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

Abstract

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.