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.

Modeling the ship white water wake in the midwave infrared.

We have modeled the white water wake of a ship as a single layer of bubbles packed on the sea surface within the perimeter of the trailing turbulent wake. The size of the bubbles is considered greater than the midwave infrared wavelengths such that the optical geometrical approximation remains valid. The upper half bubble hemisphere is meshed into facets, and we calculate the probability density function of their slopes and constrain that distribution by the geometrical limits imposed by the position of the receiver through the shadowing of facets by other bubbles and of facets that are facing away from the receiver. For the facets that are visible, we compute the midwave infrared emitted and reflected radiance for the white water wake for atmospheric, solar, and sea conditions that prevailed during a ship wake measurement trial using a homegrown simulation code, the Sea Surface Radiance Simulator. The range of slopes that are visible to the receiver for the white water wake greatly exceeds those that are present in the turbulent wake and in the sea background. Consequently, the variability in the white water wake radiance is substantial. As a function of the downstream distance astern of the ship, we have ad hoc assumed that the white water wake fraction decays linearly or proportionally to the turbulent intensity in the wake. Comparing to measurements, we find an agreement in trend behavior of the midwave radiance contrast of the white water wake with downstream distance for a white water wake fraction that decays proportionally to the square of the turbulence intensity.

Modeling the turbulent trailing ship wake in the infrared.

The sea surface turbulent trailing wake of a ship, which can be rather easily observed in the infrared by airborne surveillance systems, is a consequence of the difference in roughness and temperature between the wake and the sea background. We have developed a phenomenological model for the infrared radiance of the turbulent wake by assuming that the sea surface roughness is dependent upon the turbulent intensity near the sea surface. Describing the sea surface roughness with a Cox and Munk probability distribution function of slopes, we distinguish on the sea surface between the sea background and the turbulent wake by the variance of sea surface slopes, σCM2=constant and σTW2(x,y)≠constant. The latter dependence is assumed to be inversely proportional to the turbulent intensity of the wake, Urms(x,y). Given the incident solar, atmospheric, and sky infrared radiances, we calculate the reflected and emitted sea surface radiance from both the wake and the background. We compare the infrared contrast of the wake with infrared image data obtained in an airborne trial. Our predictions and the measurements agree very well in trend over a significant range of observer zenith angles. Our calculations reveal the strong dependence of the wake radiance on the observer zenith angle, allowing for positive and negative contrasts with the background.