OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 37, Iss. 33 — Nov. 20, 1998
  • pp: 7897–7905

Light Scattering from an Optically Active Sphere into a Circular Aperture

J. David Pendleton and David L. Rosen  »View Author Affiliations

Applied Optics, Vol. 37, Issue 33, pp. 7897-7905 (1998)

View Full Text Article

Acrobat PDF (378 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



To show how apertures affect measurements of the circularly polarized components of light scattered to a detector, we develop two methods of averaging the V and I Stokes parameters over a circular aperture that collects light scattered from an optically active sphere. One method uses a two-dimensional numerical integration that is appropriate for small apertures, and the other gives analytical expressions for scattering into a solid angle of any size. We identify the aperture locations that, independent of aperture size, give an average V (and an effective degree of circular polarization) of zero for scattering from an optically inactive sphere and of nonzero for scattering from an optically active sphere.

© 1998 Optical Society of America

OCIS Codes
(010.1110) Atmospheric and oceanic optics : Aerosols
(260.2110) Physical optics : Electromagnetic optics
(260.5430) Physical optics : Polarization
(290.0290) Scattering : Scattering
(290.4020) Scattering : Mie theory

J. David Pendleton and David L. Rosen, "Light Scattering from an Optically Active Sphere into a Circular Aperture," Appl. Opt. 37, 7897-7905 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. A. Vitkin, “Polarized light and the asymmetry of life,” Opt. Photon. News 7(7), 30–33 (1996).
  2. A. Lakhtakia, ed., Selected Papers on Natural Optical Activity (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990).
  3. D. L. Rosen and J. D. Pendleton, “Detection of biological particles by the use of circular dichroism measurements improved by scattering theory,” Appl. Opt. 34, 5875–5884 (1995).
  4. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983), pp. 45–53, 62–65, 94–95, 100–101, 114, 185–193.
  5. C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29, 458–462 (1974).
  6. D. J. Gordon, “Mie scattering by optically active particles,” Biochemistry 11, 413–420 (1972).
  7. C. F. Bohren, “Scattering of electromagnetic waves by an optically active spherical shell,” J. Chem. Phys. 62, 1566–1571 (1975).
  8. C. F. Bohren, “Scattering of an optically active cylinder,” J. Colloid Interface Sci. 66, 105–109 (1978).
  9. M. S. Kluskens and E. H. Newman, “Scattering by a multilayer chiral cylinder,” IEEE Trans. Antennas Propag. 39, 91–96 (1991).
  10. M. F. R. Cooray and I. R. Ciric, “Wave scattering by a chiral spheroid,” J. Opt. Soc. Am. A 10, 1197–1203 (1993).
  11. W. H. Pierce, “Numerical integration over the planar annulus,” J. Soc. Ind. Appl. Math. 5, 66–73 (1957).
  12. P. Chylek, “Mie scattering into the backward hemisphere,” J. Opt. Soc. Am. 63, 1467–1471 (1973).
  13. W. J. Wiscombe and P. Chylek, “Mie scattering between any two angles,” J. Opt. Soc. Am. 67, 572–573 (1977).
  14. W. P. Chu and D. M. Robinson, “Scattering from a moving spherical particle by two crossed coherent plane waves,” Appl. Opt. 16, 619–626 (1977).
  15. J. D. Pendleton, “Mie scattering into apertures,” J. Opt. Soc. Am. 72, 1029–1033 (1982).
  16. J. D. Pendleton, “A generalized Mie theory solution and its application to particle sizing interferometry,” Ph.D. dissertation (University of Tennessee, Knoxville, Tenn. 1982), p. 90.
  17. J. Y. Son, W. M. Farmer, and T. V. Giel, Jr., “New optical geometry for the particle sizing interferometer,” Appl. Opt. 25, 4332–4337 (1986).
  18. J. Y. Son, “Multiple methods for obtaining particle size distribution with a particle sizing interferometer,” Ph.D. dissertation (University of Tennessee, Knoxville, Tenn., 1985).
  19. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 746.
  20. J. D. Pendleton and S. C. Hill, “Collection of emission from an oscillating dipole inside a sphere: analytical integration over a circular aperture,” Appl. Opt. 36, 8729–8737 (1997).
  21. M. E. Rose, Elementary Theory of Angular Momentum (Dover, New York, 1995), p. 50.
  22. G. Arfken, Mathematical Methods for Physicists, 3rd. ed. (Academic, San Diego, Calif., 1985), pp. 198–200, 253, 678.
  23. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), pp. 34, 124.
  24. A. N. Lowan, N. Davids, and A. Levenson, “Table of the zeros of the Legendre polynomials of order 1–16 and the weight coefficients for Gauss’ mechanical quadrature formula,” Bull. Am. Math. Soc. 48, 739–743 (1942); errata 49, 939 (1943).
  25. S. L. Belousov, Tables of Normalized Associated Legendre Polynomials (Pergamon, New York, 1962).
  26. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 401.
  27. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1964).
  28. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), pp. 1005, 1008.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited