Elastic electron scattering using the finite element method. Forward and inverse problems

Denis Aubry (1) , Ann-Lenaig Hamon (1) , Guillaume Puel (1)

1 MSSMat - Laboratoire de mécanique des sols, structures et matériaux

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.

Keywords: elastic scattering; TEM; inverse problem; adjoint state; regularization

Domains: Engineering Sciences [physics]; Mechanics [physics.med-ph]

Denis Aubry, Ann-Lenaig Hamon, Guillaume Puel. Elastic electron scattering using the finite element method. Forward and inverse problems. Revue Européenne de Mécanique Numérique/European Journal of Computational Mechanics, 2010, 19 (1-2-3), pp.117-128. ⟨hal-00707978⟩