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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 51, Iss. 10 — Oct. 1, 1961
  • pp: 1050–1054

Closed Solutions of Rayleigh's Diffraction Integral for Axial Points

HAROLD OSTERBERG and LUTHER W. SMITH  »View Author Affiliations

JOSA, Vol. 51, Issue 10, pp. 1050-1054 (1961)

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Rayleigh's diffraction integral is solved in closed form as regards all axial points when a divergent or a convergent spherical wave is specified as the electromagnetic disturbance incident upon a circular aperture or obstacle. Diffraction of divergent waves is treated briefly. The method is applied more fully to the diffraction of convergent waves by circular apertures. It is shown that the axial "focal point" of the converged spherical wave falls inside, at, or outside the geometrical focal point according as the angular semi-aperture θm of the lens is less than, equal to, or greater than a particular angle that falls near 70.5°. The magnitudes of the departures of the focal point from the geometrical focal point are illustrated by examples for both the radar and optical regions.

HAROLD OSTERBERG and LUTHER W. SMITH, "Closed Solutions of Rayleigh's Diffraction Integral for Axial Points," J. Opt. Soc. Am. 51, 1050-1054 (1961)

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  1. C. J. Bouwkamp, Repts. Progr. Phys. 17, (1954), Eq. (2.7), 39.
  2. R. K. Luneberg, Mathematical Theory of Optics (Brown University Press, Providence, Rhode Island, 1944), p. 356.
  3. See reference 1, pp. 49 and 50.
  4. Consequently, the authors have a strong preference for Rayleigh's diffraction integral.
  5. See reference 2, pp. 361–363.
  6. See reference 2, p. 363.
  7. G. W. Farnell, J. Opt. Soc. Am. 48, 643–47 (1958).
  8. See reference 7, p. 644.

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