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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN 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)
http://dx.doi.org/10.1364/AO.38.003134


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Abstract

It is shown that where ?¯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 ?¯0sn, where ?¯0 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 ?¯0 exp[?bd(1 ? ?¯s)]. For water bodies in which loss of upward-scattered photons through the surface is small enough to be disregarded, the value of ?¯c (the average cosine of all the photons instantaneously present in the water column) for any given incoming flux of photons with average cosine ?¯0 is determined entirely by the inherent optical properties of the water in accordance with ?¯c= ?¯0/[1 + (b/a)(1 ? ?¯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

Citation
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)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-15-3134

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