Elastic electron scattering using the finite element method

Forward and inverse problems

Authors

  • Denis Aubry Laboratoire MSSMat (Ecole Centrale Paris - CNRS UMR 8579) Grande Voie des Vignes, F-92290 Châtenay-Malabry
  • Ann- Lenaig Hamon Laboratoire MSSMat (Ecole Centrale Paris - CNRS UMR 8579) Grande Voie des Vignes, F-92290 Châtenay-Malabry
  • Guillaume Puel Laboratoire MSSMat (Ecole Centrale Paris - CNRS UMR 8579) Grande Voie des Vignes, F-92290 Châtenay-Malabry

DOI:

https://doi.org/10.13052/EJCM.19.117-128

Keywords:

elastic scattering, TEM, inverse problem, adjoint state, regularization

Abstract

We address here the case of electron-matter elastic interaction as it occurs in Transmission Electron Microscopy (TEM) experiments. In the forward problem, we show that it is possible to derive the scattered electron wave function as the solution of a Helmholtz equation. This equation depends on the spatial potential associated with the analyzed sample, and can be relevantly solved using the Finite Element Method (FEM). Then we present an inverse formulation dealing with the determination of the sample’s potential when the total wave function is measured at the exit plane of the sample.

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Published

2010-08-06

How to Cite

Aubry, D. ., Lenaig Hamon, A.-., & Puel, G. . (2010). Elastic electron scattering using the finite element method: Forward and inverse problems. European Journal of Computational Mechanics, 19(1-3), 117–128. https://doi.org/10.13052/EJCM.19.117-128

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Original Article