So, why is there a lens at all? Spherical mirrors like this one are subject to a particular kind of distortion called spherical aberration. A famous design of reflecting telescope, the Schmidt, overcomes the problem by a cunning combination of lens and mirror. Scallop eyes seem to solve the problem in a slightly different way. Spherical {176} aberration can theoretically be overcome by a special kind of lens whose shape is called a ‘Cartesian oval’. Figure 5,I8e is a diagram of a theoretically ideal Cartesian oval. Now look again at the profile of the actual lens of the .scallop eye (Figure 5.18d). On the basis of the striking resemblance, Professor Land suggests that the lens is there as a corrector for the spherical aberration of the mirror which is the main image-forming device.
As for the origin of the curved mirror eye on the lower slopes of its region of the mountain, we can make an educated guess. Reflecting layers behind retinas are common in the animal kingdom, but for a different purpose, not image forming, as in scallops. If you go out into the woods with a bright spotlight you will see numerous twin beams glaring straight back at you. Many mammals, especially nocturnal ones like Figure 5.19b's golden potto or angwantibo from West Africa, have a tapetum, a reflecting layer behind the retina. What the tapetum does is provide a second chance of catching photons that the photocells failed to stop: each photon is reflected straight back to the very photocell that missed it coming the other way, so the image is not distorted. Invertebrates, too, have discovered the tapetum. A bright torch in the woods is an excellent way to find certain kinds of spider. Indeed, looking at the portrait of a wolf spider (Figure 5.19a), you wonder why the ‘cats’ eyes’ that mark our roads are not called ‘spider eyes’. Tapetums for capturing every last photon may well have evolved in ancestral cup eyes before lenses. Perhaps the tapetum is the pre-adaptation which, in a few isolated creatures, has become modified to form a reflecting telescope kind of eye. Or the mirror may have arisen from another source. It is hard to be sure.
Lenses and curved mirrors are two ways of sharply focusing an image. In both cases the image is upside-down and left — right reversed. A completely different kind of eye, which produces an image the right way up, is the compound eye, favoured by insects, crustaceans, some worms and molluscs, king crabs (strange marine creatures said to be closer to spiders than to real crabs) and the large group of now extinct trilobites. Actually there are several different kinds of compound eye. I'll begin with the most elementary kind, the so-called apposition compound eye. To understand how the apposition eye {177}
Figure 19 Saving photons by reflecting them back. Glowing tapeta behind the eyes of (a) a wolf spider, Geolycosa sp., and (b) a golden potto.
works, we go back nearly to the bottom of Mount Improbable. As we have seen, if you want an eye to see an image or indeed go beyond signalling the mere intensity of light, you need more than one photocell, and they must pick up light from different directions. One way {178} to make them look in different directions is to place them in a cup, backed by an opaque screen. All the eyes we have so far talked about have been descendants of this concave cup principle. But perhaps an even more obvious solution to the problem is to place the photocells on the convex, outside surface of a cup, thereby causing them to look outwards in different directions. This is a good way to think of a compound eye, at its simplest.
Remember when we first introduced the problem of forming an image of a dolphin. I pointed out that the problem could be regarded as the problem of having too many images. An infinite number of ‘dolphins’ on the retina, every way up and in every position on the retina, adds up to no visible dolphin at all (Figure 5.20a). The pinhole eye worked because it filtered out almost all the rays, leaving only the minority that cross each other in the pinhole and form a single upside-down image of the dolphin. We treated the lens as a more sophisticated version of the same principle. The {179}
Figure 5.20 (a) reproduction of Figure 5.6; (b) the cup turned inside out. Principle of the apposition compound eye.
apposition compound eye solves the problem in an even simpler way.
The eye is built as a dense cluster of long straight tubes, radiating out in all directions from the roof of a dome. Each tube is like a gunsight which sees only the small part of the world in its own direct line of fire. In terms of our filtering metaphor, we could say that rays coming from other parts of the world are prevented, by the walls of the tube and the backing of the dome, from hitting the back of the tube where the photocells are.
That's basically how the apposition compound eye works. In practice, each of the little tube eyes, called an ommatidium (plural omma-tidia), is a bit more than a tube. It has its own private lens, and its own tiny ‘retina’ of, usually, half a dozen or so photocells. Insofar as each ommatidium produces an image at all at the bottom of the narrow tube, that image is upside-down: the ommatidium works like a long, poor-quality, camera eye. But the upside-down images of the individual ommatidia are ignored. The ommatidium reports only how much light comes down its tube. The lens serves only to gather more light rays from the ommatidium's gunsight direction and focus them on to the retina. When all the ommatidia are taken together, their summed ‘image’ is the right way up, as shown in Figure 5.20b.
As always, ‘image’ doesn't have to mean what we humans would think of as an image: an accurate, Technicolor perception of an entire scene. Instead, we are talking about any kind of ability to use the eyes to distinguish what is going on in different directions. Some insects might, for example, use their compound eyes only to track moving targets. They might be blind to still scenes. The question of whether animals see things in the same way as we do is partly a philosophical one and it may be a more than usually difficult task trying to answer it.
The compound-eye principle works well enough for, say, a dragonfly zeroing in on a moving fly but, in order for a compound eye to see as much detail as we see, it would need to be hugely bigger than the kind of simple camera eye that we possess. Here is approximately why this is. Obviously, the more ommatidia you have, all looking in slightly different directions, the more fine detail you can see. A dragonfly may have 30,000 ommatidia and it is pretty good at hawking insects on the wing (Figure 5.21). But in order to see as much detail {180}
Figure 5.21 Large compound eyes in a visually hunting aerial predator, the dragonfly Aeshna cyanea.
as we can see, you'd need millions of ommatidia. The only way to fit in millions of ommatidia is to make them exceedingly tiny. And unfortunately there is a strict limit on how small an ommatidium can be. It is the same limit as we met in talking about very small pinholes, and it is called the diffraction limit. The consequence is that, in order to make a compound eye see as precisely as the human camera eye, the compound eye would have to be ludicrously large: twenty-four metres in diameter! The German scientist Kuno Kirschfeld dramatized this by drawing what a man would look like if he could see as well as a normal man can see, but using compound eyes (Figure 5.22). The honeycomb pattern on the drawing is impressionistic, by the way. Each facet drawn actually stands for 10,000 ommatidia. The reason the man's compound eyes are only about one metre across instead of twenty-four is that Kirschfeld made allowance for the fact that we humans see very precisely only in the centre of our retina. He took an average of our precise central vision and our much less precise vision towards the edges of our retina, and came up with the one metre eye shown. Whether one metre across or twenty-four, a compound eye this large is impractical. The moral is, if you want to see precise, detailed images of the world, use a simple camera eye with a {181}
Figure 5.22 Kuno Kirschfelds picture of
how a man with compound eyes would
look if he wanted to see as well as a
normal human.
single, good lens, not a compound eye. Dan Nilsson even remarks of compound eyes that ‘It is only a small exaggeration to say that evolution seems to be fighting a desperate battle to improve a basically disastrous design.’
Why, then, don't insects and
crustaceans abandon the compound eye and evolve camera eyes instead? It may be one of those cases of becoming trapped the wrong side of a valley on the massif of Mount Improbable. To change a compound eye into a camera eye, there has to be a continuous series of workable intermediates: you cannot travel down into a valley as a prelude to mounting a higher peak. So, what is the problem about intermediates between a compound eye and a camera eye?
At least one outstanding difficulty comes to mmd. A camera eye forms an upside-down image. A compound eye's image is the right way up. Finding an intermediate between those two is a tough proposition, to put it mildly. A possible intermediate is no image at all. There are some animals, living in the deep sea or otherwise in near total darkness, who have so few photons to play with that they give {182} up on images altogether. All that they can hope for is to know whether there is light at all. An animal such as this could lose its image-processing nervous apparatus altogether and hence be in a position to make a fresh start up a completely different slope of the mountain. It could therefore constitute an intermediate on the path from a compound eye to a camera eye.
Some deep-sea crustaceans have large compound eyes but no lenses or optical apparatus at all. Their ommatidia have lost their tubes and their photocells are exposed right at the outer surface of where they will pick up what few photons there are, regardless of direction. From there it would seem but a small step to the remarkable eye of Figure 5.23. It belongs to a crustacean, called Ampelisca, which doesn't live particularly deep — perhaps it is on the way back up again from deep-sea ancestors. Ampelisca's eye works as a camera eye, with a single lens forming an upside-down image on a retina. But the retina is clearly derived from a compound eye and consists of the remains of a bank of ommatidia. A small step, maybe, but only if, during the interregnum of near total blindness, the brain had enough evolutionary time to ‘forget’ all about processing right-way-up images.
That is an example of evolution from compound eye to camera eye (yet another example, by the way, of the ease with which eyes seem to evolve independently all around the animal kingdom). But {183}
Figure 5.23 A camera eye
with a compound eye in its
ancestral history. The
remarkable eye of Ampelisca.
how did the compound eye evolve in the first place? What do we find on the lower slopes of this particular peak of Mount Improbable?
Once again we may be helped by looking around the modern animal kingdom. Outside the arthropods (insects, crustaceans and their kin), compound eyes are found only in some Polychaet worms (ragworms and tubeworms) and in some bivalve molluscs (again, presumably independently evolved). The worms and molluscs are helpful to us as evolutionary historians because they also include among their number some primitive eyes which look like plausible intermediates strung out along the lower slopes of Mount Improbable leading to a compound-eye peak. The eyes in Figure 5.24 come from two different worm species. Once again, these are not ancestors, they are modern species and they are probably not even descended from the true intermediates. But they could easily be giving us a glimpse of what the evolutionary progression might have been like, from a loose clustering of photocells on the left to a proper compound eye on the right. This slope is surely just as gentle as the one we strolled up to reach the ordinary camera eye.
Ommatidia, as we have so far discussed them, depend for their effectiveness on being isolated from their neighbours. The gunsight that is looking at the dolphin's tailtip must not pick up rays from other parts of the dolphin, or we should be back with our original {184}
Figure 5.24 Possibly primitive compound eyes from two kinds of worms.
problem of millions of dolphin images. Most ommatidia achieve isolation by having a sheath of dark pigment around the tube. But there are times when this has bad side effects. Some sea creatures rely on transparency for their camouflage. They live in sea water and they look like sea water. The essence of their camouflage, then, is to avoid stopping photons. Yet the whole point of dark screens around ommatidia is to stop photons. How to escape from this cruel contradiction?
There are some deep-sea crustaceans who have come up with an ingenious partial solution (Figure 5.25). They don't have screening pigment, and their ommatidia are not tubes in the ordinary sense. Instead, they are transparent light guides, working just like man-made fibre-optic systems. Each light guide swells, at its front end, into a tiny lens, of varying refractive index like a fish eye. Lens and all, the light guide as a whole concentrates a large amount of light on to the {185}
Figure 5.25 Eye of a deep-sea crustacean with fibre-optic light guides.
photocells at its base. But this includes only light coming from straight in the line of the gunsight. Beams coming sideways at a tube, instead of being shielded by a pigment screen, are reflected back and don't enter the light guide.
Not all compound eyes even try to isolate their private supply of light. It is only eyes of the apposition type that do. There are at least three different kinds of ‘superposition compound eye which do something more subtle. Far from trapping rays in tubes or fibre-optic light guides, they allow rays that pass through the lens of one omma-tidium to be picked up by a neighbouring ommatidium's photocells. There is an empty, transparent zone, shared by all ommatidia. The lenses of all ommatidia conspire together to form a single image on a shared retina which is jointly put together from the light-sensitive cells of all the ommatidia. Figure 5.26 is Michael Land's picture of {186}
Figure 5.26 Charles Darwin's portrait, photographed by Michael Land through a firefly's compound lens.
Charles Darwin, seen through the compound lens of a firefly's superposition compound eye.
The image in a superposition compound eye, like that of apposition compound eyes but unlike that of camera eyes or that of Figure 5.23's Ampelisca, is the right way up. This is what you'd expect, assuming that superposition eyes are derived from apposition ancestors. It makes historical sense, and it must have made for an effortless transition as far as the brain was concerned. But it is still a very remarkable fact. For consider the physical problems of constructing a single right-way-up image in this way. Each individual ommatidium in an apposition eye has a normal lens in front of it which, if it makes an image at all, makes an upside-down one. To convert an apposition eye into a superposition one, therefore, the rays, as they pass through each lens, have somehow to be turned the right way up. Not only this, all the separate images from the different lenses have to be carefully superimposed to give one shared image. The advantage of doing this is that the shared image is much brighter. But the physical difficulties of turning the rays round are formidable. Amazingly, not only has the problem been solved in evolution, it has been solved in at least three independent ways: using fancy lenses, using fancy mirrors and using fancy neural circuitry. The details are so intricate that to spell them out would unbalance this already quite complicated chapter, and I'll deal with them only briefly.
A single lens turns the image upside-down. By the same token another lens, a suitable distance behind it, would turn it the right way up again. The combination is used in an instrument called a Keplerian telescope. The equivalent effect can be achieved in a single complex lens, using fancy gradations of refractive index. As we have seen, living lenses, unlike man-made ones, are good at achieving gradations of refractive index. This method of simulating the effect of a Keplerian telescope is used by mayflies, lacewings, beetles, moths, caddises and members of five different groups of crustaceans. The distance of their cousinship suggests that at least several of these groups evolved the same Keplerian trick independently of one another. An equivalent trick is pulled by three groups of crustaceans, using mirrors. Two of these three groups also contain members that {187} do the lens trick. Indeed, if you look at which animal groups have adopted which of the several different kinds of compound eye, you notice a fascinating thing. The different solutions to problems pop up here, there and everywhere, suggesting, yet again, that
they evolve rapidly and at the drop of a hat.
'Neural superposition or ‘wired-up superposition has evolved in the large and important group of two-winged insects, the flies (fireflies, by the way, such as those mentioned in Figure 5.26, are not flies at all, but beetles). A similar system occurs in water boatmen, where it seems to have evolved — yet again — independently. Neural superposition is fiendishly cunning. In a way it shouldn't be called superposition at all, because the ommatidia are isolated tubes just as in apposition eyes. But they achieve a superposition-like effect by ingenious wiring of nerve cells behind the ommatidia. Here's how. You'll remember that the ‘retina’ of a single ommatidium is made up of about half a dozen photocells. In ordinary apposition eyes, the firing of all six photocells is simply added together, which is why I put ‘retina’ in quotation marks: all photons that shoot down the tube are counted, regardless of which photocell they hit. The only point of having several photocells is to increase the total sensitivity to light. This is why it doesn't matter that the tiny image at the bottom of an apposition ommatidium is technically upside-down.
Climbing Mount Improbable Page 18