Application of the Projective Standard Deviation to STEM Imaging and Analysis

The radon transformation has demonstrated tremendous utility for the processing of tomographic reconstructions, though it remains largely unapplied to problems of imaging in scanning transmission electron microscopy (STEM). A complete radon transformation projects image intensities onto lines oriented at different angles relative to the image. When orientated normal to a lattice vector, the projection becomes dominated by the intensity fluctuations determined by the interplanar spacing, as seen in the red trace in Figure 1. Projections away from these conditions result in flatter intensities as shown in the black trace in Figure 1. The standard deviation of these projected intensities thus scales with the degree to which an angle corresponds to a lattice vector. We have recently shown that the standard deviation of the normalized radon transformation as a function of angle, herein called the projective standard deviation (PSD), serves as a critical tool to enable the elimination of drift related distortions using the revolving-STEM (RevSTEM) method [1]. Furthermore, its utility extends far beyond the RevSTEM method.