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Reconstructing Crystalline Structures from Few Images Under High Resolution Transmission Electron Microscopy

In: Mathematics — Key Technology for the Future

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  • Peter Gritzmann

    (Zentrum Mathematik, Technische Universität München)

  • Sven de Vries

    (Zentrum Mathematik, Technische Universität München)

Abstract

The present paper is motivated by the demand from material sciences to reconstruct crystalline structures given through their images under high resolution transmission electron microscopy (HRTEM) in a certain limited number of directions. In particular, [31] and [22] show how a quantitative analysis of images from high resolution transmission electron microscopy can be used to determine the number of atoms on atomic columns in certain directions; see Sects. 2 and 3. Mathematically, this leads to the problem of reconstructing finite lattice sets from certain of their marginal sums; see Sect. 4.

Suggested Citation

  • Peter Gritzmann & Sven de Vries, 2003. "Reconstructing Crystalline Structures from Few Images Under High Resolution Transmission Electron Microscopy," Springer Books, in: Willi Jäger & Hans-Joachim Krebs (ed.), Mathematics — Key Technology for the Future, pages 441-459, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55753-8_36
    DOI: 10.1007/978-3-642-55753-8_36
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