Zernike-Bessel representation and its application to Hankel transforms
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/vjbo/abstract.cfm?URI=josaa-24-6-1609
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