Table of Contents
Textures and Microstructures
Volume 21 (1993), Issue 2-3, Pages 161-176

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

MIFI (Moscow Engineering Physical Institute), Kashirskoye shosse 31, Moscow 115409, Russia

Received 10 May 1992; Accepted 30 December 1992

Copyright © 1993 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.