Optimizing Structure Factors From Four-dimensional Scanning Transmission Electron Microscopy via the Scattering Matrix

Quantitative potential retrieval in scanning transmission electron microscopy (STEM) is of much importance for detailed material characterization but is often hindered by substantial multiple scattering effects in thicker samples. Here, we propose a gradient-descent-based optimization algorithm to obtain the quantitative potential from thick samples from a four-dimensional (4D) STEM dataset using the scattering matrix (S-matrix), which is an operator to calculate the exit-surface wavefunction in the presence of multiple scattering. This optimization uses optimum bright-field STEM data as an initial guess of potential and a loss function based on measured and estimated 4D STEM datasets without the regularization terms commonly used in iterative potential retrieval techniques in STEM. We show the capabilities of our approach through systematic simulations across a range of sample thicknesses, doses, and degrees of spatial incoherence and by applying it to experimental data. The extension of our algorithm from pixelated to segmented detectors is also investigated.