Table of Contents
Textures and Microstructures
Volume 33 (1999), Issue 1-4, Pages 343-355

Optimization of Texture Measurements—Part I: Method: Optimal Grid Parameter

Joint Institute for Nuclear Research, Frank Laboratory of Neutron Physics, Moscow Region, Dubna 141980, Russia

Received 1 October 1997

Copyright © 1999 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.


In texture experiments one always measures a sample with some constrained number of grains N (see the discussion in Bunge (1996). Proc. of Workshop “Math. Methods of Texture Analysis”, Textures and Microstructures 25, 71–108). It is clear that the orientation distribution function (ODF) and pole figures (PFs) measured for this limited N may differ from actual ones. How well do texture measurements reproduce the actual distribution densities? The statistical relevance of such measurements is the main area of interest in the present paper.

In this article the RP-value is adopted as the value quantitatively characterizing this relevance. From this point of view the problem of evaluation of true distribution densities means the minimization of the RP-value over some variables. For evaluation of the pole density (for some PF), we consider the parameter of the measurement grid as the variable of the minimization problem. The number of grains N and the sharpness of the texture are the additional parameters of the problem.

Two approaches to solve the mentioned problem are proposed. One is the numerical simulation of the given distribution as the normal (Gaussian) distribution. The other is based on some estimation of the expected RP-value between the actual and experimental PFs.

It turns out that for the given type of the measurement grid (an equidistant grid) the optimal measurement grid parameter exists. This is one that minimizes the RP-value in dependence on the number of grains N in the sample and sharpness of the texture.