Beta-lattice multiresolution of quasicrystalline Bragg peaks

Avi Elkharrat; Jean-Pierre Gazeau; Françoise Dénoyer

doi:10.1117/12.736021

27 September 2007 Beta-lattice multiresolution of quasicrystalline Bragg peaks

Avi Elkharrat, Jean-Pierre Gazeau, Françoise Dénoyer

Proceedings Volume 6701, Wavelets XII; 670113 (2007) https://doi.org/10.1117/12.736021
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

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.

Citation Download Citation

Avi Elkharrat, Jean-Pierre Gazeau, and Françoise Dénoyer "Beta-lattice multiresolution of quasicrystalline Bragg peaks", Proc. SPIE 6701, Wavelets XII, 670113 (27 September 2007); https://doi.org/10.1117/12.736021

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