Optimal Calculation of ODF with the Canonical Normal Distribution on the Rotation Group

摘要

Macroscopic physical properties of mostpolycrystalline materials are controlled by orientation distributionof their grains. The orientation distribution function (ODF) of apolycrystal is seldom if ever determined directly from anexperiment. Usually experimental data are represented by a set ofpole figures (PFs), these latter are some integral projections of theODF. The main problem of quantitative texture analysis is torecover ODF from its corresponding PFs. With any set of PFs thesolution of this problem is non-unique. That is why someassumptions about ODF structure are necessary. We consider ODFas super-position of the canonical normal distribution (CND) onthe rotation group SO(3).