Asymptotic optical attenuation

The spectral irradiance attenuation coefficient normally varies with depth near the surface. It approaches a constant value in infinitely deep, homogeneous waters at depths below which all fluorescent or bioluminescent sources occur. The attenuation coefficient can equal the asymptotic coefficient for all depths, however, for a special surface illumination; when this equality occurs the angular dependence of the radiance does not change with depth. The attenuation coefficient for homogeneous waters of finite depth never approaches a constant, and the same is true for some examples of infinitely deep waters with spatially varying properties. A by‐product of the analysis is a demonstration of the importance of understanding the eigenvalue spectrum of the radiative transfer equation.