title: Matched Backprojection Operator for Combined Scanning Transmission Electron Microscopy Tilt- and Focal Series.
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.
authors.affiliation: 1German Research Center for Artificial Intelligence GmbH (DFKI),66123 Saarbrücken,Germany.
authors.forename: Tim
authors.initials: T
authors.lastname: Dahmen
authors.affiliation: 2Department of Mathematics,KTH Royal Institute of Technology,Lindstedtsvägen 25,Stockholm,SE 100 44,Sweden.
authors.forename: Holger
authors.initials: H
authors.lastname: Kohr
authors.affiliation: 3INM Leibniz Institute for New Materials,66123 Saarbrücken,Germany.
authors.forename: Niels
authors.initials: N
authors.lastname: de Jonge
authors.affiliation: 1German Research Center for Artificial Intelligence GmbH (DFKI),66123 Saarbrücken,Germany.
authors.forename: Philipp
authors.initials: P
authors.lastname: Slusallek
mesh_terms: D000465:Algorithms; D021621:Imaging, Three-Dimensional / Q000379:methods*; D017348:Microscopy, Electron, Scanning Transmission / Q000379:methods*; D008962:Models, Theoretical
keywords: 3D; STEM; back projection; depth of field; focal series; iterative reconstruction; tomography