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- Title
Convergence of the hyperspherical harmonic expansion for crystallographic texture.
- Authors
Mason, Jeremy K.; Johnson, Oliver K.
- 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.
- Subjects
HARMONIC analysis (Mathematics); CRYSTAL texture; PROBABILITY density function; SPHERICAL harmonics; HARMONIC functions; COEFFICIENTS (Statistics)
- Publication
Journal of Applied Crystallography, 2013, Vol 46, Issue 6, p1722
- ISSN
0021-8898
- Publication type
Article
- DOI
10.1107/S0021889813022814