A mysid shrimp carrying a pair of binoculars

In water as well as on land, light intensities usually vary with direction in a rather predictable way (Lythgoe, 1979). On land, the sky is rich in ultraviolet whereas the ground and vegetation are not. Under water, the predominant direction for light of all wavelengths is from above. For both compound eyes and simple eyes, this angular predictability is an important reason for regional variations across the retina (Land, 1989a,b). Different parts of the visual field also contain different kinds of visual information, providing another reason for regional variations in retinal design (Land, 1989b; Stavenga, 1992). The direction of locomotion is yet another factor responsible for regional variations in eyes. Hence, forward vision is often more acute than vision in other directions (Land, 1989b).

For a compound eye, acute vision is expensive in terms of eye surface. The ultimate limit for optical resolution is diffraction at the lens aperture. Diffraction reduces the content of high spatial frequencies in the image and puts a definite limit to spatial resolving power, which is proportional to the diameter of the lens aperture (for a recent review, see Warrant and McIntyre, 1993). This implies that a doubling of the optical resolution requires a doubling of the facet diameter. To exploit fully this increase in optical quality, the retina would need to sample with twice the spatial density. For a compound eye, this means twice the number of facets in each row and twice the number of rows. Naturally, a simultaneous increase in both facet diameter and the number of facets dramatically increases the surface area it occupies (Kirschfeld, 1976). If the eye as a whole is not to be any bigger, resolution can be increased only in a restricted part of the visual field and only at the expense of resolution in the rest of the eye. The fact that compound eyes have to economize on the eye surface spent on vision in different directions means that acute zones are dearly paid for and are always indicative of important visual needs for whatever species they are found in.

The most impressive acute zones are those involved in finding mates or prey. Land (1989b) distinguishes between forward-pointing and upward-pointing regions of acute vision. Many male dipteran flies have a more or less forward-pointing acute zone for chasing females (Land and Eckert, 1985; Hardie et al. 1981). These specializations are evidently devoted to sexual behaviour because they are less pronounced in females. Forward-pointing acute zones that are not sexually dimorphic, and are known to be for prey detection, are found in dipterans such as robber flies (Dietrich, 1909), but have been more thoroughly studied in the eyes of the praying mantis (Barrós-Pita and Maldonado, 1970; Rossel, 1979) and the predatory water flea Polyphemus pediculus (Nilsson and Odselius, 1983; Odselius and Nilsson, 1983).

In both insects and crustaceans, there are a number of very conspicuous dorsal acute zones designed for the detection of small targets against the homogeneous background of the sky or the water surface. In insects such as bibionid flies, mayflies and honeybees, these areas are male-specific and are used in swarming behaviour (Zeil, 1983; Stavenga, 1992). Predatory insects such as owlflies and dragonflies have dorsal acute zones in both sexes (Schneider et al. 1978; Horridge, 1978). Among crustaceans, similar specializations are found in many hyperiid amphipods (Land, 1989a) and euphausiid shrimps (Land et al. 1979).

The two basic types of arthropod compound eye, apposition and superposition, offer fundamentally different possibilities for making acute zones. With the optically independent ommatidia of apposition eyes, photon catch and spatial sampling frequency can change to any extent across the eye, but each image point requires its own facet on the eye surface. In superposition eyes the situation is more complicated. Upright images from many optical units (corneal lenses and crystalline cones) are superimposed to form the overall retinal image, which implies that neighbouring optical units must have the same image magnification (Nilsson, 1989). Although this does not entirely exclude regional variations in imaging, it prevents steep changes across the eye. Superposition optics does, however, allow the retinal sampling array to vary independently of the array of facets on the eye surface. If the facets are made larger and fewer, diffraction can be decreased without making the eye any bigger. The improved image quality can then be exploited by having narrower and more numerous rhabdoms. To accomplish this, some ommatidia would have to produce a rhabdom but no corneal lens or crystalline cone. Such cases are actually known from the dorsal eyes of male mayflies (Wolburg-Bucholz, 1976; Zimmer, 1898) and from the dorsal acute zone of euphausiid shrimps (Chun, 1896; Land et al. 1979). Larval stages of the euphausiid Thysanopoda tricuspidata have only seven facets but about 90 rhabdoms in the retina (Land, 1981, 1984). The animal studied in this paper, the Caribbean shallow-water mysid Dioptromysis paucispinosa, has carried this principle to its extreme by having a single giant optical system supplying light to a retinal acute zone of 120 rhabdoms. But there is more to it than that: the acute zone of Dioptromysis is pointing almost directly backwards!

The mysid shrimps, Dioptromysis paucispinosa (Brattegard, 1969), were collected at the barrier reef of Belize, Central America. The catch site was in shallow water (<1.5 m) in the back reef lagoon north of Carrie Bow Cay (16°48’N, 88°05’W), among dead coral covered in algal turf (see Modlin, 1987). The midday light intensity at the catch site was 3.6×10¹⁶ quanta cm⁻²s⁻¹. The animals were collected with hand-held nets and transferred to small fish tanks for behavioural studies, or taken directly for optical experiments and histology. All work with live animals was carried out at Carrie Bow Cay research station.

For histology, the eyes were cut off into sea water with 2.5 % glutaraldehyde and left refrigerated for at least 2 h. They were then rinsed in cacodylate buffer, stained in 1 % OsO₄ for 1 h, dehydrated in an alcohol series and embedded in Epon resin. Semi-thin sections for light microscopy were cut with a glass knife and stained with Methylene Blue and Azure Blue. For electron microscopy, sections were cut with a diamond knife and stained with lead citrate and uranyl acetate.

Visual fields were measured on live animals mounted in a submerged Leitz goniometer and observed through a microscope with a ×3.2/0.07 objective fitted with a coverslip in front to allow immersion into sea water. The eye was illuminated with incident white light, which produced a distinct black pseudopupil surrounded by yellow-white facets.

Recordings of eye movements were made on animals placed in a small dish and observed through a dissecting microscope with a Sony Hi-8 video camera. The video tapes were copied to Super VHS standard and analysed frame by frame.

Behavioural studies were made on animals caught the same day and placed in a fish tank with coral rocks from the catch site. Their presumably natural behaviour and their responses to various visual stimuli were recorded on video and subsequently analyzed from the screen.

The stalked compound eyes of Dioptromysis paucispinosa have a diameter of about 0.4 mm, which is not exceptional in any way considering the body length of 5 mm. The general appearance of the eyes is like that of other shallow-water mysids, with the addition of the unmistakable feature of the Dioptromysis genus: a large single lens wedged in at the posterior margin of the compound eye (Brattegard, 1969). The large lens is equally developed in males and females. From above, the protruding single lens seems to be pointing straight backwards (Fig. 1A). Viewing the live animal from behind (Fig. 1B) gives an almost uncanny feeling of being observed. The large lens forms a perfectly circular black aperture, which is seen in both eyes at the same time. Beside the large aperture is a much smaller one that is not covered by any obvious lens.

Semi-thin sections cut horizontally along the equator of the eye reveal that the posterior apertures are specialized parts of the compound eye (Fig. 2). To understand the posterior modifications of the eye, it is first necessary to describe the normal part of the eye. The structure of this part does not differ from that of the compound eyes of other shallow-water mysids (see Hallberg, 1977): the design is quite obviously that of a refracting superposition eye, with a clear zone separating the crystalline cones from the rhabdoms (see Nilsson, 1989, 1990). Each ommatidium has a thin corneal lens that, together with the crystalline cone, forms an optical unit. The proximal tips of the crystalline cones project slightly into the clear zone through holes in a double layer of screening pigment. The outer layer is whitish and probably gives the eye its sandy white colour. The inner layer is dark brown and probably serves as a field stop for the exit pupils of the optical units. The rhabdoms are short and spindle-shaped, with a conspicuous eighth cell rhabdomere (see Hallberg, 1977), which alone forms the distal 20 % of the length. Although the rhabdom layer in the normal part of the eye contains dark screening pigment, it does not appear to be enough to shield the individual rhabdoms completely from each other. Sitting on top of each rhabdom is a needle-like refracting structure, the ‘epirhabdom’, which is typical of the compound eyes of mysids (Hallberg, 1977).

The part of the eye behind the large posterior lens seems to be grossly distorted compared with the normal eye (Fig. 2). A giant crystalline cone obviously belongs to the large corneal lens, but, apart from being almost three times larger, this optical unit looks very similar to those in the normal part of the eye. A second crystalline cone, which appears to be functional, lies between the giant cone and the rest of the eye. This cone, for which there is no corneal lens, is responsible for the small secondary aperture seen in the live animal. The specialized posterior region also contains about 10 more-or-less reduced crystalline cones, which must be non-functional because they do not penetrate the pigment layer and are thus unable to supply light to the retina. Most of the reduced cones form a kinked row at the border with the normal eye, but one is placed at the opposite side of the giant cone (Fig. 2). As judged from the number of cell nuclei around the giant cone, this region contains many additional ommatidia that do not produce crystalline cones at all.

The retina receiving light from the modified posterior optics is an astonishingly dense array of very thin and long rhabdoms. There are 120 rhabdoms under the large cone, and their distal tips form a slightly concave retina which is distinctly separated from the retina of the normal eye (Fig. 2). There can be no doubt that the posterior specialization constitutes an acute zone of the eye. Of the 120 ommatidia, only one forms a complete optical unit. If the secondary functional cone of the posterior part is included, there are 118 ommatidia that only contribute to the retina and not to the optics. Serial cross-sectioning through the ommatidium with the giant cone surprisingly demonstrated that its corresponding rhabdom is not in the centre of the acute zone, but in the second or third row in from the junction with the normal eye.

Rhabdoms belonging to the acute zone are easily distinguished because they all point towards the giant cone, such that they come closest together distally and separate from each other proximally, quite contrary to the arrangement in the normal eye. The absence of epirhabdoms is another distinguishing feature, although a few rhabdoms in the row next to the normal eye have retained these enigmatic structures.

If, in a caudal cross section of rhabdoms, the centre of each rhabdom is joined with lines to its immediate neighbours, the retinal packing geometry is revealed (Fig. 3). Although the acute zone is much more densely packed and physically somewhat separated from the rest of the retina, the hexagonal packing array is continuous between the normal eye and the acute zone. This indicates that the formation of the acute zone has involved no loss of retinal elements, just a loss of optical units.

There are many differences between the rhabdoms of the acute zone and those of the normal eye region. Apart from being increasingly longer and thinner towards the centre of the acute zone, all rhabdoms belonging to the acute zone are surrounded by a distinct palisade of empty extracellular space (Fig. 4), whereas palisades are absent from rhabdoms in the rest of the eye. The acute-zone rhabdoms are shaped like long tapering rods, whereas those of the normal eye are stubby and spindle shaped. These differences imply that light guiding is important in the acute zone, but not in the normal eye. Retinal pigmentation in the acute zone displays a related peculiarity: there is no screening pigment between the most densely packed rhabdoms. This is probably an adaptation to reduce attenuation, because a significant fraction of the guided light is propagated outside the boundaries of thin rhabdoms (Nilsson et al. 1988; van Hateren, 1989).

Electron microscopy also reveals that the rhabdoms of both the acute zone and the normal eye have microvilli arranged orthogonally in alternating tiers (Fig. 4), which is the common arrangement in most malacostracan crustaceans (Waterman, 1961). The microvillar alignment is horizontal and vertical in all rhabdoms along the equator of the eye.

The proliferation zone of the eye is at the frontal margin. The oldest ommatidia in the eye would thus be located at the opposite margin, which is just ventral to the acute zone. This implies that the acute zone ommatidia are laid down fairly early during ontogenetic development. External observations of Dioptromysis larvae show the giant corneal lens in stage 3, but not in earlier stages.

Despite the extreme specializations of both optics and the retina in the acute zone, there are no obvious correlates in the thickness or stratification of the optic ganglia. The only notable feature is a fold on the lamina, making it concave below the acute zone (Fig. 2).

Owing to the dark retinal pigmentation, the live shrimps display a black pseudopupil in the ommatidia pointing towards the observer. The pseudopupil is thus an indicator, marking both the size and position of the eye’s aperture. With the animal mounted in a goniometer, the pseudopupil can be used for measurements of interommatidial angles in the normal part of the eye and for visual fields in the acute zone. Interommatidial angles measured in this way gave average values of 4.2° with very small variations across the normal part of eye. Semi-thin sections cut along equatorial rows of facets were used for control measurements of interommatidial angles. Lines connecting rhabdom centres with facet centres diverge by 4–5 ° between neighbouring ommatidia. Close to the acute zone the values decrease to about 3°.

The agreement between pseudopupil measurements and histological measurements provides a firm basis for calibrating the retinal sampling array in angular units. It is not immediately possible to compare the retinal sampling array in the acute zone with that of the normal eye. The reason is that image magnification could very well differ between the acute zone and the rest of the eye. The fact that all acute-zone rhabdoms point towards the pigment aperture of the giant crystalline cone certainly seems to allow for separate imaging. The pigment curtain projecting partly into the clear zone between the giant cone and the rest of the eye provides a further indication of an optically independent acute zone. The difference in clear zone depth adds to the evidence. It thus seems necessary to obtain an independent angular calibration of the sampling array of the acute zone. This was achieved simply by measuring the vertical and horizontal visual fields of the acute zone in live animals, using the pseudopupil in the giant corneal lens as an indicator (Fig. 5). The acute zone was found to cover a visual field of 25° vertically and 17° horizontally.

The anatomical array of rhabdoms in the retina was analysed on semi-thin sections. Tangential sections of the retinal surface, cut from slightly different angles in six different animals, gave the necessary data for reconstruction of the retinal sampling array in the posterior field of the right eye, including the acute zone. It turns out that the independent angular calibrations required the acute-zone retina to be magnified by 5 % relative to the retina of the normal eye. Observations of the pseudopupil moving from the giant corneal lens to the normal eye showed that there is neither a gap nor a visual overlap between the acute zone and the rest of the eye (Fig. 5). The sampling array of the acute zone was therefore placed to be contiguous with the rest of the retina in the angular map of Fig. 6. This seems to be correct because the triangular shape of the acute zone then fits perfectly to the margin of the normal eye visual field. The angular plot of Fig. 6 relies on the assumption that acute zone imaging is upright, as in the rest of the eye. Support for this assumption comes from the similarities in shape and proportion of the optical units and also from the behaviour of the pseudopupil (Fig. 5).

The angular sampling array of Fig. 6 resembles the anatomical pattern (Fig. 3), except for the relative size and placement of the acute zone. It is evident from Fig. 6 that the acute zone makes a smooth transition from the coarse sampling of the normal eye to the extremely dense sampling in the centre.

Observations with the animal mounted in a goniometer demonstrate an 8–10 ° field of binocular vision in the acute zone. This implies that the densest part of the retina is pointing directly back and thus coincides with the same part of the contralateral eye. In the normal eye there is hardly any binocular overlap: the pseudopupil slides out of one eye at the same time as it moves into the other. The animal has a total visual field of roughly 360 ° both vertically and horizontally, and there is only a small dead angle below the acute zone.

The variation in sampling and rhabdom angular subtense along the equator of the eye is plotted in Fig. 7A. From the normal eye to the centre of the acute zone, the separation of visual axes drops from 4.14 to 0.64 ° and the angle that each rhabdom subtends drops from 2.32 to 0.5 °. There is a similar gradient in rhabdom length (Fig. 7B). From the normal eye to the opposite edge of the acute zone, the length of the rhabdoms increases steadily. The longest rhabdoms in the acute zone are three times longer than those in the normal eye. For all optical considerations, the distal retinal surface, or image plane, can be assumed to be at the junction between the distal rhabdomere R8 and the main rhabdom segment. There are two reasons for making this assumption: (i) retinal pigmentation extends up to the level of the junction, and (ii) so does the palisade around the acute zone rhabdoms.

A further assessment of the performance of the acute zone relative to the rest of the eye requires information about the apertures through which light enters the eye. The function of the secondary aperture of the acute zone deserves some attention in this respect. In live animals, the secondary aperture appears dark over much the same angles as does the giant lens. It is, however, notable that the secondary aperture is dark brown over most of this angle, but neutral black when the pseudopupil is about to move over to the normal eye. A possible explanation is that the secondary aperture only contributes light to the retina in the angles where it appears black. The pigment curtain projecting into the clear zone from the giant cone actually prevents the crystalline cone of the secondary aperture from contributing any light to the majority of acute-zone rhabdoms. The brown colour seen over large angles in the secondary aperture would then simply be the curtain of screening pigment showing through the optics. The conclusion is that the secondary aperture contributes light only to a narrow transition zone on the retina and it does so through an opening that is much smaller than both the giant lens of the acute zone and the superposition aperture of the normal eye. The impact that the secondary aperture has on imaging must, therefore, be minimal and it can be safely ignored.

The aperture of the acute zone is the single 44 μm corneal lens. A reasonably accurate measure of the finest detail that can be reproduced by such a lens is the half-width of the diffraction blur spot, the Airy disc, which is given by λ/D (rad), where A is the wavelength of light and D is the diameter of the aperture causing diffraction (Snyder, 1977). If the wavelength is 500 nm, the Airy disc behind the 44 μm corneal lens has a half-width of 0.65 ° of visual angle. The rhabdom separation in the densest part of the acute zone is 0.64 °, implying that the system is diffraction-limited (Fig. 7A).

In the normal part of the eye the facet diameter is 16 μm in all regions. This produces an Airy disc of 1.8 ° half-width, but the rhabdom separation is more than 4 °, and diffraction is not the limiting factor here (Fig. 7A). Since it is a superposition eye, the photon catch is not dependent on facet size but on the superposition aperture, which has a diameter of 3–4 facets along the equator of the eye (estimated from the black part of the pseudopupil). This makes a light-admitting aperture of about 56 μm, which is actually bigger than that of the acute zone. There is, however, a dorsoventral gradient in size of the superposition aperture ranging from 40 μm dorsally to 100 μm ventrally. There is thus a very definite ‘up’ and ‘down’ in the superposition eye.

The difference in closeness to a diffraction-limited design points towards an optimization to lower light intensities in the normal eye than in the acute zone (Fig. 7A). This is supported by the observation that dark-adapted eyes display an eye glow in the normal eye, but not in the acute zone. The low photon catch in the narrow acute-zone rhabdoms is probably not adaptable to vision at low light intensities.

Another optically important parameter is the focal length. In a spherical superposition eye this is half the eye radius or, more accurately, the radius of the retinal surface (Land et al. 1979). With an eye diameter of 400 μm, the focal length becomes 100 μm, and this agrees exactly with the radius of the retinal surface. The focal length of the acute zone can be derived from the image magnification: f=x/[2tan(θ /2)], where f is the focal length, x is a known distance in the image, and θ is the angle that x subtends at the nodal point. Using the vertical extent of the acute-zone retina as the known distance x, the focal length becomes 95 μm. Recall that the retina of the acute zone was magnified by a factor of 1.05 relative to the normal eye in order to reconstruct the angular sampling map in Fig. 6. This would make the focal length of the acute zone 100 μm/1.05, which comes to 95.2 μm, in perfect agreement with the previous estimate.

Observations of animals kept in tanks with rocks and algae from the catch site demonstrate a primarily epibenthic life-style. Dioptromysis seems to prefer horizontal clearings in the algal mat. When undisturbed, they mostly remain in one place on the substratum, showing no sign of life other than occasional eye movements. In a dense population, the animals apparently disturb each other. If one individual comes too close to another, the one being approached rapidly swims up to the intruder, and for a few seconds the two swim upwards and around each other in a frenzied manner before they settle at some distance from each other.

A few crude attempts were made to test their reaction to simple visual stimuli. The fish tank with the shrimps was exposed to the midday sun, only a few hundred metres from the shallow catch site. With these presumably normal light intensities, moving and stationary visual stimuli were presented just outside the glass walls of the tank. The stimuli were black and white paper discs of various sizes mounted on thin posts. The outcome of these trials was somewhat disappointing because the shrimps took no major action in response to any stimulus, not even to a large fast-moving disc. The only obvious responses were rapid eye movements when something changed in the visual surrounding. Unfortunately, the shrimps were too small, both for the video camera and for the naked eye, to determine the nature of the eye movements.

Being convinced that Dioptromysis is not particularly interested in paper discs, we took another approach: gut content analysis. From the few individuals that had their stomachs teased apart and examined microscopically, the diet was found to be diatoms and epiphytic cyanophyta. There was also some unidentified amorphous material, but no obvious remains of the prey that we had hoped to find.

The search for a behavioural explanation of the backward-pointing acute zone gave some useful by-products. Video recordings of live animals taken from various angles revealed the normal body posture. When Dioptromysis is sitting on a horizontal surface, which they seem to prefer, the abdomen is held straight and horizontal. From the visual field measurements described earlier, we found the ventral margin of the acute-zone visual field to coincide with the axis of the abdomen. This makes the centre of the acute zone point about 12 ° above the horizon behind the animal.

Investigations of the extent by which eye movements may alter the direction of view of the acute zone were made with single animals placed in a small vial with sea water. Although this is hardly a natural environment, it did allow close observations of eye movements through a dissecting microscope. For most of the time the eyestalks were held in the position shown in Fig. 1 but, occasionally, rapid eye movements were observed. The eye movements were recorded on video and analysed frame by frame. The results reveal two degrees of freedom of eye movement: turning in the horizontal plane and rotation around the axis of the eyestalk. Both types of eye movement were perfectly coordinated between left and right eyes. The binocularity of the acute zone thus appears to be preserved at all times. There even seems to be a mechanical connection between the two eyes because if, in a recently dead animal, one eyestalk is pushed forward in the horizontal plane, the other automatically turns backwards. The maximum turning and rotation of the eyestalks recorded on video was quite impressive (Fig. 8). In the horizontal plane, the eyestalks were seen to turn ±60 ° from their rest position. Eyestalk rotation was as much as 130 °, always making the dorsal part of the eye rotate forwards. This means that the acute zone can be made to point forwards about 40 ° above the horizon. Of the 14 recorded occasions of eye movement, 11 were combinations of turning and rotation. The change of eye orientation occurred very rapidly and the new orientation was held for 0.4–1.3 s. The 130 ° frontward rotation shown in Fig. 8 was completed in 0.16 s, after which the eye remained stationary for 0.4 s and then returned to the resting position in 0.07 s. Since the animals were kept in a 10 mm vial with only 4 mm of water, it is possible, and even likely, that the recorded eye movements were initiated by stress rather than by more natural causes. The results, therefore, can only be used as indications of by how much and how fast Dioptromysis is able to move its eyes. It is still possible that the eyes can be moved both further and faster than they did in the recordings.

Large eyes generally perform better than small eyes simply because the lenses are bigger (Kirschfeld, 1976). Diffraction, which is inversely proportional to the diameter of the imaging lens, allows more fine detail to be reproduced behind a larger lens. Light capture, which determines photon shot noise, is also improved by a larger lens (Snyder, 1977). For any size of eye the best solution to vision is thus a single lens supplying light to the entire retina. If, as in apposition compound eyes, the available surface area of the eye is divided into one private lens for each point sampled in the image, then the space taken by the eye is utilized in the least economic way possible. The superposition-type of compound eye offers the same potential for good photon capture as the camera-type eye does. But, in terms of diffraction, the small facets make superposition eyes no better than apposition eyes. This is the probable reason why superposition eyes are predominantly found in animals that are active in dim light, where photon catch is the prime limitation to visual performance (Land, 1981; Nilsson, 1989; Warrant and McIntyre, 1993). However, at high intensities, when diffraction dictates the optimal design, superposition eyes can be pushed to better performance if the array of rhabdoms is made independent of the array of facets and crystalline cones. Fewer and larger facets and crystalline cones will decrease diffraction blurring and allow for thinner, more numerous and more densely packed rhabdoms. As mentioned in the Introduction, this is exactly what seems to have happened in the superposition eyes of a few mayflies and euphausiid shrimps. The ultimate development is that found in the acute zone of Dioptromysis paucispinosa: a large single facet and crystalline cone supplying light to a common retina of numerous rhabdoms. There can be no further improvement along this line and, in the acute zone, Dioptromysis has reached the ideal design for a compound eye. Ironically, the ideal compound eye is not really a compound eye at all. It has been turned into a simple eye in order to exploit the advantages of imaging through a single aperture. There is thus little reason for surprise over the unique design in Dioptromysis. It would be more appropriate to wonder why Dioptromysis does not share its ingenious solution with other crustaceans or with insects.

From the behaviour of the pseudopupil (Fig. 5), and also from anatomy, there are good reasons to believe that the optics of the acute zone has retained the upright imaging present in normal superposition ommatidia. This seems like an unnecessary complication when there is just a single facet. Magnification, brightness and diffraction blur of the optical image in the acute zone would be perfectly mimicked by a single thin lens of 95 μm focal length. The only difference between such a lens and the real optics of the acute zone is the image orientation: inverted behind the single lens and upright behind the real optics. If Dioptromysis had managed neurally to switch from an upright to an inverted interpretation of the acute-zone image, they could have done away with the crystalline cone and achieved the same optical performance with just the corneal lens if it had a focal length of 95 μm. In this way, the physical length of the optical system would have been significantly shortened (Fig. 9). On the question of why this has not happened, the obvious answer is the absence of functional intermediates between upright and inverted images, regarding both the optics and the neural connections. Making both changes in a single miraculous mutation would be a bit much to ask, and there is no selection favouring such a development in numerous small steps. As a result, Dioptromysis is stuck with its unnecessarily complicated acute-zone optics.

A three-lens model of the acute-zone optics is derived in Fig. 9. The model produces upright images with the same brightness, resolution, magnification and visual field as the real system. The physical dimensions of the model also fit well into the space occupied by the corneal lens and crystalline cone. A model with a few thin lenses is, of course, only a crude representation of the crystalline cone, which must rely on continuous refraction in a radial refractive index gradient. The model, nevertheless, shows that we can be confident with our assumption of an upright image.

A useful by-product of modelling is the F-number, which determines the angle of the cone of light that reaches the retina from a point source. The angle of incidence of the marginal ray to the optical axis, θ, is related to the F-number, F, by: 1/(2F)=tan θ. With an F-number of 2.16, θ becomes 13 °, making a total light cone of 26 °. The immediate question is whether the long thin rhabdoms can trap and guide light over such a large angle. The largest angle of light that can be trapped and guided by a cylindrical rhabdom, θ_max, is determined by the critical angle of total internal reflection inside the rhabdom. The maximum angle can be calculated by: sinθ_max=√[(n_r/n₀)²-1] (Warrant and McIntyre, 1993), where n_r and n₀ are the refractive indices of the rhabdom and its surrounding medium respectively. If the surrounding refractive index is that of water, n₀=1.335, then an incident angle of 13 ° requires a rhabdom refractive index of 1.368 in order to trap all the light from the optical system. Reliable estimates of rhabdom refractive index are exclusively from insects and centre around 1.36 (see Nilsson and Howard, 1989). The required value in Dioptromysis is only slightly higher and is perfectly realistic. These calculations do show, however, that the acute zone rhabdoms are operating at the very limit for light guiding, thus explaining the presence of palisades around these rhabdoms.

In the normal part of the eye, the superposition aperture has a diameter of 56 μm in the equatorial region and the focal length is 100 μm. This gives an F-number of 1.79 and a cone of light on the retina of 31.3 °. Clearly, this angle is too wide to allow for complete light-guiding in the rhabdoms. Not surprisingly, palisades are absent around these rhabdoms, and there is obviously no attempt made to guide light in the retina of the normal eye.

The optical performance of the acute zone and the rest of the eye can be analysed and compared by calculating two important values, the resolution and the sensitivity (Land, 1981; Warrant and McIntyre, 1993). These can be calculated from the anatomical and optical data already obtained. The resolution, or spatial sampling frequency, expressed as cycles per degree, is 1/(√3 Δ ϕ) for a hexagonal array of photoreceptors (Snyder, 1977), where Δ ϕ is the divergence of visual axes of neighbouring rhabdoms. The retinal sampling frequency of the normal superposition eye is only 0.14 cycles degree⁻¹, whereas the centre of the acute zone reaches 0.9 cycles degree⁻¹. These sampling frequencies can be compared with the highest spatial frequencies that can be passed through the facet lenses. Diffraction sets the ultimate limit to this cut-off frequency (Snyder, 1977), and it is given by π D/180λ, where D is the facet diameter and A is the wavelength of light, here taken to be 500 nm. The 16 μm facets of the normal eye can pass spatial frequencies up to 0.56 cycles degree⁻¹. Since the sampling frequency is much lower (0.14 cycles degree⁻¹), diffraction does not impose a limit to vision in the normal eye. In the acute zone, however, the 44 μm facet lens has a cut-off frequency of 1.54 cycles degree⁻¹, which is not far from the sampling frequency of 0.9 cycles degree⁻¹. It should be noted here that at the optical cut-off frequency there is no image modulation for any object. For something to be visible to the animal, the object must make a modulation of the retinal signal which exceeds the photoreceptor’s noise. Allowing for a certain amount of noise, and also for objects of moderate contrast, the highest useful sampling frequency should be clearly below the optical cut-off frequency. It thus seems that the centre of the acute zone is close enough to the diffraction limit to exploit the full optical potential of the 44 μm aperture. The variation in sampling frequency along the equator of the eye is plotted in Fig. 10A. The resolution of the acute zone is impressive even in relation to the eyes of large insects (Land, 1989b). Only the dorsal acute zones of large dragonflies will safely win a competition (Sherk, 1978).

Apparently the centre of the acute zone is pushing vision to its very limit, not only for diffraction but also for photon noise. This means that there is no way to improve visual performance unless the giant corneal lens is made even larger. If this were done, the focal length would have to be increased too, because the F-number is already at the limit for light-guiding in the rhabdoms. However, the acute zone already occupies considerable depth in the eye. Evidently, Dioptromysis has reached every physical limit in its attempt to squeeze extreme visual capacity into its 0.4 mm eyes.

Comparing the acute-zone centre with the rest of the eye, reveals a 6.4-fold better resolution but about a log unit lower sensitivity. A human looking through a pair of modern compact binoculars would experience a similar increase in resolution and also a drop in sensitivity. The binocular overlap between the acute zone of the two eyes, and the restricted visual field, makes vision through these zones even more like that through a pair of binoculars.

Among the most common reasons for vision are general navigation and detection of prey, predators and mates. Pronounced acute zones with narrow visual fields, like that of Dioptromysis, are thoroughly unsuited for general navigation and for seeing predators or other dangers (Land, 1989b). The small visual field in particular would give a predator good opportunities to sneak up from a direction outside the visual field. In addition, the low sensitivity makes the acute zone useful only under favourable conditions. A prey relying on the security gained from such an acute zone would be a predator’s dream and definitely its breakfast.

There can be no doubt that the acute zone is designed for finding mates or prey. The fact that the acute zone is equally developed in males and females speaks against its use in courtship, although it does not entirely rule out the possibility. The most plausible explanation must be that Dioptromysis is a predator using its high resolution to spot small prey at long distances. The binocular overlap between the widely separated acute zones offers ideal conditions for computation of object distance (Schwind, 1989), which is yet another indication of a prey detector. It is only unfortunate that neither the gut content analysis nor the behavioural studies were successful in providing a candidate prey.

An additional complication is of course the backward orientation of the acute zone. In Fig. 11 both sides of the sampling array behind the animal are plotted on the visual sphere. The visual field of the acute zone rests on the horizon behind the animal, just above its abdomen. For Dioptromysis to pursue a prey it would have to move backwards, and it would reach the prey in a highly unconventional manner! The behavioural studies do not in any way support such a use of the acute zone.

A solution to the problem comes from the eye-movement studies. The eyestalks can be turned through 60 ° to either side and rotated by 130 ° around their axes such that the acute zone points forward about 40 ° above the horizon. The values come from a very limited number of recorded eye movements, so it is possible that the eyestalks can be rotated even further. The part of the visual field that then becomes accessible to the acute zone is illustrated in Fig. 12. Because the horizontal turning of the eyestalk has no effect when the acute zone is rotated to a dorsal position, the accessible visual field is effectively split into two triangular parts, one anterior and one posterior. Hence, the primary direction of interest is not upwards, because there the eye movements only have one degree of freedom. It is more likely that Dioptromysis uses its acute zone primarily for forward vision.

For what reason then is the acute zone normally held pointing backwards? The low sensitivity of the acute zone may offer the explanation here. As argued above, the acute zone is optimized for small target detection at high intensities, but is unsuited for other visual tasks. The forward visual field is probably too important for normal vision to have it constantly occupied by a highly specialized zone of low sensitivity. If this interpretation is correct, the acute zone is held in the backward-pointing position when it is not in use and occasionally turned forwards to analyse potential prey and to guide pursuit. As fantastic as this hypothesis may seem, there is really no other explanation to the large, rapid and coordinated eye movements.

The binoculars analogy becomes even more appropriate in this new context. A person with binoculars, say a bird-watcher walking through a forest, would probably carry the binoculars on a strap around the neck. Only when something potentially interesting is to be seen, and the conditions permit it, would he actually look through the binoculars. An attempt to use the binoculars while walking would rapidly prove the importance of large-field general vision. It seems that evolution has taught Dioptromysis a similar lesson.

There are a few odd consequences of the rotating eye that deserve attention. Because the proliferation zone of the eye, which is typically frontal in crustaceans (Elofsson and Dahl, 1970), occupies this location when the eye is in the resting position, the acute zone can hardly have originated as a frontal specialization. At the most, it may have started as a dorsal specialization that gradually has moved backwards as the manoeuvrability of the eyestalk has increased. During such a process, the nervous system must have been gradually altered to interpret correctly a caudal eye region that is occasionally turned frontally to be used. The dorsoventral size gradient of the superposition aperture demonstrates that there is a functional up and down in the normal eye, which makes sense only when the acute zone is in its caudal rest position. When the eyes are rotated to make the acute zone aim forwards, the normal eye is very definitely upside down and unmatched to the downwelling light.

Turning the eye upside down also has other, possibly more serious, consequences. Motion detector neurones which register the flowfield around the moving animal, would experience a reversal between backward and forward motion. Having the entire spatial representation suddenly shifted by 130 ° is another intricate problem which Dioptromysis must have solved.

The intriguing fact is that the orientation of the normal eye makes best sense when the acute zone is pointing backwards, whereas the acute zone itself makes best sense when it is pointing forwards. Are the two eye regions switched on and off depending on eyestalk orientation? And what happens to vision during the short time it takes to change from backward-to forward-pointing acute zone? At least the last question lends itself to some analysis. All the recorded rotations of the eyestalks occurred very fast. Typically, 90 ° of rotation was accomplished within 0.1 s, which gives an angular velocity of 900 degrees s⁻¹. For the eye to see during the rotation, the temporal sampling frequency should be roughly the angular velocity times the spatial frequency. For the normal eye, this would mean a temporal sampling frequency of 126 cycles s⁻¹, which is perhaps not unreasonable. But the centre of the acute zone would need to sample at a rate of 810 cycles s⁻¹, which is clearly out of reach even for the fastest photoreceptors (Howard et al. 1984; Laughlin and Weckström, 1993) and theoretically quite impossible with the poor photon catch of this region. Consequently, at least the acute zone must be neurally ignored during the rapid rotations of the eyestalk. It thus seems that the optic lobes of Dioptromysis need several kinds of neural circuitry that other visual systems do not.

We are grateful to Dr Eric Warrant for critical reading of the manuscript and to Mrs Rita Wallen for the histological work. Travel and work at the Carrie Bow Cay marine station was partly financed by the Swedish Fulbright Commission and the Smithsonian Institution’s Caribbean Coral Reef Ecosystem Program (CCRE), which is partly supported by the Exxon Corporation. This is contribution number 399 from the CCRE, Smithsonian Institution. The work was also supported by The Swedish Natural Science Research Council.