多晶衍射花样定向取样的改进
Improved Orientation Sampling for Indexing Diffraction Patterns of Polycrystalline Materials
摘要：
取向映射是揭示多晶样品微观结构的一种广泛使用的技术。样品中每个点的晶体取向通过分析衍射图案来确定，这一过程称为图案索引。图案索引的最新发展是使用蛮力方法，由此模拟大量晶体取向的衍射图案，并与实验观察到的衍射图案进行比较，以确定最可能的取向。虽然该方法可以在存在噪声的情况下鲁棒地识别取向，但它具有非常高的计算要求。在这篇文章中，通过开发一种接近最优的方向采样方法来减少计算负担。利用方位的四元数表示，证明了最优采样问题等价于四维球面上点的最优分布问题。在这样做时，实现索引期望精度所需的取向样本的数量显著减少。以这种方式为所有劳厄组生成一系列大小的方向集，并在线提供以便于使用。
英文摘要：
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.
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