OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 70, Iss. 9 — Sep. 1, 1980
  • pp: 1075–1079

Semiuniform asymptotic expansions of the diffraction integral

E. Loh, Jr.  »View Author Affiliations

JOSA, Vol. 70, Issue 9, pp. 1075-1079 (1980)

View Full Text Article

Acrobat PDF (510 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Previous asymptotic expansions of the diffraction integral are valid for only certain regions in the observation plane. This paper gives a method for calculating semiuniform expansions that are valid in the intermediate regions. They are especially useful and simple for the near-axis field of a circularly symmetric aperture. The case for circularly symmetric ρ2v. aberrations is presented.

© 1980 Optical Society of America

E. Loh, Jr., "Semiuniform asymptotic expansions of the diffraction integral," J. Opt. Soc. Am. 70, 1075-1079 (1980)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. R. Ingarden, "A generalization of the Young–Rubinowicz principle in the theory of diffraction," Acta Phys. Pol. 14, 77–91 (1955).
  2. J. Keller, "Diffraction by an aperture," J. Appl. Phys. 28, 426–444 (1957).
  3. J. Keller, "Geometrical theory of diffraction," J. Opt. Soc. Am. 52, 116–130 (1962).
  4. N. Chako, "Développement asymptotique d’intégrales doubles que l’on rencontre dans la théorie de la diffraction," C. R. Acad. Sci. Paris 247, 436–438 (1953); "Application de la méthode de la phase stationnaire dans la théorie de la diffraction des images optiques," ibid. 247, 580–582 (1958).
  5. N. Van Kampen, "An asymptotic treatment of diffraction problems," Physica (Utrecht) 14, 575–589 (1949).
  6. D. Jones and M. Kline, "Asymptotic expansion of multiple integrals and the method of stationary phase," J. Math. Phys. 37, 1–28 (1958).
  7. M. Kline and I. Kay, Electromagnetic Theory and Geometrical Optics (Wiley-Interscience, New York, 1965), Chap. XII.
  8. J. Focke, "Asymptotische Entwicklungen Mittels der Methode der Stationären Phase," Ber. Sächs. Geo. (Akad.) Wiss. 101 (1954), Heft. 3.
  9. N. Bleistein and R. Handelsman, Asymptotic Expansion of Integrals (Holt, Rinehart and Winston, New York, 1975).
  10. W. Thomson, "On the waves produced by a single impulse in water of any depth, or in a dispersive medium," Proc. R. Soc. London A 42, 80–83 (1887).
  11. G. Watson, "The limits of applicability of the principle of stationary phase," Proc. Cambridge Philos. Soc. 19, 49–55 (1918).
  12. J. van der Corput, "On the method of critical points," K. Ned. Akad. Wet. Indag. Math. 10, 201–209 (1948).
  13. A. Erdélyi, "Asymptotic representations of Fourier integrals and the method of stationary phase," J. Soc. Ind. Appl. Math. 3, 17–27 (1955).
  14. I. Gradshteyn and I. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1965), Formula 6.631, Number 6.

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited