Eyes and Vision

Michael F. Land

University of Sussex, Brighton

Insect eyes are of two basic types: compound (or multifaceted) and simple (or single chambered). In adults, the principal organs of sight are nearly always compound eyes, although simple eyes—often quite good ones—are frequently present in immatures. Despite the major differences in their form and construction, compound and simple eyes perform essentially the same job of splitting up the incoming light according to its direction of origin (Fig. 1). Compound eyes are of two distinct and optically different kinds: apposition eyes, in which each receptor cluster has its own lens, and superposition eyes, in which the image at any point on the retina is the product of many lenses.

APPOSITION EYES History of Insect Optics

The facets of compound eyes of insects are too small to be resolved with the naked eye, and it required the invention of the microscope in the 17th century before they could be properly depicted. The process of working out how compound eyes functioned took more than 2 centuries from Robert Hooke's first drawing of "The Grey Drone Fly" (probably a male horse fly) in his Micrographia of 1665 to

FIGURE 1 The three types of eye found in insects. (A) Simple, or single-chambered, (B) apposition compound, (C) superposition compound. The receptors are shown stippled. (Reproduced, with permission, from Land and Nilsson, 2002.)

the essentially modern account by Sigmund Exner in 1891. The first person to look through the optical array of an insect eye was Antoni van Leeuwenhoek, and his observations caused a controversy that was not fully resolved until the 1960s. The following quotation comes from a letter from Leeuwenhoek to the Royal Society of London, which was published in 1695.

Last summer I looked at an insect's cornea through my microscope. The cornea was mounted at some larger distance from the objective as it was usually done when observing small objects. Then I moved the burning flame of a candle up and down at such a distance from the cornea that the candle shed its light through it. What I observed by looking into the microscope were the inverted images of the burning flame: not one image, but some hundred images. As small as they were, I could see them all moving.

Evidently, each facet of the eye (at least in apposition eyes) does produce an inverted image, even though the geometry of the eye as a whole dictates that the overall image is erect (Fig. 1). What, then, does the insect see? Do the receptors (typically eight) beneath each lens resolve the inverted images, or do they just indicate the average intensity across the field of view of the ommatidium? (An ommatidium is the "unit" of a compound eye, consisting of the lens, receptors, and associated structures. See Fig. 2A).

FIGURE 2 (A) Basic structure of an apposition eye, showing its construction from ommatidial elements. (B) Definitions of the interommatidial angle, Aty, and rhabdom acceptance angle, Ap. (Reproduced, with permission, from Land and Nilsson, 2002.)

Remarkably, the answer depends on the animal. By the 1870s histological studies had shown that in most apposition eyes the eight receptor cells in each ommatidium contribute to a single radial structure, known as a rhabdom (Greek for rod; Figs. 2 and 3). Much later, in the 1950s, this material was found to be made up of photoreceptive membrane covering large numbers of long narrow microvilli, but even by the time that Exner wrote his monograph in 1891 it was

FIGURE 3 Optical comparison of an apposition eye (A,B) and a neural superposition eye (C,D). In an apposition eye each rhabdom (hatched) views light from a slightly different direction (arrows), and the rhabdoms (B), although made up from eight receptors, have a fused structure that acts as a single light guide. UV, B, and G indicate the receptor elements that respond to ultraviolet, blue, and green in an ommatidium from the eye of a worker bee. In neural superposition eyes, light from a single direction is imaged onto different rhabdomeres in adjacent ommatidia (C). The axons from all receptors imaging the same point collect together in the first synaptic layer (the lamina, Fig. 5) so that here the image has the same structure as in an ordinary apposition eye. The section (D) shows the arrangement of the separated rhabdomeres in an ommatidium from a fly. The six outer rhabdomeres (1-6) all send axons to different adjacent laminar "cartridges" (as in C). The central pair (7 overlying 8) bypass the lamina and go straight to the next ganglion, the medulla. (Reproduced, with permission, from Land and Nilsson, 2002.)

clear that the rhabdom was the structure sensitive to light. Optically, each ommatidium works as follows. The inverted image that Leeuwenhoek saw is focused onto the distal tip of the rhabdom. Having a slightly higher refractive index than its surroundings, the rhabdom behaves as a light guide, so that the light that enters its distal tip travels down the structure, trapped by total internal reflection. Any spatial information in the image that enters the rhabdom tip is lost, scrambled by the multiple reflections within the light guide, so that the rhabdom itself acts as a photocell that averages all the light that enters it. Its field of view is defined, in geometric terms, by the angle that the tip subtends at the nodal point of the corneal lens (Ap; Fig. 2B), and in a typical apposition eye this acceptance angle is approximately the same as the angle between the ommatidial axes (the interom-matidial angle, A^ Fig. 2B). Thus the field of view of one rhabdom abuts (or "apposes," hence the name) the field of its neighbor, producing an overall erect image made up of a mosaic of adjacent fields of view.

Although the eight receptors that contribute to the rhabdom share the same visual field, it does not mean that they supply the same information. The labels UV, B, and G on the cross section of a bee rhabdom in Fig. 3B indicate the regions of the spectrum that the cells respond to best. Most

FIGURE 4 The spectral sensitivity curves for the three human cone mechanisms (and rods, dotted) and the corresponding three curves for a bee. The spectrum shows the colors as they appear to human eyes. (Reproduced, with permission, from Land and Nilsson, 2002.)

insects have trichromatic color vision, just as humans do, although their visible spectrum is shifted toward shorter wavelengths compared with ours (Fig. 4). Some butterflies and dragonflies have four-color vision.

The second feature of the bee rhabdom (Fig. 3B) is that the microvilli making up the structure are arranged in orthogonal sets. It has been known since the work of Karl von Frisch in the 1940s that bees can navigate using the pattern of polarized light in the sky. This capacity arises from the way the photoreceptor molecules are arranged on the microvilli. A geometric consequence of the cylindrical shape of the microvilli is that there will be twice as many lightsensitive chromophore groups of the rhodopsin molecules aligned parallel to the long axis of each microvillus than at right angles to it. This, in turn, means that the receptors respond best to light polarized parallel to this axis. In fact bees use a special dorsal region of the eye (the POL area) to analyze sky polarization; in the rest of the eye the receptors are twisted to abolish polarization sensitivity, so that it does not interfere with color vision. Polarization vision is also used by some insects, such as the water bug Notonecta, to detect water surfaces, which polarize light strongly.

The description of apposition optics given above holds for most diurnal insects (e.g., bees, grasshoppers, and dragonflies), but it does not apply to the true (two-winged) flies, the Diptera. Since 1879, when Grenacher observed that the receptors in fly ommatidia have separate photoreceptive structures (rhabdomeres) that do not contribute to a common rhabdom, there had been suspicions that flies might actually be resolving the Leeuwenhoek images. In the focal plane of the lens of a fly ommatidium, the distal tips of the rhabdomeres are separated from each other and form a characteristic pattern (Fig. 3D) that resolves the image into seven parts (there are eight receptors, but the central pair lie one above the other). This raises the obvious question: how are these seven-pixel inverted images welded together to form the overall erect image, if indeed that is what occurs? Kuno Kirschfeld finally solved this conundrum in 1967. It turns out that the angle between the fields of view of adjacent rhabdomeres within an ommatidium (about 1.5° in a blow fly) is identical to the angle between neighboring ommatidial axes. Furthermore, the fields of each of the six peripheral rhabdomeres in one fly ommatidium are aligned, in the space around the fly, with the field of the central rhabdomere of one of the neighboring ommatidia (Fig 3C). Thus, each point in space is viewed by seven rhabdomeres in seven adjacent ommatidia. What does this complicated and seemingly redundant arrangement achieve? To answer this it is necessary to know what happens to the signals from the seven receptors that view the same point, and that turns out to be the most astonishing part of the story. Beneath each ommatidium, the emerging receptor axon bundle undergoes a 180° twist before the individual neurons disperse to nearby regions of the first optic ganglion (the lamina) that correspond to the adjacent ommatidia. The net result of this impressive

FIGURE 5 The interchange of axons that occurs between retina and lamina of a blow fly (Calliphora), which makes possible the neural superposition mechanism of Fig. 3C.

feat of neural knitting (Fig. 5) is that all the axons that "look at" the same point in space finish up making connections with the same cells in the lamina. Thus, as far as the lamina is concerned, the image is exactly the same as it would be in a conventional apposition eye, except that the signal, in terms of photon captures, is seven times stronger. One advantage of the extra signal is that it provides flies with a short period at dawn and dusk when they can see well, but when the eyesight of their predators and competitors is less sensitive and so less effective at detecting small objects.

Kirschfeld called this arrangement "neural superposition," because, as in optical superposition (see later), the contributions of a number of ommatidia are superimposed in the final image. One might ask: could the signal not have been made stronger simply by increasing the diameter of the rhabdom in a conventional apposition eye? Indeed it could, but that would mean increasing the rhabdom acceptance angle (Ap; Fig. 2B) at the same time, which in turn would mean a loss of resolution for the eye as a whole. The beauty of the fly solution, and undoubtedly the reason why it evolved, is that it involves no increase in acceptance angle, provided the rhabdomeres are properly aligned. There are strong hints that something like neural superposition occurs in other insect groups (some beetles, earwigs, water bugs, and crane flies) but it is only in the advanced flies that the perfect nearest-neighbors arrangement is known to be achieved.

Imaging Mechanisms

The structures that form the images in the ommatidia of apposition eyes are quite varied (Fig. 6). In terrestrial insects, as in terrestrial vertebrates, the simplest way to produce an image is to make the cornea curved (Fig. 6A). Ordinary spherical-surface optics then apply, and an image is formed about four radii of curvature behind the front face. In aquatic insects such as the water bug Notonecta, the external surface of the cornea has little power because of the reduction in refractive index difference (Fig. 6B). It is augmented by two other surfaces, the rear of the lens and an unusually curved

FIGURE 6 Four mechanisms of image formation in apposition eyes. (A) Corneal lens (bee, fly). (B) Multisurface lens (water bugs). (C) Lens/lens-cylinder afocal combination (butterflies). Details in text. (Reproduced, with permission, from Land and Nilsson, 2002.)

interface in the center of the lens whose function may be to correct one of the defects of spherical surfaces—spherical aberration.

The eyes of butterflies, which resemble ordinary apposition eyes in nearly all respects, have an optical system that is subtly different from the arrangement in Fig. 6A. Instead of forming an image at the rhabdom tip, as in the eye of a bee or locust, the image lies within the crystalline cone. The proximal part of the cone contains a very powerful lens cylinder that makes the focused light parallel again, so that it reaches the rhabdom as a beam that just fits the rhabdom (Figs. 6C, and 17). This arrangement, known as afocal apposition because there is no external focus, has much in common with the superposition optical system of moths, to which butterflies are closely related, and will be considered later.

Resolution

For any eye, the resolution of the image seen by the brain is determined by the fineness with which the ommatidial mosaic samples the environment, represented by the interommatidial angle, A9 (Fig. 2B), and by the quality of the image received by each rhabdom, represented by the rhabdom acceptance angle Ap (Fig. 2B). (Although the eight receptors that contribute to each rhabdom usually have different spectral and polarization responses, they all share a common field of view.) In asymmetric eyes (which most are) A9 may be different along different axes of the facet array, but for present purposes A9 is taken to be the average of the angle measured along each of the three axes of the array. In the central region of a bee eye, A9 is about 1.7°. An extensive table of values can be found in a recent review by Land in 1997.

One would expect that apposition eyes would show a rough match between the interommatidial angle and the acceptance angle (Ap) of a single rhabdom, the argument being that no individual rhabdom can resolve detail finer than Ap, so there is no point spacing the directions of view of ommatidia closer than this angle. The acceptance angle Ap

FIGURE 7 (A) The acceptance angle (Ap) of an ommatidium results from a combination of the Airy diffraction pattern (point-spread function), given by X/D (right), and the geometrical angular width of the rhabdom (d/f) at the nodal point of the lens (left). (B) Light is trapped in a rhabdom by total internal reflection, which occurs when the angle the light makes with a normal to the wall is greater than the critical angle, given by sin 9cdt = nx/n2, the ratio of the refractive indices outside and inside the rhabdom. A typical rhabdom can trap a cone of light about 22° wide. (C) In narrow lightguiding structures some of the light is actually outside the fiber, and can potentially be caught by adjacent fibers and so spoil resolution.

FIGURE 7 (A) The acceptance angle (Ap) of an ommatidium results from a combination of the Airy diffraction pattern (point-spread function), given by X/D (right), and the geometrical angular width of the rhabdom (d/f) at the nodal point of the lens (left). (B) Light is trapped in a rhabdom by total internal reflection, which occurs when the angle the light makes with a normal to the wall is greater than the critical angle, given by sin 9cdt = nx/n2, the ratio of the refractive indices outside and inside the rhabdom. A typical rhabdom can trap a cone of light about 22° wide. (C) In narrow lightguiding structures some of the light is actually outside the fiber, and can potentially be caught by adjacent fibers and so spoil resolution.

is actually a combination of the contributions of ray and wave optics (Fig. 7A). Geometrically, Apray is the angle subtended by the rhabdom tip at the nodal point of the facet lens, i.e., the rhabdom diameter divided by the focal length (d/f radians). Typical values (for a bee) are 2 ||m for d and 60 ||m for f, which makes Apray 0.033 radians, or 1.9°. In wave optics, the limit to image quality is set by diffraction, specifically by the angle subtended by the Airy disk (the diffraction image of a point source), and this is given by X/D radians. If the wavelength (X) is 0.5 |lm and the facet diameter (D ) is 25 |lm, then Apwave is 0.02 radians, or 1.1°. To obtain the final value for Ap, Apray and Apwave have to be combined, and unfortunately the proper way of doing this (convolution, taking the wave-guide properties of the rhabdom into account) is very complicated. A simple approximation is given by Ap2 = Apray2 + Apwave2. This is adequate for most purposes but tends to overestimate Ap slightly. Using this approximation, Ap for the bee data is 2.2°, somewhat larger than A^. Typically in light-adapted diurnal insects the ratio of Ap to A^ is about 1:1.

The neural superposition eyes of dipterans have an additional constraint, namely that the separation of the tips of the rhabdomeres must match the interommatidial angle. In a house fly, A^ is about 2°, and with an ommatidial focal length of 70 | m, this means that the tip separation must be 2.4 |lm, which does not leave a great deal of room (Fig. 3D). Because narrow light guides, such as rhabdomeres, tend to be

"leaky," with a substantial fraction of the light energy outside the guide itself (Fig. 7C), there needs to be an adequate gap between one rhabdomere and the next to prevent cross talk. In flies there is a 1-|m gap between adjacent rhabdomeres (Fig. 3D), which means that the rhabdomeres themselves must be very narrow. They have a distal tip diameter that is also about 1 | m, making them among the narrowest photoreceptors in any animal. In most other respects, however, neural superposition eyes are optically similar to other apposition eyes.

Diffraction and Eye Size

In a short and remarkable article titled "Insect sight and the defining power of compound eyes," published in 1894, Henry Mallock, an optical instrument maker, described insect vision in these terms: "The best of the eyes... would give a picture about as good as if executed in rather coarse wool-work and viewed at a distance of a foot."

Why is insect vision so poor? The problem, as Mallock recognized for the first time, is diffraction. Compound eyes have very small lenses compared with the lenses of single-chambered eyes, and because the size of the diffraction blur circle (the Airy disk) is inversely proportional to aperture diameter, the blur circles are large and the resolution correspondingly poor (Fig. 7A). A 25-|m diameter facet of a bee produces an Airy disc that is just over 1° wide in angular terms. One degree is about the size of a thumbnail at arm's length, so one can imagine a bee's world made up of pixels of about that size. In terms of the acuity of our own eyes (A^ about 0.01°), this is not very good at all.

Mallock's article goes on to discuss what a compound eye with human resolution would look like, and he came to the astonishing conclusion that it would need to be more than 20 m in diameter, or bigger than a house. The reason for this is clear: the human eye achieves high resolution by having a daylight pupil diameter of 2 mm, 80 times the diameter of a bee lens. For a bee to have the same resolution, diffraction requires that all its lenses would need to have this diameter, and to exploit all the detail in the scene they would need to be spaced at 0.5 arcmin angular intervals, the same as the receptors in our fovea. In a spherical eye, the interommatidial angle (A^) is the angle subtended by one lens diameter at the center of the eye (D/r radians, where r is the eye radius), which gives r = D/A^. With A^ = 0.5 arcmin of arc (0.000145 radians; 1 radian = 57.3° and 1° = 60 arcmin), and D = 2 mm, the radius of curvature will be 13.8 m and the diameter twice this. (Kirschfeld has pointed out that this calculation is a little unfair because resolution in the human eye falls off dramatically away from the fovea, to a tenth of its maximum value at 20° from the fovea, and even less farther out. Taking this into account the "human" compound eye can be shrunk in size considerably, to an irreducible 1 m diameter, which still looks very clumsy). Dragonflies seem to approach the limit of what it is possible with an apposition eye. Their eyes are 8 mm or more in diameter, have up to 30,000 facets each, and resolve about 0.25° in their most acute region. This is still poor compared with what is achievable by any camera-type eye of the same diameter.

The outcome of this discussion is that it is very hard for an apposition eye to improve its resolution; it simply gets too big. Space is thus at a premium; a little extra resolution here must be bought by a bit less there, and for this reason the different visual priorities of arthropods with different lifestyles show up in the distribution of interommatidial angles, and often facet sizes, across the eye.

Sensitivity

The sensitivity of an eye is the ratio of the amount of light received by a single photoreceptor to the amount emitted by the surface that eye is imaging. It can be used to work out the numbers of photons that individual receptors receive, and this determines the way in which the eye will perform under dim light conditions. Sensitivity can be calculated from the formula S = 0.62 D2 Ap2, where D is the lens diameter and Ap the rhabdom acceptance angle (Figs. 2B and 7A) (we ignore the effect of receptor length here). Although D is roughly 100 times greater in a human eye than in a bee ommatidium, Ap is about 100 times smaller (approximately 0.015° compared with 1.5°), so that the value of S is very similar in the bee and the human. Thus, the range of illumination conditions over which an insect with an apposition eye can operate is similar to that of a mammal using its cone system. Mammals can also see at much lower intensities, by pooling the responses of rods over quite large retinal areas (effectively increasing Ap). It is unlikely that pooling occurs to any great extent in insect eyes.

When discussing sensitivity, "adaptation" can have two meanings. Different eyes may be adapted in the evolutionary sense to work permanently under conditions of high or low illumination, e.g., night or day, deep sea or surface. Alternatively, the same eye can be said to be light- or dark-adapted via reversible and temporary changes in its optical anatomy. In both cases, the above equation is the key to interpreting changes and differences.

Light and Dark Adaptation

Temporary light and dark adaptation mechanisms take a number of forms in apposition eyes. Some are illustrated in Fig. 8 and include the following: (A) an iris mechanism just above the distal tip of the rhabdom that restricts the effective value of Ap. In the case of crane flies (Tipulidae), which have an arrangement of six outer and two central rhabdomeres, the iris cuts off the outer six in the light, leaving only the central pair. (B) A "longitudinal pupil" consisting of large numbers of very small pigment granules that move into the region immediately around the rhabdom in the light and withdraw in the dark is a second form. The main effect of

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