Maximal Resolution from the Ronchigram: Human vs. Deep Learning

Abstract

Real-space atomic-resolution imaging with aberration-corrected scanning transmission electron microscopy (STEM) has revolutionized material characterization. Maximizing resolution, contrast, and total usable beam current is critically dependent on the ability to determine the largest convergence angle (objective aperture) permitted by lens aberrations. However, this quantity is difficult to accurately measure in real charged particle optical systems. For STEM, the electron Ronchigram encodes the optimal convergence angle, but is challenging to quantifiably assess and currently is most accurately evaluated with human expertise [1]. Here we present a deep regression framework which predicts the optimal convergence angle for maximal probe quality and imaging resolution from a simulated Ronchigram. Our neural network operates 500 times faster with 6 times less error than trained microscopists and outperforms common heuristic algorithms that are unrealistically given perfect knowledge of the aberration function. The widely accepted criteria for selecting a convergence angle for STEM imaging is Rayleigh's quarter-wave rule, which promises good image quality for less than a quarter-wave of primary spherical aberration (χ