Convergence of the hyperspherical harmonic expansion for crystallographic texture

Abstract

Advances in instrumentation allow a material texture to be measured as a collection of spatially resolved crystallite orientations rather than as a collection of pole figures. However, the hyperspherical harmonic expansion of a collection of spatially resolved crystallite orientations is subject to significant truncation error, resulting in ringing artifacts (spurious oscillations around sharp transitions) and false peaks in the orientation distribution function. This article finds that the ringing artifacts and the accompanying regions of negative probability density may be mitigated or removed entirely by modifying the coefficients of the hyperspherical harmonic expansion by a simple multiplicative factor. An addition theorem for the hyperspherical harmonics is derived as an intermediate result.