Hennelly, Bryan M. and Sheridan, John T. (2005) Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms. Journal of the Optical Society of America A., 22 (5). pp. 917-927. ISSN 1084-7529

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Abstract

By use of matrix-based techniques it is shown how the space–bandwidth product (SBP) of a signal, as indicated by the location of the signal energy in the Wigner distribution function, can be tracked through any quadratic-phase optical system whose operation is described by the linear canonical transform. Then, applying the regular uniform sampling criteria imposed by the SBP and linking the criteria explicitly to a decomposition of the optical matrix of the system, it is shown how numerical algorithms (employing interpolation and decimation), which exhibit both invertibility and additivity, can be implemented. Algorithms appearing in the literature for a variety of transforms (Fresnel, fractional Fourier) are shown to be special cases of our general approach. The method is shown to allow the existing algorithms to be optimized and is also shown to permit the invention of many new algorithms.

Item Type:	Article
Keywords:	matrix-based techniques; space–bandwidth product (SBP); Wigner distribution function; numerical algorithms; fractional Fourier transform; Fresnel transform; linear canonical transform;
Academic Unit:	Faculty of Science and Engineering > Computer Science Faculty of Science and Engineering > Electronic Engineering Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	8724
Identification Number:	https://doi.org/10.1364/JOSAA.22.000917
Depositing User:	Dr. Bryan Hennelly
Date Deposited:	04 Sep 2017 14:35
Journal or Publication Title:	Journal of the Optical Society of America A.
Publisher:	Optical Society of America
Refereed:	Yes
Funders:	Enterprise Ireland, Science Foundation Ireland, Irish Research Council for Science Engineering and Technology (IRCSET)
URI:	https://www.osapublishing.org
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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