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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 29, Iss. 31 — Nov. 1, 1990
  • pp: 4646–4657

Diffraction of light by an opaque sphere. 1: Description and properties of the diffraction pattern

Gary E. Sommargren and H. Joseph Weaver  »View Author Affiliations


Applied Optics, Vol. 29, Issue 31, pp. 4646-4657 (1990)
http://dx.doi.org/10.1364/AO.29.004646


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Abstract

In this paper we discuss the diffraction pattern resulting from the propagation of light past an opaque obstacle with a circular cross section. A mathematical description of the diffraction pattern is obtained in the Fresnel region using scalar diffraction theory and is presented in terms of the Lommel functions. This description is shown experimentally to be quite accurate, not only for near axis points within the shadow region but also well past the shadow’s edge into the directly illuminated region. The mathematical description is derived for spherical wave illumination and an isomorphic relation is developed relating it to plane wave illumination. The size of the central bright spot (as well as the subsequent diffraction rings), the axial intensity, and the intensity along the geometric shadow are characterized in terms of point source location and the distance of propagation past the circular obstacle.

© 1990 Optical Society of America

History
Original Manuscript: October 2, 1989
Published: November 1, 1990

Citation
Gary E. Sommargren and H. Joseph Weaver, "Diffraction of light by an opaque sphere. 1: Description and properties of the diffraction pattern," Appl. Opt. 29, 4646-4657 (1990)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-29-31-4646


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References

  1. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. iii.
  2. S. G. Lipson, H. Lipson, Optical Physics (Cambridge U.P., London, 1969), p. 4.
  3. G. Mie, “Beitrage zur Optik Truber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
  4. Ref. 1, Sec. 13.5.
  5. C. J. Bouwkamp, Dissertation, Groningen (1941).
  6. H. Osterberg, L. W. Smith, “Closed Solutions of Rayleigh’s Diffraction Integral for Axial Points,” J. Opt. Soc. Am. 51, 1050–1054 (1961). [CrossRef]
  7. V. N. Mahajan, “Axial Irradiance and Optimum Focusing of Laser Beams,” Appl. Opt. 22, 3042–3053 (1983). [CrossRef] [PubMed]
  8. R. E. English, N. George, “Diffraction Patterns in the Shadow of Disks and Obstacles,” Appl. Opt. 27, 1581–1587 (1988). [CrossRef] [PubMed]
  9. Ref. 1, p. 438. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 438.
  10. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. P., London, 1922), pp. 540–542.
  11. H. J. Weaver, Applications of Discrete and Continuous Fourier Analysis (Wiley, New York, 1983), pp. 217–223.
  12. J. Spanier, K. B. Oldham, An Atlas of Functions (Hemisphere Publishing, Washington, DC, 1987), p. 509.

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