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Matched Backprojection Operator for Combined Scanning Transmission Electron Microscopy Tilt- and Focal Series

Published online by Cambridge University Press:  05 June 2015

Tim Dahmen*
German Research Center for Artificial Intelligence GmbH (DFKI), 66123 Saarbrücken, Germany
Holger Kohr
Department of Mathematics, KTH Royal Institute of Technology, Lindstedtsvägen 25, Stockholm, SE 100 44, Sweden
Niels de Jonge
INM Leibniz Institute for New Materials, 66123 Saarbrücken, Germany
Philipp Slusallek
German Research Center for Artificial Intelligence GmbH (DFKI), 66123 Saarbrücken, Germany
*Corresponding author.
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Combined tilt- and focal series scanning transmission electron microscopy is a recently developed method to obtain nanoscale three-dimensional (3D) information of thin specimens. In this study, we formulate the forward projection in this acquisition scheme as a linear operator and prove that it is a generalization of the Ray transform for parallel illumination. We analytically derive the corresponding backprojection operator as the adjoint of the forward projection. We further demonstrate that the matched backprojection operator drastically improves the convergence rate of iterative 3D reconstruction compared to the case where a backprojection based on heuristic weighting is used. In addition, we show that the 3D reconstruction is of better quality.

Techniques and Equipment Development
© Microscopy Society of America 2015 

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