OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 59, Iss. 9 — Sep. 1, 1969
  • pp: 1158–1161

Exact Calculation of the Field Due to a Single Fresnel Zone by the Use of the Maggi-Rubinowicz Contour Integral

RASHAD MOUNIR SHOUCRI  »View Author Affiliations


JOSA, Vol. 59, Issue 9, pp. 1158-1161 (1969)
http://dx.doi.org/10.1364/JOSA.59.001158


View Full Text Article

Acrobat PDF (430 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The exact calculation of the field at a point due to a single Fresnel zone is carried out by using the Maggi—Rubinowicz contour integral. The result agrees with the Fresnel theorem in the limit for k very large, k being the propagation constant of the incident wave. The results obtained suggest a new interpretation of the physical meaning of the Maggi—Rubinowicz contour integral in diffraction theory as representing a contribution of elementary or Fresnel zones, in exactly the same manner that the Kirchhoff integral does when considered as an expression of Huygens’ principle.

© 1969 Optical Society of America

Citation
RASHAD MOUNIR SHOUCRI, "Exact Calculation of the Field Due to a Single Fresnel Zone by the Use of the Maggi-Rubinowicz Contour Integral," J. Opt. Soc. Am. 59, 1158-1161 (1969)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-59-9-1158


Sort:  Author  |  Journal  |  Reset

References

  1. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p. 373.
  2. B. A. Lippmann, J. Opt. Soc. Am. 55, 360 (1965).
  3. A. Rubinowicz, Die Beugungswelle in der Kirchliojfschen Theorie der Beugung (Springer Verlag, Berlin, 1967).
  4. R. W. Ditchbum, Light (Blackie and Son Ltd, London, 1963), pp. 167, 172.
  5. A calculation using the principle of interference of elementary vibrations is given by R. M. Shourcri, Thèse de Maîtrise, Université Laval, Quebec, p. 36 (1968). The answer is identical to Eq. (9). The factor -2i is omitted in the result given by R. W. Ditchburn.
  6. A. Rubinowicz, in Progress in Optics, IV, E. Wolf Ed., (North—Holland Publ. Co., Amsterdam, 1965). See also Ref. 3, p. 88.
  7. E. W. Marchand and E. Wolf, J. Opt. Soc. Am. 56, 1712 (1966).
  8. A. Boivin, Théorie et calcul des figures de diffraction de revolution (Les Presses de I'Université Laval, Québec; Gauthier-Villars, Paris, 1964), p. 446.

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