Analysis of Angular Distribution of Power Spectrum

In order to quantitate the orientation, the summation of the power spectrum within a narrow fan-shaped area is calculated. For this purpose, the power spectrum transformed in a polar system, \P(r, 6)\2, is more convenient than the Cartesian system (Fig. 7). The function P(r, 6) is decomposed into ps(r) for each 6 and pr (6) for each r, yielding a pair of functions [p6(r), pr (6)] to be used by a texture operator. The intensity of the orientation at an angle 6, F(6), is indicated by summation of the power spectrum within a fan-shaped area and written as

This function can be incorporated in theories to define the degree of the anisotropy and estimation of the mechanical properties of the anisotropic materials.

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