Three-Dimensional Texture Analysis After Bunge and Roe: Correspondence Between the Respective Mathematical Techniques

Abstract

Bunge's and Roe's three-dimensional texture analysis methods, although both founded on harmonic analysis, show some differences between the various mathematical techniques used.This paper establishes the correspondence relation between the respective mathematical techniques allowing one to compare works done in either variant. Taking the latest developments in three dimensional texture analysis into account, the correspondence relations hold for the odd degrees l as well as for the even ones.Finally numerical tables give the extension of the symmetry coefficients B:l4mμ (after Bunge) and R4nμl (after Roe) to all the degrees l of the series expansion, even and odd, including l = 34.