Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms

Not Accessible

Your library or personal account may give you access

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.

© 2005 Optical Society of America

Full Article  |  PDF Article
More Like This
Fast numerical algorithm for the linear canonical transform

Bryan M. Hennelly and John T. Sheridan
J. Opt. Soc. Am. A 22(5) 928-937 (2005)

Fast linear canonical transforms

John J. Healy and John T. Sheridan
J. Opt. Soc. Am. A 27(1) 21-30 (2010)

Digital computation of the complex linear canonical transform

Changgeng Liu, Dayong Wang, John J. Healy, Bryan M. Hennelly, John T. Sheridan, and Myung K. Kim
J. Opt. Soc. Am. A 28(7) 1379-1386 (2011)

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (2)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (62)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved