Physical wavelets: applications in optics

Sylvain Deschenes; Yunlong Sheng

doi:10.1117/12.458750

8 March 2002 Physical wavelets: applications in optics

Sylvain Deschenes, Yunlong Sheng

Author Affiliations +

Proceedings Volume 4738, Wavelet and Independent Component Analysis Applications IX; (2002) https://doi.org/10.1117/12.458750
Event: AeroSense 2002, 2002, Orlando, FL, United States

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.

Citation Download Citation

Sylvain Deschenes and Yunlong Sheng "Physical wavelets: applications in optics", Proc. SPIE 4738, Wavelet and Independent Component Analysis Applications IX, (8 March 2002); https://doi.org/10.1117/12.458750

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

;

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE