Successive Computations of an ODF while Measuring its Corresponding PDFs with Respect to Progressively Locally Refined Spherical Grids

摘要

Due to a novel method of pole intensity to orientation density inversion applying radial basis functions and an implementation employing fast Fourier transform algorithms for S2,S2×S2 , and SO(3) it is now possible to process intensity data arbitrarily scattered on the pole sphere and successively compute numerical approximations of an ODF explaining the data while they are being measured. Therefore we suggest an adaptive successive refinement of an initial coarse uniform grid to a locally refined grid where the progressive refinement corresponds to the pattern of preferred crystallographic orientation. At each level of refinement an ODF is computed, and die refinement is terminated if some stopping rule is accomplished.