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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

  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 6 — Jun. 1, 2007
  • pp: 1609–1616

Zernike–Bessel representation and its application to Hankel transforms

Charles Cerjan  »View Author Affiliations


JOSA A, Vol. 24, Issue 6, pp. 1609-1616 (2007)
http://dx.doi.org/10.1364/JOSAA.24.001609


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Abstract

The duality between the well-known Zernike polynomial basis set and the Fourier–Bessel expansion of suitable functions on the radial unit interval is exploited to calculate Hankel transforms. In particular, the Hankel transform of simple truncated radial functions is observed to be exact, whereas more complicated functions may be evaluated with high numerical accuracy. The formulation also provides some general insight into the limitations of the Fourier–Bessel representation, especially for infinite-range Hankel transform pairs.

© 2007 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(050.1960) Diffraction and gratings : Diffraction theory
(070.2590) Fourier optics and signal processing : ABCD transforms
(100.3020) Image processing : Image reconstruction-restoration
(100.6890) Image processing : Three-dimensional image processing

ToC Category:
Image Processing

History
Original Manuscript: October 27, 2006
Revised Manuscript: January 3, 2007
Manuscript Accepted: January 5, 2007
Published: May 9, 2007

Virtual Issues
Vol. 2, Iss. 7 Virtual Journal for Biomedical Optics

Citation
Charles Cerjan, "Zernike-Bessel representation and its application to Hankel transforms," J. Opt. Soc. Am. A 24, 1609-1616 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-6-1609


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References

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