Fast Radon transforms for high-precision EBSD orientation determination using PyEBSDIndex

The automated indexing and orientation determination of backscattered Kikuchi patterns is an essential step in electron backscattered diffraction (EBSD) analysis. Here a new Radon-transform-based algorithm is developed within the software package PyEBSDIndex, which features a number of key improvements over what has been traditionally available. The Radon convolutions use derivatives of Gaussian kernels that more closely match EBSD band profiles, which is combined with sub-pixel localization of the peaks in the Radon transform. Additionally, the weighted quaternion estimator algorithm (QUEST) is leveraged to provide the final estimation of the crystal orientation. The combination of these techniques allows for high-accuracy indexing and precise orientation determination, with tests on simulated patterns showing mean orientation errors as low as 0.037° and a 95% confidence level of 0.073°. Additional testing of the effect of pattern noise shows that PyEBSDIndex performs similarly to the spherical harmonic transform indexing methods except in the most extreme levels of low pattern quality. A test case of indexing a dual-phase Ti-6Al-4V EBSD map finds that PyEBSDIndex differentiates phases equivalently to the commercial Hough indexing solution, with orientation noise 75% lower than the commercial solution. Finally, it is shown that PyEBSDIndex, by performing the image processing calculations on the GPU, is able to analyze patterns at unprecedented speeds, in some cases at over 45 000 patterns s⁻¹, thereby providing sufficient speed for newer, high-speed detectors. PyEBSDIndex is open source and available at https://github.com/USNavalResearchLaboratory/PyEBSDIndex.