  Scanning transmission electron microscopy (STEM) has become the technique of
choice for quantitative characterization of atomic structure of materials,
where the minute displacements of atomic columns from high-symmetry positions
can be used to map strain, polarization, octahedra tilts, and other physical
and chemical order parameter fields. The latter can be used as inputs into
mesoscopic and atomistic models, providing insight into the correlative
relationships and generative physics of materials on the atomic level. However,
these quantitative applications of STEM necessitate understanding the
microscope induced image distortions and developing the pathways to compensate
them both as part of a rapid calibration procedure for in situ imaging, and the
post-experimental data analysis stage. Here, we explore the spatiotemporal
structure of the microscopic distortions in STEM using multivariate analysis of
the atomic trajectories in the image stacks. Based on the behavior of principal
component analysis (PCA), we develop the Gaussian process (GP)-based regression
method for quantification of the distortion function. The limitations of such
an approach and possible strategies for implementation as a part of in-line
data acquisition in STEM are discussed. The analysis workflow is summarized in
a Jupyter notebook that can be used to retrace the analysis and analyze the
reader's data.
