Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space–bandwidth product
JOSA A, Vol. 27, Issue 8, pp. 1885-1895 (2010)
http://dx.doi.org/10.1364/JOSAA.27.001885
Enhanced HTML 
Acrobat PDF (220 KB)
Abstract
Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space–frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space–frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space–bandwidth product. The bicanonical width product, which is a generalization of the space–bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.
© 2010 Optical Society of America
OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.2590) Fourier optics and signal processing : ABCD transforms
(080.2730) Geometric optics : Matrix methods in paraxial optics
(070.2025) Fourier optics and signal processing : Discrete optical signal processing
(070.2575) Fourier optics and signal processing : Fractional Fourier transforms
(050.5082) Diffraction and gratings : Phase space in wave options
ToC Category:
Fourier Optics and Signal Processing
History
Original Manuscript: March 29, 2010
Manuscript Accepted: May 25, 2010
Published: July 30, 2010
Citation
Figen S. Oktem and Haldun M. Ozaktas, "Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space–bandwidth product," J. Opt. Soc. Am. A 27, 1885-1895 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-8-1885
You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.
Contact your librarian or system administrator
or
Log in to access OSA Member Subscription
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.
Contact your librarian or system administrator
or
Log in to access OSA Member Subscription
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.
Contact your librarian or system administrator
or
Log in to access OSA Member Subscription
You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.
Contact your librarian or system administrator
or
Log in to access OSA Member Subscription
Related Journal Articles 
- Phase-space rotations and orbital Stokes parameters (OL)
- Eigenfunctions and self-imaging phenomena of the two-dimensional nonseparable linear canonical transform (JOSAA)
- Fundamental structure of Fresnel diffraction: natural sampling grid and the fractional Fourier transform (OL)
- Discrete linear canonical transforms based on dilated Hermite functions (JOSAA)
- Phase-space window and degrees of freedom of optical systems with multiple apertures (JOSAA)
Related Conference Papers
- Programmable Spectral Design Using the Binary Supergrating (BSG)
- Swept Source Fourier Domain Optical Coherence Tomography
- Optimization of FTS Phase Correction Parameters
- Investigation of Hyperspectral Interferometer Infrared Cloud Top Retrievals Using High Altitude Aircraft Measurements
- Fourier Domain Functional Optical Coherence Tomography
OSA is a member of 