A new approach is proposed for the indexing of electron back-scattered diffraction (EBSD) patterns. The algorithm employs a spherical master EBSD pattern and computes its cross-correlation with a back-projected experimental pattern using the spherical harmonic transform (SHT). This approach is significantly faster than the recent dictionary indexing algorithm, but shares the latter's robustness against noise. The underlying theory is presented, followed by example applications, one on a series of Ni EBSD data sets recorded with decreasing signal-to-noise ratio, the other on a large shot-peened Al data set. The dependence of indexing speed and memory usage on the SHT bandwidth is explored. The speed gains of the new algorithm are achieved by executing real-valued Fast Fourier Transforms, explicitly incorporating crystallographic symmetry in the cross-correlation computation, and using efficient loop ordering to improve the caching behavior. The algorithm produces a cross-correlation array in the zyz Euler space; an orientation refinement procedure is proposed based on analytical derivatives of the Wigner d functions. The new approach can be applied to any diffraction modality for which the scattered intensity can be represented on a spherical surface.

中文翻译：

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电子背散射衍射图案索引的球谐变换方法

提出了一种用于对电子背散射衍射 (EBSD) 图案进行索引的新方法。该算法采用球面主 EBSD 模式，并使用球谐变换 (SHT) 计算其与反投影实验模式的互相关。这种方法比最近的字典索引算法快得多，但与后者的抗噪声鲁棒性相同。介绍了基本理论，然后是示例应用，一个是在一系列以降低的信噪比记录的 Ni EBSD 数据集上，另一个是在大型喷丸铝数据集上。探索了索引速度和内存使用对 SHT 带宽的依赖性。新算法的速度增益是通过执行实值快速傅立叶变换来实现的，在互相关计算中明确结合晶体对称性，并使用有效的循环排序来改善缓存行为。算法在zyz欧拉空间产生互相关数组；基于 Wigner d 函数的解析导数提出了一种取向细化程序。新方法可以应用于任何可以在球面上表示散射强度的衍射模态。