This paper develops a mathematical model for the radiance distribution of light penetrating a homogeneous hydrosol on the basis of the general theory of radiative transfer. It is proved that the radiance distribution approaches an asymptotic pattern at great depths. This is in accord with previous field measurements of the directional patterns in underwater light and with L. V. Whitney's conjecture that there is at some depth in natural waters a characteristic diffuse light symmetrically distributed around the vertical. The angular form of this equilibrium light pattern is derived in terms of the mathematical model presented.
Preisendorfer, Rudolph W.. 1959. "Theoretical proof of the existence of characteristic diffuse light in natural waters." Journal of Marine Research 18, (1). https://elischolar.library.yale.edu/journal_of_marine_research/943