Application of Normal Distributions on SO(3) and Sn for Orientation Distribution Function Approximation

Abstract

The orientation distribution function (ODF) in a polycrystalline sample is of special interest in texture analysis. Its determination from pole figures leads to an ill-posed problem, the solution of which is non-unique.In the present paper the properties of normal distributions on the rotation group SO(3) proposed by Parthasarathy (1964), Savyolova (1984) are discussed. A method for ODF determination based on the superposition of the normal distributions is proposed. The parameters of normal distributions are determined from the experimental pole figures. The application of this method is demonstrated for a rolling texture of beryllium.