Bayesian inference of atomic column positions in scanning transmission electron microscopy images

Atomic-resolution scanning transmission electron microscopy combined with two-dimensional Gaussian fitting enables the accurate and precise identification of atomic column positions within a few picometers. The measurement performance significantly depends on the signal-to-noise ratio of the atomic columns. In areas with low signal-to-noise ratios, such as near surfaces, the measurement performance was lower than that of the bulk. However, previous studies evaluated the accuracy and precision only in bulk areas, underscoring the need for a method that quantitatively evaluates the accuracy and precision of each atomic column position with various signal-to-noise ratios. This study introduced Bayesian inference to assess the accuracy and precision of determining individual atomic column positions under various signals. We applied this method to simulated and experimental images and demonstrated its effectiveness in identifying statistically significant displacements, particularly near surfaces with signal degradation. The use of vector maps and kernel density estimate plots obtained from Bayesian inference provided a probabilistic understanding of the atom displacement. Therefore, this study highlighted the potential benefits of Bayesian inference in high-resolution imaging to reveal material properties.