Improved Orientation Sampling for Indexing Diffraction Patterns of Polycrystalline Materials

TL;DR

This paper introduces a nearly-optimal orientation sampling method using quaternion representation to significantly reduce computational costs in diffraction pattern indexing of polycrystalline materials.

Contribution

It develops a quaternion-based sampling technique for orientations, optimizing the distribution on a 4D sphere to improve efficiency in pattern indexing.

Findings

Reduced the number of samples needed for accurate indexing.

Generated orientation sets for all Laue groups and made them publicly available.

Demonstrated robustness of the method in noisy data conditions.

Abstract

Orientation mapping is a widely used technique for revealing the microstructure of a polycrystalline sample. The crystalline orientation at each point in the sample is determined by analysis of the diffraction pattern, a process known as pattern indexing. A recent development in pattern indexing is the use of a brute-force approach, whereby diffraction patterns are simulated for a large number of crystalline orientations, and compared against the experimentally observed diffraction pattern in order to determine the most likely orientation. Whilst this method can robust identify orientations in the presence of noise, it has very high computational requirements. In this article, the computational burden is reduced by developing a method for nearly-optimal sampling of orientations. By using the quaternion representation of orientations, it is shown that the optimal sampling problem is equivalent to that of optimally distributing points on a four-dimensional sphere. In doing so, the number of orientation samples needed to achieve a indexing desired accuracy is significantly reduced. Orientation sets at a range of sizes are generated in this way for all Laue groups, and are made available online for easy use.