Underwater binocular imaging of aerial objects versus the position of eyes relative to the flat water surface

The apparent position, size, and shape of aerial objects viewed binocularly from water change as a result of the refraction of light at the water surface. Earlier studies of the refraction-distorted structure of the aerial binocular visual field of underwater observers were restricted to either vertically or horizontally oriented eyes. Here we calculate the position of the binocular image point of an aerial object point viewed by two arbitrarily positioned underwater eyes when the water surface is flat. Assuming that binocular image fusion is performed by appropriate vergent eye movements to bring the object's image onto the foveae, the structure of the aerial binocular visual field is computed and visualized as a function of the relative positions of the eyes. We also analyze two erroneous representations of the underwater imaging of aerial objects that have occurred in the literature. It is demonstrated that the structure of the aerial binocular visual field of underwater observers distorted by refraction is more complex than has been thought previously.