OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 10 — May. 10, 2010
  • pp: 10551–10556

Reconstruction of optical fields with the Quasi-discrete Hankel transform

Andrew W. Norfolk and Edward J. Grace  »View Author Affiliations


Optics Express, Vol. 18, Issue 10, pp. 10551-10556 (2010)
http://dx.doi.org/10.1364/OE.18.010551


View Full Text Article

Enhanced HTML    Acrobat PDF (674 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Unlike the FFT, the Quasi Discrete Hankel Transform (QDHT) is not sampled on a uniform grid; in particular the field may no longer be sampled on axis. We demonstrate how the generalised sampling theorem may be applied to optical problems, evaluated with the QDHT, to efficiently and accurately reconstruct the optical field at any point. Without sacrificing numerical accuracy this is demonstrated to be typically 50× faster than using an equivalent 2D FFT.

© 2010 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(080.2720) Geometric optics : Mathematical methods (general)
(350.5500) Other areas of optics : Propagation

ToC Category:
Physical Optics

History
Original Manuscript: October 27, 2009
Revised Manuscript: March 18, 2010
Manuscript Accepted: April 26, 2010
Published: May 6, 2010

Citation
Andrew W. Norfolk and Edward J. Grace, "Reconstruction of optical fields with the Quasi-discrete Hankel transform," Opt. Express 18, 10551-10556 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-10-10551


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. D. Feit and J. A. Fleck, Jr., “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3998(1978). [CrossRef] [PubMed]
  2. A. E. Siegman, “Quasi fast Hankel transform,” Opt. Lett. 1, 13–15 (1977). [CrossRef] [PubMed]
  3. L. Yu, M. Huang, M. Chen, W. Chen, W. Huang, and Z. Zhu, “Quasi-discrete Hankel transform,” Opt. Lett. 23(6), 409–411 (1998). [CrossRef]
  4. . M. Guizar-Sicairos and J. C. Guti`errez-Vega, “Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields,” J. Opt. Soc. Am. A 21, 53–58 (2004). [CrossRef]
  5. P. Srisungsitthisunti, O. K. Ersoy, and X. Xu, “ Beam propagation modeling of modified volume Fresnel zone plates fabricated by femtosecond laser direct writing,” J. Opt. Soc. Am. A 26(1), 188–194 (2009). [CrossRef]
  6. A. W. Norfolk and E. J. Grace, “New beat length for writing periodic structures using Bessel beams,” Opt. Commun. 283(3), 447–450 (2010). [CrossRef]
  7. D. Ding and X. Liu, “Approximate description for Bessel, Bessel-Gauss, and Gaussian beams with finite aperture,” J. Opt. Soc. Am. A 16, 1286–1293 (1999). [CrossRef]
  8. H. P. Kramer, “A Generalized Sampling Theorem,” J. Math. & Phys. 38, 68–72 (1959).
  9. A. J. Jerri and D. W. Kreisler, “Sampling Expansions with Derivatives for Finite Hankel and Other Transforms,” SIAM J. Math. Anal. 6(2), 262–267 (1975). [CrossRef]
  10. L. L. Campbell, “A comparison of the sampling theorems of Kramer and Whittaker,” J. Soc. Indust. Appl. Math. 12, 117–130 (1964). [CrossRef]
  11. J. P. Boyd, Chebyshev and Fourier Spectral Methods (Dover Publications, 2001).
  12. M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93(2), 216–231 (2005). [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.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited