Inverse electronic scattering by singular values decomposition within the Fresnel–Kirchhoff formalism

The inverse scattering technique we presented previously to enable a sample reconstruction from the diffraction figures obtained by electronic projection microscopy is reformulated within the Fresnel–Kirchhoff formalism, which describes the sample as a two-dimensional mask. The method relies on the use of singular values decomposition techniques, thus providing the best least-squares solutions and enabling a reduction of noise. The technique is applied to the analysis of a two-dimensional nanometric sample that is observed in Fresnel conditions with an electronic energy of 40 eV. The algorithm turns out to provide results with a mean relative error around 1% and to be very stable against random noise.