Scattering Matrix Determination in Crystalline Materials from 4D Scanning Transmission Electron Microscopy at a Single Defocus Value

Recent work has revived interest in the scattering matrix formulation of electron scattering in transmission electron microscopy as a stepping stone toward atomic-resolution structure determination in the presence of multiple scattering. We discuss ways of visualizing the scattering matrix that make its properties clear. Through a simulation-based case study incorporating shot noise, we shown how regularizing on this continuity enables the scattering matrix to be reconstructed from 4D scanning transmission electron microscopy (STEM) measurements from a single defocus value. Intriguingly, for crystalline samples, this process also yields the sample thickness to nanometer accuracy with no a priori knowledge about the sample structure. The reconstruction quality is gauged by using the reconstructed scattering matrix to simulate STEM images at defocus values different from that of the data from which it was reconstructed.

Automated summary

Recent research has reignited interest in the use of the scattering matrix in transmission electron microscopy for atomic-resolution structure determination in the presence of multiple scattering. Through simulation-based case studies, it has been shown that the scattering matrix can be reconstructed from 4D STEM measurements with nanometer accuracy without prior knowledge of the sample structure. The reconstruction quality can be evaluated by simulating STEM images at different defocus values using the reconstructed scattering matrix.