There are only three types of eyes that are fundamentally different: simple eyes (like ours), apposition compound eyes (found in most insects) and superposition compound eyes (less common, but found in lobsters, for example). But hidden beyond this relative uniformity, there lies an enormous diversity. Every species is the product of evolution, and different environments place very different demands on the eyes. When you think of vision, you probably think of your own highly mobile, forward-facing eyes. But for most of the animal kingdom, vision is something very different.
A particularly striking example of specialized vision can be found in marine animals that live about 200 to 800 meters beneath the surface (Land, 2000; Land & Nilsson, 2002). A little bit of sunlight still penetrates to these depths. Sunlight obviously comes from above, so these midwater creatures live in an environment where everything below them is pretty much completely dark and everything above them is, during daytime at least, relatively light. This is a peculiar environment to live in and it has given rise to a peculiar type of vision.
Essentially, midwater animals have two pairs of eyes. One pair looks up at the surface, and one pair looks down into the dark deep. This is true for a wide variety of midwater species, regardless of what type of eyes they have, which in itself is a beautiful illustration of convergent evolution.
Some animals do not really have two distinct pairs of eyes, but rather a single pair with specialized optics to look simultaneously up and down (a recently discovered example is described in Wagner, Douglas, Frank, Roberts, & Partridge, 2009). Or animals may swim sideways, with one eye facing up and one eye facing down, as some squid do. Still other animals have more than two pairs of eyes. But the basic pattern is clear: There are dorsal eyes (from the latin dorsum, which means “back”) to look at the surface and ventral eyes (from venter, which means “belly”) to look down.
There is another consistent pattern in midwater vision: The dorsal eyes are much more sensitive and have a much higher resolution than the ventral eyes. This is weird and at first glance it seems that nature has gotten it the wrong way around. Since the bottom of the ocean is dark and difficult to see, shouldn't the ventral, downward-pointing eyes be the good ones? The answer is yes, if you assume that the ventral and dorsal eyes serve the same purpose. So rather than second-guessing evolution, we conclude that they must do something different.
The dorsal, surface-facing eyes appear to scan for food, which can be droppings from other animals or, of course, other animals. This is a challenging task, because the light is dim (the threshold of human vision is reached at a depth of a little over 600 meters). To make things worse, many aquatic animals go through great pains to be invisible from below. Their underside generally has a bright color, to match the color of the surface, either passively (counter-shading) or because their underside actively gives off light (bioluminescence; this type of camouflage is called counter-illumination). Therefore, midwater animals need good dorsal eyes to spot other animals dwelling near the surface.
But if spotting food near the surface is hard, spotting food in the depths of the ocean is a lost cause. There is simply too little sunlight, and even the best possible eyes would be of little help. So why do they have ventral eyes at all? It is a good bet that these eyes are used to look for bioluminescent animals. Bioluminescence is common among deep water animals and, because the surroundings are so dark, it is easy to spot even the faintest signal. Therefore, the ventral, downward-pointing eyes of midwater animals don't have to be very good: There is basically nothing to see, except for the occasional bioluminescent creature, which you can't miss!
Land, M. F. (2000). On the functions of double eyes in midwater animals. Philosophical Transactions of the Royal Society B: Biological Sciences, 355(1401), 1147-1150.
Land, M. F., & Nilsson, D. E. (2002). Animal eyes. New York: Oxford University Press.
Wagner, H.-J., Douglas, R. H., Frank, T. M., Roberts, N. W., & Partridge, J. C. (2009). A novel vertebrate eye using both refractive and reflective optics. Current Biology, 19(2), 108-114.