A solution to the radiative transfer equation is presented which describes the apparent radiance of underwater optical targets of simple shapes. The solution is an exponential, the coefficient of which varies with distance and depends on four quantities: the volume attenuation coefficient, the integrated volume scattering function, the target size, and the illuminating beam size. The solution is compared with data taken by the authors and explains a discrepancy with the generally employed constant coefficient exponential dependence. A comparison with Monte Carlo calculations of point spread functions further supports the validity of the solution.
S. H. Koeppen,
R. E. Walker,
"Effective Radiance Attenuation Coefficients For Underwater Imaging", Proc. SPIE 0064, Ocean Optics IV, (10 November 1975); doi: 10.1117/12.954497; https://doi.org/10.1117/12.954497