Scattering Matrix Determination in Crystalline Materials from 4D Scanning Transmission Electron Microscopy at a Single Defocus Value

Findlay, Scott D.; Brown, Hamish G.; Pelz, Philipp M.; Ophus, Colin; Ciston, Jim; Allen, Leslie J.

doi:10.1017/s1431927621000490

Title: Scattering Matrix Determination in Crystalline Materials from 4D Scanning Transmission Electron Microscopy at a Single Defocus Value

Journal Article · 26 July 2021 · Microscopy and Microanalysis

DOI: https://doi.org/10.1017/s1431927621000490 · OSTI ID:1841721

^[1]; Brown, Hamish G. ^[2]; Pelz, Philipp M. ^[3]; Ophus, Colin ^[4]; Ciston, Jim ^[4]; Allen, Leslie J. ^[5]

Monash Univ., Melbourne, VIC (Australia)
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Molecular Foundry; Univ. of Melbourne (Australia)
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Molecular Foundry; Univ. of California, Berkeley, CA (United States)
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Molecular Foundry
Univ. of Melbourne (Australia)

Recent work has revived interest in the scattering matrix formulation of electron scattering in transmission electron microscopy as a stepping stone toward atomic-resolution structure determination in the presence of multiple scattering. Here, we discuss ways of visualizing the scattering matrix that make its properties clear. Through a simulation-based case study incorporating shot noise, we shown how regularizing on this continuity enables the scattering matrix to be reconstructed from 4D scanning transmission electron microscopy (STEM) measurements from a single defocus value. Intriguingly, for crystalline samples, this process also yields the sample thickness to nanometer accuracy with no a priori knowledge about the sample structure. The reconstruction quality is gauged by using the reconstructed scattering matrix to simulate STEM images at defocus values different from that of the data from which it was reconstructed.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: Australian Research Council; National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22), Chemical Sciences, Geosciences & Biosciences Division (SC-22.1)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1841721

Journal Information:: Microscopy and Microanalysis, Journal Name: Microscopy and Microanalysis Journal Issue: 4 Vol. 27; ISSN 1431-9276

Publisher:: Microscopy Society of America (MSA)Copyright Statement

Country of Publication:: United States

Language:: English

References (56)

Ptychography Rodenburg, John; Maiden, Andrew Springer Handbook of Microscopy, p. 819-904 https://doi.org/10.1007/978-3-030-00069-1_17	book	January 2019
Lattice-resolution contrast from a focused coherent electron probe. Part II Findlay, S. D.; Allen, L. J.; Oxley, M. P. Ultramicroscopy, Vol. 96, Issue 1 https://doi.org/10.1016/S0304-3991(02)00381-9	journal	July 2003
CCPi-Regularisation toolkit for computed tomographic image reconstruction with proximal splitting algorithms Kazantsev, Daniil; Pasca, Edoardo; Turner, Martin J. SoftwareX, Vol. 9 https://doi.org/10.1016/j.softx.2019.04.003	journal	January 2019
An improved ptychographical phase retrieval algorithm for diffractive imaging Maiden, Andrew M.; Rodenburg, John M. Ultramicroscopy, Vol. 109, Issue 10 https://doi.org/10.1016/j.ultramic.2009.05.012	journal	September 2009
Position averaged convergent beam electron diffraction: Theory and applications LeBeau, James M.; Findlay, Scott D.; Allen, Leslie J. Ultramicroscopy, Vol. 110, Issue 2 https://doi.org/10.1016/j.ultramic.2009.10.001	journal	January 2010
Simulation of scanning transmission electron microscope images on desktop computers Dwyer, C. Ultramicroscopy, Vol. 110, Issue 3 https://doi.org/10.1016/j.ultramic.2009.11.009	journal	February 2010
Aberration-compensated large-angle rocking-beam electron diffraction Koch, Christoph T. Ultramicroscopy, Vol. 111, Issue 7 https://doi.org/10.1016/j.ultramic.2010.12.014	journal	June 2011
Efficient phase contrast imaging in STEM using a pixelated detector. Part II: Optimisation of imaging conditions Yang, Hao; Pennycook, Timothy J.; Nellist, Peter D. Ultramicroscopy, Vol. 151 https://doi.org/10.1016/j.ultramic.2014.10.013	journal	April 2015
Towards quantitative, atomic-resolution reconstruction of the electrostatic potential via differential phase contrast using electrons Close, R.; Chen, Z.; Shibata, N. Ultramicroscopy, Vol. 159 https://doi.org/10.1016/j.ultramic.2015.09.002	journal	December 2015
Phase contrast STEM for thin samples: Integrated differential phase contrast Lazić, Ivan; Bosch, Eric G. T.; Lazar, Sorin Ultramicroscopy, Vol. 160 https://doi.org/10.1016/j.ultramic.2015.10.011	journal	January 2016
Measurement of atomic electric fields and charge densities from average momentum transfers using scanning transmission electron microscopy Müller-Caspary, Knut; Krause, Florian F.; Grieb, Tim Ultramicroscopy, Vol. 178 https://doi.org/10.1016/j.ultramic.2016.05.004	journal	July 2017
Practical aspects of diffractive imaging using an atomic-scale coherent electron probe Chen, Z.; Weyland, M.; Ercius, P. Ultramicroscopy, Vol. 169 https://doi.org/10.1016/j.ultramic.2016.06.009	journal	October 2016
Analysis of depth-sectioning STEM for thick samples and 3D imaging Bosch, Eric G. T.; Lazić, Ivan Ultramicroscopy, Vol. 207 https://doi.org/10.1016/j.ultramic.2019.112831	journal	December 2019
A multiple scattering algorithm for three dimensional phase contrast atomic electron tomography Ren, David; Ophus, Colin; Chen, Michael Ultramicroscopy, Vol. 208 https://doi.org/10.1016/j.ultramic.2019.112860	journal	January 2020
Direct measurement of electrostatic potentials at the atomic scale: A conceptual comparison between electron holography and scanning transmission electron microscopy Winkler, Florian; Barthel, Juri; Dunin-Borkowski, Rafal E. Ultramicroscopy, Vol. 210 https://doi.org/10.1016/j.ultramic.2019.112926	journal	March 2020
Relative roles of multiple scattering and Fresnel diffraction in the imaging of small molecules using electrons Gureyev, T. E.; Quiney, H. M.; Kozlov, A. Ultramicroscopy, Vol. 218 https://doi.org/10.1016/j.ultramic.2020.113094	journal	November 2020
Efficient large field of view electron phase imaging using near-field electron ptychography with a diffuser Allars, Frederick; Lu, Peng-Han; Kruth, Maximilian Ultramicroscopy, Vol. 231 https://doi.org/10.1016/j.ultramic.2021.113257	journal	December 2021
High Dynamic Range Pixel Array Detector for Scanning Transmission Electron Microscopy Tate, Mark W.; Purohit, Prafull; Chamberlain, Darol Microscopy and Microanalysis, Vol. 22, Issue 1 https://doi.org/10.1017/S1431927615015664	journal	January 2016
Advanced Phase Reconstruction Methods Enabled by Four-Dimensional Scanning Transmission Electron Microscopy Ophus, Colin; Harvey, Tyler R.; Yasin, Fehmi S. Microscopy and Microanalysis, Vol. 25, Issue S2 https://doi.org/10.1017/S1431927619000783	journal	August 2019
Exploiting Colorimetry for Fidelity in Data Visualization Waters, Michael J.; Walker, Jessica M.; Nelson, Christopher T. Chemistry of Materials, Vol. 32, Issue 13 https://doi.org/10.1021/acs.chemmater.0c00933	journal	June 2020
Simultaneous atomic-resolution electron ptychography and Z-contrast imaging of light and heavy elements in complex nanostructures Yang, H.; Rutte, R. N.; Jones, L. Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms12532	journal	August 2016
Atomic electric fields revealed by a quantum mechanical approach to electron picodiffraction Müller, Knut; Krause, Florian F.; Béché, Armand Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms6653	journal	December 2014
Electron ptychographic microscopy for three-dimensional imaging Gao, Si; Wang, Peng; Zhang, Fucai Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-00150-1	journal	July 2017
Electron ptychography of 2D materials to deep sub-ångström resolution Jiang, Yi; Chen, Zhen; Han, Yimo Nature, Vol. 559, Issue 7714 https://doi.org/10.1038/s41586-018-0298-5	journal	July 2018
Quantitative electron phase imaging with high sensitivity and an unlimited field of view Maiden, A. M.; Sarahan, M. C.; Stagg, M. D. Scientific Reports, Vol. 5, Issue 1 https://doi.org/10.1038/srep14690	journal	October 2015
Invited Article: A unified evaluation of iterative projection algorithms for phase retrieval Marchesini, S. Review of Scientific Instruments, Vol. 78, Issue 1 https://doi.org/10.1063/1.2403783	journal	January 2007
Diffractive imaging of the dumbbell structure in silicon by spherical-aberration-corrected electron diffraction Morishita, Shigeyuki; Yamasaki, Jun; Nakamura, Keisuke Applied Physics Letters, Vol. 93, Issue 18 https://doi.org/10.1063/1.3003582	journal	November 2008
Electron diffractive imaging of nano-objects using a guided method with a dynamic support Dronyak, Roman; Liang, Keng S.; Stetsko, Yuri P. Applied Physics Letters, Vol. 95, Issue 11 https://doi.org/10.1063/1.3227837	journal	September 2009
Bad Colour Maps Hide Big Features and Create False Anomalies Kovesi, Peter ASEG Extended Abstracts, Vol. 2015, Issue 1 https://doi.org/10.1071/ASEG2015ab107	journal	December 2015
The Calculation of Electron Diffraction Intensities Sturkey, Lorenzo Proceedings of the Physical Society, Vol. 80, Issue 2 https://doi.org/10.1088/0370-1328/80/2/301	journal	August 1962
General framework for quantitative three-dimensional reconstruction from arbitrary detection geometries in TEM Van den Broek, Wouter; Koch, Christoph T. Physical Review B, Vol. 87, Issue 18 https://doi.org/10.1103/PhysRevB.87.184108	journal	May 2013
Method for Retrieval of the Three-Dimensional Object Potential by Inversion of Dynamical Electron Scattering Van den Broek, Wouter; Koch, Christoph T. Physical Review Letters, Vol. 109, Issue 24 https://doi.org/10.1103/PhysRevLett.109.245502	journal	December 2012
Inversion of Dynamical Scattering from Large-Angle Rocking-Beam Electron Diffraction Patterns Wang, Feng; Pennington, Robert S.; Koch, Christoph T. Physical Review Letters, Vol. 117, Issue 1 https://doi.org/10.1103/PhysRevLett.117.015501	journal	June 2016
Structure Retrieval at Atomic Resolution in the Presence of Multiple Scattering of the Electron Probe Brown, H. G.; Chen, Z.; Weyland, M. Physical Review Letters, Vol. 121, Issue 26 https://doi.org/10.1103/PhysRevLett.121.266102	journal	December 2018
Inversion of Many-Beam Bragg Intensities for Phasing by Iterated Projections: Removal of Multiple Scattering Artifacts from Diffraction Data Donatelli, Jeffrey J.; Spence, John C. H. Physical Review Letters, Vol. 125, Issue 6 https://doi.org/10.1103/PhysRevLett.125.065502	journal	August 2020
Movable Aperture Lensless Transmission Microscopy: A Novel Phase Retrieval Algorithm Faulkner, H. M. L.; Rodenburg, J. M. Physical Review Letters, Vol. 93, Issue 2 https://doi.org/10.1103/PhysRevLett.93.023903	journal	July 2004
Retrieval of a Complex-Valued Object from its Diffraction Pattern McBride, W.; O'Leary, N. L.; Allen, L. J. Physical Review Letters, Vol. 93, Issue 23 https://doi.org/10.1103/PhysRevLett.93.233902	journal	December 2004
Quantitative structure retrieval using scanning transmission electron microscopy Findlay, S. D. Acta Crystallographica Section A Foundations of Crystallography, Vol. 61, Issue 4 https://doi.org/10.1107/S0108767305011293	journal	June 2005
Direct Inversion of Dynamical Electron Diffraction Patterns to Structure Factors Spence, J. C. H. Acta Crystallographica Section A Foundations of Crystallography, Vol. 54, Issue 1 https://doi.org/10.1107/S010876739700874X	journal	January 1998
Electron Ptychography. II. Theory of Three-Dimensional Propagation Effects Plamann, T.; Rodenburg, J. M. Acta Crystallographica Section A Foundations of Crystallography, Vol. 54, Issue 1 https://doi.org/10.1107/S0108767397010507	journal	January 1998
Inversion of dynamical electron diffraction data including absorption Allen, L. J.; Faulkner, H. M. L.; Leeb, H. Acta Crystallographica Section A Foundations of Crystallography, Vol. 56, Issue 2 https://doi.org/10.1107/S0108767399014798	journal	March 2000
Atomic Resolution Imaging of a Carbon Nanotube from Diffraction Intensities Zuo, J. M. Science, Vol. 300, Issue 5624 https://doi.org/10.1126/science.1083887	journal	May 2003
Electron ptychography achieves atomic-resolution limits set by lattice vibrations Chen, Zhen; Jiang, Yi; Shao, Yu-Tsun Science, Vol. 372, Issue 6544 https://doi.org/10.1126/science.abg2533	journal	May 2021
Total Generalized Variation Bredies, Kristian; Kunisch, Karl; Pock, Thomas SIAM Journal on Imaging Sciences, Vol. 3, Issue 3 https://doi.org/10.1137/090769521	journal	January 2010
Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later Moler, Cleve; Van Loan, Charles SIAM Review, Vol. 45, Issue 1 https://doi.org/10.1137/S00361445024180	journal	January 2003
A fast image simulation algorithm for scanning transmission electron microscopy Ophus, Colin Advanced Structural and Chemical Imaging, Vol. 3, Issue 1 https://doi.org/10.1186/s40679-017-0046-1	journal	May 2017
Sub-Ångstrom electric field measurements on a universal detector in a scanning transmission electron microscope Hachtel, Jordan A.; Idrobo, Juan Carlos; Chi, Miaofang Advanced Structural and Chemical Imaging, Vol. 4, Issue 1 https://doi.org/10.1186/s40679-018-0059-4	journal	August 2018
Phase retrieval by iterated projections Elser, Veit Journal of the Optical Society of America A, Vol. 20, Issue 1 https://doi.org/10.1364/JOSAA.20.000040	journal	January 2003
Ptychographic transmission microscopy in three dimensions using a multi-slice approach Maiden, A. M.; Humphry, M. J.; Rodenburg, J. M. Journal of the Optical Society of America A, Vol. 29, Issue 8 https://doi.org/10.1364/JOSAA.29.001606	journal	January 2012
Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint Fienup, J. R. Journal of the Optical Society of America A, Vol. 4, Issue 1 https://doi.org/10.1364/JOSAA.4.000118	journal	January 1987
Noise-robust coherent diffractive imaging with a single diffraction pattern Martin, A. V.; Wang, F.; Loh, N. D. Optics Express, Vol. 20, Issue 15 https://doi.org/10.1364/OE.20.016650	journal	January 2012
Improved success rate and stability for phase retrieval by including randomized overrelaxation in the hybrid input output algorithm Köhl, Martin; Minkevich, A. A.; Baumbach, Tilo Optics Express, Vol. 20, Issue 15 https://doi.org/10.1364/OE.20.017093	journal	January 2012
Overcoming information reduced data and experimentally uncertain parameters in ptychography with regularized optimization Schloz, Marcel; Pekin, Thomas Christopher; Chen, Zhen Optics Express, Vol. 28, Issue 19 https://doi.org/10.1364/OE.396925	journal	January 2020
Overcoming information reduced data and experimentally uncertain parameters in ptychography with regularized optimization Schloz, Marcel; Pekin, Thomas Christopher; Van den Broek, Wouter Zenodo https://doi.org/10.5281/zenodo.3924495	dataset	January 2020
Ptychographic transmission microscopy in three dimensions using a multi-slice approach Maiden, A. M.; Humphry, M. J.; Rodenburg, J. M. Figshare https://doi.org/10.6084/m9.figshare.c.3753704.v1	collection	January 2012
Phase imaging and atomic-resolution imaging by electron diffractive imaging Yamasaki, Jun; Morishita, Shigeyuki; Shimaoka, Yuki Japanese Journal of Applied Physics, Vol. 58, Issue 12 https://doi.org/10.7567/1347-4065/ab50d7	journal	November 2019

Similar Records

Resolution of Virtual Depth Sectioning from Four-Dimensional Scanning Transmission Electron Microscopy

Journal Article · 2023 · Microscopy and Microanalysis · OSTI ID:1989425

Terzoudis-Lumsden, E. W. C.; Petersen, T. C.; Brown, H. G.; +3 more

Denoising atomic resolution 4D scanning transmission electron microscopy data with tensor singular value decomposition

Journal Article · 2020 · Ultramicroscopy · OSTI ID:1849893

Zhang, Chenyu; Han, Rungang; Zhang, Anru R.; +1 more

A Fast Algorithm for Scanning Transmission Electron Microscopy Imaging and 4D-STEM Diffraction Simulations

Journal Article · 2021 · Microscopy and Microanalysis · OSTI ID:1815403

Pelz, Philipp M.; Rakowski, Alexander; Rangel DaCosta, Luis; +3 more

Related Subjects

36 MATERIALS SCIENCE
4D STEM
phase retrieval
scattering matrix

Title: Scattering Matrix Determination in Crystalline Materials from 4D Scanning Transmission Electron Microscopy at a Single Defocus Value

Citation Formats

References (56)

Similar Records

Related Subjects