Indexing of superimposed Laue diffraction patterns using a dictionary–branch–bound approach

Abstract

X-ray Laue diffraction is an important method for characterizing the local crystallographic orientation and elastic strain in polycrystalline materials. Existing analysis methods are designed mainly to index a single or a few Laue diffraction pattern(s) recorded in a detector image. In this work, a novel method called dictionary–branch–bound (DBB) is presented to determine the crystallographic orientations of multiple crystals simultaneously illuminated by a parallel X-ray incident beam, using only the spot positions in a detector image. DBB is validated for simulated X-ray Laue diffraction data. In the simulation, up to 100 crystals with random crystallographic orientations are simultaneously illuminated. Fake spots are randomly added to the detector image to test the robustness of DBB. Additionally, spots are randomly removed to test the resilience of DBB against true spots that are undetected due to background noise and/or spot overlap. Poisson noise is also added to test the sensitivity of DBB to less accurate positions of detected spots. In all cases except the most challenging one, a perfect indexing with a mean angular error below 0.08° is obtained. To demonstrate the potential of DBB further, it is applied to synchrotron microdiffraction data. Finally, guidelines for using DBB in experimental data are provided.