A 3D Hough transform for indexing EBSD and Kossel patterns

A three-dimensional Hough transform is designed for the detection of conic curves (hyperbolae and ellipses) formed by the gnomonic projection of diffraction Kossel cones. This new procedure is applied to a high-angular-accuracy analysis of electron backscatter diffraction (EBSD) patterns and to a fully automatic indexing of X-ray Kossel patterns in the SEM. The high-accuracy analysis of EBSD patterns allows for the determination of local elastic strains, without any reference pattern, and with a spatial resolution of a few tens of nanometres. An accuracy of 2 x 10(-4) is achieved on geometrically calculated diagrams. This paper presents also the first fully automatic indexing of Kossel patterns. This automatic indexing procedure can be applied to local texture analysis, as well as to local elastic strain measurements. Although the spatial resolution of Kossel is about 1 microm, the accuracy of strain measurement is in this case much higher than that presently obtained on EBSD.