A multiple scattering algorithm for three dimensional phase contrast atomic electron tomography
Abstract
Electron tomography is used in both materials science and structural biology to image features well below the optical resolution limit. Here, we present a new method for high-resolution 3D transmission electron microscopy (TEM) which approximately reconstructs the electrostatic potential of a sample at atomic resolution in all three dimensions. We use phase contrast images captured through-focus and at varying tilt angles, along with an implicit phase retrieval algorithm that accounts for dynamical and strong scattering, providing more accurate results with much lower electron doses than current atomic electron tomography methods. We test our algorithm using simulated images of a synthetic needle geometry dataset composed of an amorphous silicon dioxide shell around a silicon core. By simulating various levels of electron dose, tilt and defocus, missing projections, and regularization methods, we identify a configuration that allows us to accurately determine both atomic positions and species. We also test the ability of our method to recover randomly positioned vacancies in light elements such as silicon, and to accurately reconstruct strongly-scattering elements such as tungsten.
- Authors:
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES), Chemical Sciences, Geosciences & Biosciences Division; National Science Foundation (NSF)
- OSTI Identifier:
- 1573259
- Alternate Identifier(s):
- OSTI ID: 1760197
- Grant/Contract Number:
- AC02-05CH11231; DMR1548924
- Resource Type:
- Published Article
- Journal Name:
- Ultramicroscopy
- Additional Journal Information:
- Journal Name: Ultramicroscopy Journal Volume: 208 Journal Issue: C; Journal ID: ISSN 0304-3991
- Publisher:
- Elsevier
- Country of Publication:
- Netherlands
- Language:
- English
- Subject:
- 42 ENGINEERING; Transmission electron microscopy; phase retrieval; multiple scattering; optimization; atomic electron tomography
Citation Formats
Ren, David, Ophus, Colin, Chen, Michael, and Waller, Laura. A multiple scattering algorithm for three dimensional phase contrast atomic electron tomography. Netherlands: N. p., 2020.
Web. doi:10.1016/j.ultramic.2019.112860.
Ren, David, Ophus, Colin, Chen, Michael, & Waller, Laura. A multiple scattering algorithm for three dimensional phase contrast atomic electron tomography. Netherlands. doi:10.1016/j.ultramic.2019.112860.
Ren, David, Ophus, Colin, Chen, Michael, and Waller, Laura. Wed .
"A multiple scattering algorithm for three dimensional phase contrast atomic electron tomography". Netherlands. doi:10.1016/j.ultramic.2019.112860.
@article{osti_1573259,
title = {A multiple scattering algorithm for three dimensional phase contrast atomic electron tomography},
author = {Ren, David and Ophus, Colin and Chen, Michael and Waller, Laura},
abstractNote = {Electron tomography is used in both materials science and structural biology to image features well below the optical resolution limit. Here, we present a new method for high-resolution 3D transmission electron microscopy (TEM) which approximately reconstructs the electrostatic potential of a sample at atomic resolution in all three dimensions. We use phase contrast images captured through-focus and at varying tilt angles, along with an implicit phase retrieval algorithm that accounts for dynamical and strong scattering, providing more accurate results with much lower electron doses than current atomic electron tomography methods. We test our algorithm using simulated images of a synthetic needle geometry dataset composed of an amorphous silicon dioxide shell around a silicon core. By simulating various levels of electron dose, tilt and defocus, missing projections, and regularization methods, we identify a configuration that allows us to accurately determine both atomic positions and species. We also test the ability of our method to recover randomly positioned vacancies in light elements such as silicon, and to accurately reconstruct strongly-scattering elements such as tungsten.},
doi = {10.1016/j.ultramic.2019.112860},
journal = {Ultramicroscopy},
number = C,
volume = 208,
place = {Netherlands},
year = {2020},
month = {1}
}
DOI: 10.1016/j.ultramic.2019.112860
Web of Science
Works referenced in this record:
Cryo-electron tomography: The challenge of doing structural biology in situ
journal, August 2013
- Lučić, Vladan; Rigort, Alexander; Baumeister, Wolfgang
- The Journal of Cell Biology, Vol. 202, Issue 3
Recent Advances in the Application of Electron Tomography to Materials Chemistry
journal, August 2012
- Leary, Rowan; Midgley, Paul A.; Thomas, John Meurig
- Accounts of Chemical Research, Vol. 45, Issue 10
Electron tomography and holography in materials science
journal, April 2009
- Midgley, Paul A.; Dunin-Borkowski, Rafal E.
- Nature Materials, Vol. 8, Issue 4
Three-dimensional atomic imaging of crystalline nanoparticles
journal, February 2011
- Van Aert, Sandra; Batenburg, Kees J.; Rossell, Marta D.
- Nature, Vol. 470, Issue 7334
Three-Dimensional Atomic Imaging of Colloidal Core–Shell Nanocrystals
journal, August 2011
- Bals, Sara; Casavola, Marianna; van Huis, Marijn A.
- Nano Letters, Vol. 11, Issue 8
Three-dimensional coordinates of individual atoms in materials revealed by electron tomography
journal, September 2015
- Xu, Rui; Chen, Chien-Chun; Wu, Li
- Nature Materials, Vol. 14, Issue 11
Deciphering chemical order/disorder and material properties at the single-atom level
journal, February 2017
- Yang, Yongsoo; Chen, Chien-Chun; Scott, M. C.
- Nature, Vol. 542, Issue 7639
Comparison of intensity distributions in tomograms from BF TEM, ADF STEM, HAADF STEM, and calculated tilt series
journal, December 2005
- Friedrich, H.; McCartney, M. R.; Buseck, P. R.
- Ultramicroscopy, Vol. 106, Issue 1
GENFIRE: A generalized Fourier iterative reconstruction algorithm for high-resolution 3D imaging
journal, September 2017
- Pryor, Alan; Yang, Yongsoo; Rana, Arjun
- Scientific Reports, Vol. 7, Issue 1
Efficient linear phase contrast in scanning transmission electron microscopy with matched illumination and detector interferometry
journal, February 2016
- Ophus, Colin; Ciston, Jim; Pierce, Jordan
- Nature Communications, Vol. 7, Issue 1
In-line three-dimensional holography of nanocrystalline objects at atomic resolution
journal, February 2016
- Chen, F. -R.; Van Dyck, D.; Kisielowski, C.
- Nature Communications, Vol. 7, Issue 1
Correcting nonlinear drift distortion of scanning probe and scanning transmission electron microscopies from image pairs with orthogonal scan directions
journal, March 2016
- Ophus, Colin; Ciston, Jim; Nelson, Chris T.
- Ultramicroscopy, Vol. 162
Studying Atomic Structures by Aberration-Corrected Transmission Electron Microscopy
journal, July 2008
- Urban, K. W.
- Science, Vol. 321, Issue 5888
Determination of the 3D shape of a nanoscale crystal with atomic resolution from a single image
journal, September 2014
- Jia, C. L.; Mi, S. B.; Barthel, J.
- Nature Materials, Vol. 13, Issue 11
Unraveling the 3D Atomic Structure of a Suspended Graphene/hBN van der Waals Heterostructure
journal, February 2017
- Argentero, Giacomo; Mittelberger, Andreas; Reza Ahmadpour Monazam, Mohammad
- Nano Letters, Vol. 17, Issue 3
Restoration of weak phase-contrast images recorded with a high degree of defocus: The “twin image” problem associated with CTF correction
journal, August 2008
- Downing, Kenneth H.; Glaeser, Robert M.
- Ultramicroscopy, Vol. 108, Issue 9
Radiation damage in the TEM and SEM
journal, August 2004
- Egerton, R. F.; Li, P.; Malac, M.
- Micron, Vol. 35, Issue 6
Comparison of optimal performance at 300keV of three direct electron detectors for use in low dose electron microscopy
journal, December 2014
- McMullan, G.; Faruqi, A. R.; Clare, D.
- Ultramicroscopy, Vol. 147
Single-particle cryo-electron microscopy
journal, December 2015
- Doerr, Allison
- Nature Methods, Vol. 13, Issue 1
Structural biology in situ—the potential of subtomogram averaging
journal, April 2013
- Briggs, John AG
- Current Opinion in Structural Biology, Vol. 23, Issue 2
Advances in Single-Particle Electron Cryomicroscopy Structure Determination applied to Sub-tomogram Averaging
journal, September 2015
- Bharat, Tanmay A. M.; Russo, Christopher J.; Löwe, Jan
- Structure, Vol. 23, Issue 9
When to use the projection assumption and the weak-phase object approximation in phase contrast cryo-EM
journal, January 2014
- Vulović, Miloš; Voortman, Lenard M.; van Vliet, Lucas J.
- Ultramicroscopy, Vol. 136
Automatic software correction of residual aberrations in reconstructed HRTEM exit waves of crystalline samples
journal, November 2016
- Ophus, Colin; Rasool, Haider I.; Linck, Martin
- Advanced Structural and Chemical Imaging, Vol. 2, Issue 1
Structure retrieval in HREM
journal, November 1991
- Gribelyuk, M. A.
- Acta Crystallographica Section A Foundations of Crystallography, Vol. 47, Issue 6
A method for crystal potential retrieval in HRTEM
journal, December 1993
- Beeching, M. J.; Spargo, A. E. C.
- Ultramicroscopy, Vol. 52, Issue 3-4
Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy
journal, August 1996
- Coene, W. M. J.; Thust, A.; Op de Beeck, M.
- Ultramicroscopy, Vol. 64, Issue 1-4
Reconstruction of the projected crystal potential in transmission electron microscopy by means of a maximum-likelihood refinement algorithm
journal, May 2000
- Lentzen, M.; Urban, K.
- Acta Crystallographica Section A Foundations of Crystallography, Vol. 56, Issue 3
Reconstruction of the projected electrostatic potential in high-resolution transmission electron microscopy including phenomenological absorption
journal, April 2010
- Lentzen, M.
- Ultramicroscopy, Vol. 110, Issue 5
An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations
journal, December 1973
- Misell, D. L.
- Journal of Physics D: Applied Physics, Vol. 6, Issue 18
Nonlinear high resolution image processing of conventional transmission electron micrographs
journal, January 1982
- Kirkland, Earl J.
- Ultramicroscopy, Vol. 9, Issue 1-2
Phase retrieval from series of images obtained by defocus variation
journal, November 2001
- Allen, L. J.; Oxley, M. P.
- Optics Communications, Vol. 199, Issue 1-4
Exit wave reconstruction at atomic resolution
journal, July 2004
- Allen, L. J.; McBride, W.; O'Leary, N. L.
- Ultramicroscopy, Vol. 100, Issue 1-2
Ptychographic transmission microscopy in three dimensions using a multi-slice approach
journal, January 2012
- Maiden, A. M.; Humphry, M. J.; Rodenburg, J. M.
- Journal of the Optical Society of America A, Vol. 29, Issue 8
High-Resolution Multislice X-Ray Ptychography of Extended Thick Objects
journal, February 2014
- Suzuki, Akihiro; Furutaku, Shin; Shimomura, Kei
- Physical Review Letters, Vol. 112, Issue 5
Learning approach to optical tomography
journal, January 2015
- Kamilov, Ulugbek S.; Papadopoulos, Ioannis N.; Shoreh, Morteza H.
- Optica, Vol. 2, Issue 6
Machine learning for 3D microscopy
journal, July 2015
- Waller, Laura; Tian, Lei
- Nature, Vol. 523, Issue 7561
Electron ptychographic microscopy for three-dimensional imaging
journal, July 2017
- Gao, Si; Wang, Peng; Zhang, Fucai
- Nature Communications, Vol. 8, Issue 1
Invertible propagator for plane wave illumination of forward-scattering structures
journal, January 2017
- Samelsohn, Gregory
- Applied Optics, Vol. 56, Issue 14
Multi-slice ptychographic tomography
journal, February 2018
- Li, Peng; Maiden, Andrew
- Scientific Reports, Vol. 8, Issue 1
3D intensity and phase imaging from light field measurements in an LED array microscope
journal, January 2015
- Tian, Lei; Waller, Laura
- Optica, Vol. 2, Issue 2
The scattering of electrons by atoms and crystals. I. A new theoretical approach
journal, October 1957
- Cowley, J. M.; Moodie, A. F.
- Acta Crystallographica, Vol. 10, Issue 10, p. 609-619
General framework for quantitative three-dimensional reconstruction from arbitrary detection geometries in TEM
journal, May 2013
- Van den Broek, Wouter; Koch, Christoph T.
- Physical Review B, Vol. 87, Issue 18
Method for Retrieval of the Three-Dimensional Object Potential by Inversion of Dynamical Electron Scattering
journal, December 2012
- Van den Broek, Wouter; Koch, Christoph T.
- Physical Review Letters, Vol. 109, Issue 24
Inverse dynamical photon scattering (IDPS): an artificial neural network based algorithm for three-dimensional quantitative imaging in optical microscopy
journal, January 2016
- Jiang, Xiaoming; Van den Broek, Wouter; Koch, Christoph T.
- Optics Express, Vol. 24, Issue 7
Image formation in holographic tomography
journal, January 2008
- Kou, Shan Shan; Sheppard, Colin J. R.
- Optics Letters, Vol. 33, Issue 20
Nanostructured Ultrafast Silicon-Tip Optical Field-Emitter Arrays
journal, August 2014
- Swanwick, Michael E.; Keathley, Phillip D.; Fallahi, Arya
- Nano Letters, Vol. 14, Issue 9
Towards three-dimensional structural determination of amorphous materials at atomic resolution
journal, September 2013
- Zhu, Chun; Chen, Chien-Chun; Du, Jincheng
- Physical Review B, Vol. 88, Issue 10
Si — O bond-length modification in pressure-densified amorphous
journal, June 1987
- Devine, R. A. B.; Arndt, J.
- Physical Review B, Vol. 35, Issue 17
Electron microscopy image enhanced
journal, April 1998
- Haider, Maximilian; Uhlemann, Stephan; Schwan, Eugen
- Nature, Vol. 392, Issue 6678
Sub-ångstrom resolution using aberration corrected electron optics
journal, August 2002
- Batson, P. E.; Dellby, N.; Krivanek, O. L.
- Nature, Vol. 418, Issue 6898
Background, status and future of the Transmission Electron Aberration-corrected Microscope project
journal, August 2009
- Dahmen, U.; Erni, R.; Radmilovic, V.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 367, Issue 1903, p. 3795-3808
SiO2 / Si Interfaces Studied by Scanning Tunneling Microscopy and High Resolution Transmission Electron Microscopy
journal, March 1992
- Niwa, M.; Matsumoto, M.; Iwasaki, H.
- Journal of The Electrochemical Society, Vol. 139, Issue 3
A reassessment of electron escape depths in silicon and thermally grown silicon dioxide thin films
journal, January 1988
- Hochella, M. F.; Carim, A. H.
- Surface Science, Vol. 197, Issue 3
Electron Microscopy Characterization of Silicon Dioxide Nanotubes
journal, July 2004
- Krumeich, F.; Wark, M.; Ren, L.
- Zeitschrift für anorganische und allgemeine Chemie, Vol. 630, Issue 7
In Situ Transmission Electron Microscopy Probing of Native Oxide and Artificial Layers on Silicon Nanoparticles for Lithium Ion Batteries
journal, October 2014
- He, Yang; Piper, Daniela Molina; Gu, Meng
- ACS Nano, Vol. 8, Issue 11
Entropic Comparison of Atomic-Resolution Electron Tomography of Crystals and Amorphous Materials
journal, October 2017
- Collins, S. M.; Leary, R. K.; Midgley, P. A.
- Physical Review Letters, Vol. 119, Issue 16
Deterministic phase retrieval: a Green’s function solution
journal, January 1983
- Teague, Michael Reed
- Journal of the Optical Society of America, Vol. 73, Issue 11
Transport of Intensity phase imaging by intensity spectrum fitting of exponentially spaced defocus planes
journal, January 2014
- Jingshan, Zhong; Claus, Rene A.; Dauwels, Justin
- Optics Express, Vol. 22, Issue 9
Experimental robustness of Fourier ptychography phase retrieval algorithms
journal, January 2015
- Yeh, Li-Hao; Dong, Jonathan; Zhong, Jingshan
- Optics Express, Vol. 23, Issue 26
Proximal Algorithms
journal, January 2014
- Parikh, Neal
- Foundations and Trends® in Optimization, Vol. 1, Issue 3
Nonlinear total variation based noise removal algorithms
journal, November 1992
- Rudin, Leonid I.; Osher, Stanley; Fatemi, Emad
- Physica D: Nonlinear Phenomena, Vol. 60, Issue 1-4
Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems
journal, November 2009
- Beck, A.; Teboulle, M.
- IEEE Transactions on Image Processing, Vol. 18, Issue 11
Accelerated cryo-EM structure determination with parallelisation using GPUs in RELION-2
journal, November 2016
- Kimanius, Dari; Forsberg, Björn O.; Scheres, Sjors HW
- eLife, Vol. 5
Quantitative evaluation of temporal partial coherence using 3D Fourier transforms of through-focus TEM images
journal, November 2013
- Kimoto, Koji; Sawada, Hidetaka; Sasaki, Takeo
- Ultramicroscopy, Vol. 134
Practical computation of amplitudes and phases in electron diffraction
journal, January 1983
- Self, P. G.; O'Keefe, M. A.; Buseck, P. R.
- Ultramicroscopy, Vol. 11, Issue 1
Works referencing / citing this record:
Atomic electron tomography in three and four dimensions
journal, April 2020
- Zhou, Jihan; Yang, Yongsoo; Ercius, Peter
- MRS Bulletin, Vol. 45, Issue 4