Looking into the water with a facet eye

The apparent velocity and apparent size of objects approaching an animal strongly depend on their size, their position within the visual field and on the path along which they move. It also makes a considerable difference whether both the animal and the objects are in air, or whether the animal looks from one medium into the other, as is the case in animals that live at the water surface. To systematically investigate this situation we calculated apparent velocity and size in the midsagittal plane of approaching objects of flat horizontal, rodlike vertical and spherical shape. We confine our investigation to object movements along straight horizontal and vertical paths and consider the situation for eyes with and without acute zones. The apparent velocity of an approaching object is low in the far field and increases rapidly close to the eye in both air and water. Along horizontal paths and close to the animal it is higher in water than in air. Along vertical paths and close to the animal it is higher in air than in water. Both relationships are exaggerated when there is an acute zone for vertical resolution along the animal's horizon. Boundary curves are calculated along which an approaching object is seen by a linearly increasing number of receptors. The change of apparent size is characterized by the density of these lines. Below the water surface the change of apparent size is similar to that of the apparent velocity.(ABSTRACT TRUNCATED AT 250 WORDS)