The task of determining the orientations of crystals is usually performed by indexing reflections detected on diffraction patterns. The well known underlying principle of indexing methods is universal: they are based on matching experimental scattering vectors to some vectors of the reciprocal lattice. Despite this, the standard attitude has been to devise algorithms applicable to patterns of a particular type. This paper provides a broader perspective. A general approach to indexing of diffraction patterns of various types is presented. References are made to formally similar problems in other research fields, e.g. in computational geometry, computer science, computer vision or star identification. Besides a general description of available methods, concrete algorithms are presented in detail and their applicability to patterns of various types is demonstrated; a program based on these algorithms is shown to index Kikuchi patterns, Kossel patterns and Laue patterns, among others.

中文翻译：

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用于确定晶体取向的衍射图的索引

确定晶体取向的任务通常是通过索引在衍射图样上检测到的反射来完成的。索引方法的众所周知的基本原理是通用的：它们基于将实验性散射矢量与倒易晶格的某些矢量匹配的基础。尽管如此，标准的态度是设计适用于特定类型模式的算法。本文提供了更广阔的视野。提出了索引各种类型的衍射图的通用方法。参考了其他研究领域中形式上相似的问题，例如在计算几何，计算机科学，计算机视觉或恒星识别方面。除了对可用方法的一般描述之外，还详细介绍了具体算法，并展示了它们对各种类型的模式的适用性；展示了基于这些算法的程序来索引Kikuchi模式，Kossel模式和Laue模式等。