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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. 16, Iss. 3 — Mar. 1, 1999
  • pp: 613–615

Analytic expression for Fresnel diffraction: comment

P. L. Overfelt and D. J. White  »View Author Affiliations


JOSA A, Vol. 16, Issue 3, pp. 613-615 (1999)
http://dx.doi.org/10.1364/JOSAA.16.000613


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Abstract

In a recent paper by WangP. [J. Opt. Soc. Am. A 15, 684 (1998)] an analytic expression for calculating Fresnel diffraction is presented. Several mathematical problems with this analysis have been observed. In this comment, corrections to the analysis of Wang et al. are offered as well as an alternative view of this analysis. New formulas based on series of exponential polynomials that are everywhere convergent are derived. These new formulas eliminate the need to split the computational problem into two distinct regions. New series representations for two of the most important combinations of the Lommel functions of two variables are offered.

© 1999 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(260.3160) Physical optics : Interference

History
Original Manuscript: July 27, 1998
Manuscript Accepted: October 1, 1998
Published: March 1, 1999

Citation
P. L. Overfelt and D. J. White, "Analytic expression for Fresnel diffraction: comment," J. Opt. Soc. Am. A 16, 613-615 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-3-613


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References

  1. P. Wang, Y. Xu, W. Wang, Z. Wang, “Analytic expression for Fresnel diffraction,” J. Opt. Soc. Am. A 15, 684–688 (1998). [CrossRef]
  2. G. N. Watson, Treatise on the Theory of Bessel Functions (Cambridge U. Press, London, 1958), Chap. 16.
  3. J. Walker, The Analytical Theory of Light (Cambridge U. Press, London, 1904).
  4. P. L. Overfelt, C. S. Kenney, “Comparison of the propagation characteristics of Bessel, Bessel–Gauss, and Gaussian beams diffracted by a circular aperture,” J. Opt. Soc. Am. A 8, 732–745 (1991). [CrossRef]
  5. J. Spanier, K. Oldham, An Atlas of Functions (Hemisphere, New York, 1987).
  6. P. L. Overfelt, “Partial summation of the Wang series,” (Naval Air Warfare Center Weapons Division, China Lake, Calif., July1998).

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