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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 19, Iss. 9 — Sep. 1, 2002
  • pp: 1763–1773

Wigner distribution moments in fractional Fourier transform systems

Martin J. Bastiaans and Tatiana Alieva  »View Author Affiliations


JOSA A, Vol. 19, Issue 9, pp. 1763-1773 (2002)
http://dx.doi.org/10.1364/JOSAA.19.001763


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Abstract

It is shown how all global Wigner distribution moments of arbitrary order in the output plane of a (generally anamorphic) two-dimensional fractional Fourier transform system can be expressed in terms of the moments in the input plane. Since Wigner distribution moments are identical to derivatives of the ambiguity function at the origin, a similar relation holds for these derivatives. The general input–output relationship is then broken down into a number of rotation-type input–output relationships between certain combinations of moments. It is shown how the Wigner distribution moments (or ambiguity function derivatives) can be measured as intensity moments in the output planes of a set of appropriate fractional Fourier transform systems and thus be derived from the corresponding fractional power spectra. The minimum number of (anamorphic) fractional power spectra that are needed for the determination of these moments is derived. As an important by-product we get a number of moment combinations that are invariant under (anamorphic) fractional Fourier transformation.

© 2002 Optical Society of America

OCIS Codes
(030.5630) Coherence and statistical optics : Radiometry
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(110.6980) Imaging systems : Transforms
(120.4800) Instrumentation, measurement, and metrology : Optical standards and testing

History
Original Manuscript: February 20, 2002
Revised Manuscript: April 12, 2002
Manuscript Accepted: April 24, 2002
Published: September 1, 2002

Citation
Martin J. Bastiaans and Tatiana Alieva, "Wigner distribution moments in fractional Fourier transform systems," J. Opt. Soc. Am. A 19, 1763-1773 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-9-1763

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