An estimate of the average cosine for the radiance distribution resulting from a point source in the ocean

We have shown in an earlier paper that by measuring the decay of the irradiance field due to a point source, the absorption coefficient of the medium can be determined. A central parameter in this method is the average cosine of the radiance distribution at each measurement point. From measurements of the Point Spread Function (PSF), an estimate of the average cosine can be determined. However, experimentally the PSF is routinely measured only to 12 degrees. We have also previously shown a method which relates the small angle PSF measurements to an empirically derived analytic formulation of the Beam Spread Function (BSF) which extends to 90 degrees. We will present an independent test of this method, and then use the BSF to determine the average cosine for varying ranges (from the point source) and water properties. In this way we can estimate how rapidly the average cosine varies, and its relative importance in the field measurements of the absorption coefficient with these techniques.