Abstract
Inverse problems as direct solutions of electron scattering equations can be deduced using either an invertible linearized eigenvalue system or a discretized form of the diffraction equations. The analysis is based on the knowledge of the complex electron wave at the exit plane of an object reconstructed for single reflections by electron holography or other wave reconstruction techniques. In principle, this enables the direct retrieval of the local thickness and orientation of a sample as well as the refinement of potential coefficients or the determination of the atomic displacements, caused by a crystal lattice defect, relative to the atom positions of the perfect lattice. Considering the sample orientation as perturbation the solution is given by a generalized and regularized Moore-Penrose inverse. Extracting solely the atomic displacements the latter are given by the zeros of a function with an incompletely known Fourier spectrum. The numerical algorithms resulting from the fundamental relations imply ill-posed inverse problems.
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Scheerschmidt, K. (1997). Retrieval of object information from electron diffraction as Ill-posed inverse problems. In: Chavent, G., Sabatier, P.C. (eds) Inverse Problems of Wave Propagation and Diffraction. Lecture Notes in Physics, vol 486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105761
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DOI: https://doi.org/10.1007/BFb0105761
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