Radiance of the ocean horizon

Cox and Munk used aerial photographs of Sun glint to determine the statistical distribution of ocean capillary wave slopes as a function of wind velocity [ J. Opt. Soc. Am.44, 838 ( 1954)]. When their equation connecting the slope distribution with Sun glint is used on the horizon, however, an infinite glint is predicted even though Sun glint never exceeds solar radiance. An integral equation connecting the capillary wave slope distribution with ocean radiance is derived. The integral predicts a finite Sun glint on the ocean horizon and, away from the horizon, reduces to the algebraic form used by Cox and Munk.