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Proceedings Paper

Beta-lattice multiresolution of quasicrystalline Bragg peaks
Author(s): Avi Elkharrat; Jean-Pierre Gazeau; Françoise Dénoyer
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Paper Abstract

We present a method for analyzing and classifying 2d-pure-point (pp) diffraction spectra (i.e. set of Bragg peaks) of certain self-similar structures with scaling factor β > 1, like quasicrystals. The 2d-pp diffraction spectrum is viewed as a point set in the complex plane in which each point is assigned a positive number, its Bragg intensity. Then, by using a nested sequence of self-similar subsets called beta-lattices, a multiresolution analysis is carried out on the spectrum, leading to a partition of it at once in geometry, in scale, and in intensity ("fingerprint" of the spectrum). As an illustration of our approach, the method is experimented on pp diffraction spectra of a few mathematical structures.

Paper Details

Date Published: 27 September 2007
PDF: 15 pages
Proc. SPIE 6701, Wavelets XII, 670113 (27 September 2007); doi: 10.1117/12.736021
Show Author Affiliations
Avi Elkharrat, APC, CNRS, Univ. Paris Diderot (France)
Jean-Pierre Gazeau, APC, CNRS, Univ. Paris Diderot (France)
Françoise Dénoyer, LPS, CNRS, Univ. Paris-Sud (France)

Published in SPIE Proceedings Vol. 6701:
Wavelets XII
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)

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