Statistical formulation for an inhomogeneous random water surface: a basis for optical remote sensing of oceans

A statistical formulation for a stationary ocean surface has been fully developed in the angular spectral domain. The angular spectral formulation can be found in the theory of radiometry and optical coherence. The present theory is a rigorous generalization of the conventional framework of ocean-wave statistics, which represent the surface displacement in two-dimensional wave-number space. The present theory is applicable to an inhomogeneous (spatially nonstationary) surface as well as a homogeneous surface. A number of formulas for the statistical functions, such as the cross spectrum, the correlation function for the surface displacement, and the correlation function for the surface slopes, have been derived in connection with the spectrum that characterizes the ocean surface. By taking an adequate spectral model for the surface wave and using the present formalism, it is possible to treat statistically the light emitted from and scattered by the ocean surface, which is characterized by its spectrum. Optical statistical understanding of random ocean surface is essential for optical remote sensing of water and oceans.