Point-spread function associated with underwater imaging through a wavy air–water interface: theory and laboratory tank experiment

The point-spread function needed for imaging underwater objects is theoretically derived and compared with experimental results. The theoretical development is based on the emergent-ray model, in which the Gram-Charlier series for the non-Gaussian probability-density function for emergent angles through a wavy water surface was assumed. To arrive at the point-spread model, we used a finite-element methodology with emergent-ray angular probability distributions as fundamental building functions. The model is in good agreement with the experiment for downwind conditions. A slight deviation between theory and experiment was observed for the crosswind case; this deviation may be caused by the possible interaction of standing waves with the original air-ruffled capillary waves that were not taken into account in the model.