A spherical harmonic transform approach to the indexing of electron back-scattered diffraction patterns

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.