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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 5 — Feb. 28, 2011
  • pp: 4786–4794

Effective scattering phase functions for the multiple scattering regime

Jacek Piskozub and David McKee  »View Author Affiliations

Optics Express, Vol. 19, Issue 5, pp. 4786-4794 (2011)

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The propagation of light through turbid media is of fundamental interest in a number of areas of optical science including atmospheric and oceanographic science, astrophysics and medicine amongst many others. The angular distribution of photons after a single scattering event is determined by the scattering phase function of the material the light is passing through. However, in many instances photons experience multiple scattering events and there is currently no equivalent function to describe the resulting angular distribution of photons. Here we present simple analytic formulas that describe the angular distribution of photons after multiple scattering events, based only on knowledge of the single scattering albedo and the single scattering phase function.

© 2011 OSA

OCIS Codes
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(290.4210) Scattering : Multiple scattering
(290.7050) Scattering : Turbid media

ToC Category:

Original Manuscript: January 26, 2011
Manuscript Accepted: February 16, 2011
Published: February 25, 2011

Virtual Issues
Vol. 6, Iss. 3 Virtual Journal for Biomedical Optics

Jacek Piskozub and David McKee, "Effective scattering phase functions for the multiple scattering regime," Opt. Express 19, 4786-4794 (2011)

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  2. H. C. van de Hulst, Multiple Light Scattering, Vol. 1 (Academic Press, 1980).
  3. H. C. van de Hulst, Multiple Light Scattering, Vol. 2 (Academic Press, 1980).
  4. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge Univ. Press, 2006).
  5. A. A. Kokhanovsky, Cloud Optics (Springer, 2006).
  6. M. Sydor, “Statistical treatment of remote sensing reflectance from coastal ocean water: proportionality of reflectance from multiple scattering to source function b/a,” J. Coast. Res. 235, 1183–1192 (2007). [CrossRef]
  7. N. Pfeiffer and G. H. Chapman, “Successive order, multiple scattering of two-term Henyey-Greenstein phase functions,” Opt. Express 16(18), 13637–13642 (2008). [CrossRef] [PubMed]
  8. P. Flatau, J. Piskozub, and J. R. V. Zaneveld, “Asymptotic light field in the presence of a bubble-layer,” Opt. Express 5(5), 120–124 (1999). [CrossRef] [PubMed]
  9. Z. Otremba and J. Piskozub, “Modelling the bidirectional reflectance distribution function (BRDF) of seawater polluted by an oil film,” Opt. Express 12(8), 1671–1676 (2004). [CrossRef] [PubMed]
  10. J. Piskozub, A. R. Weeks, J. N. Schwarz, and I. S. Robinson, “Self-shading of upwelling irradiance for an instrument with sensors on a sidearm,” Appl. Opt. 39(12), 1872–1878 (2000). [CrossRef]
  11. D. McKee, J. Piskozub, and I. Brown, “Scattering error corrections for in situ absorption and attenuation measurements,” Opt. Express 16(24), 19480–19492 (2008). [CrossRef] [PubMed]
  12. G. Marsaglia, The Diehard Battery of Tests of Randomness (1995), http://www.stat.fsu.edu/pub/diehard/ .
  13. L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941). [CrossRef]
  14. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters. (Academic, 1994).
  15. T. J. Petzold, T. J. SIO Ref. 72–78, Scripps Institute of Oceanography (U. California, 1972).
  16. G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994). [CrossRef]
  17. J. L. Forand and G. R. Fournier, “Particle distributions and index of refraction estimation for Canadian waters,” Proc. SPIE 3761, 34–44 (1999). [CrossRef]
  18. I. Turcu and M. Kirillin, “Quasi-ballistic light scattering – analytical models versus Monte Carlo simulations,” J. Phys.: Conf. Ser. 182, 012035 (2009). [CrossRef]

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