Spheres, or more usually spherical surfaces, are important in electron backscatter diffraction. Both electron backscatter patterns (EBSPs) and pole figure texture data are more accurately represented on the spherical surface, S2; and unit quaternions, which are the optimal method for orientation calculations, exist on the surface of the hypersphere, S3.
This paper is split into two distinct parts. The first shows a little of the history of the EBSP technique, including the use of spheres to assemble a spherical Kikuchi map (SKM) and as calibration artefacts. The second part relates new developments in the analysis of EBSPs on the surface of a sphere, a new spherical Hough transform and ideas for fully automatic, ab initio analysis of unknown phases using collections of EBSPs assembled as spherical Kikuchi maps.