Abstract
A set of differential equations is derived to relate the light field and its derivative to the inherent optical properties of sea water (volume-scattering function and beam-attenuation coefficient) when the light field is axially symmetric. From these equations, the volume-scattering function and the beam-attenuation coefficient can be calculated if the light field and its derivative with depth are known. The equations are then used to provide an alternate proof for the asymptotic light field hypothesis. The shape of the asymptotic light field is derived as a function of the inherent optical properties and the asymptotic decay constant. It is finally shown that if the shape of the asymptotic light field and the asymptotic decay constant are known, the inherent optical properties can be calculated.
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