Table of Contents
Textures and Microstructures
Volume 33, Issue 1-4, Pages 357-363

Optimization of Texture Measurements—Part II: Further Applications: Optimal Smoothing

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 our previous paper (Luzin, 1997. Proc. of Workshop “Neutron Textures and Stress Analysis”) the basic principles of the quantitative approach to optimize the texture measurements were outlined. This paper is the report of advances in this direction.

The quantitative approach is used to solve the smoothing problem. Smoothing by singular integrals with an integral kernel used by Nikolayev and Ullemeyer (1996). Proc. of Workshop “Math. Methods of Texture Analysis”, Textures and Microstructures25, 149– 158 is used in this paper. It is shown how the optimal smoothing parameter depends on the grain statistics, i.e. the number of grains in the sample. The algorithm for optimal smoothing of real pole density data (pole figures) is proposed.

Also, the application of optimal smoothing for solving the central problem of quantitative texture analysis (QTA), i.e. orientation distribution function (ODF) reproduction, is discussed.