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Proceedings Paper

Physical wavelets: applications in optics
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Paper Abstract

During the last decade, the optics community has shown interest in building bridges between mathematical wavelets and optical phenomena. In a first time, we review some of the previous works done on the subject. Namely, we discuss the optical implementation of the transform, as well as its utilization in relation with optical pattern matching. A short discussion on works, unfortunately falling short to explain scalar diffraction in terms of a wavelet transform, is presented. At this point, we introduce the physical wavelet (Psi) . After portraying the mathematical properties of (Psi) , we describe its contributions to the optical world. Actually, this wavelet being a solution of Maxwell's equations, we derive interesting optical properties from its mathematical behavior. For instance, looking more closely to the scalar projection of this wavelet, we demonstrate the equivalence between Huygens' diffraction principle and the wavelet transform using y as the transformation kernel. Another application involves a closely related form of this wavelet that can be used to generate limited diffraction beams.

Paper Details

Date Published: 8 March 2002
PDF: 10 pages
Proc. SPIE 4738, Wavelet and Independent Component Analysis Applications IX, (8 March 2002); doi: 10.1117/12.458750
Show Author Affiliations
Sylvain Deschenes, Ctr. de Recherche du CHUM and Ecole de Technologie Superieure (Canada)
Yunlong Sheng, COPL/Univ. Laval (Canada)

Published in SPIE Proceedings Vol. 4738:
Wavelet and Independent Component Analysis Applications IX
Harold H. Szu; James R. Buss, Editor(s)

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