OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 59, Iss. 1 — Jan. 1, 1969
  • pp: 79–85

Diffraction at Small Apertures in Black Screens

E. W. MARCHAND and E. WOLF  »View Author Affiliations


JOSA, Vol. 59, Issue 1, pp. 79-85 (1969)
http://dx.doi.org/10.1364/JOSA.59.000079


View Full Text Article

Acrobat PDF (1092 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In an earlier paper dealing with a consistent formulation of Kirchhoff’s theory, an extension of the theory was proposed which seems to be applicable to treatment of diffraction at very small apertures in black screens. The extension consists of the addition to Kirchhoff’s solution of the effect of waves arising from multiple diffraction at the edge of the aperture. In the present paper, calculations based on this modified theory are presented. Corrections to Kirchhoff’s theory are obtained for the case of a plane wave incident normally on a small circular aperture in a black screen. Appreciable departures from Kirchhoff’s theory are found only when the diameter of the aperture is small compared with the wavelength of the incident wave or when the angles of diffraction are very large. It is also shown that in the asymptotic limit ka → ∞ (k is the wave number, a the radius of the aperture) our results are consistent with those obtained on the basis of Keller’s geometrical theory of diffraction.

Citation
E. W. MARCHAND and E. WOLF, "Diffraction at Small Apertures in Black Screens," J. Opt. Soc. Am. 59, 79-85 (1969)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-59-1-79


Sort:  Author  |  Journal  |  Reset

References

  1. There are a number of studies relating to diffraction at small apertures in conducting screens. For references and review see C. J. Bouwkamp, Rept. Prog. Phys. 18, 35 (1954).
  2. E. W. Marchand and E. Wolf, J. Opt. Soc. Am. 56, 1712 (1966).
  3. J. B. Keller, (a) J. Appl. Phvs. 28, 426 (1957); (b) J. Appl. Phys. 28, 570 (1957) (with R. M. Lewis and D. Seckler); (c) in Calculus of Variations, L. M. Graves, Ed. (McGraw-Hill Book Co., New York, 1958) p. 27; (d) J. Opt. Soc. Am. 52, 116 (1962).
  4. In this connection, see also articles byF. J. Kottler, in Progress in Optics, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, and J. Wiley & Sons, New York) 4, 281 (1965); 6, 331 (1967), and the preface to Vol. 4.
  5. A. Rubinowicz (a) Ann. Phys. (Leipzig) 53, 257 (1917); (b) Die Beugungswelle in der Kirchhoffschen Theorie der Beugung, Zweite Aufl. (Springer-Verlag, Berlin, 1966).
  6. M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon Press, London and New York, 1965).
  7. Explicit expressions for the multiply scattered waves are given in § 5 of Ref. 2.
  8. The choice of our normalization of A2 and AK is based on the behavior of these quantities for small values of ka. It may be shown that, for sufficiently small values of ka, A2(ψ; ka)≈(ka/4π), AK(ψ; ka)≈-(i/2)(ka)2 COS2(ψ/2).

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