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

V Luzin

doi:10.1155/tsm.33.357

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.

Highlights

The problem of the optimal texture experiment was formulated by the author in his other article (Luzin, 1997)
In the Bunge method, 03op coincides with the actual position of the RPmin(calc, true). These results show the advantages and validity of optimal smoothing
After that the smoothed pole figures (PFs) can be used for the second approximation of the texture and the estimate of the optimal smoothing parameters

Summary

INTRODUCTION

The problem of the optimal texture experiment was formulated by the author in his other article (Luzin, 1997). In this paper the smoothing procedure in the form used by Nikolayev et al (1996) is applied: l"-h Yk). The main attention is paid to the fact that the optimal smoothing parameter (degree of smoothing) depends on the size of the investigated sample (or the number ofgrains) in the texture experiment and the sharpness of the texture. Both facts are built into the consideration in the same way as it was done in (Luzin, 1997). Optimal smoothing can be carded out in a self-contained way even if the texture is not initially known (Section 3)

THE OPTIMAL SMOOTHING PROCEDURE

SMOOTHING OF THE REAL EXPERIMENTAL DATA

CONCLUSION