Calibration-sample free distortion correction of electron diffraction patterns using deep learning

The information that can be extracted from electron diffraction patterns is limited by the presence of optical distortions. Existing distortion characterization techniques typically require knowledge of the reciprocal lattice of either the observed object or a separate calibration sample. The latter of these requires a sample exchange, thus adding time and inconvenience to the sample observation. To overcome this limitation, we have developed the Python library EMicroML, which features a deep learning (DL) framework for measuring and correcting combinations of pincushion, spiral, elliptical, and parabolic optical distortions in convergent beam electron diffraction (CBED) patterns that does not require a separate calibration sample. Performance tests of our DL model are conducted using datasets of artificially distorted CBED patterns of MoS₂ on amorphous C, with varying sizes of CBED disks, that are generated using multislice simulations. The test results of our DL approach are benchmarked against those obtained using a conventional technique that uses the radial gradient maximization (RGM) technique and knowledge of the reciprocal lattice system. While the RGM approach outperforms our DL approach for the patterns with very small disks, our DL approach outperforms the RGM approach for the patterns with medium-sized disks, as well as those with large overlapping disks. The results suggest that our DL approach, which does not require knowledge of the sample, achieves a good compromise between convenience and accuracy. We also show how our DL framework can be used to improve experimental ptychographic reconstructions, and to correct distortion in experimental selected area electron diffraction patterns.