Electronic diffraction tomography by Green's functions and singular valuesdecompositions - art. no. 035408

An inverse scattering technique is developed to enable a three-dimensional sample reconstruction from the diffraction figures obtained for different s ample orientations by electronic projection microscopy, thus performing a d iffraction tomography. In its Green's-functions formulation, this technique takes account of all orders of diffraction by performing an iterative reco nstruction of the wave function on the observation screen and in the sample . In a final step, these quantities enable a reconstruction of the potentia l-energy distribution, which is assumed real valued. The method relies on t he use of singular values decomposition techniques, thus providing the best least-squares solutions and enabling a reduction of noise. The technique i s applied to the analysis of a three-dimensional nanometric sample that is observed in Fresnel conditions with an electron energy of 40 eV. The algori thm turns out to provide results with a mean relative error around 3% and t o be stable against random noise.