Fresnelets - A new wavelet basis for digital holography
Journal
Proceedings of SPIE - The International Society for Optical Engineering
Journal Volume
4478
Date Issued
2001-12-01
Author(s)
Abstract
We present a new class of wavelet bases-Fresnelet-which is obtained by applying the Fresnel transform operator to a wavelet basis of L2. The thus constructed wavelet family exhibits properties that are particularly useful for analyzing and processing optically generated holograms recorded on CCD-arrays. We first investigate the multiresolution properties (translation, dilation) of the Fresnel transform that are needed to construct our new wavelet. We derive a Heisenberg-like uncertainty relation that links the localization of the Fresnelets with that of the original wavelet basis. We give the explicit expression of orthogonal and semi-orthogonal Fresnelet bases corresponding to polynomial spline wavelets. We conclude that the Fresnel B-splines are particularly well suited for processing holograms because they tend to be well localized in both domains.
Subjects
B-splines | Digital holography | Fresnel transform | Fresnelets | Wavelets
Type
conference paper