Abstract

It is shown that where μ̅s 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 μ̅0μ̅s 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 - μ̅s)]. For water bodies in which loss of upward-scattered photons through the surface is small enough to be disregarded, the value of μ̅c (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 μ̅c= μ̅0/[1 + (b/a)(1 - μ̅s)], where a and b are the absorption and scattering coefficients.

© 1999 Optical Society of America

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