A spherical harmonic transform approach to the indexing of electron back-scattered diffraction patterns
A spherical harmonic transform approach to the indexing of electron back-scattered diffraction patterns
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DOI：
10.1016/j.ultramic.2019.112841
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发表时间：
2019-12-01
期刊：
影响因子：
2.2
通讯作者：
De Graef, M.
中科院分区：
文献类型：
--
作者：
Lenthe, W. C.;Singh, S.;De Graef, M.
提出了一种新的电子背散射衍射（EBSD）图的标定方法。该算法采用球面主EBSD模式，并使用球谐变换（SHT）计算其与反向投影实验模式的互相关。这种方法明显快于最近的字典索引算法，但共享后者的鲁棒性对噪声。的基本理论，然后通过示例应用程序，一个在一系列的Ni EBSD数据集记录的信噪比下降，另一个在一个大的喷丸铝数据集。索引速度和内存使用的SHT带宽的依赖性进行了探讨。新算法的速度增益是通过执行实值快速傅立叶变换，明确地将晶体对称性的互相关计算，并使用有效的循环排序，以提高缓存行为。该算法产生一个互相关阵列中的zyz欧拉空间，提出了一个方向的细化过程的基础上的维格纳d函数的解析导数。新的方法可以适用于任何衍射模态，散射强度可以表示在球面上。
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.