Discrete spherical harmonic functions for texture representation and analysis

A basis of discrete harmonic functions for efficient representation and analysis of crystallographic texture is presented. Discrete harmonics are a numerical representation of the harmonics on the sphere. A finite element formulation is utilized to calculate these orthonormal basis functions, which provides several advantageous features for quantitative texture analysis. These include high‐precision numerical integration, a simple implementation of the non‐negativity constraint and computational efficiency. Simple examples of pole figure and texture interpolation and of Fourier filtering using these basis sets are presented. This paper describes the discrete harmonics basis set on S2 and S3 spheres using the finite element method for texture representation.