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Applied Optics

Applied Optics


  • Vol. 38, Iss. 15 — May. 20, 1999
  • pp: 3134–3140

Multiple scattering of a photon flux: implications for the integral average cosine of the underwater light field

John T. O. Kirk  »View Author Affiliations

Applied Optics, Vol. 38, Issue 15, pp. 3134-3140 (1999)

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It is shown that where μ̅ s is the average cosine of scattering, then for any set of photons that undergoes exactly n scatterings per photon, the average cosine after scattering is μ̅0μ̅ s n , where μ̅0 is the average cosine of the photon flux before scattering. For a set of photons that has traversed distance d through a medium with scattering coefficient b, the average cosine is μ̅0 exp[-bd(1 - μ̅ s )]. For water bodies in which loss of upward-scattered photons through the surface is small enough to be disregarded, the value of μ̅ c (the average cosine of all the photons instantaneously present in the water column) for any given incoming flux of photons with average cosine μ̅0 is determined entirely by the inherent optical properties of the water in accordance with μ̅ c = μ̅0/[1 + (b/a)(1 - μ̅ s )], where a and b are the absorption and scattering coefficients.

© 1999 Optical Society of America

OCIS Codes
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.1310) Atmospheric and oceanic optics : Atmospheric scattering
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(010.7340) Atmospheric and oceanic optics : Water

Original Manuscript: January 20, 1999
Published: May 20, 1999

John T. O. Kirk, "Multiple scattering of a photon flux: implications for the integral average cosine of the underwater light field," Appl. Opt. 38, 3134-3140 (1999)

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  1. J. T. O. Kirk, “Volume scattering function, average cosines, and the underwater light field,” Limnol. Oceanogr. 36, 455–467 (1991). [CrossRef]
  2. R. A. Maffione, K. J. Voss, R. C. Honey, “Measurement of the spectral absorption coefficient in the ocean with an isotropic source,” Appl. Opt. 32, 3273–3279 (1993). [CrossRef] [PubMed]
  3. R. A. Maffione, J. S. Jaffe, “The average cosine due to an isotropic light source in the ocean,” J. Geophys. Res. 100, 13,179–13,192 (1995). [CrossRef]
  4. R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Int. Union Geodesy Geophys. Monogr. 10, 11–30 (1961).
  5. N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976).
  6. J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29, 350–356 (1984). [CrossRef]
  7. J. Berwald, D. Stramski, C. D. Mobley, D. A. Kiefer, “Influences of absorption and scattering on vertical changes in the average cosine of the underwater light field,” Limnol. Oceanogr. 40, 1347–1357 (1995). [CrossRef]
  8. T. J. Petzold, “Volume scattering functions for selected ocean waters,” (Scripps Institution of Oceanography, University of California, San Diego, La Jolla, Calif., 1972).
  9. J. T. O. Kirk, “Characteristics of the light field in highly turbid waters: a Monte Carlo study,” Limnol. Oceanogr. 39, 702–706 (1994). [CrossRef]

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