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Electron tomography: A short overview with an emphasis on the absorption potential model for the forward problem
Sidec AB, Kista, Sweden.ORCID iD: 0000-0002-1118-6483
University of Florens.
2008 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 24, no 1, 013001- p.Article in journal (Refereed) Published
Abstract [en]

This review of the development and current status of electron tomography deals mainly with the mathematical and algorithmic aspects. After a very brief description of the role of electron tomography in structural biology, we turn our attention to the derivation of the forward operator. Starting from the Schrodinger equation, the electron - specimen interaction is modelled as a diffraction tomography problem and the picture is completed by adding a description of the optical system of the transmission electron microscope. The first- order Born approximation enables one to explicitly express the intensity for any finite wavenumber in terms of the propagation operator acting on the specimen convolved with a point spread function, derived from the optics in the transmission electron microscope. Next, we focus on the difficulties that cause the reconstruction problem to be quite challenging. Special emphasis is put on explaining the extremely low signal- to- noise ratio in the data combined with the incomplete data problems, which lead to severe ill- posedness. The next step is to derive the standard phase contrast model used in the electron tomography community. The above- mentioned expression for the intensity generalizes the standard phase contrast model which can be obtained by replacing the propagation operator by its high- energy limit, the x- ray transform, as the wavenumber tends to infinity. The importance of more carefully including the wave nature of the electron - specimen interaction is supported by performing an asymptotic analysis of the intensity as the wavenumber tends to infinity. Next we provide an overview of the various reconstruction methods that have been employed in electron tomography and we conclude by mentioning a number of open problems. Besides providing an introduction to electron tomography written in the 'language of inverse problems', the authors hope to raise interest among experts in integral geometry and regularization theory for the mathematical and algorithmic difficulties that are encountered in electron tomography.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2008. Vol. 24, no 1, 013001- p.
Keyword [en]
Electron tomography, inverse scattering, electron scattering, diffraction tomography, regularisation, phase contrast tomography
National Category
Mathematical Analysis Atom and Molecular Physics and Optics Structural Biology
Research subject
SRA - Molecular Bioscience; SRA - E-Science (SeRC)
Identifiers
URN: urn:nbn:se:kth:diva-71134DOI: 10.1088/0266-5611/24/1/013001ISI: 000254150900002OAI: oai:DiVA.org:kth-71134DiVA: diva2:486606
Funder
Swedish e‐Science Research Center
Note
QC 20120131Available from: 2012-01-30 Created: 2012-01-30 Last updated: 2017-12-08Bibliographically approved

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Öktem, Ozan

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