OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 21, Iss. 1 — Jan. 1, 2004
  • pp: 53–58

Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields

Manuel Guizar-Sicairos and Julio C. Gutiérrez-Vega  »View Author Affiliations


JOSA A, Vol. 21, Issue 1, pp. 53-58 (2004)
http://dx.doi.org/10.1364/JOSAA.21.000053


View Full Text Article

Enhanced HTML    Acrobat PDF (216 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The method originally proposed by Yu [Opt. Lett. 23, 409 (1998)] for evaluating the zero-order Hankel transform is generalized to high-order Hankel transforms. Since the method preserves the discrete form of the Parseval theorem, it is particularly suitable for field propagation. A general algorithm for propagating an input field through axially symmetric systems using the generalized method is given. The advantages and the disadvantages of the method with respect to other typical methods are discussed.

© 2004 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
(350.5500) Other areas of optics : Propagation

History
Original Manuscript: June 11, 2003
Revised Manuscript: August 26, 2003
Manuscript Accepted: September 9, 2003
Published: January 1, 2004

Citation
Manuel Guizar-Sicairos and Julio C. Gutiérrez-Vega, "Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields," J. Opt. Soc. Am. A 21, 53-58 (2004)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-1-53


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. E. Siegman, “Quasi fast Hankel transform,” Opt. Lett. 1, 13–15 (1977). [CrossRef] [PubMed]
  2. G. P. Agrawal, M. Lax, “End correction in the quasi-fast Hankel transform for optical-propagation problems,” Opt. Lett. 6, 171–173 (1981). [CrossRef] [PubMed]
  3. D. R. Mook, “An algorithm for the numerical calculation of Hankel and Abel transforms,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 979–985 (1983). [CrossRef]
  4. E. C. Cavanagh, B. D. Cook, “Numerical evaluation of Hankel transforms via Gaussian–Laguerre polynomial expansions,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 361–366 (1979). [CrossRef]
  5. E. W. Hansen, “Fast Hankel transform algorithms,” IEEE Trans. Acoust. Speech Signal Process. ASSP-33, 666–671 (1985). [CrossRef]
  6. E. W. Hansen, “Correction to ‘Fast Hankel transform algorithms’,” IEEE Trans. Acoust. Speech Signal Process. ASSP-34, 623–624 (1986). [CrossRef]
  7. V. Magni, G. Cerullo, S. De Silvestri, “High-accuracy fast Hankel transform for optical beam propagation,” J. Opt. Soc. Am. A 9, 2031–2033 (1992). [CrossRef]
  8. J. A. Ferrari, “Fast Hankel transform of order zero,” J. Opt. Soc. Am. A 12, 1812–1813 (1995). [CrossRef]
  9. R. Barakat, E. Parshall, B. H. Sandler, “Zero-order Hankel transformation algorithms based on Filon quadrature philosophy for diffraction optics and beam propagation,” J. Opt. Soc. Am. A 15, 652–659 (1998). [CrossRef]
  10. Li Yu, M. Huang, M. Chen, W. Chen, W. Huang, Z. Zhu, “Quasi-discrete Hankel transform,” Opt. Lett. 23, 409–411 (1998). [CrossRef]
  11. J. Markham, J. A. Conchello, “Numerical evaluation of Hankel transforms for oscillating functions,” J. Opt. Soc. Am. A 20, 621–630 (2003). [CrossRef]
  12. A. V. Oppenheim, G. V. Frish, D. R. Martinez, “An algorithm for the numerical evaluation of the Hankel transform,” Proc. IEEE 66, 264–265 (1978). [CrossRef]
  13. A. V. Oppenheim, G. V. Frish, D. R. Martinez, “Computation of the Hankel transform using projections,” J. Acoust. Soc. Am. 68, 523–529 (1980). [CrossRef]
  14. W. E. Higgins, D. C. Munson, “An algorithm for computing general integer-order Hankel transforms,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 86–97 (1987). [CrossRef]
  15. J. A. Ferrari, D. Perciante, A. Dubra, “Fast Hankel transform of nth order,” J. Opt. Soc. Am. A 16, 2581–2582 (1999). [CrossRef]
  16. S. M. Candel, “Dual algorithms for fast calculation of the Fourier–Bessel transform,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 963–972 (1981). [CrossRef]
  17. P. K. Murphy, N. C. Gallagher, “Fast algorithm for thecomputation of the zero-order Hankel transform,” J. Opt. Soc. Am. 73, 1130–1137 (1983). [CrossRef]
  18. B. W. Suter, “Fast nth order Hankel transform algorithm,” IEEE Trans. Signal Process. 39, 532–536 (1991). [CrossRef]
  19. A. Agnesi, G. C. Reali, G. Patrini, A. Tomaselli, “Numerical evaluation of the Hankel transform: remarks,” J. Opt. Soc. Am. A 10, 1872–1874 (1993). [CrossRef]
  20. L. Knockaert, “Fast Hankel transform by fast sine and cosine transforms: the Mellin connection,” IEEE Trans. Signal Process. 48, 1695–1701 (2000). [CrossRef]
  21. B. W. Suter, R. A. Hedges, “Understanding fast Hankel transforms,” J. Opt. Soc. Am. A 18, 717–720 (2001). [CrossRef]
  22. G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists (Harcourt–Academic, San Diego, Calif., 2001).
  23. A. L. Garcı́a, Numerical Methods for Physics (Prentice-Hall, Englewood Cliffs, N.J., 2000).
  24. N. M. Temme, “An algorithm with Algol60 program for the computation of the zeros of ordinary Bessel functions and those of their derivatives,” J. Comput. Phys. 32, 270–279 (1979). [CrossRef]
  25. The propagation of optical fields by applying the angular spectrum of plane waves is well documented in literature, e.g., J. W. Goodman, Introduction to Fourier Optics (McGraw Hill, New York, 1996).
  26. J. C. Gutiérrez-Vega, R. Rodrı́guez-Masegosa, S. Chávez-Cerda, “Focusing evolution of generalized propagation invariant optical fields,” Pure Appl. Opt. 5, 276–282 (2003). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited