Optimal STEM Convergence Angle Selection using a Convolutional Neural Network and the Strehl Ratio

TL;DR

This paper presents a machine learning approach using a convolutional neural network trained on the Strehl ratio to rapidly and accurately select optimal convergence angles in STEM, outperforming experienced microscopists and enabling automated microscope alignment.

Contribution

The study introduces a CNN trained on the Strehl ratio for convergence angle selection, significantly improving speed and accuracy over traditional heuristics and expert judgment.

Findings

CNN outperforms microscopists in convergence angle selection

Achieves 85% proximity to optimal probe size

Operates at millisecond speeds, reducing assessment time by over 99%

Abstract

Selection of the correct convergence angle is essential for achieving the highest resolution imaging in scanning transmission electron microscopy (STEM). Use of poor heuristics, such as Rayleigh's quarter-phase rule, to assess probe quality and uncertainties in measurement of the aberration function result in incorrect selection of convergence angles and lower resolution. Here, we show that the Strehl ratio provides an accurate and efficient to calculate criteria for evaluating probe size for STEM. A convolutional neural network trained on the Strehl ratio is shown to outperform experienced microscopists at selecting a convergence angle from a single electron Ronchigram using simulated datasets. Generating tens of thousands of simulated Ronchigram examples, the network is trained to select convergence angles yielding probes on average 85% nearer to optimal size at millisecond speeds (0.02% human assessment time). Qualitative assessment on experimental Ronchigrams with intentionally introduced aberrations suggests that trends in the optimal convergence angle size are well modeled but high accuracy requires extensive training datasets. This near immediate assessment of Ronchigrams using the Strehl ratio and machine learning highlights a viable path toward rapid, automated alignment of aberration-corrected electron microscopes.