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Optics Letters

Optics Letters


  • Vol. 6, Iss. 12 — Dec. 1, 1981
  • pp: 604–606

Sampling theorem for rotationally symmetric systems based on Dini expansion

Stanisław Szapiel  »View Author Affiliations

Optics Letters, Vol. 6, Issue 12, pp. 604-606 (1981)

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A new formulation of the sampling theorem for circular apertures is proposed that uses a Dini series approach instead of a Fourier–Bessel one. The results obtained are especially convenient for the fast evaluation of point-spread functions: even the case of thin-ring aperture is not troublesome.

© 1981 Optical Society of America

Original Manuscript: August 31, 1981
Published: December 1, 1981

Stanisław Szapiel, "Sampling theorem for rotationally symmetric systems based on Dini expansion," Opt. Lett. 6, 604-606 (1981)

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), Chaps. 8 and 9.
  2. R. Barakat, “Application of the sampling theorem to optical diffraction theory,” J. Opt. Soc. Am. 54, 920–930 (1964). [CrossRef]
  3. R. Barakat, “The calculation of integrals encountered in optical diffraction theory,” in The Computer in Optical Research, B. R. Frieden, ed. (Springer-Verlag, New York, 1980), pp. 35–80. [CrossRef]
  4. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), Chap. 5.
  5. A. Boivin, Théorie et Calcul des Figures de Diffraction de Révolution (Laval U. Press, Quebec, 1964), pp. 164, 197–199.
  6. H. Bateman, A. Erdélyi, Higher Transcendental Functions (McGraw-Hill, New York, 1953), Vol. II, Sec. 7.10.4.
  7. S. Szapiel, “Maréchal intensity criteria modified for circular apertures with nonuniform intensity transmission: Dini series approach,” Opt. Lett. 2, 124–126 (1978). [CrossRef] [PubMed]
  8. F. W. J. Olver, ed., Royal Society Mathematics Tables, Vol. VII, Bessel Functions, Part III: Zeros and Associated Values (Cambridge U. Press, Cambridge, 1960), Tables I and VI.

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