title: Multiple scattering of a photon flux: implications for the integral average cosine of the underwater light field.
abstract: It is shown that where micros 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 micro(0)micro(s)(n), where micro(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 micro(0) exp[-bd(1 - micro(s))]. For water bodies in which loss of upward-scattered photons through the surface is small enough to be disregarded, the value of micro(c) (the average cosine of all the photons instantaneously present in the water column) for any given incoming flux of photons with average cosine micro(0) is determined entirely by the inherent optical properties of the water in accordance with micro(c)= micro(0)/[1 + (b/a)(1 - micro(s))], where a and b are the absorption and scattering coefficients.
authors.affiliation: jtokirk@ozemail.com.au
authors.forename: J T
authors.initials: JT
authors.lastname: Kirk