Analytical Methods for Superresolution Dislocation Identification in Dark-Field X-ray Microscopy

In this work, we develop several inference methods to estimate the position of dislocations from images generated using dark-field X-ray microscopy (DFXM) -- achieving superresolution accuracy and principled uncertainty quantification. Using the framework of Bayesian inference, we incorporate models of the DFXM contrast mechanism and detector measurement noise, along with initial position estimates, into a statistical model coupling DFXM images with the dislocation position of interest. We motivate several position estimation and uncertainty quantification algorithms based on this model. We then demonstrate the accuracy of our primary estimation algorithm on synthetic realistic DFXM images of edge dislocations in single crystal aluminum. We conclude with a discussion of our methods' impact on future dislocation studies and possible future research avenues.