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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. 18, Iss. 3 — Mar. 1, 2001
  • pp: 717–720

Understanding fast Hankel transforms

Bruce W. Suter and Robert A. Hedges  »View Author Affiliations


JOSA A, Vol. 18, Issue 3, pp. 717-720 (2001)
http://dx.doi.org/10.1364/JOSAA.18.000717


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Abstract

Recently Ferrari et al. [J. Opt. Soc. Am. A 16, 2581 (1999)] presented an algorithm for the numerical evaluation of the Hankel transform of nth order. We demonstrate that this formulation can be interpreted as an application of the projection slice theorem.

© 2001 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
(070.6020) Fourier optics and signal processing : Continuous optical signal processing

History
Original Manuscript: June 7, 2000
Revised Manuscript: September 21, 2000
Manuscript Accepted: September 21, 2000
Published: March 1, 2001

Citation
Bruce W. Suter and Robert A. Hedges, "Understanding fast Hankel transforms," J. Opt. Soc. Am. A 18, 717-720 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-3-717


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References

  1. J. A. Ferrari, D. Perciante, A. Dubra, “Fast Hankel transform of nth order,” J. Opt. Soc. Am. A 16, 2581–2582 (1999). [CrossRef]
  2. E. W. Hansen, “Fast Hankel transform algorithms,” IEEE Trans. Acoust. Speech Signal Process. ASSP-33, 666–671 (1985). [CrossRef]
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  7. B. W. Suter, “Fast nth order Hankel transform algorithm,” IEEE Trans. Signal Process. 39, 532–536 (1991). [CrossRef]
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  10. A. M. Cormack, “Representation of a function by its line integrals with some radiological applications,” J. Appl. Phys. 34, 2722–2727 (1963). [CrossRef]
  11. A. M. Cormack, “Representation of a function by its line integrals with some radiological Applications II,” J. Appl. Phys. 35, 2908–2913 (1964). [CrossRef]
  12. G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1968).
  13. M. J. Lighthill, Introduction to Fourier Analysis and Generalized Functions (Cambridge University, Cambridge, UK, 1962).
  14. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, 1978).
  15. S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, New York, 1983).

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