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Optics Letters

Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Vol. 1, Iss. 1 — Jul. 1, 1977
  • pp: 13–15

Quasi fast Hankel transform

A. E. Siegman  »View Author Affiliations


Optics Letters, Vol. 1, Issue 1, pp. 13-15 (1977)
http://dx.doi.org/10.1364/OL.1.000013


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Abstract

We outline here a new algorithm for evaluating Hankel (Fourier–Bessel) transforms numerically with enhanced speed, accuracy, and efficiency. A nonlinear change of variables is used to convert the one-sided Hankel transform integral into a two-sided cross-correlation integral. This correlation integral is then evaluated on a discrete sampled basis using fast Fourier transforms. The new algorithm offers advantages in speed and substantial advantages in storage requirements over conventional methods for evaluating Hankel transforms with large numbers of points.

© 1977 Optical Society of America

History
Original Manuscript: March 25, 1977
Published: July 1, 1977

Citation
A. E. Siegman, "Quasi fast Hankel transform," Opt. Lett. 1, 13-15 (1977)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-1-1-13


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References

  1. D. G. Gardner, J. C. Gardner, G. Lausch, W. W. Meinke, “Method for the analysis of multi-component exponential decays,” J. Chem. Phys. 31, 987 (1959).
  2. J. Schlesinger, “Fit to experimental data with exponential functions using the fast fourier transform,” Nucl. Instrum. Methods 106, 503 (1973). [CrossRef]
  3. M. R. Smith, S. Cohn-Sfetcu, “Comments on fit to experimental data with exponential functions using the fast fourier transform,” Nucl. Instrum. Methods 114, 171 (1974). [CrossRef]
  4. S. Cohn-Sfetcu, M. R. Smith, S. T. Nichols, P. L. Henry, “A digital technique for analysing a class of multicomponent signals,” Proc. IEEE 63, 1460 (1975). [CrossRef]
  5. S. Cohn-Sfetcu, M. R. Smith, S. T. Nichols, “On the representation of signals by basis kernels with product argument,” Proc. IEEE 63, 326 (1975). [CrossRef]

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