ray Diffraction Microscopy
journal, March 2008

  • Suter, R. M.; Hefferan, C. M.; Li, S. F.
  • Journal of Engineering Materials and Technology, Vol. 130, Issue 2
  • DOI: 10.1115/1.2840965

X-ray image reconstruction from a diffraction pattern alone
journal, October 2003