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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 72, Iss. 10 — Oct. 1, 1982
  • pp: 1382–1384

Simple derivation of formulas for Fraunhofer diffraction at polygonal apertures

Jiří Komrska  »View Author Affiliations

JOSA, Vol. 72, Issue 10, pp. 1382-1384 (1982)

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The Abbe transform is used to derive rigorous algebraic formulas for the wave function describing Fraunhofer diffraction at apertures in the form of arbitrary polygons. Two remarks bring the Abbe transform and the Abbe theorem into the context of the history of diffraction.

© 1982 Optical Society of America

Jiří Komrska, "Simple derivation of formulas for Fraunhofer diffraction at polygonal apertures," J. Opt. Soc. Am. 72, 1382-1384 (1982)

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  1. W. Sillitto, "Fraunhofer diffraction at straight-edged apertures," J. Opt. Soc. Am. 69, 765–770 (1979).
  2. R. M. Sillitto and W. Sillitto, "A simple Fourier approach to Fraunhofer diffraction by triangular apertures," Opt. Acta 22, 999–1010 (1975).
  3. I. E. Golberg, B. E. Kinber, and V. B. Tzeitlin, "Diffraction by the bodies with broken edges," Radiotech. Elektron. 20, 1582–1591 (1975).
  4. J. Komrska, "Fraunhofer diffraction at apertures in the form of regular polygons. I," Opt. Acta 19, 807–816 (1972).
  5. J. Komrska, "Fraunhofer diffraction at apertures in the form of regular polygons. II," Opt. Acta 20, 549–563 (1973).
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  9. R. Straubel, Über die Berechnung der Fraunhoferschen Beugungserscheinungen durch Randintegrale mit besonderer Berück-Sichtigung der Theorie der Beugung in Heliometer (Frommansche Buchdruckerei, Jena, Germany, 1888).
  10. M. v. Laue, "Bemerkung über Fraunhofersche Beugung," Sitzungsber. Preuss. Akad. Wiss. Phys. Math. KI. 89–91 (1936).
  11. M. v. Laue, "Die äussere Form der Kristalle in ihrem Einfluss auf die Interferenzerscheinungen an Raumgittern," Ann. Phys. (Leipzig) 26, 55–68 (1936).
  12. R. W. James, The Optical Principles of the Diffraction of X-Rays (Bell, London, 1967), pp. 548–555.
  13. A. Rubinowicz, "Die Rolle der Beugungswelle in der Fraunhoferschen Beugungserscheinungen," Acta Phys. Pol. 13, 3–13 (1954).
  14. A. Rubinowicz, Die Beugungswelle in der Kirchhoffschen Theorie der Beugung, 2nd ed. (Springer-Verlag, Berlin, 1966), pp. 214–225.
  15. R. Straubel, "Zwei allgemeine Sätze über Fraunhofersche Beugungserscheinungen," Ann. Phys. Chemie, Neue Folge 56, 746–761 (1895); cf. pp. 757–758.
  16. J. Komrska, "Abbe transform and Abbe theorem in the theory of Fraunhofer diffraction," Cesk. Cas. Fys. (A) 27, 579–586 (1977).
  17. F. M. Schwerd, Die Beugungserscheinungen aus den Fundamehtalgesetzen der,Undulationstheorie analytisch entwickelt und in Bildern dargestellt (Schwan und Goetz'sche Hofbuchhandlung, Mannheim, Germany, 1835), Sec. 182, p. 117.
  18. Ref. 2, Fig. 4(a).
  19. J. Larmor, "The stellate appendages of telescopic and entoptic diffraction," Proc. Cambridge Philos. Soc. 21, 410–413 (1923).
  20. A. Sommerfeld, Optics (Academic, New York, 1954), pp. 233–237.

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