THE AVERAGE COSINE DUE TO AN ISOTROPIC LIGHT-SOURCE IN THE OCEAN

The average cosine ($) over bar mu of the light field created by an is otropic point source (IFS) embedded in a homogeneous ocean is investig ated with a Monte Carlo model. Two volume scattering functions (VSFs) are used in the model, taken from Petzold (1972), to compute the radia nce distributions at various distances from the source. The simulated radiance distributions are compared with measurements of the point spr ead function made at Lake Pend Oreille, Idaho, during the 1992 optical closure experiment, An analytic model is presented for ($) over bar m u which is valid to at least 15 optical lengths from the source, The m odel shows that the mean light path, derived from ($) over bar mu, is a strong function of the single scattering albedo and the VSF. We foun d that errors in estimating the absorption coefficient by neglecting t he increase in the mean light path, which is due to scattering, vary b etween 5% and 12% for nearly all natural waters, A mathematical proof is given that ($) over bar mu --> 1 as the distance to the IPS goes to zero. An analytic expression is derived for ($) over bar mu close to a finite diffuse-isotropic source which shows that ($) over bar mu app roaches one as the distance decreases, but at extremely close distance s, ($) over bar mu --> 1/2 as the distance to the surface of the sourc e goes to zero. At distances beyond one attenuation length, for finite sources small compared to an attenuation length, ($) over bar mu beha ves essentially as it would for a point source. An asymptotic model fo r ($) over bar mu as a function of the single scattering albedo is giv en with coefficients that depend on the VSF. Model results and compari sons with measured PSFs reveal the surprising result that the light fi eld from an embedded isotropic point source in the ocean does not exhi bit asymptotic behavior as far as 15 attenuation lengths from the sour ce.