Inverse electronic scattering from shifted projections within the Fresnel-Kirchhoff formalism

Abstract

The inverse scattering technique we presented previously to achieve a sample reconstruction from the diffraction patterns obtained by electronic projection microscopy is extended to cope with the problem of automatically finding the characteristics of the incident wave (i.e., its amplitude and the source-sample distance). The underlying formalism is that of Fresnel-Kirchhoff, which describes the sample as a two-dimensional mask. By processing simultaneously the projections associated with a given sample translation, the accuracy of the reconstruction is improved and the evaluation of the source-sample distance is more efficient. The technique is applied to the analysis of a two-dimensional nanometric sample that is observed in Fresnel conditions with an electron energy of 40 eV. The parameters of the incident state are recovered precisely and reconstructions with a mean relative error around 1% are achieved.