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Convergence of the hyperspherical harmonic expansion for crystallographic texture
Author(s) -
Mason Jeremy K.,
Johnson Oliver K.
Publication year - 2013
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889813022814
Subject(s) - harmonics , spurious relationship , multiplicative function , ringing , harmonic , texture (cosmology) , truncation (statistics) , orientation (vector space) , crystallite , spherical harmonics , mathematical analysis , physics , mathematics , geometry , crystallography , computer science , chemistry , acoustics , quantum mechanics , statistics , telecommunications , enhanced data rates for gsm evolution , voltage , artificial intelligence , image (mathematics)
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.