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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)

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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

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)

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  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.

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