497 The Journal of Experimental Biology 202, 497–511 (1999) Printed in Great Britain © The Company of Biologists Limited 1999 JEB1713 PHYSIOLOGICAL OPTICS IN THE HUMMINGBIRD HAWKMOTH: A COMPOUND EYE WITHOUT OMMATIDIA ERIC WARRANT1,2,*, KLAUS BARTSCH3 AND CLAUDIA GÜNTHER3,‡ of Zoology, University of Lund, Helgonavägen 3, S-22362 Lund, Sweden, 2Institute for Advanced Study, Wallotstrasse 19, D-14193 Berlin, Germany and 3Lehrstuhl für Biokybernetik, Universität Tübingen, Auf der Morgenstelle 28, D-72076 Tübingen, Germany 1Department *e-mail: [email protected] ‡Present address: Public Communication Networks Group, Siemens AG, Siemensdamm 50, D-13623 Berlin, Germany Accepted 7 December 1998; published on WWW 3 February 1999 Summary angular packing of the overlying corneal facets. In fact, this The fast-flying day-active hawkmoth Macroglossum eye has many more rhabdoms than facets, with up to four stellatarum (Lepidoptera: Sphingidae) has a remarkable rhabdoms per facet in the frontal eye, a situation which refracting superposition eye that departs radically from the means that M. stellatarum does not possess ommatidia in classical principles of Exnerian superposition optics. the accepted sense. The size of the facets and the area of Unlike its classical counterparts, this superposition eye is the superposition aperture are both maximal at the frontal highly aspherical and contains extensive gradients of retinal acute zone. By having larger facets, a wider resolution and sensitivity. While such features are well aperture and denser rhabdom packing, the frontal acute known in apposition eyes, they were thought to be zone of M. stellatarum provides the eye with its sharpest impossible in superposition eyes because of the imaging and brightest image and samples the image with the densest principle inherent in this design. We provide the first photoreceptor matrix. It is this eye region that M. account of a superposition eye where these gradients are stellatarum uses to fixate flower entrances during hovering not only possible, but also produce superposition eyes of and feeding. This radical departure from classical unsurpassed quality. Using goniometry and Exnerian principles has resulted in a superposition eye ophthalmoscopy, we find that superposition images formed which has not only high sensitivity but also outstanding in the eye are close to the diffraction limit. Moreover, the spatial resolution. photoreceptors of the superposition eyes of M. stellatarum are organised to form local acute zones, one of which is frontal and slightly ventral, and another of which provides improved resolution along the equator of the eye. This Key words: hummingbird hawkmoth, Macroglossum stellatarum, superposition eye, compound eye, diffraction limit, optics, vision. angular packing of rhabdoms bears no resemblance to the Introduction The hummingbird hawkmoth Macroglossum stellatarum is one of Europe’s most delightful insects. Active almost exclusively in bright daylight, this moth is not only a fast and aerobatic flier but also an excellent hoverer, sucking nectar from flowers in much the same way as its namesake the hummingbird. Its visual behaviour has been the subject of study since the early part of this century (Knoll, 1922), more recently with regard to visual stabilisation of flight (Kern, 1994, 1998; Kern and Varju, 1994, 1998; Farina et al., 1995), distance perception (Pfaff and Varju, 1991; Farina et al., 1994), colour vision (Kelber, 1996; Kelber and Henique, 1999) and flower recognition (Kelber, 1997; Kelber and Pfaff, 1997). Whilst much information has been obtained regarding the visual behaviour of M. stellatarum, very little is known about its eyes. There are many paradoxes associated with the eyes of M. stellatarum. First, despite being day-active, it has superposition eyes with well-developed tapeta, a compound eye design more typical of insects active at night. Second, the eyes are extremely aspherical and inhomogeneous, and thereby fail to adhere to the accepted optical construction necessary to form a superposition image on the retina. In the accepted model, first developed by Sigmund Exner over 100 years ago (Exner, 1891), superposition eyes are spherical and maintain a constant focal length and angular magnification throughout the eye. Most superposition eyes conform more or less to this classical model. In a future publication (E. Warrant, K. Bartsch and C. Günther, in preparation), we will show that the eyes of M. stellatarum not only form crisp superposition images but also possess the sharpest angular sensitivities yet known for a superposition eye. In the present study, we take a closer look E. WARRANT, K. BARTSCH AND C. GÜNTHER at the optics of the eye in an attempt to understand how Exner’s rules can be broken and still permit excellent superposition vision. In attempting to unravel this paradox, we discovered that the eye had two remarkable properties. First, as in many apposition eyes, there are gradients of resolution and sensitivity throughout the eye. Gradients in resolution were previously deemed impossible for superposition eyes. Second, there is not one corneal facet per rhabdom as in a conventional compound eye, but as many as four, the exact ratio depending on the location in the eye. Because an ommatidium contains one rhabdom and one facet, this means that M. stellatarum does not have ommatidia in the functional sense, and the concept of an interommatidial angle is meaningless. The eyes of M. stellatarum represent a remarkable optimisation of the superposition design for vision in bright light, and their physiological optics are described here for the first time. An abstract of this work has been published previously (Bartsch and Warrant, 1994). Materials and methods Animals Macroglossum stellatarum L. (Lepidoptera: Sphingidae) was reared in a laboratory culture that was regularly restocked with wild-caught moths from Southern Europe. Full details of the rearing and maintenance of hummingbird hawkmoths can be found elsewhere (Farina et al., 1994). Coordinates All visual field coordinates used in this study comply to the conventions given in Fig. 1. Angles of latitude and longitude were defined with the origin (0 °,0 °) located at the lateral (side) point of the eye (L). Longitudes anterior (A) to this point are positive, those that are posterior (P) are negative. The same convention applies to latitude: latitudes dorsal (D) of the lateral point are positive, those that are ventral (V) are negative. Goniometry Corneal measurements of eye glow area, facet diameter and inter-facet angle were made using a large goniometer together with a low-power microscope whose objective could be placed at any position on the surface of an imaginary hemisphere centred on the eye of a living hawkmoth. Attached to the microscope was a camera. The hawkmoth was restrained within an Eppendorf tube whose tip had been sliced off to allow the moth’s head to protrude. The head was lightly fixed to the tube with a small quantity of beeswax to prevent it from moving. Excess scales and hairs were carefully plucked from the head to allow a full view of the eye. Chalk dust was then sprinkled lightly onto the eye to provide landmarks. A mount holding an oriented glass coverslip was then placed over the end of the objective. This coverslip, oriented at 45 ° to the objective’s long axis, acted as a beam splitter which diverted orthodromic light from a small lamp, placed to the side of the objective, down onto the eye. This light caused a bright eye glow which could be seen through the microscope. The details D AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA Longitude AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA L AAAAAAAAAAAAAAAAAAAAAA 80° 70° 60° 50° P 40° Latitude 498 30° 20° -40° -30° 80° 70° 10° -20° -10° 0° A 10° 20° 30° 40° 50° 60° -10° -20° V Fig. 1. The coordinate system used in this study. The origin (0 °,0 °) was defined at the lateral point (L) of the eye, and angles of latitude and longitude were defined in the manner shown. D, dorsal; V, ventral; A, anterior; P, posterior. and operation of the goniometer are described by Dahmen (1991). The experimental procedure was as follows. The goniometer was used to move the microscope through steps of 10 ° longitude. At each longitude, the microscope was moved through steps of 10 ° latitude, beginning as far ventrally as possible and progressing dorsally until the microscope had no further travel. At each position, the eye glow was photographed, and the photographs were used to determine the size, shape and facet content of the eye glow. Facet diameter was also determined at each position. On the basis of the number of facets traversed by the eye glow during the 10 ° transition from one photograph to the next, it was possible to measure the angle separating neighbouring facets at each eye position (using a method analogous to that used by Horridge, 1978, and Dahmen, 1991, in apposition eyes). Ophthalmoscopy Retinal measurements of line-spread functions, point-spread functions and the angular packing density of rhabdoms were made using ophthalmoscopic techniques (for a full explanation, see Land, 1984a). These methods allow the retina, and any images formed on it, to be viewed through the eyes’ own optics. A short description of the principal methods used will be given below. Specific details of some procedures – best explained in the context of the Results – are given at the appropriate places in the Results section. For measurements of the packing density of rhabdoms, the Physiological optics in the hummingbird hawkmoth ophthalmoscope was a converted Zeiss photoscope. This contained a half-silvered mirror which diverted light from a laterally placed light path through the objective (Fig. 2). The light was produced by a xenon arc lamp and filtered by an interference filter transmitting light in the wavelength range 550–650 nm. Hawkmoths, restrained as described above, were placed on a small goniometer that could be used together with the rotating microscope stage to position the moth at a chosen latitude and longitude under the objective. A Bertrand lens inserted into the beam path (Fig. 2) allowed the retina to be viewed in angular space. Slits, pin-holes, letters and gratings placed at the position of the angular diaphragm could then be imaged on the retina. Images so produced could be intensified by an image intensifier, collected by a CCD camera, enhanced with an electronic image-analysis system and printed on a video printer. Removal of the Bertrand lens allowed the corneal surface to be viewed. For optical measurements of rhabdom acceptance functions, the ophthalmoscope was a bench-mounted arrangement of Spindler and Hoyer optical components (for a full description, see Land, 1984a). Images were photographed with an Olympus OM-2 camera using Kodak TMAX400 black-and-white slide film and developed in TMAX developer. The resulting negatives, which contained an intensity range of over 3 logarithmic units (sufficient for quantitative microdensitometry), were illuminated from below by a 0.075 mm wide circular pin-hole of light. Densitometry was performed by reading the voltage output of a photodiode placed above the negative as the light source was moved beneath the negative in 0.05 mm steps. To convert voltage readings into intensities and to standardise readings between different films, a slide made up of strips of known neutral density (strips made from gelatin) was photographed on every film. This slide provided the calibration curve for the film. Electron microscopy Whole eyes were placed for 2 h at 4 °C in standard fixative (2.5 % glutaraldehyde and 3 % paraformaldehyde in 150 mmol l−1 sodium cacodylate buffer, pH 7.2). Following a Fig. 3. The eye of Macroglossum stellatarum in horizontal section. This longitudinal view, in the plane of the eye’s equator, very clearly shows the highly nonspherical nature of the eye. Because neither the retina (r) nor the cornea (c) is spherical or concentric, the clear zone of the eye (cz) varies in size throughout the eye. The lamina (l) and medulla (m) of the optic lobe are also visible. a, anterior; p, posterior. Scale bar, 200 µm. Video printer 499 Image analysis CCD camera Image intensifier Angular diaphragm Xenon arc lamp Shutter A AA A Field diaphragm Bertrand lens Half-silvered mirror Spectral Lens filter Objective lens Goniometer with animal Fig. 2. The ophthalmoscopic apparatus. A converted Zeiss photoscope, containing a half-silvered mirror, diverted light (600 nm, ∆λ=100 nm) from a xenon arc source to the eye of a hawkmoth placed on a goniometer beneath the objective. Placement of a Bertrand lens in the beam path allowed the retina to be imaged. Slits, pin-holes, letters and gratings placed at the position of the angular diaphragm could then be imaged on the retina. Images could be intensified, captured by a CCD camera and printed on a video printer. A regular camera could also be used in place of the intensifier and CCD camera. rinse in buffer, the eyes were added to 1 % OsO4 for 1 h. Dehydration was performed in an alcohol series, and the eyes were embedded in Araldite. Ultrathin sections for electron microscopy were stained with lead citrate and uranyl acetate. Results An aspherical superposition eye The refracting superposition eye of M. stellatarum is highly aspherical (Fig. 3), and ommatidial anatomy and optics vary 500 E. WARRANT, K. BARTSCH AND C. GÜNTHER throughout the eye. The aspherical nature of the eye is clearly seen in horizontal (equatorial) longitudinal sections (Fig. 3). Neither the corneal surface nor the retinal surface is concentric or spherical, and the size of the clear zone and the lengths of the rhabdoms vary throughout the eye. In this respect alone, the eyes depart radically from the classical Exnerian norm of sphericity and homogeneity. As we shall see, this departure also extends to other aspects of the eye. Despite this, angularsensitivity functions with acceptance angles as small as 1.3 ° can be recorded from the photoreceptors, indicating that image quality on the retina is very good (the anatomy and physiology of the eye will be expanded upon by E. Warrant, K. Bartsch and C. Günther, in preparation). Optical image quality To assess image quality, we used the ophthalmoscopic techniques pioneered for insect eyes by Land (1984a). These methods allow the retina, and any images formed on it, to be viewed through the eyes’ own optics. One way of assessing the optical quality of the eye is to use the ophthalmoscope to look at retinal structures, such as the array of photoreceptors. If the array is clearly visible, the optical quality is good. Because the image we see has passed only once through the optics of the eye (outwards from the retina), any measurements made from these images are referred to as ‘single-pass’. An alternative way of assessing the optical quality is to place objects (such as points, lines and gratings) outside the eye and then examine their images on the retina. Such measurements are ‘doublepass’ because light from an object is imaged twice by the optical system: once on its way to the retina, and once again on its way back out. The image of relevance to the animal is that formed on the inward journey to the retina: the single-pass image. Luckily, any double-pass images we capture in the ophthalmoscope can be converted to single-pass images using standard procedures (which are very clearly explained by Land, 1984a). As a qualitative indication of image quality in M. stellatarum, we projected letters and square-wave gratings Fig. 4. Ophthalmoscopic images of the retina in Macroglossum stellatarum; lateral eye (0 °,0 °). (A) The clearly visible matrix of rhabdoms. (B) A musical ‘natural’ sign (height 18.4 °) imaged on the retina. The original object was placed in the plane of the ophthalmoscope’s angular diaphragm (see Fig. 2). Scale bar (for both parts), 4 °. onto the retina using the ophthalmoscope (Figs 4, 5). The retinal photoreceptor array of the lateral eye (0 °,0 °; see Fig. 1) was clearly visible (Fig. 4A), indicating that the eyes are well focused. It also indicates that the quality of the optical system in this part of the eye is better than the retinal ‘grain’, i.e. that the angular separation of neighbouring rhabdoms (∆φ) is greater than the angular half-width (in object space) of the receptive field of each rhabdom (∆ρ). According to Land (1984a), the photoreceptor array will only be visible when ∆φ exceeds 0.9∆ρ. In the lateral eye ∆φ≈2.0 ° and ∆ρ≈1.8 ° (see below), so this indeed seems to be the case. In this regard, M. stellatarum can be compared with two other diurnal lepidopteran species (measurements made by Land, 1984a): the eyes are at least as well focused as those of the agaristid moth Phalaenoides tristifica and somewhat better focused than those of the skipper butterfly Ocybadistes walkeri. Interestingly, in the frontal part of the retina of M. stellatarum, the packing of the rhabdoms becomes much denser and the ophthalmoscope can only just resolve the photoreceptor array. It seems that in this part of the retina ∆ρ approaches or is slightly larger than ∆φ. This notion is supported by electrophysiological measurements of ∆ρ (1.3–1.4 °: E. Warrant, K. Bartsch and C. Günther, in preparation) and optical measurements of ∆φ (approximately 1.1 °; see below). Double-pass images of objects placed outside the eye are Fig. 5. High-contrast square-wave gratings of various angular periods imaged on the equatorial frontal retina (longitude 70 °). (A) 12 ° period (0.08 cycles degree−1); (B) 8 ° period (0.13 cycles degree−1); (C) 6 ° period (0.17 cycles degree−1); (D) 4 ° period (0.25 cycles degree−1). All gratings are clearly resolvable on the retina, except the 4 ° grating whose contrast has declined markedly. Scale bar (for all parts), 5 °. Physiological optics in the hummingbird hawkmoth also clearly visible, with a musical ‘natural’ sign of 18.4 ° height being easily seen (Fig. 4B). When high-contrast squarewave gratings are projected (Fig. 5), those of lowest spatial frequency (0.08 cycles degree−1) are easily resolved (Fig. 5A), although the sharp edges of the grating object are lost in the image (due to diffraction). Gratings are still very clear even at 0.17 cycles degree−1 (Fig. 5C), but by 0.25 cycles degree−1 they are difficult to discern (Fig. 5D). Quantitative measurements of optical quality can be made by optically measuring the acceptance functions of single rhabdoms. This was performed by observing the image of a 0.49 ° point source centred on a single rhabdom in the lateral eye (Fig. 6, inset) and measuring the distribution of light in this image using densitometry. Whilst almost all of the light in the photographed image arises from the single central rhabdom, some light does arise from the neighbouring six rhabdoms. Because the light is emitted through the same aperture from which it entered, the resulting light distribution should be identical to the rhabdom’s acceptance function whose halfwidth is ∆ρ (the acceptance angle). Moreover, this distribution should also be ‘single-pass’ because a single rhabdom accepts and emits almost all of the incoming point source blur-circle. Note that the image shown in the inset of Fig. 6 is somewhat elliptical, a phenomenon that is often encountered. Acceptance functions were measured by making a densitometric scan along the long axis of the elliptical image. The scan appears roughly Gaussian (circular symbols in Fig. 6) and, in fact, can be 1.0 Relative intensity 0.8 Rhabdom acceptance function 0.6 1.81° 0.4 0.2 0 -6 -4 -2 0 2 Angle (degrees) 4 6 Fig. 6. The acceptance function of a single rhabdom in the lateral eye (0 °,0 °) of Macroglossum stellatarum measured optically from the image of a point source on the retina (inset). Point-source images, which were essentially single-pass (see text), were generated by centring the image of a pin-hole of light (0.49 ° wide) on a single rhabdom. Experimental data (circles) were obtained from several densitometric scans across the image shown in the inset. A theoretical acceptance function (heavy continuous line) was then derived by fitting these data to equation 1 (see text). This function, of half-width 1.81 °, fits the data better than a single Gaussian function of the same half-width (thin continuous line). The inset image measures 4 °×4 °. 501 accurately fitted by a function R(θ) composed of the sum of two Gaussian functions, one having a higher amplitude and narrower half-width, and the other having a lower amplitude and broader half-width: 2 θ 2 + A exp − –– θ , R(θ) = A1exp − –– 2 a2 a1 冤 冢 冢冤 冤 冢 冢冤 (1) where θ is a variable (angle), A1, a1, A2 and a2 are constants and A1+A2=1. The half-width hi of each Gaussian function is related to the constant ai (the ‘natural radius’) via the simple relationship ai=0.6hi. The receptive field data shown in Fig. 6 can be accurately fitted by equation 1 with the following bestfit constants: a1=0.89 °, A1=0.621, a2=1.65 ° and A2=0.379 (correlation coefficient r2=0.98). The half-width of the total function is 1.81 °. The data can almost be fitted by a single Gaussian function of the same half-width (thin inner profile in Fig. 6), but the data points lie above the flanks of this profile. This is the ‘image flare’ we observed in the photographed image (Fig. 6 inset). Whilst not extremely large in M. stellatarum, it does have the potential to reduce image contrast significantly and thus to make vision worse (Land, 1984a). Interestingly, exactly the same thing is seen in electrophysiologically measured acceptance functions (E. Warrant, K. Bartsch and C. Günther, in preparation), implying that these flanks have a real effect on cellular receptive fields. The acceptance functions of rhabdoms in the lateral eye thus have acceptance angles (∆ρ) of 1.81 °. Knowing this angle also makes it possible to estimate the half-width ∆ρl of the blurred point source image (or blur-circle) formed on the retina. The acceptance function is the mathematical convolution of the blur-circle and the circular top-hat function representing the stop at the tip of the rhabdom. This stop is defined by the cylindrical sheath of tracheal tubes that surrounds each rhabdom and internally reflects light from the blur-circle into the rhabdom (Land, 1984a; Warrant and McIntyre, 1991; E. Warrant, K. Bartsch and C. Günther, in preparation). Using a method described by Land (see Land, 1984a, Fig. 9), it is possible to derive ∆ρl from ∆ρ and the angular width of the stop (∆ρr). In the lateral eye of M. stellatarum, ∆ρr≈1.73 °. With ∆ρ=1.81 °, this gives ∆ρl=1.27 °. How does this value of ∆ρl compare with the value expected if the blur-circle quality was limited only by the diffraction of light at each corneal facet? Images formed by an optical system can never be sharper than this diffraction limit. In a diffractionlimited eye, ∆ρl=180λ/πD, where λ is the wavelength of incoming light and D is the diameter of a single facet (Land, 1981). In the lateral eye of M. stellatarum D=29 µm (see Fig. 8). Taking λ=0.6 µm (the median wavelength used during these experiments) gives ∆ρl=1.19 °. This is narrower than our experimental value of 1.27 ° by 0.08 °, implying that the lateral eye of M. stellatarum, whilst being close to the diffraction limit, may suffer very slightly from image-degrading aberrations. Diffraction-limited superposition eyes have been found in the diurnal agaristid moth Phalaenoides tristifica, but in the diurnal skipper butterfly Ocybadistes walkeri the 502 E. WARRANT, K. BARTSCH AND C. GÜNTHER hovering (not shown in Fig. 8). In more posterior regions of the eye, the facets lose their perfect hexagonal shape and become compressed in the anterior–posterior direction (Figs 7A, 8B). In the dorso-ventral direction, facets are largest and most hexagonal at the equator, reaching diameters of approximately 29 µm (Fig. 8A). Both above and below the equator, facets become smaller but remain fairly hexagonal. Eye glow The superposition eye of M. stellatarum possesses a reflective tapetum, which lies in the retina. Light rays that have not been absorbed within the eye can be reflected by the tapetum and returned to a distant observer through the same aperture of facets as they entered. If the eye is illuminated and viewed coaxially with the illumination (i.e. orthodromic illumination), a bright patch of blue-green light can be seen on the eye surface (E. Warrant, K. Bartsch and C. Günther, in preparation). This patch, called the eye glow, represents the pupil through which light reaches the retina: a larger eye glow represents a larger pupil and a greater light catch. In most nocturnal superposition eyes, a bright eye glow is usually associated with a dark-adapted and fully open pupil. Continued illumination of such an eye normally causes screening pigments within the eye to migrate and ‘close’ the pupil. The eye glow then fades. Remarkably, in many diurnal superposition eyes including those of M. stellatarum, the pupil is always fully open, as if in the dark-adapted state, even though the animals themselves fly only in bright sunshine (E. Warrant, K. Bartsch and C. Günther, in preparation). The pupil can be partially closed, but only using unnaturally bright light (Warrant and McIntyre, 1996; E. Warrant, K. Bartsch and C. Günther, in preparation). The significance of this is not understood at present. Fig. 7. The facet matrix at two different equatorial locations: longitudes −15 ° (A) and +60 ° (B). The top, bottom, left and right edges of each panel represent the dorsal, ventral, posterior and anterior directions respectively. Facets are larger and more regularly hexagonal at the front of the eye (B). Scale bar (for both parts), 30 µm. superposition eyes are somewhat worse than the diffraction limit (Land, 1984a). M. stellatarum lies somewhere in between, but closer to Phalaenoides than to Ocybadistes. Corneal facet diameter The corneal facets of M. stellatarum maintain neither a constant diameter nor a perfectly hexagonal shape throughout the eye (Figs 7, 8). This is not uncommon in many apposition eyes, but for superposition eyes it is very unusual. Facets are largest and most hexagonal in the anterior part of the eye, with diameters exceeding 30 µm along the equator at longitudes around 60 ° (Fig. 8B). For longitudes further anterior, the facets maintain this shape and maximum diameter ventrally of the equator, notably in the region of the eye used by M. stellatarum to fixate the entrance of a flower during Lateral Ventral Dorsal Posterior Lateral Anterior 32 D Facet diameter (µm) 30 P D A A P V V 28 26 24 D A P 22 A V B 20 -100 -80 -60 -40 -20 0 20 Latitude (degrees) 40 60 80 100 -60 -40 -20 0 20 40 60 80 100 Longitude (degrees) Fig. 8. Facet diameter along the dorso-ventral meridian (longitude 0 °; A) and along the equator (latitude 0 °; B). Facet diameters were measured at each of the three possible orientations (inset in A), with curves for each represented by circles, squares and triangles respectively. Facets are largest and most regularly hexagonal at the equator and front of the eye. D, dorsal; V, ventral; A, anterior; P, posterior. Physiological optics in the hummingbird hawkmoth 503 Area (mm2) Number of facets D D 0.08 140 0.10 160 0.12 180 0 20 0. 16 L 0.1 8 A A 0.20 0.22 0.24 340 280 300 320 24 0 26 0 L 0.16 220 240 0 26 14 0. Fig. 9. The area of the superposition aperture (eye glow), and the number of facets comprising it, in different parts of the eye. Both the area and the facet number increase in a smooth gradient towards the ventral front of the eye and decrease in smooth gradients dorsally and ventrally. D, dorsal; V, ventral; A, anterior; L, lateral. 4 0.1 0 22 (mm2) 22 0 200 0. 12 0.1 0.0 0 8 V In a classical Exnerian superposition eye, the size and shape of the eye glow remain constant in different parts of the eye. Again, M. stellatarum breaks this classical rule: both the size and shape of the eye glow vary significantly (Fig. 9) and in a way that shows parallels to the facet variations. The eye glow becomes largest and roundest in the anterior part of the eye, with regard to both its area and the number of facets which constitute it. Its largest size (350 facets, 0.25 mm2) occurs approximately 10 ° below the equator at longitudes between 70 ° and 80 °. This region of the eye is used by M. stellatarum for fixating the entrance of the flower during hovering. Away from this region, the eye glow becomes smaller, decreasing in size in smooth gradients (Fig. 9). The eye glow becomes smallest and somewhat elliptical towards the edges of the eye. Over large regions of the lateral eye, the eye glow maintains approximately the same circular shape and an area of between 0.14 and 0.16 mm2. Interestingly, the eye glow area increases slightly towards the back of the eye. Rhabdom packing in the retina Using the ophthalmoscope, it is possible to scan a narrow slit across the retina and accumulate a bright image of rhabdom rows using an image intensifier. The angle between these rows in each orientation was measured from video prints calibrated for angle. Such images show that the angular separation of V rhabdom rows varies considerably in different parts of the eye. For instance, at different locations along the equator, there are rhabdom rows oriented dorso-ventrally, and the angular separation between these rows ∆φ decreases towards the front of the eye (Fig. 10). At an equatorial longitude of 20 °, the rows are 1.73 ° apart (Fig. 10A), but at a longitude of 70 ° they are only 1.17 ° apart (Fig. 10C). Similar reductions in the angular separations of rhabdom rows in the other two row directions are also seen towards the front of the eye (see Fig. 11). To quantify these changes, measurements of row separations were made at 10 ° intervals along the posterior–anterior equator (latitude 0 ° line) and along different dorso-ventral meridians, in two moths (Fig. 11). At each angular position, the animal was rotated under the ophthalmoscope in order to pick out rows in each of the three rhabdom row orientations. We then measured the separation of rows in the three orientations (inset, Fig. 11A). Large variations in row separation were found in both moths. Along meridians running dorso-ventrally (longitude lines 15 ° in Fig. 11A and 0 ° in Fig. 11B), the separation of dorso-ventral rows (squares in Fig. 11) remains roughly constant. In contrast, the separation of rows in the other two orientations (triangles and circles in Fig. 11) reaches a minimum at the equator and increases in both the dorsal and ventral directions. For instance, along the 0 ° longitude line (Fig. 11B), the dorso-ventral rows remain separated by Fig. 10. Images of dorso-ventral rhabdom rows at three different equatorial locations: longitudes 20 ° (A), 45 ° (B) and 70 ° (C). The images were made by scanning a narrow slit of light across the retina parallel to the desired rhabdom row orientation. During scanning, the image was accumulated by the image intensifier and analysis apparatus (see Fig. 2). The angular separation of rows (∆φ) decreases in a smooth gradient towards the front of the eye. ∆φ is 1.73 ° in A, 1.44 ° in B and 1.17 ° in C. Scale bar (for all parts), 2 °. 504 E. WARRANT, K. BARTSCH AND C. GÜNTHER Animal 1 Animal 2 Lateral Dorsal 2.2 Lateral Dorsal 2.2 2.0 P 2.0 A V 1.8 1.8 1.6 1.6 D D 1.4 75° P A A V 1.2 -60 -40 -20 0 20 40 60 Latitude (degrees) Lateral 80 1.4 90° P B V 1.2 0 20 40 60 -60 -40 -20 Latitude (degrees) Lateral Anterior 2.2 2.2 2.0 V 1.8 80 D A P A Anterior D Inter-row angle (degrees) Fig. 11. The angles separating rhabdom rows in two Macroglossum stellatarum along two different dorsoventral meridians (longitudes 15 ° in A and 0 ° in B) and along the anterior–posterior equator (latitude 0 °; C,D). The rhabdom matrix contains rows in three different orientations, and the angles separating rows in each of these orientations are shown by squares, circles and triangles respectively (inset in A). The angular packing of rhabdoms is not constant within the eye but instead forms local acute zones, one at the front of the eye and another along the equator, the equatorial one becoming weaker posteriorly. D, dorsal; V, ventral; A, anterior; P, posterior. Inter-row angle (degrees) D 2.0 A P V 1.8 1.6 1.6 1.4 1.4 1.2 1.2 C D 1.0 1.0 -20 0 20 40 60 Longitude (degrees) approximately 1.9 °, whereas rows in the other two orientations reach a minimum separation of 1.3–1.4 ° at the equator, increasing to well over 2 ° dorsally. The separations of rows in these latter two orientations appears to be greater and to occur more rapidly in the dorsal direction than in the ventral direction. Measurements along the equator (Fig. 11C,D) reveal that, even though the dorso-ventral rows are usually separated by a much larger angle than rows in the other two orientations, the separation of all rows decreases towards the front of the eye. Frontally, the separations of rows in all three orientations become very similar (approximately 1.1–1.2 °), indicating that the angular packing of rhabdoms becomes regularly hexagonal in this part of the eye. The angular packing of rhabdoms in the eye indicates the presence of retinal ‘acute zones’, a feature that is not reflected in the packing of facets in the overlying cornea (see below). Acute zones are regions of the eye where spatial resolution is improved (and also quite often sensitivity) and are a wellknown adaptation in apposition eyes (Land, 1989). In M. stellatarum, there is an acute zone along the equator of the eye 80 -20 0 20 40 60 80 Longitude (degrees) because the rhabdoms are mostly densely packed here (Fig. 11A,B). This equatorial acute zone becomes even more intense anteriorly, the region of the eye possessing the densest packing of rhabdoms. When we use an ophthalmoscope to look at the retina, we do not see rhabdoms in their true physical arrangement (i.e. with their physical separations in micrometres). Instead, we see the rhabdoms projected in angular space, and their angular packing may bear little resemblance to their physical packing. The angular separation of rhabdoms ∆φ (degrees) is related to their physical separation d (µm) via the local focal length f (µm): ∆φ=180d/πf. If changes in ∆φ from one part of the retina to the other are accompanied by appropriate changes in f, d could remain constant. If this were so, then one would not expect to see significant differences in the physical spacing of rhabdoms within the eye. Conversely, changes in ∆φ could also be obtained by changes in d at a fixed f, in which case the physical spacing of rhabdoms would vary significantly within the eye. To determine whether the changes in angular packing we have observed can be explained by changes in f or d or Physiological optics in the hummingbird hawkmoth both, we made electron microscope sections from two equatorial locations within the same eye: laterally (at longitude 0 °) and frontally (at longitude 70 °). These sections show that the physical packing of rhabdoms is indeed denser frontally than laterally (Fig. 12 and see Fig. 14E,F), but not dense enough to explain the observed differences in angular packing. This means that simultaneous changes in both d and f are Fig. 12. Transverse electron microscope sections through the retina at two different equatorial locations, approximately at longitudes 70 ° (A) and 0 ° (B), in the same moth. The physical rhabdom packing is denser frontally (A) than laterally (B). Sections show the rings of tracheal tubes which surround each rhabdom and act as a reflective sheath for trapping light (Land, 1984a; Warrant and McIntyre, 1991). The section in B is slightly more distal than the section in A and is, unfortunately, not exactly perpendicular to the rhabdom axis (which slightly exaggerates the more dilute packing present here). Calculations based on this section (see text) have been corrected for this. Scale bar (for both parts), 5 µm. 505 responsible for the changes in angular packing we have observed. Estimations of focal length Knowledge of the angular (∆φ) and physical (d) separations of rhabdom rows (Fig. 11 and see Fig. 14E,F) allows us to calculate the focal length (f) at the lateral and frontal equator of the eye. At both locations in the eye, the calculated focal length is different for each of the three different rhabdom row orientations. In the lateral eye, f=319 µm for the dorso-ventral orientation and 350 µm and 380 µm for the other two orientations. An ‘average’ focal length for these three values is 350 µm. In the frontal eye, the three focal lengths are 387 µm, 424 µm and 417 µm, with an average of 409 µm. Thus, not only do the focal lengths differ in different parts of the eye (being longer towards the front), they also differ between different rhabdom orientations at any single location in the eye. In all optical systems, including eyes, the focal length is defined as the distance between the system’s optical ‘nodal point’ and its focal plane. In a classical superposition eye, there is a single nodal point located at the eye’s centre of curvature, and the focal plane is located at the distal tips of the rhabdoms. Because classical superposition eyes are also spherical, the distal tips of the rhabdoms lie on a spherical surface whose centre of curvature is the nodal point. This means that the focal length is the same in all parts of the eye. The fact that the focal length of the eye of M. stellatarum is so variable suggests that the position of the nodal point may vary with retinal location. The fact that the focal length differs with orientation even at single retinal locations confirms this suggestion. Facet packing in the cornea The angles between neighbouring facet rows in the cornea were determined from angular displacements of the eye glow measured using a goniometer. Angles between facet rows were measured at 10 ° intervals along the posterior–anterior equator (latitude 0 ° line) and along the dorso-ventral meridian (longitude 0 ° line). At each angular position, we measured the angular divergence of rows in each of the three facet row orientations (inset, Fig. 13A). As with rhabdom rows, one of the facet rows has a dorso-ventral orientation (squares, Fig. 13). For a large range of latitudes above and below the equator, the angles between facet rows in all three orientations have values of approximately 1.8–2.0 ° (Fig. 13A). For latitudes more dorsal than 60 ° and more ventral than −50 °, the angle between rows in all orientations increases markedly, with angles between some rows reaching nearly 3.0 °. Along the equator (Fig. 13B), the angles between facet rows remain similar for all three orientations, but decline steadily towards the front of the eye until a longitude of approximately 60 °. For longitudes more anterior than 60 °, the angle separating dorsoventral rows suddenly increases dramatically, reaching a value of nearly 3 ° at 90 ° longitude. E. WARRANT, K. BARTSCH AND C. GÜNTHER Angle between facet rows (degrees) 506 Lateral Ventral 3.0 Posterior Lateral Anterior A D B D A P 2.5 Dorsal A P V V 2.0 D P A V 1.5 -80 -60 -40 -20 0 20 40 60 80 -60 -40 -20 0 20 40 60 80 100 Longitude (degrees) Latitude (degrees) Fig. 13. The angles separating facet rows along the dorso-ventral meridian (longitude 0 °; A) and along the posterior–anterior equator (latitude 0 °; B). As with rhabdom rows, there are also three different orientations of facet rows, with the angular separation between rows from each orientation shown by squares, circles and triangles respectively (inset in A). The angle separating facets is not constant in the eye, but varies in smooth gradients. D, dorsal; V, ventral, A, anterior; P, posterior. The number of rhabdoms per facet To some degree the angles between the facet rows do reflect the angles between the rhabdom rows lying directly beneath. The facet row angles, like the rhabdom row angles, are small near the equator (Fig. 13A) and generally decline along the equator towards the front of the eye (Fig. 13B). However, an inspection of Figs 11 and 13 quickly reveals that, even though this loose relationship does exist, the angles between facets are much larger in all parts of the eye than the angle between rhabdoms. This can be readily seen in a comparison of the angular packing matrices of rhabdoms and facets at two equatorial locations on the eye (Fig. 14): laterally (at longitude 0 °) and frontally (at longitude 70 °). The angular packing of facets at the frontal equator (Fig. 14B) is slightly denser than at the lateral equator (Fig. 14A), as we have already seen in Fig. 13. The same trend is also seen in the angular packing of rhabdoms, but the density is very much greater (and the packing more regularly hexagonal) at the frontal equator (Fig. 14D) than at the lateral equator (Fig. 14C). Most important, though, is the fact that the rhabdoms are much more densely packed in both parts of the eye than are the facets that lie above them. If this is the case in all parts of the eye, then this means that there must be many more rhabdoms than facets. Is this actually the case? To answer this question, we used the data shown in Figs 11 and 13 to calculate the local densities of rhabdoms and facets, and Fig. 14. The physical and angular packing of rhabdoms and facets in the eye at two different equatorial locations, laterally (longitude 0 °; A,C,E) and frontally (longitude 70 °; B,D,F). The small circles represent the centres of rhabdoms and facets. Both the angular (C,D) and physical (E,F) packing of rhabdoms is denser at the front of the eye than at the side, but the relative change is greater for angular packing. The angular packing of facets (A,B) remains rather similar, but much less dense, than the packing of the underlying rhabdoms. Equatorial, lateral Equatorial, frontal Facet packing (angular) Facet packing (angular) B A 2° 2° Rhabdom packing (angular) Rhabdom packing (angular) C D 2° 2° Rhabdom packing (physical) Rhabdom packing (physical) E F 10 µm 10 µm Physiological optics in the hummingbird hawkmoth Lateral 3.5 Number of rhabdoms per facet Fig. 15. The number of rhabdoms per facet along the dorso-ventral meridian (longitude 0 °; A) and along the posterior–anterior equator (latitude 0 °; B). Except for the extreme dorsal (and possibly the extreme ventral) part of the eye, the number of rhabdoms always exceeds the number of facets. Based on data from two different animals. Data points are the averages of 3 calculations made at each retinal location; error bars represent their total spread. D, dorsal; V, ventral; A, anterior; P, posterior. 3.0 Lateral Dorsal D Anterior D P A P 507 V A V 2.5 2.0 1.5 1.0 -60 B A -40 -20 0 20 40 Latitude (degrees) thereby the number of rhabdoms per facet, at 10 ° intervals along the posterior–anterior equator (latitude 0 ° line) and along the dorso-ventral meridian (longitude 0 ° line). At all positions we tested along the equator, there are at least two rhabdoms per facet, increasing to possibly as many as four rhabdoms per facet in the extreme anterior part of the eye (Fig. 15B). Along the dorso-ventral meridian, the number of rhabdoms per facet is greatest near the equator (two rhabdoms per facet) and falls systematically both dorsally and ventrally (Fig. 15A). In the extreme dorsal part of the eye (and possibly also in the extreme ventral part), the number of rhabdoms per facet falls to one. As far as we can tell, these are the only places in the eye where the number of rhabdoms and facets become equal. Spot checks in several other parts of the eye always revealed at least one rhabdom per facet, with most checks revealing much higher ratios. The only conclusion that one can draw from these results is that the eyes of M. stellatarum possess many more rhabdoms than facets, a most remarkable situation. In a classical superposition eye, and indeed in all compound eyes, there should be one rhabdom per facet in all parts of the eye. After all, an ommatidium is supposed to contain one facet lens and one rhabdom. The fact that this is clearly not the case in M. stellatarum is yet another indication of how significantly this eye departs from classical Exnerian principles. Discussion Deviations from classical superposition design The refracting superposition eye of the hummingbird hawkmoth is, in many ways, the most remarkable superposition eye ever described. Its deviation from the principles of classical Exnerian superposition optics is so profound that at first glance it is hard to imagine how the eye can form a decent image at all. Yet it does, and with arguably the sharpest receptive fields yet recorded from a superposition eye, with acceptance angles as small as 1.3 ° in the frontal eye (E. Warrant, K. Bartsch and C. Günther, in preparation). There 60 80 -20 0 20 40 60 80 Longitude (degrees) is no question that the departure of M. stellatarum from classical superposition optics has given it an eye of outstanding quality. The eye is very non-spherical and has a retina with rhabdoms whose packing density varies throughout the eye. The size of the facets, the area of the superposition aperture and the focal length also vary markedly. All these properties are at extreme odds with the classical model of Exner (1891). In this model, superposition eyes are spherical and maintain a constant focal length and angular magnification throughout the eye (i.e. the eye has a single nodal point). One would also expect an Exnerian superposition eye to have rhabdoms of equal length and separation and to have facets of equal size. The variable focal length is of particular interest, because it adds an extra degree of freedom in the design of the eye. A single glass lens which is not circularly symmetrical, but elongated, will often be astigmatic: the focal length in one orientation (say X) will be different from that in the perpendicular orientation (say Y). Because the nodal point in a glass lens is the same for all orientations, the image planes in the X and Y orientations will not coincide and the image quality will be poor. Astigmatism is not a problem for M. stellatarum. Because the nodal point can differ for different orientations at a single retinal location, differences in focal length that occur at that location need not mean that the image planes lack coincidence. On the contrary, the image planes coincide exactly on the retinal surface. Moreover, differences in focal length mean that the image can be differently magnified in different orientations (magnification is proportional to 1/f). This extra degree of design freedom would permit improvements in local spatial resolution simply by having a magnified image (in one or more orientations). To take advantage of this magnification, the underlying rhabdoms may even be packed more densely. Variations in the size of the superposition aperture have also been noted in another diurnal moth, the agaristid Phalaenoides tristifica (Horridge et al., 1977). In this moth, the aperture gradually decreases from a maximum width of 15 facets in the 508 E. WARRANT, K. BARTSCH AND C. GÜNTHER centre of the eye to much smaller values near the edge. In the dorsal part of the eye, the aperture diameter falls to approximately four facets. The eye of P. tristifica is much more spherical than that of M. stellatarum, and it is not known whether it possesses retinal acute zones. The superposition eyes of M. stellatarum apparently depart from Exnerian rules to achieve a single major benefit: the production of local acute zones. The frontal but slightly ventral acute zone not only has a higher spatial resolution but also collects more light from each point in space (i.e. has larger superposition apertures). In this region of the eye, the rhabdoms have a rhabdom separation (∆φ) of just 1.1–1.2 ° (Fig. 11C,D) compared with more than 2 ° in some other parts of the eye, which represents an approximately fourfold increase in packing density. In addition to this frontal acute zone, there is also an equatorial acute zone (Fig. 11A,B), a kind of horizontal ‘visual streak’ to borrow the vertebrate term. In an apposition eye, increases in ∆φ are directly visible from the appearance of the pupil and the angular packing of facets in the cornea (Stavenga, 1979; Land, 1989). In M. stellatarum, however, changes in ∆φ occur only within the retina. They are not measurable from either the pupil or the packing of facets. According to classical Exnerian principles, acute zones should be impossible in a superposition eye. To quote Land (1989): ‘the option of inserting small higher resolution regions (in superposition eyes) does not seem to be available, because the image-forming system will not work if there are local variations. There are superposition eyes with regions of different resolution – in euphausiid crustaceans for example (Land et al., 1979) – but here there are really two eyes joined together rather than a single one with an optical gradient.’ The eyes of M. stellatarum are the first superposition eyes known to possess pronounced resolution gradients. Why does the hummingbird hawkmoth have acute zones? The rhabdom packing that leads to acute zones in the superposition eye of M. stellatarum is actually remarkably similar to the ommatidial packing found in the apposition eyes of several other insects. Just as with the rhabdoms of M. stellatarum, the ommatidia of many bees, butterflies, wasps and locusts have their densest packing at the front of the eye, with a smooth decrease in density occurring posteriorly along the equator, especially between the dorso-ventral ommatidial rows (Baumgärtner, 1928; del Portillo, 1936; Autrum and Wiedemann, 1962; Horridge, 1978; Land, 1989). And, just as in M. stellatarum, they also possess a horizontal visual streak. Remarkably, the same optical adaptations have evolved in two completely different eye designs via two completely different methods. Equatorial gradients of spatial resolution are thought to be an adaptation for forward flight through a textured environment (Land, 1989). When an insect (or any animal) moves forward, it experiences the movement of its surroundings as it passes them, a so-called ‘flow field’ of moving features (Gibson, 1950; Wehner, 1981; Buchner, 1984). Features directly ahead appear to be almost stationary, while features to the side of this forward ‘pole’ appear to move with a velocity that becomes maximal when they are located at the side of the eye, 90 ° from the pole. If the photoreceptors have a fixed integration time ∆t (which is not necessarily the case), the motion of flow-field images from front to back across the eye will cause blurring. An object moving past the side of the eye (with velocity v) will appear as a horizontal spatial smear whose angular size (in degrees) will be approximately v∆t. This effectively widens the local optical acceptance angle (∆ρ) to a new value of √[∆ρ2+(v∆t)2] (Srinivasan and Bernard, 1975; Snyder, 1977). The extent of this widening is worse at the side of the eye (higher v) than at the front (lower v). To maintain an optimum sampling ratio of ∆ρ/∆φ (Snyder, 1977, 1979), the equatorial increase in ∆ρ posteriorly should be matched by an increase in ∆φ, as indeed seems to be the case. A very fast flying insect such as M. stellatarum can easily experience a velocity of 100 ° s−1 at the side of the eye. In the lateral eye, ∆ρ=1.81 ° (Fig. 6), and assuming a value of 15 ms for ∆t, we arrive at a new widened acceptance angle of 2.35 °, an increase of approximately 0.5 °. The separation (∆φ) of dorso-ventral rhabdom rows in the lateral eye is approximately 1.9 ° (Fig. 11). If we assume that the ratio of these ∆ρ and ∆φ values is the optimum for sampling (in this case 2.35 °/1.9 °≈1.2), then we can use this ratio to predict ∆ρ frontally (say at approximately 70 °) where widening due to motion-blurring would be minimal. We know the value of ∆φ is approximately 1.2 ° here (Fig. 11) and, using a sampling ratio of 1.2, leads to a ∆ρ of 1.2×1.2 °≈1.4 °. This is exactly the same acceptance angle as we have measured electrophysiologically in the same part of the eye (E. Warrant, K. Bartsch and C. Günther, in preparation). In the case of M. stellatarum, the denser packing of rhabdoms at the front of the eye is not just a response to lower flow-field velocities. This acute zone also serves quite another purpose: to fixate the entrances of flowers. When M. stellatarum hovers and sucks nectar, it uses the frontal, and slightly ventral, part of the eye to maintain its distance to the flower (Knoll, 1922). If the wind blows and the flower bobs around, it is amazing just how rapidly and effortlessly M. stellatarum can follow the movements. To a human observer, the moth seems almost ‘glued’ to the flower entrance by its outstretched proboscis. This stunning ability must in part be due to the extensive binocular overlap (E. Warrant, K. Bartsch and C. Günther, in preparation) and excellent resolution found in the acute zone viewing the flower entrance. The ability of M. stellatarum to follow flower-like movements and to hold its distance has recently been the subject of excellent behavioural studies (Pfaff and Varju, 1991; Farina et al., 1994; Kern, 1998; Kern and Varju, 1998). Moreover, movement-sensitive cells with frontal receptive fields have recently been identified in the optic lobe of M. stellatarum that would be perfect inputs to binocular circuits designed to detect the looming of a flower blown towards the moth (Wicklein, 1994; O’Carroll et al., 1997). The horizontal ‘visual streak’ possessed by M. stellatarum, and by other fast-flying insects which live in open terrain, is Physiological optics in the hummingbird hawkmoth possibly an adaptation for horizon detection. The horizon is a major visual cue in natural scenes, a large contrasting border between a blue-ultraviolet sky and a green-brown landscape. In many insects, the ocelli play a major role in detecting this horizon (Wilson, 1978; Stange, 1981), but in M. stellatarum, which has no ocelli, the eyes are solely responsible. A surprising number of visually interesting things are located at the horizon, familiar landmarks for instance. Because of this, visual streaks have evolved which sample the horizon much more densely than other parts of the vertical visual field. Visual streaks are common in vertebrates (for a review, see Hughes, 1977) and in the compound eyes of arthropods (for reviews, see Wehner, 1987; Land, 1989). They have never before been reported in a superposition eye. Hovering insects such as M. stellatarum may find the horizon very useful for preventing themselves from ‘rolling’ around their long axes during hovering. Interestingly, cells have recently been described in the ventral nerve cord of M. stellatarum that respond strongly to upward and downward motion of laterally placed horizontal edges (Kern, 1994, 1998; Kern and Varju, 1998). Moreover, the response of these putative roll detectors is strongest when a horizontal edge moves over the equator of the eye, a result that fits very well with the presence of an equatorial visual streak. A compound eye without ommatidia The superposition eye of the hummingbird hawkmoth is a compound eye without functional ommatidia. An ommatidium contains one set of rhabdomeres, which together constitute a rhabdom, and one pair of lenses, the corneal facet lens and the crystalline cone. In M. stellatarum, there are clearly many more rhabdoms than facets (Figs 14, 15), and therefore the ommatidial ratio of one rhabdom per facet has been abandoned. Simply put, there are no ommatidia in the functional sense, and there is no interommatidial angle. Instead, there is a matrix of photoreceptors and an overlying imaging system made out of a completely independent matrix of lens elements. In a sense, this is a compound eye that has developed into a kind of simple eye, like that in a spider: a retina with a fovea receiving a bright sharp image from an independent lens. What does M. stellatarum gain by lacking true ommatidia? First, because the rhabdoms are not constrained by an ommatidial matrix, they are free to aggregate and to form acute zones in a way impossible for a normal superposition eye. Second, because the facets are not constrained by the rhabdom matrix, they are free to vary optically and morphologically, and this they do spectacularly. Their optical variation has allowed them to develop a gradient of superposition apertures, the largest of which are centred exactly over the frontal acute zone in the retina, the region responsible for flower fixation (Fig. 9). Not only this, the facets here are also the largest in the eye (Fig. 8), and larger facets are less affected by the image-degrading effects of diffraction. The flower-fixating part of the eye produces the brightest, sharpest image on the acutest part of the retina. This 509 region has the highest sensitivity and the greatest resolution of the entire eye, and entirely due to the eye’s radical departure from the classical superposition design. Superposition eyes without ommatidia, whilst rare, are not unheard of. Cases are known from the dorsal eyes of male mayflies (Zimmer, 1898; Wolburg-Buchholz, 1976; P. Brännström and D.-E. Nilsson, in preparation), the dorsal acute zones of euphausiid shrimps (Chun, 1896; Land et al., 1979) and the larval eye of the euphausiid Thysanopoda tricuspidata, which has 90 rhabdoms but only seven facets (Land, 1981, 1984b). The most extreme example is the mysid shrimp Dioptromysis paucispinosa, which has a superposition eye that in all respects is quite classical apart from the presence of a single enormous facet supplying light to its own private acute zone of 120 rhabdoms (Nilsson and Modlin, 1994). But, as we mentioned above, if any changes in resolution are seen in these eyes, it is because of the presence of two separate regions, each with uniform resolution, that have been joined together to form a single eye. The superposition eye of M. stellatarum is the first documented example of a superposition eye with true gradients. Interestingly, new data from the nocturnal hawkmoth Deilephila elphenor also show weak gradients, but in an eye that looks quite spherical and has the same number of rhabdoms as facets (P. Brännström and Y. Arroyo Yanguas, in preparation). It is not yet understood how superposition eyes can develop with an unequal number of facets and rhabdoms. It would seem that during the manufacture of ommatidia some must develop without lenses. How can M. stellatarum break all the rules and get away with it? Unfortunately, the answer to this question still remains a mystery. The fact that the focal length varies at different points in the eye, and even at the same point, presents a major conceptual difficulty in understanding this eye. Quite clearly, the optical nodal point has no single location and probably has nothing at all to do with the local curvature of the retina, as it does in a classical superposition eye. Both the retina and the overlying cornea are highly aspherical and are not concentric, which means that the depth of the clear zone varies all over the eye. The depth of the clear zone indicates the distance between the optics and the image plane at the distal tips of the rhabdoms (McIntyre and Caveney, 1985). The fact that it varies means there must be a compensatory change in the optics to maintain a crisp image on the rhabdom tips. This must somehow be achieved by systematically altering the optics and morphology of the lenses, something that is difficult to conceive because the same crystalline cone can be used to focus light from two entirely different incident angles to two entirely different locations on the retina. How can a single crystalline cone manage two different clear zone depths, compensating for the difference by bending light by different amounts for the two different locations? This would require that the angular magnifications of individual cones are not constant (as in Exnerian eyes), but vary with the angle of incidence of 510 E. WARRANT, K. BARTSCH AND C. GÜNTHER incoming light. Interestingly, recent work suggests that this could indeed be the case in the unusual dorsal superposition eyes of krill and mayflies, which have highly curved corneal surfaces and flat retinas (D.-E. Nilsson, P. Brännström and L. Gislén, in preparation). The same problem arises when thinking about the variable superposition aperture. A single crystalline cone could be optically functional in two different superposition apertures. Again it is difficult to understand how this can work unless the optical magnifications of individual cones can vary with the angle of incident light. Land (1989) was not being naive by claiming that gradients are impossible in superposition eyes. They really do seem impossible. Obviously, however, they are not only possible, they also produce superposition eyes of unsurpassed quality. Exactly how is still unclear. This study is dedicated to Professor Dezsö Varju on the occasion of his retirement from the Chair of Biological Cybernetics at the University of Tübingen. The authors are extremely grateful to Dan-Eric Nilsson for critically reading the manuscript and for many fruitful discussions. Both he, HansJürgen Dahmen and Mike Land graciously allowed us to use their equipment and willingly assisted us with its operation. Dezsö Varju, Hans-Jürgen Dahmen, Mike Land, Martina Wicklein, Almut Kelber and Michael Pfaff were also a source of rich insight. We are extremely indebted to Rita Wallén and Lina Hansen for expert histological work. This study would have been impossible without the gratefully acknowledged assistance of a Twinning Grant provided by the European Science Foundation. K.B. is grateful for support from the Deutsche Forschungsgemeinschaft (SFB 307). E.J.W. is deeply grateful for the ongoing support of the Swedish Natural Science Research Council and for the generous hospitality extended to him by Professor Varju and the other members of his Tübingen department during many memorable visits. This paper was completed during a Fellowship at the Institute of Advanced Study in Berlin, for whose support and marvellous working environment E.J.W. is particularly grateful. References Autrum, H. and Wiedemann, I. (1962). Versuche über den Strahlengang im Insektenauge. Z. Naturforsch. 17b, 480–482. Bartsch, K. and Warrant, E. J. (1994). The non-spherical superposition eye of Macroglossum stellatarum (Lepidoptera, Sphingidae). In Göttingen Neurobiology Report 1994 (ed. N. Elsner and H. Breer), p. 434. Stuttgart, New York: Georg Thieme Verlag. Baumgärtner, H. (1928). Der Formensinn und die Sehschärfe der Bienen. Z. Vergl. Physiol. 7, 56–143. Buchner, E. (1984). 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