The average cosine due to an isotropic light source in the ocean

Abstract

The average cosine of the light field created by an isotropic point source (IPS) embedded in a homogeneous ocean is investigated with a Monte Carlo model. Two volume scattering functions (VSFs) are used in the model, taken from Petzold (1972), to compute the radiance distributions at various distances from the source. The simulated radiance distributions are compared with measurements of the point spread function made at Lake Pend Oreille, Idaho, during the 1992 optical closure experiment. An analytic model is presented for which is valid to at least 15 optical lengths from the source. The model shows that the mean light path, derived from , is a strong function of the single scattering albedo and the VSF. We found that errors in estimating the absorption coefficient by neglecting the increase in the mean light path, which is due to scattering, vary between 5% and 12% for nearly all natural waters. A mathematical proof is given that as the distance to the IPS goes to zero. An analytic expression is derived for close to a finite diffuse‐isotropic source which shows that approaches one as the distance decreases, but at extremely close distances, as the distance to the surface of the source goes to zero. At distances beyond one attenuation length, for finite sources small compared to an attenuation length, behaves essentially as it would for a point source. An asymptotic model for as a function of the single scattering albedo is given with coefficients that depend on the VSF. Model results and comparisons with measured PSFs reveal the surprising result that the light field from an embedded isotropic point source in the ocean does not exhibit asymptotic behavior as far as 15 attenuation lengths from the source.