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Computationally Efficient Handling of Partially Coherent Electron Sources in (S)TEM Image Simulations via Matrix Diagonalization

Published online by Cambridge University Press:  15 September 2022

Zhongbo Li Open the ORCID record for Zhongbo Li [Opens in a new window] ,
Harald Rose ,
Jacob Madsen ,
Johannes Biskupek ,
Toma Susi  and
Ute Kaiser
Zhongbo Li*
Affiliation:
Electron Microscopy Group of Materials Science, University of Ulm, Ulm 89081, Germany
Harald Rose
Affiliation:
Electron Microscopy Group of Materials Science, University of Ulm, Ulm 89081, Germany
Jacob Madsen
Affiliation:
Faculty of Physics, University of Vienna, Vienna 1090, Austria
Johannes Biskupek
Affiliation:
Electron Microscopy Group of Materials Science, University of Ulm, Ulm 89081, Germany
Toma Susi
Affiliation:
Faculty of Physics, University of Vienna, Vienna 1090, Austria
Ute Kaiser
Affiliation:
Electron Microscopy Group of Materials Science, University of Ulm, Ulm 89081, Germany
*
*Corresponding author: Zhongbo Li, E-mail: zhongbo.lee@uni-ulm.de
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Abstract

We introduce a novel method to improve the computational efficiency for (S)TEM image simulation by employing matrix diagonalization of the mixed envelope function (MEF). The MEF is derived by taking the finite size and the energy spread of the effective electron source into account, and is a component of the transmission cross-coefficient that accounts for the correlation between partially coherent waves. Since the MEF is a four-dimensional array and its application in image calculations is time-consuming, we reduce the computation time by using its eigenvectors. By incorporating the aperture function into the matrix diagonalization, only a small number of eigenvectors are required to approximate the original matrix with high accuracy. The diagonalization enables for each eigenvector the calculation of the corresponding image by employing the coherent model. The individual images are weighted by the corresponding eigenvalues and then summed up, resulting in the total partially coherent image.

Keywords

matrix diagonalizationmixed envelope functionpartially coherent sourceSTEM image simulationTEM image simulationtransmission cross-coefficient
Type
Original Article
Information
Microscopy and Microanalysis , First View , pp. 1 - 9
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of the Microscopy Society of America

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