Modeling the short wavelength infrared laser radiance reflection on the sea surface

The sea surface is a complex dynamic structure dependent on atmospheric conditions, and for which physical and chemical properties change from water to foam. Its roughness determines how the surface reflects, absorbs, and emits radiance, and depends on multiple parameters such as wind speed and direction, and foam and turbulence induced from natural waves or from object displacement. In this paper, a model description is given for laser reflection on the sea surface in open water driven by the wind. The model allows calculation of the reflected laser radiance from the sea surface toward a receiver as a function of the incoming laser radiance with a known beam intensity profile. Each subarea of the sea surface seen by one pixel of the receiver is considered as an ensemble of facets, where each facet is defined by its x and y directional slopes. The wind speed and orientation determine the probability density function of the sea surface facet slope occurrence. In this paper, we have analytically expressed the reflected radiance on the sea surface as a function of the wind speed, receiver range, receiver heading, laser position, laser output aperture, and laser incoming radiance. Using the tolerance ellipse, the reflected radiance expression was approximated, and both direct and approximated results were compared. The richness in behavior of the reflected radiance and its dependence on the geometry of the problem were studied showing the impact of the receiver position, the laser position, heading, and beam divergence.