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Microsc Microanal. 2015 Jun;21(3):725-38. doi: 10.1017/S1431927615000525. Epub 2015 Jun 5.

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

Author information

1
1German Research Center for Artificial Intelligence GmbH (DFKI),66123 Saarbrücken,Germany.
2
2Department of Mathematics,KTH Royal Institute of Technology,Lindstedtsvägen 25,Stockholm,SE 100 44,Sweden.
3
3INM Leibniz Institute for New Materials,66123 Saarbrücken,Germany.

Abstract

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.

KEYWORDS:

3D; STEM; back projection; depth of field; focal series; iterative reconstruction; tomography

PMID:
26046398
DOI:
10.1017/S1431927615000525
[Indexed for MEDLINE]

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