Probabilistic Model for Laser Light Propagation Through a Random Water Surface
Abstract
The general problem of laser light propagating through a random water surface is investigated. A theoretical model is established for characterizing this complex process and its predictions are compared with measurements made in a laboratory tank. The experiment has been designed to allow channeling a variable speed air flow over the water surface so as to induce a controlled amount of surface roughness. The resulting small scale capillary wave structure of the airwater interface is probed with a laser and a 1dimensional lateral effects position sensor in both the crosswind and downwind directions. The surface wave angle probability density is found to be approximately Gaussian for air speeds below 3.7 m/s. The wave angle mean and standard deviation follow the driving air speed in a nearly linear manner. The surface wave spectral densities are computed and show peak values at spatial frequencies that depend on the air speed. Surface correlation times are found to decrease rapidly and to approach a constant as the air speed increases. Narrow bundles of rays refracted through the surface are dispersed into emergent angle probability densities that are modelled as a GramCharlier series. The fit in the downwind direction has been observed to be extremely good, but it is not as good in the crosswind direction. A finite element model has been constructed, based upon the GramCharlier models for emergent rays. This has allowed the prediction of complex light distributions above the surface for arbitrary submerged sources. The first use of this model has been to predict the point spread function of a simple camera system placed above the random surface and imaged on a number of submerged objects. The theoretically predicted point spread function agrees very well with measured ones. With the use of the predicted point spread function, it has been possible to effect image restorations of those blurred and distorted by the random surface. The restoration filter employed was a Wiener filter, and it was found to perform moderately well in the presence of additive noise.
 Publication:

Ph.D. Thesis
 Pub Date:
 1990
 Bibcode:
 1990PhDT........58B
 Keywords:

 WATER SURFACE;
 SUBMARINE COMMUNICATIONS;
 Physics: Optics; Mathematics; Engineering: Electronics and Electrical;
 Laser Beams;
 Light Transmission;
 Probability Theory;
 Surface Roughness;
 Surface Waves;
 Water;
 Wave Propagation;
 Air Flow;
 Air Water Interactions;
 Capillary Waves;
 Finite Element Method;
 Laser Outputs;
 Mathematical Models;
 Wind Direction;
 Lasers and Masers