Orientation sampling for dictionary-based diffraction pattern indexing methods

A general framework for dictionary-based indexing of diffraction patterns is presented. A uniform sampling method of orientation space using the cubochoric representation is introduced and used to derive an empirical relation between the average disorientation between neighboring sampling points and the number of grid points sampled along the semi-edge of the cubochoric cube. A method to uniformly sample misorientation iso-surfaces is also presented. This method is used to show that the dot product serves as a proxy for misorientation. Furthermore, it is shown that misorientation iso-surfaces in Rodrigues space are quadractic surfaces. Finally, using the concept of Riesz energies, it is shown that the sampling method results in a near optimal covering of orientation space.