Visual Neuroscience (1992), 9, 571-580. Printed in the USA. Copyright © 1992 Cambridge University Press 0952-5238/92 $5.00 + .00
The Limulus-eye view of the world
ERIK D. HERZOG AND ROBERT B. BARLOW, JR. Institute for Sensory Research, Syracuse University, Syracuse (RECEIVED February 3, 1992; ACCEPTED May
19,
1992)
Abstract The compound lateral eye of the adult horseshoe crab, Limulus polyphemus, views the world with approximately 1000 ommatidia. Their optical properties and orientation determine the eye's resolution, field of view, and light collecting ability. Optic axes of adjacent ommatidia diverge from 1-15 deg with an average value of 5.5 deg yielding an average resolution of 0.1 cycles/deg. Resolution is not uniform across the eye: along horizontal planes, it is maximal in the anterior region of the eye (0.22 cycle/deg) and minimal in the posterior region (0.07 cycle/deg); along vertical planes, it is maximal near or just below the horizon (0.23 cycle/deg) and minimal above the horizon (0.04 cycle/deg). Together the ommatidia of one eye view approximately 60% of the hemispheric world on one side of the body. There is little binocular overlap ( < 1 % of total field). Ommatidial facets of up to 320 /im in diameter (among the largest known in the animal kingdom) make the eye a superb light collector. Limulus are known to use vision to find mates both day and night. Apparently, the optics of the lateral eye sample a large enough part of the world with sufficient resolution and light-collecting ability for the animal to succeed at this essential task. Keywords: Resolution, Spatial sampling frequency, Optics and transformation, Pseudopupil
each ommatidium (acceptance angle, Ap). The smaller the interommatidial angle, the greater the potential resolving power of the eye (Snyder, 1977). Resolution is proportional to the reciprocal of A. The field of view of individual ommatidia, Ap, is determined by the properties of the corneal lens and location of the retinular cells. The field of view of the eye is determined by the orientation of the most peripheral ommatidia. Previous studies of the Limulus eye investigated interommatidial angles (von Campenhausen, 1967; Kirschfeld & Reichardt, 1964), ommatidial packing (French et al., 1977), and fields of view of individual ommatidia (Waterman, 1954o; Kirschfeld & Reichardt, 1964). These studies provided new information, but they did not give a complete picture of the eye's optical transformation. We report here on the resolution and field of view of the lateral eye and illustrate how the eye's optics transform the visual world. Preliminary results have been reported (Herzog & Barlow, 1990).
Introduction
The Limulus lateral eye has been an exceptionally useful model for investigating basic mechanisms of vision. Much has been learned from it about the physiology and anatomy of retinal processing of visual information (Ratliff & Hartline, 1974; Barlow et al., 1989; Chamberlain & Barlow, 1987). Also, much has been learned about what the animal can see in its natural habitat (Barlow et al., 1987; Powers et al., 1991). However, little is known about the optical interface between the retina and the world. Here, we describe the properties of the dioptric apparatus of the lateral eye. The basic unit of the dioptric apparatus is a lens and crystalline cone embedded in the cornea. Together they form a refracting cylinder lens (Exner, 1891; Land, 1979) that focuses an inverted image onto a cluster of photoreceptor (retinular) cells. The lens-receptor complex forms the functional unit called an ommatidium, approximately 1000 of which make up the apposition eye of an adult. The ommatidia and compound eyes of Limulus are among the largest of living animals. Individual ommatidia are large enough to be seen with the unaided eye. Each ommatidium acts as a light meter looking at a small patch of the visual world and is most sensitive to light entering along its optic axis.
Methods Maintenance of animals
Understanding how the eye processes spatial information requires knowledge of the angle between optic axes of adjacent ommatidia (interommatidial angle, A) and the field of view of
Reprint requests to: E. Herzog, Institute for Sensory Research, Merrill Lane, Syracuse, NY 13244-5290, USA.
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Male horseshoe crabs (Limulus polyphemus) measuring 1927 cm across the carapace were used in this study. Animals were obtained from the Marine Biological Laboratory (Woods Hole, MA) and stored under natural lighting conditions in tanks with circulating artificial seawater (Instant Ocean, Aquarium Systems, Eastlake, OH) in the animal cold room at the Institute for Sensory Research, Syracuse University (Syracuse, NY). We fed the animals fresh clams biweekly.
572 Eye plane The orientation of the lateral eyes varies from animal to animal. To compare the orientation of eyes from different animals, we defined the "eye plane" as that plane which is tangential to the cornea at its geometric center. The ommatidium located at this point is termed the "central ommatidium." To measure the eye plane, we mounted a live crab on the platform of a two-dimensional goniometer. The animal was aligned on the platform so that it rotated about a line parallel to its longitudinal axis and passing through the central ommatidium. The beam of a HeNe laser (Spectra-Physics, Model 916-1, 0.9 mW, 632.8 nm) was then rotated about an axis perpendicular to the platform's axis of rotation and passing through the central ommatidium. The laser beam illuminated the central ommatidium and its immediate neighbors. Both the laser beam and platform were rotated until the laser beam reflected back from the central ommatidium to the face of the laser. The platform angle gives the dorsoventral tilt of the eye plane and the laser angle gives the antero-posterior tilt. The average of ten measurements of both angles defined the eye plane. A small hole (< 180 /xm diameter) was drilled in the cornea directly over the central ommatidium and filled with permanent acrylic paint (Liquitex, Permanent Pigments, Inc., Cincinnati, OH). This operation did not interfere with the reflection of the laser beam by the cornea. Because Limulus is strictly marine, an analysis of the eye's optics must be done underwater to avoid the effects of refraction at the air-cornea interface. The eye plane provided an essential landmark for studying the excised eye underwater. We preferred to fix the eyes so that measurements could be made
B
E.D. Herzog and R.B. Barlow, Jr. at any time without deterioration of the tissue. Control experiments showed that fixation did not affect optical measurements. We fixed the eye in the animal by subretinal injection of fixative (4.5% sucrose, 3% NaCl, 0.8% glutaraldehyde, and 5% paraformaldehyde in 0.1 M Sorensen's phosphate buffer, pH 7.2). After 30 min, the eye was excised with surrounding carapace and stored overnight in fixative. To avoid any systematic error resulting from known circadian changes in morphology (Chamberlain & Barlow, 1987), we fixed all eyes (n = 17) in their daytime state. To align the excised eye for optical measurements, we mounted it on a second two-dimensional goniometer and reestablished the eye plane using the same laser reflection technique described above. The eye was then immersed in filtered sea water to minimize errors due to refraction and illuminated with collimated light. The observer viewed the eye through one ocular of a dissecting microscope at lOx or 15.75X magnification.
Optic axis of an ommatidium Our preferred technique for measuring the optic axis of an ommatidium takes advantage of the light reflected from pigment cells at the base of the corneal lens within an ommatidium. The radial arrangement of pigment cells forms an aperture that controls the amount of light incident upon the underlying retinular cells. The aperture defines the optic axis of the ommatidium. Under axial illumination, the pigment cells reflect light back to the observer forming a bright spot within an ommatidium (Fig. 1). This bright spot overlies the aperture. The daytime aperture is too small (-17 jim in diameter; Barlow et al., 1980)
Fig. 1. A: Under axial illumination, the pseudopupil of the compound lateral eye of Limulus appears as a conspicuous bright cluster of ommatidia. The ommatidia within the cluster are oriented towards the observer and reflect light back to the observer. B: A 4x magnification of the pseudopupil in A. A bright spot of light is apparent within several ommatidia of the cluster. When the bright spot is centered within an ommatidium (arrow), the optic axis of that ommatidium is oriented towards the observer. Facets of single ommatidia are -200 /im in diameter. Scale bar =
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The Limulus-eye view of the world to be resolved by our light microscope. By rotating the eye about the two orthogonal axes of the goniometer, one can center the bright spot (and, thus, the aperture) within each ommatidium. The angular settings of the goniometer then define the orientation of the optic axis of that ommatidium relative to the eye plane. Interommatidial angle A The divergence between the optic axes of adjacent ommatidia is the interommatidial angle, A, which we measured with two methods: aperture and center of the pseudopupil. Aperture The aperture method takes advantage of the spot of light reflected from within an ommatidium. As described above, we determined the optic axis of an ommatidium by centering the bright spot within the facet of a given ommatidium. We then determined the optic axis of an adjacent ommatidium. The difference between the two optic axes is A(f>. We repeated these measurements for pairs of ommatidia located within specific regions and along specific planes of the mounted eye. Center of the pseudopupil The center of the pseudopupil method utilizes the pseudopupil (Fig. 1) which is a conspicuous ring of ommatidia that appear dark surrounding one or more ommatidia that glow brightly (Leydig, 1855). We counted the number of ommatidia traversed by the center of the pseudopupil as the eye was rotated through 10 deg. Dividing 10 deg by the number of facets traversed yielded the average interommatidial angle, A, for that cluster of facets. This method has been used with the compound eyes of many insects and some crustaceans (cf. Horridge, 1978, and Stavenga, 1979, for reviews). Optical resolution and sampling frequency The optical resolution of the eye is determined by the relationship between interommatidial angle, A, and acceptance angle, Ap. Previous physiological studies show that A equals Ap in the central region of the Limulus lateral eye (see Discussion). In this paper, we measure resolution in terms of A. For convenience, we describe the resolution of the eye in terms of spatial sampling frequency which is defined by the spatial frequency of the finest grating that the optics will reliably pass. Based on geometry, the highest sampling frequency passed by an array of hexagonally packed ommatidia is / = [A * v 3 j ~ ' w h e r e / is the spatial sampling frequency in cycles/degree and A is the interommatidial angle in degrees (Snyder, 1979). The 3 ~ l / 2 term is based on hexagonal packing of the ommatidial array (Snyder, 1979). Although Limulus ommatidia are not packed in a perfect hexagonal array, it is the best approximation of the geometry of the array. Following Land's (1989) convention, we plot on polar coordinates the square root of sampling frequency to compensate for the areal distortion of polar plots resulting from the increase in circumference with distance from the origin. We analyzed the distribution of resolution throughout the eye by measuring A within nine regions and along four horizontal and four vertical "planes" (great circular sections passing through the front-rear or top-bottom poles of the eye). The four horizontal planes were the actual horizon, 30 and 10 deg
above the horizon, and 20 deg below the horizon. One vertical plane, the lateral plane, is perpendicular to the longitudinal axis of the animal. The other three planes were 50 and 20 deg anterior to lateral and 30 deg posterior to lateral. The nine regions were located as shown in the inset in Fig. 4. We averaged ten A measures within each region. In addition, we studied the size and shape of the pseudopupil as indicators of how the eye samples its visual world. Pseudopupil size (A) is defined as the product of the number of ommatidia along the radii of the major (a) and minor (b) axes of the pseudopupil times w (i.e. A = wab). The major axis of the pseudopupil represents the axis of greater sampling. The edges of the pseudopupil are not well-defined; some ommatidia are not completely dark (see Fig. I). Our convention was to include in the pseudopupil all ommatidia that appeared at least half dark. We measured the size of the pseudopupil at 10-deg increments throughout the eye and omitted it at the margins of the eye where it was incomplete. Field of view of the eye The optic axes of the most peripheral ommatidia of an eye define its field of view. We determined the field of view along horizontal planes of an eye by measuring the number of degrees separating the optic axes of the ommatidia at the anterior and posterior margins of the eye. Along vertical planes, we used the optic axes of the most dorsal and ventral ommatidia. Facet size In most compound eyes, light collecting ability increases with facet diameter. Facet diameter and density are reciprocally related as can be light-collecting ability and resolution. Facet diameters are generally not the same throughout an eye and often their distribution indicates whether resolution is sacrificed for overall sensitivity. To test these ideas in Limulus, we measured the diameters of the facets throughout several eyes. Eyes with the retina removed from the cornea were illuminated from behind and viewed with a dissecting light microscope (model SZH, Olympus Corp.) fitted with a video camera. We made measurements from digitized, calibrated video images of the eyes in various positions with an image analysis software package (Cue-2 Image Analyzer, Olympus Corp., Version 3.0, 1989).
Results Figs. 2-4 give the field of view and the distribution of resolution of the lateral eye. In each figure, the filled symbols give the resolution in terms of the square root of sampling frequency as explained above. We give the overall field of view of the eye, the range of interommatidial angles (A$s), and their resulting sampling frequency. Field of view of the eye The Limulus lateral eyes see a large portion of the world. Fig. 2A gives for one animal the field of view of the right eye along the horizontal plane. Optic axes along this plane diverge by 209 deg, 93 deg anterior, and 116 deg posterior to a perpendicular to the animal's longitudinal axis. Fig. 2B shows the field of view of the eye along a vertical plane 20 deg anterior to lat-
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A
Posterior
Anterior
Midline Dorsal
Horizon
Sampling Frequency
Ventral
Fig. 2. Distribution of resolution along two orthogonal planes of one lateral eye. Resolution is given in terms of the square root of sampling frequency (see Methods) and plotted on polar coordinates. Dotted lines indicate the limits of the field of view of the eye along each plane. A: Filled circles show that resolution increases from posterior to anterior regions along the animal's horizon. The crab and this horizontal plane are viewed from above. B: Filled squares show that resolution along the vertical is highest just below the animal's horizon. This vertical plane is situated 20 deg anterior to lateral (see Methods). We view this dorsoventral plane from the front of the crab.
eral. This eye sees an angular sector of 95 deg along this plane beginning 56 deg above and extending 39 deg below the horizon. Figs. 3A and 3B summarize the fields of view of six eyes from as many animals. On average, the eye views 204 ± 9 deg (mean ± S.D.) along the animal's horizon. That is, the eye looks 98 ± 11 deg anterior and 107 ± 15 deg posterior to lateral. Along vertical planes, the average visual field is 106 ± 12 deg. The eye splits the world into roughly equal halves with 51 ± 12 deg above and 55 + 7 deg below the animal's horizon. In some cases, the optic axes of the most peripheral ommatidia could not be seen directly because the goniometric apparatus blocked the observers' view. In such instances, we extrapolated the complete field of view by multiplying the number of ommatidia from the last measurable ommatidium to the edge of the eye by the average divergence (see archetypal eye below) for that region of the eye. This extrapolated visual angle was added to the measured angle to yield the complete field of view.
Inlerommatidial
right lateral eyes using the aperture technique. For comparison, we measured A0s from three of the same eyes with the center of the pseudopupil method. The two methods yielded different absolute A measures but similar A ranges and trends. Interommatidial angles range from less than 1 deg to nearly 15 deg. In general, A$s increase from anterior to posterior and are larger in the dorsal half of the eye. In addition, the A# between an ommatidium and its vertical neighbor can differ by several degrees from that between its horizontal neighbor. The narrowest average A measured by the aperture method of the nine regions examined for four eyes is 3 ± 2 deg (mean ± S.D.; n = 80) for vertical neighbors in the ventro-anterior region and 4 ± I deg (n = 92) for horizontal neighbors in the dorso-anterior region of the eye (Fig. 6, inset). The widest average A is 9 ± 3 deg (n = 80) for vertical neighbors in the dorso-posterior region and 7 ± 2 deg (n = 116) for horizontal neighbors in the dorsolateral and dorso-posterior regions of the eye. The axes of ommatidia in the middle of the eye diverge by 6 ± 2 deg (n = 30) both horizontally and vertically.
angle
The optics of the eye are not uniform. We measured interommatidial angles, A#s, of about 20% of the ommatidia in five
The lateral eye does not resolve uniformly all parts of its visual field. Figs. 2A and 2B show the distribution of resolution along representative horizontal and vertical planes for the right eye of one animal. Sampling frequencies range from 0.04-0.27 cycle/ deg along the animal's horizon and from 0.08-0.23 cycle/deg along the plane 20 deg anterior to lateral. The distribution of resolution shown in Figs. 2A and 2B is indicative of that of other eyes. For each eye studied, we analyzed optical resolution along at least four horizontal and four vertical planes. Cumulative data in Fig. 3 from the eight planes of four eyes show that resolution increases anteriorly along horizontal planes and near the animal's horizon along vertical planes. In general, resolution changes gradually across the visual field, but occasional local irregularities exist. Archetypal eye Fig. 4 gives a generalized or archetypal eye that summarizes the field of view and resolution data of six adult eyes. Resolution along all horizontal planes of the archetypal eye is highest in the anterior visual field, i.e. vertically oriented bars should be best resolved in the forward or anterior visual field. Resolution along vertical planes is highest at or just below the animal's horizon, i.e. horizontally oriented bars should be best resolved in the lower portion of the visual field.
Pseudopupil size and shape The size and shape of the pseudopupil change dramatically across the eye. Fig. 5 plots the number of ommatidia in the pseudopupil as a function of the location in the eye. The pseudopupil is largest in the anterior region of the eye near the horizon (82 ommatidia) and smallest in the dorso-posterior region (six ommatidia). The changes in pseudopupil size are gradual. The shape of the pseudopupil is circular along the horizon, elongated dorso-ventrally in the ventral portion and elongated antero-posteriorly in the dorsal portion of the eye. Pseudopupil size in a given region of the eye indicates the number of ommatidia viewing a part of a scene, thus resolution is related to pseudopupil size. We compared the average size of
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The Limulus-eye view of the world
Dorsal Posterior
Anterior
+50
+20
+30°
Horizon Midline
+ 10°
-30' 0°
-20°
Fig. 3. Distribution of resolution along eight planes of four eyes. Each graph pools data from the four eyes. The numbered dotted lines indicate the limits of the fields of view of each eye. A: Along each of the four horizontal planes, resolution is maximal in the anterior visual field. B: Along each of the four vertical planes, resolution is highest just below the horizon.
the pseudopupil with archetypal resolution in various regions of the eye (n = 10 eyes). Fig. 6A shows that the size of (number of ommatidia within) the pseudopupil of an eye increases monotonically with resolution. In regions of the eye where the pseudopupil is elliptical, resolution is always higher in the direction of the major axis of the pseudopupil. Fig. 6B shows that the number of ommatidia along the major axis of the pseudopupil increases monotonically with resolution along that axis. Along the middle of the eye, where the pseudopupil is circular, the number of ommatidia along the vertical axis of the pseudopupil increases with resolution along the vertical plane just as number along the horizontal increases with resolution along the horizontal.
Facet size Average facet size increases with eye size and towards the posterior region of the eye. We measured the diameter of 150 facets from each of two eyes and 100 facets from a third eye (approximately 15% of the total number of facets per eye). The largest eye (11.8 mm antero-posterior by 4.96 mm dorsoventral) had the largest average and smallest variation in facet diameter of 244 ± 29 urn (mean ± S.D.). The smallest eye (9.6 mm x
4.3 mm) had the smallest average and largest variation in facet diameter of 202 ± 42 ^m. Average diameter of facets of all three eyes was significantly smaller anteriorly, 167 ± 19 fim, and larger posteriorly, 238 ± 17 ^m (Student's Mest, P = 0.05). Discussion The optics of the Limulus compound eye provide the first level of spatial filtering of the visual system. They sample a large enough part of the world with sufficient resolution for the animals to succeed at the crucial task of finding mates (see below). In addition, they collect enough light for the retina, driven to high sensitivity by a circadian clock, to detect objects under the very darkest nighttime conditions. The optical properties (Figs. 2-5) can now be incorporated into an existing computational model of the eye (Barlow et al., 1991) to investigate the information the eye must send to the brain for the animal to see. Field of view Humans and Limulus have comparable monocular fields of view. We see approximately 65% (4.18 steradians) of the visual world with one eye and Limulus sees 59% (3.68 steradians) with one
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A
Anterior
Dorsal + 50
Midline Horizon + 10°
-20°
Fig. 4. Distribution of resolution for the archetypal Limulus lateral eye. Filled symbols give local averages of resolution measured from the four eyes in Fig. 3. Unfilled symbols give regional averages from two eyes in Fig. 3 and two additional eyes. Inset shows the nine regions of the eyes studied with their corresponding average values of A0 (mean ± S.D.) along horizontal (top number in each pair) and vertical (bottom number) planes. In general, the regional averages agree well with the more detailed local averages. A: Resolution changes gradually along horizontal planes reaching a maximum in the anterior visual field. Highest horizontal resolution occurs below the horizon. Local averages were computed for 20-deg bin widths (•). B: Resolution is highest along the vertical plane oriented lateral to the animal's long axis and just below the animal's horizon. Local averages (•) were computed for 10-deg bin widths.
pseudopupil size (# of ommatidia) 80
Posterior
40
0
40
80
Anterior
Fig. 5. Pseudopupil size changes with position in the eye. The pseudopupil is smallest when viewed at an angle of 40 deg above the horizon (o) and largest when viewed from the anterior direction. The other four horizontal planes shown are 20 deg (A) and 10 deg (D) above the horizon, at the horizon (•), and 10 deg below the horizon (A).
eye on its side of the body. For both us and Limulus, about half of the visual field is above the horizon and half below (Fig. 3). However, binocular overlap differs greatly for humans and horseshoe crabs. Both of our eyes see nearly 60 deg across our midline giving us about 25% overlap. In Limulus, both eyes see only 7 ± 11 deg across the midline giving them less than 1% overlap beginning about 33 cm in front of the animal. In sum, Limulus views more of the world with both eyes than we do, but with less binocular overlap.
Spatial filtering: trends in the optics The lateral eye of an adult Limulus reconstructs the visual world with approximately 1000 receptors. They are not uniformly spaced across the eye. The region of highest density and, consequently, highest resolution, lies in the forward direction and close to the horizon. Resolution changes gradually across
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The Limulus-eye view of the world
tip. These values of Ap are about equal to the average value of &4> of 6 ± 2 deg (Fig. 4) we measured for the middle of the eye. Thus, in the middle of the Limulus eye Ap = A$ suggesting resolution is optimally related to light collection. £..14 -
Light-collecting ability
.06 10
20
30 Size or Pseudopupil
40 SO (Ommalidia)
60
.18-
i.14 -
I10 .06 3
4
5 6 7 8 9 10 Major Axis of Pseudopupil (Ommatidia)
11
Fig. 6. Pseudopupil size and shape are related to resolution. A: Resolution is plotted on the ordinate as a function of the size of the pseudopupil on the abscissa. Measurements were made in the dorsal (+0), middle (•o), and ventral (BO) regions of the eye. Resolution increases monotonically with pseudopupil size along both horizontal (filled symbols) and vertical (unfilled) planes. B: Resolution also increases with the length of the major axis of the pseudopupil measured in number of ommatidia. In the middle of the eye, resolution increases monotonically with the length of the horizontal (•) and the vertical (o) axes of the pseudopupil. Resolution increases with the length of the vertical axis of the pseudopupil (x) in the dorsal region and with the length of the horizontal axis in the ventral region (a).
the eye as evidenced by the smooth changes in regional averages of interommatidial angles (Figs. 2-4) and pseudopupil size and shape (Figs. 5-6) along the eye. Does the Limulus eye sacrifice resolution for light-collecting ability? Rossel (1979) showed that in an optimally designed eye, the interommatidial angle, A, equals the acceptance angle, Ap, although exceptions have been noted (Snyder, 1979). In any compound eye, if Ap were less than A 5 for some deep sea crustaceans that operate in dim light conditions (Stavenga, 1975; see Horridge, 1977 for review). Values for the eye parameter of the adult Limulus range from 4-84 which rank among the largest known for any species. Such large/? values are a consequence of Limulus having unusually large facets. Limulus may have no peers regarding light-collecting ability. The eye performs extremely well at low intensities. Light-collecting ability and resolution depend in part on the size of the eye. As the eye grows at each molt, new, small ommatidia appear at the anterior margin and the existing, larger ommatidia move posteriorly (Marler et al., 1983). Facets in the posterior region of the eye are thus the largest in the eye. Their optic axes also diverge more from their neighbors than those in the anterior region of the eye. As a consequence, the eye parameter and light-collecting ability are not constant across the eye. In sum, light-collecting ability is inversely distributed with resolution: largest in the posterior region and smallest towards the anterior region. Day-to-night changes in visual resolution Does Limulus see as well at night as during the day? The lateral eyes of Limulus undergo pronounced daily physiological and structural changes driven by a circadian clock in the brain. At night, sensitivity increases by as much as six orders of magnitude nearly compensating for the decrease in available light (Barlow, 1983, 1988) by increasing quantum catch (Barlow et al., 1977, 1984, 1987) and decreasing retinal noise (Kaplan & Barlow, 1980). Associated with these endogenously driven changes at night is an increase in Ap (Barlow et al., 1980) and a decrease in temporal resolution (Batra & Barlow, 1990). Assuming that the angle separating neighboring optic axes does not change while the acceptance angle of each ommatidium increases, spatial resolution is sacrificed for increased light collection at night. Yet, behavioral experiments show that Limulus sees about equally well night and day (Powers et al., 1991). Reduction of spatial resolution at night does not appear to significantly affect the animal's ability to see. Relation of eye design to behavior For what, then, does the horseshoe crab use vision? All animals need to mate, eat, and not be eaten. Vision clearly has a role in Limulus mating behavior. It may also have a role in predator avoidance, but is apparently not involved in feeding behavior. During the summer months along the Atlantic Coast of North America, horseshoe crabs congregate at the water's edge to lay eggs and mate. Barlow et al. (1982, 1987) showed that males use vision to approach underwater targets of various shapes and contrasts and suggested that vision is used in the
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same way to find females. With their highest visual resolution forward and along the horizon, males moving in shallow water would be well designed to find a mate ahead of them. Video records of males approaching targets show them frequently approaching at an oblique angle, as if to place the target in the portion of the field of view with highest resolution (Herzog and Barlow, unpublished results). The eye appears to segregate resolution of horizontally and vertically oriented objects. The circular pseudopupil along the horizon of the eye indicates that it resolves vertical and horizontal bars equally well. Elsewhere on the eye, the pseudopupil is elliptical. The major axis of the pseudopupil represents the axis of dominant sampling. Based upon the data in Figs. 2-4 and 6, the ventral portion of the eye resolves horizontal patterns best while the dorsal part of the eye resolves vertical bars best. What this means to the animal's behavior is unknown. The wide field of view of the Limulus eye may be advantageous in detecting predators. Adults are known to be preyed upon from above by sharks (Schuster, 1982). Nearly half of the eye sees the world above the horizon and does so with poor resolution. Observations carried out in the field (Atlantic Ocean) with SCUBA show that animals respond to a shadow cast over one eye by turning sharply in the opposite direction of the shadowed eye (Barlow, unpublished results). Such behavior may be indicative of predator avoidance and may benefit from the eyes' excellent ability to detect changes in light intensity.
What does he see in her: the optical
from Barlow et al. (1982). In Fig. 7B, we superimpose the optic axes of the male's eyes on the visual scene. Fig. 7C shows the result of convolving the angular sensitivity of each ommatidium with the light intensities it views. The grey level of each hexagon is proportional to the light available to the photoreceptors within each ommatidium. The blurring of the female is dramatic and yet he sees her! Although no holes exist in the optically transformed image, the silhouette of the female is severely degraded. Studies of Limulus mating behavior show that males reliably respond to objects placed 0.75 m away. At that distance, the optic axes of only about five receptors of the male's eye intercept the silhouette of a female. The light available for neural processing is a very rough approximation of the object intensity. Does the neural network enhance its contrast or further degrade the image? For example, a model of the optics does not include enhancement through lateral inhibition (Hartline & Ratliff, 1972; Bar-
transformation
What is the Limulus-eye view of the world? Fig. 7 illustrates the optical transformation of the central portion of the eye. We transformed a visual scene as the eye would by convolving the known contrast values of the scene with the angular sensitivities of ommatidia viewing the scene. Fig. 7A shows the scene before entering the male's eye. The silhouette of a female horseshoe crab rests underwater on a sandy bottom 0.75 m away from the male's eye. Contrast values of the scene are taken
C
Fig. 7. Optical transformation of an underwater scene by the lateral eye. A: The underwater scene simulates a female horseshoe crab (silhouette) resting on a sandy bottom as viewed from a distance of 0.75 m which is slightly less than the distance for males to see females (Powers & Barlow, 1991). The silhouette measures 0.35 m from head to tail and covers a solid angle of ~30 deg. Values of contrasts of the scene are based on measurements made in the field (Barlow et al., 1982). The sand (optical density of 0.33 log units attenuation) reflects twice as much light as the carapace (0.66 log units) and half as much as the water column (0 log units). B: White dots indicate the direction of view of ommatidia in the center of the eye viewing the scene. Optic axes of each ommatidium diverge by 6 deg, intercepting the scene at the white circles. Distortion resulting from the curvature of the eye is ignored. The field of view of each ommatidium is approximated by a Gaussian function with width of 6 deg at half-maximum sensitivity centered on the optic axis (Barlow et al., 1980). We limited the field of view of each ommatidium by setting its sensitivity to zero for all regions beyond 7.1 deg from the optic axis of the ommatidium. At 7.1 deg, sensitivity is 6% of maximum. C: The Limulus-tyt view of the scene in A. Field of view of each ommatidium was convolved with the light distribution in scene A. Grey levels within each hexagon give the light intensities passing through each lens facet. The optical transformation severely blurs the scene.
CJ,
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The Limulus-eye view of the world low, 1969; Laughlin, 1981) or degradation through angular motion, finite diameter of the rhabdom, and neural convergence (Snyder, 1977). It will be interesting to learn how the visual system uses this rudimentary information.
lumination. Investigative Ophthalmology and Visual Science (Suppl.) 29, 350. BARLOW, R.B., J R . , BOLANOWSKI, S.J. & BRACHMAN, M.L. (1977). Ef-
ferent optic nerve fibers mediate circadian rhythms in the Limulus eye. Science 197, 86-89. BARLOW, R.B., J R . , CHAMBERLAIN, S.C. & LEVINSON, J.Z. (1980). Lim-
The aperture: a reliable and novel technique for assessing A
The Limulus-eye view of the world
ERIK D. HERZOG AND ROBERT B. BARLOW, JR. Institute for Sensory Research, Syracuse University, Syracuse (RECEIVED February 3, 1992; ACCEPTED May
19,
1992)
Abstract The compound lateral eye of the adult horseshoe crab, Limulus polyphemus, views the world with approximately 1000 ommatidia. Their optical properties and orientation determine the eye's resolution, field of view, and light collecting ability. Optic axes of adjacent ommatidia diverge from 1-15 deg with an average value of 5.5 deg yielding an average resolution of 0.1 cycles/deg. Resolution is not uniform across the eye: along horizontal planes, it is maximal in the anterior region of the eye (0.22 cycle/deg) and minimal in the posterior region (0.07 cycle/deg); along vertical planes, it is maximal near or just below the horizon (0.23 cycle/deg) and minimal above the horizon (0.04 cycle/deg). Together the ommatidia of one eye view approximately 60% of the hemispheric world on one side of the body. There is little binocular overlap ( < 1 % of total field). Ommatidial facets of up to 320 /im in diameter (among the largest known in the animal kingdom) make the eye a superb light collector. Limulus are known to use vision to find mates both day and night. Apparently, the optics of the lateral eye sample a large enough part of the world with sufficient resolution and light-collecting ability for the animal to succeed at this essential task. Keywords: Resolution, Spatial sampling frequency, Optics and transformation, Pseudopupil
each ommatidium (acceptance angle, Ap). The smaller the interommatidial angle, the greater the potential resolving power of the eye (Snyder, 1977). Resolution is proportional to the reciprocal of A. The field of view of individual ommatidia, Ap, is determined by the properties of the corneal lens and location of the retinular cells. The field of view of the eye is determined by the orientation of the most peripheral ommatidia. Previous studies of the Limulus eye investigated interommatidial angles (von Campenhausen, 1967; Kirschfeld & Reichardt, 1964), ommatidial packing (French et al., 1977), and fields of view of individual ommatidia (Waterman, 1954o; Kirschfeld & Reichardt, 1964). These studies provided new information, but they did not give a complete picture of the eye's optical transformation. We report here on the resolution and field of view of the lateral eye and illustrate how the eye's optics transform the visual world. Preliminary results have been reported (Herzog & Barlow, 1990).
Introduction
The Limulus lateral eye has been an exceptionally useful model for investigating basic mechanisms of vision. Much has been learned from it about the physiology and anatomy of retinal processing of visual information (Ratliff & Hartline, 1974; Barlow et al., 1989; Chamberlain & Barlow, 1987). Also, much has been learned about what the animal can see in its natural habitat (Barlow et al., 1987; Powers et al., 1991). However, little is known about the optical interface between the retina and the world. Here, we describe the properties of the dioptric apparatus of the lateral eye. The basic unit of the dioptric apparatus is a lens and crystalline cone embedded in the cornea. Together they form a refracting cylinder lens (Exner, 1891; Land, 1979) that focuses an inverted image onto a cluster of photoreceptor (retinular) cells. The lens-receptor complex forms the functional unit called an ommatidium, approximately 1000 of which make up the apposition eye of an adult. The ommatidia and compound eyes of Limulus are among the largest of living animals. Individual ommatidia are large enough to be seen with the unaided eye. Each ommatidium acts as a light meter looking at a small patch of the visual world and is most sensitive to light entering along its optic axis.
Methods Maintenance of animals
Understanding how the eye processes spatial information requires knowledge of the angle between optic axes of adjacent ommatidia (interommatidial angle, A) and the field of view of
Reprint requests to: E. Herzog, Institute for Sensory Research, Merrill Lane, Syracuse, NY 13244-5290, USA.
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Male horseshoe crabs (Limulus polyphemus) measuring 1927 cm across the carapace were used in this study. Animals were obtained from the Marine Biological Laboratory (Woods Hole, MA) and stored under natural lighting conditions in tanks with circulating artificial seawater (Instant Ocean, Aquarium Systems, Eastlake, OH) in the animal cold room at the Institute for Sensory Research, Syracuse University (Syracuse, NY). We fed the animals fresh clams biweekly.
572 Eye plane The orientation of the lateral eyes varies from animal to animal. To compare the orientation of eyes from different animals, we defined the "eye plane" as that plane which is tangential to the cornea at its geometric center. The ommatidium located at this point is termed the "central ommatidium." To measure the eye plane, we mounted a live crab on the platform of a two-dimensional goniometer. The animal was aligned on the platform so that it rotated about a line parallel to its longitudinal axis and passing through the central ommatidium. The beam of a HeNe laser (Spectra-Physics, Model 916-1, 0.9 mW, 632.8 nm) was then rotated about an axis perpendicular to the platform's axis of rotation and passing through the central ommatidium. The laser beam illuminated the central ommatidium and its immediate neighbors. Both the laser beam and platform were rotated until the laser beam reflected back from the central ommatidium to the face of the laser. The platform angle gives the dorsoventral tilt of the eye plane and the laser angle gives the antero-posterior tilt. The average of ten measurements of both angles defined the eye plane. A small hole (< 180 /xm diameter) was drilled in the cornea directly over the central ommatidium and filled with permanent acrylic paint (Liquitex, Permanent Pigments, Inc., Cincinnati, OH). This operation did not interfere with the reflection of the laser beam by the cornea. Because Limulus is strictly marine, an analysis of the eye's optics must be done underwater to avoid the effects of refraction at the air-cornea interface. The eye plane provided an essential landmark for studying the excised eye underwater. We preferred to fix the eyes so that measurements could be made
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E.D. Herzog and R.B. Barlow, Jr. at any time without deterioration of the tissue. Control experiments showed that fixation did not affect optical measurements. We fixed the eye in the animal by subretinal injection of fixative (4.5% sucrose, 3% NaCl, 0.8% glutaraldehyde, and 5% paraformaldehyde in 0.1 M Sorensen's phosphate buffer, pH 7.2). After 30 min, the eye was excised with surrounding carapace and stored overnight in fixative. To avoid any systematic error resulting from known circadian changes in morphology (Chamberlain & Barlow, 1987), we fixed all eyes (n = 17) in their daytime state. To align the excised eye for optical measurements, we mounted it on a second two-dimensional goniometer and reestablished the eye plane using the same laser reflection technique described above. The eye was then immersed in filtered sea water to minimize errors due to refraction and illuminated with collimated light. The observer viewed the eye through one ocular of a dissecting microscope at lOx or 15.75X magnification.
Optic axis of an ommatidium Our preferred technique for measuring the optic axis of an ommatidium takes advantage of the light reflected from pigment cells at the base of the corneal lens within an ommatidium. The radial arrangement of pigment cells forms an aperture that controls the amount of light incident upon the underlying retinular cells. The aperture defines the optic axis of the ommatidium. Under axial illumination, the pigment cells reflect light back to the observer forming a bright spot within an ommatidium (Fig. 1). This bright spot overlies the aperture. The daytime aperture is too small (-17 jim in diameter; Barlow et al., 1980)
Fig. 1. A: Under axial illumination, the pseudopupil of the compound lateral eye of Limulus appears as a conspicuous bright cluster of ommatidia. The ommatidia within the cluster are oriented towards the observer and reflect light back to the observer. B: A 4x magnification of the pseudopupil in A. A bright spot of light is apparent within several ommatidia of the cluster. When the bright spot is centered within an ommatidium (arrow), the optic axis of that ommatidium is oriented towards the observer. Facets of single ommatidia are -200 /im in diameter. Scale bar =
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The Limulus-eye view of the world to be resolved by our light microscope. By rotating the eye about the two orthogonal axes of the goniometer, one can center the bright spot (and, thus, the aperture) within each ommatidium. The angular settings of the goniometer then define the orientation of the optic axis of that ommatidium relative to the eye plane. Interommatidial angle A The divergence between the optic axes of adjacent ommatidia is the interommatidial angle, A, which we measured with two methods: aperture and center of the pseudopupil. Aperture The aperture method takes advantage of the spot of light reflected from within an ommatidium. As described above, we determined the optic axis of an ommatidium by centering the bright spot within the facet of a given ommatidium. We then determined the optic axis of an adjacent ommatidium. The difference between the two optic axes is A(f>. We repeated these measurements for pairs of ommatidia located within specific regions and along specific planes of the mounted eye. Center of the pseudopupil The center of the pseudopupil method utilizes the pseudopupil (Fig. 1) which is a conspicuous ring of ommatidia that appear dark surrounding one or more ommatidia that glow brightly (Leydig, 1855). We counted the number of ommatidia traversed by the center of the pseudopupil as the eye was rotated through 10 deg. Dividing 10 deg by the number of facets traversed yielded the average interommatidial angle, A, for that cluster of facets. This method has been used with the compound eyes of many insects and some crustaceans (cf. Horridge, 1978, and Stavenga, 1979, for reviews). Optical resolution and sampling frequency The optical resolution of the eye is determined by the relationship between interommatidial angle, A, and acceptance angle, Ap. Previous physiological studies show that A equals Ap in the central region of the Limulus lateral eye (see Discussion). In this paper, we measure resolution in terms of A. For convenience, we describe the resolution of the eye in terms of spatial sampling frequency which is defined by the spatial frequency of the finest grating that the optics will reliably pass. Based on geometry, the highest sampling frequency passed by an array of hexagonally packed ommatidia is / = [A * v 3 j ~ ' w h e r e / is the spatial sampling frequency in cycles/degree and A is the interommatidial angle in degrees (Snyder, 1979). The 3 ~ l / 2 term is based on hexagonal packing of the ommatidial array (Snyder, 1979). Although Limulus ommatidia are not packed in a perfect hexagonal array, it is the best approximation of the geometry of the array. Following Land's (1989) convention, we plot on polar coordinates the square root of sampling frequency to compensate for the areal distortion of polar plots resulting from the increase in circumference with distance from the origin. We analyzed the distribution of resolution throughout the eye by measuring A within nine regions and along four horizontal and four vertical "planes" (great circular sections passing through the front-rear or top-bottom poles of the eye). The four horizontal planes were the actual horizon, 30 and 10 deg
above the horizon, and 20 deg below the horizon. One vertical plane, the lateral plane, is perpendicular to the longitudinal axis of the animal. The other three planes were 50 and 20 deg anterior to lateral and 30 deg posterior to lateral. The nine regions were located as shown in the inset in Fig. 4. We averaged ten A measures within each region. In addition, we studied the size and shape of the pseudopupil as indicators of how the eye samples its visual world. Pseudopupil size (A) is defined as the product of the number of ommatidia along the radii of the major (a) and minor (b) axes of the pseudopupil times w (i.e. A = wab). The major axis of the pseudopupil represents the axis of greater sampling. The edges of the pseudopupil are not well-defined; some ommatidia are not completely dark (see Fig. I). Our convention was to include in the pseudopupil all ommatidia that appeared at least half dark. We measured the size of the pseudopupil at 10-deg increments throughout the eye and omitted it at the margins of the eye where it was incomplete. Field of view of the eye The optic axes of the most peripheral ommatidia of an eye define its field of view. We determined the field of view along horizontal planes of an eye by measuring the number of degrees separating the optic axes of the ommatidia at the anterior and posterior margins of the eye. Along vertical planes, we used the optic axes of the most dorsal and ventral ommatidia. Facet size In most compound eyes, light collecting ability increases with facet diameter. Facet diameter and density are reciprocally related as can be light-collecting ability and resolution. Facet diameters are generally not the same throughout an eye and often their distribution indicates whether resolution is sacrificed for overall sensitivity. To test these ideas in Limulus, we measured the diameters of the facets throughout several eyes. Eyes with the retina removed from the cornea were illuminated from behind and viewed with a dissecting light microscope (model SZH, Olympus Corp.) fitted with a video camera. We made measurements from digitized, calibrated video images of the eyes in various positions with an image analysis software package (Cue-2 Image Analyzer, Olympus Corp., Version 3.0, 1989).
Results Figs. 2-4 give the field of view and the distribution of resolution of the lateral eye. In each figure, the filled symbols give the resolution in terms of the square root of sampling frequency as explained above. We give the overall field of view of the eye, the range of interommatidial angles (A$s), and their resulting sampling frequency. Field of view of the eye The Limulus lateral eyes see a large portion of the world. Fig. 2A gives for one animal the field of view of the right eye along the horizontal plane. Optic axes along this plane diverge by 209 deg, 93 deg anterior, and 116 deg posterior to a perpendicular to the animal's longitudinal axis. Fig. 2B shows the field of view of the eye along a vertical plane 20 deg anterior to lat-
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A
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Anterior
Midline Dorsal
Horizon
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Ventral
Fig. 2. Distribution of resolution along two orthogonal planes of one lateral eye. Resolution is given in terms of the square root of sampling frequency (see Methods) and plotted on polar coordinates. Dotted lines indicate the limits of the field of view of the eye along each plane. A: Filled circles show that resolution increases from posterior to anterior regions along the animal's horizon. The crab and this horizontal plane are viewed from above. B: Filled squares show that resolution along the vertical is highest just below the animal's horizon. This vertical plane is situated 20 deg anterior to lateral (see Methods). We view this dorsoventral plane from the front of the crab.
eral. This eye sees an angular sector of 95 deg along this plane beginning 56 deg above and extending 39 deg below the horizon. Figs. 3A and 3B summarize the fields of view of six eyes from as many animals. On average, the eye views 204 ± 9 deg (mean ± S.D.) along the animal's horizon. That is, the eye looks 98 ± 11 deg anterior and 107 ± 15 deg posterior to lateral. Along vertical planes, the average visual field is 106 ± 12 deg. The eye splits the world into roughly equal halves with 51 ± 12 deg above and 55 + 7 deg below the animal's horizon. In some cases, the optic axes of the most peripheral ommatidia could not be seen directly because the goniometric apparatus blocked the observers' view. In such instances, we extrapolated the complete field of view by multiplying the number of ommatidia from the last measurable ommatidium to the edge of the eye by the average divergence (see archetypal eye below) for that region of the eye. This extrapolated visual angle was added to the measured angle to yield the complete field of view.
Inlerommatidial
right lateral eyes using the aperture technique. For comparison, we measured A0s from three of the same eyes with the center of the pseudopupil method. The two methods yielded different absolute A measures but similar A ranges and trends. Interommatidial angles range from less than 1 deg to nearly 15 deg. In general, A$s increase from anterior to posterior and are larger in the dorsal half of the eye. In addition, the A# between an ommatidium and its vertical neighbor can differ by several degrees from that between its horizontal neighbor. The narrowest average A measured by the aperture method of the nine regions examined for four eyes is 3 ± 2 deg (mean ± S.D.; n = 80) for vertical neighbors in the ventro-anterior region and 4 ± I deg (n = 92) for horizontal neighbors in the dorso-anterior region of the eye (Fig. 6, inset). The widest average A is 9 ± 3 deg (n = 80) for vertical neighbors in the dorso-posterior region and 7 ± 2 deg (n = 116) for horizontal neighbors in the dorsolateral and dorso-posterior regions of the eye. The axes of ommatidia in the middle of the eye diverge by 6 ± 2 deg (n = 30) both horizontally and vertically.
angle
The optics of the eye are not uniform. We measured interommatidial angles, A#s, of about 20% of the ommatidia in five
The lateral eye does not resolve uniformly all parts of its visual field. Figs. 2A and 2B show the distribution of resolution along representative horizontal and vertical planes for the right eye of one animal. Sampling frequencies range from 0.04-0.27 cycle/ deg along the animal's horizon and from 0.08-0.23 cycle/deg along the plane 20 deg anterior to lateral. The distribution of resolution shown in Figs. 2A and 2B is indicative of that of other eyes. For each eye studied, we analyzed optical resolution along at least four horizontal and four vertical planes. Cumulative data in Fig. 3 from the eight planes of four eyes show that resolution increases anteriorly along horizontal planes and near the animal's horizon along vertical planes. In general, resolution changes gradually across the visual field, but occasional local irregularities exist. Archetypal eye Fig. 4 gives a generalized or archetypal eye that summarizes the field of view and resolution data of six adult eyes. Resolution along all horizontal planes of the archetypal eye is highest in the anterior visual field, i.e. vertically oriented bars should be best resolved in the forward or anterior visual field. Resolution along vertical planes is highest at or just below the animal's horizon, i.e. horizontally oriented bars should be best resolved in the lower portion of the visual field.
Pseudopupil size and shape The size and shape of the pseudopupil change dramatically across the eye. Fig. 5 plots the number of ommatidia in the pseudopupil as a function of the location in the eye. The pseudopupil is largest in the anterior region of the eye near the horizon (82 ommatidia) and smallest in the dorso-posterior region (six ommatidia). The changes in pseudopupil size are gradual. The shape of the pseudopupil is circular along the horizon, elongated dorso-ventrally in the ventral portion and elongated antero-posteriorly in the dorsal portion of the eye. Pseudopupil size in a given region of the eye indicates the number of ommatidia viewing a part of a scene, thus resolution is related to pseudopupil size. We compared the average size of
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The Limulus-eye view of the world
Dorsal Posterior
Anterior
+50
+20
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Horizon Midline
+ 10°
-30' 0°
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Fig. 3. Distribution of resolution along eight planes of four eyes. Each graph pools data from the four eyes. The numbered dotted lines indicate the limits of the fields of view of each eye. A: Along each of the four horizontal planes, resolution is maximal in the anterior visual field. B: Along each of the four vertical planes, resolution is highest just below the horizon.
the pseudopupil with archetypal resolution in various regions of the eye (n = 10 eyes). Fig. 6A shows that the size of (number of ommatidia within) the pseudopupil of an eye increases monotonically with resolution. In regions of the eye where the pseudopupil is elliptical, resolution is always higher in the direction of the major axis of the pseudopupil. Fig. 6B shows that the number of ommatidia along the major axis of the pseudopupil increases monotonically with resolution along that axis. Along the middle of the eye, where the pseudopupil is circular, the number of ommatidia along the vertical axis of the pseudopupil increases with resolution along the vertical plane just as number along the horizontal increases with resolution along the horizontal.
Facet size Average facet size increases with eye size and towards the posterior region of the eye. We measured the diameter of 150 facets from each of two eyes and 100 facets from a third eye (approximately 15% of the total number of facets per eye). The largest eye (11.8 mm antero-posterior by 4.96 mm dorsoventral) had the largest average and smallest variation in facet diameter of 244 ± 29 urn (mean ± S.D.). The smallest eye (9.6 mm x
4.3 mm) had the smallest average and largest variation in facet diameter of 202 ± 42 ^m. Average diameter of facets of all three eyes was significantly smaller anteriorly, 167 ± 19 fim, and larger posteriorly, 238 ± 17 ^m (Student's Mest, P = 0.05). Discussion The optics of the Limulus compound eye provide the first level of spatial filtering of the visual system. They sample a large enough part of the world with sufficient resolution for the animals to succeed at the crucial task of finding mates (see below). In addition, they collect enough light for the retina, driven to high sensitivity by a circadian clock, to detect objects under the very darkest nighttime conditions. The optical properties (Figs. 2-5) can now be incorporated into an existing computational model of the eye (Barlow et al., 1991) to investigate the information the eye must send to the brain for the animal to see. Field of view Humans and Limulus have comparable monocular fields of view. We see approximately 65% (4.18 steradians) of the visual world with one eye and Limulus sees 59% (3.68 steradians) with one
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A
Anterior
Dorsal + 50
Midline Horizon + 10°
-20°
Fig. 4. Distribution of resolution for the archetypal Limulus lateral eye. Filled symbols give local averages of resolution measured from the four eyes in Fig. 3. Unfilled symbols give regional averages from two eyes in Fig. 3 and two additional eyes. Inset shows the nine regions of the eyes studied with their corresponding average values of A0 (mean ± S.D.) along horizontal (top number in each pair) and vertical (bottom number) planes. In general, the regional averages agree well with the more detailed local averages. A: Resolution changes gradually along horizontal planes reaching a maximum in the anterior visual field. Highest horizontal resolution occurs below the horizon. Local averages were computed for 20-deg bin widths (•). B: Resolution is highest along the vertical plane oriented lateral to the animal's long axis and just below the animal's horizon. Local averages (•) were computed for 10-deg bin widths.
pseudopupil size (# of ommatidia) 80
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Fig. 5. Pseudopupil size changes with position in the eye. The pseudopupil is smallest when viewed at an angle of 40 deg above the horizon (o) and largest when viewed from the anterior direction. The other four horizontal planes shown are 20 deg (A) and 10 deg (D) above the horizon, at the horizon (•), and 10 deg below the horizon (A).
eye on its side of the body. For both us and Limulus, about half of the visual field is above the horizon and half below (Fig. 3). However, binocular overlap differs greatly for humans and horseshoe crabs. Both of our eyes see nearly 60 deg across our midline giving us about 25% overlap. In Limulus, both eyes see only 7 ± 11 deg across the midline giving them less than 1% overlap beginning about 33 cm in front of the animal. In sum, Limulus views more of the world with both eyes than we do, but with less binocular overlap.
Spatial filtering: trends in the optics The lateral eye of an adult Limulus reconstructs the visual world with approximately 1000 receptors. They are not uniformly spaced across the eye. The region of highest density and, consequently, highest resolution, lies in the forward direction and close to the horizon. Resolution changes gradually across
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The Limulus-eye view of the world
tip. These values of Ap are about equal to the average value of &4> of 6 ± 2 deg (Fig. 4) we measured for the middle of the eye. Thus, in the middle of the Limulus eye Ap = A$ suggesting resolution is optimally related to light collection. £..14 -
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Fig. 6. Pseudopupil size and shape are related to resolution. A: Resolution is plotted on the ordinate as a function of the size of the pseudopupil on the abscissa. Measurements were made in the dorsal (+0), middle (•o), and ventral (BO) regions of the eye. Resolution increases monotonically with pseudopupil size along both horizontal (filled symbols) and vertical (unfilled) planes. B: Resolution also increases with the length of the major axis of the pseudopupil measured in number of ommatidia. In the middle of the eye, resolution increases monotonically with the length of the horizontal (•) and the vertical (o) axes of the pseudopupil. Resolution increases with the length of the vertical axis of the pseudopupil (x) in the dorsal region and with the length of the horizontal axis in the ventral region (a).
the eye as evidenced by the smooth changes in regional averages of interommatidial angles (Figs. 2-4) and pseudopupil size and shape (Figs. 5-6) along the eye. Does the Limulus eye sacrifice resolution for light-collecting ability? Rossel (1979) showed that in an optimally designed eye, the interommatidial angle, A, equals the acceptance angle, Ap, although exceptions have been noted (Snyder, 1979). In any compound eye, if Ap were less than A 5 for some deep sea crustaceans that operate in dim light conditions (Stavenga, 1975; see Horridge, 1977 for review). Values for the eye parameter of the adult Limulus range from 4-84 which rank among the largest known for any species. Such large/? values are a consequence of Limulus having unusually large facets. Limulus may have no peers regarding light-collecting ability. The eye performs extremely well at low intensities. Light-collecting ability and resolution depend in part on the size of the eye. As the eye grows at each molt, new, small ommatidia appear at the anterior margin and the existing, larger ommatidia move posteriorly (Marler et al., 1983). Facets in the posterior region of the eye are thus the largest in the eye. Their optic axes also diverge more from their neighbors than those in the anterior region of the eye. As a consequence, the eye parameter and light-collecting ability are not constant across the eye. In sum, light-collecting ability is inversely distributed with resolution: largest in the posterior region and smallest towards the anterior region. Day-to-night changes in visual resolution Does Limulus see as well at night as during the day? The lateral eyes of Limulus undergo pronounced daily physiological and structural changes driven by a circadian clock in the brain. At night, sensitivity increases by as much as six orders of magnitude nearly compensating for the decrease in available light (Barlow, 1983, 1988) by increasing quantum catch (Barlow et al., 1977, 1984, 1987) and decreasing retinal noise (Kaplan & Barlow, 1980). Associated with these endogenously driven changes at night is an increase in Ap (Barlow et al., 1980) and a decrease in temporal resolution (Batra & Barlow, 1990). Assuming that the angle separating neighboring optic axes does not change while the acceptance angle of each ommatidium increases, spatial resolution is sacrificed for increased light collection at night. Yet, behavioral experiments show that Limulus sees about equally well night and day (Powers et al., 1991). Reduction of spatial resolution at night does not appear to significantly affect the animal's ability to see. Relation of eye design to behavior For what, then, does the horseshoe crab use vision? All animals need to mate, eat, and not be eaten. Vision clearly has a role in Limulus mating behavior. It may also have a role in predator avoidance, but is apparently not involved in feeding behavior. During the summer months along the Atlantic Coast of North America, horseshoe crabs congregate at the water's edge to lay eggs and mate. Barlow et al. (1982, 1987) showed that males use vision to approach underwater targets of various shapes and contrasts and suggested that vision is used in the
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same way to find females. With their highest visual resolution forward and along the horizon, males moving in shallow water would be well designed to find a mate ahead of them. Video records of males approaching targets show them frequently approaching at an oblique angle, as if to place the target in the portion of the field of view with highest resolution (Herzog and Barlow, unpublished results). The eye appears to segregate resolution of horizontally and vertically oriented objects. The circular pseudopupil along the horizon of the eye indicates that it resolves vertical and horizontal bars equally well. Elsewhere on the eye, the pseudopupil is elliptical. The major axis of the pseudopupil represents the axis of dominant sampling. Based upon the data in Figs. 2-4 and 6, the ventral portion of the eye resolves horizontal patterns best while the dorsal part of the eye resolves vertical bars best. What this means to the animal's behavior is unknown. The wide field of view of the Limulus eye may be advantageous in detecting predators. Adults are known to be preyed upon from above by sharks (Schuster, 1982). Nearly half of the eye sees the world above the horizon and does so with poor resolution. Observations carried out in the field (Atlantic Ocean) with SCUBA show that animals respond to a shadow cast over one eye by turning sharply in the opposite direction of the shadowed eye (Barlow, unpublished results). Such behavior may be indicative of predator avoidance and may benefit from the eyes' excellent ability to detect changes in light intensity.
What does he see in her: the optical
from Barlow et al. (1982). In Fig. 7B, we superimpose the optic axes of the male's eyes on the visual scene. Fig. 7C shows the result of convolving the angular sensitivity of each ommatidium with the light intensities it views. The grey level of each hexagon is proportional to the light available to the photoreceptors within each ommatidium. The blurring of the female is dramatic and yet he sees her! Although no holes exist in the optically transformed image, the silhouette of the female is severely degraded. Studies of Limulus mating behavior show that males reliably respond to objects placed 0.75 m away. At that distance, the optic axes of only about five receptors of the male's eye intercept the silhouette of a female. The light available for neural processing is a very rough approximation of the object intensity. Does the neural network enhance its contrast or further degrade the image? For example, a model of the optics does not include enhancement through lateral inhibition (Hartline & Ratliff, 1972; Bar-
transformation
What is the Limulus-eye view of the world? Fig. 7 illustrates the optical transformation of the central portion of the eye. We transformed a visual scene as the eye would by convolving the known contrast values of the scene with the angular sensitivities of ommatidia viewing the scene. Fig. 7A shows the scene before entering the male's eye. The silhouette of a female horseshoe crab rests underwater on a sandy bottom 0.75 m away from the male's eye. Contrast values of the scene are taken
C
Fig. 7. Optical transformation of an underwater scene by the lateral eye. A: The underwater scene simulates a female horseshoe crab (silhouette) resting on a sandy bottom as viewed from a distance of 0.75 m which is slightly less than the distance for males to see females (Powers & Barlow, 1991). The silhouette measures 0.35 m from head to tail and covers a solid angle of ~30 deg. Values of contrasts of the scene are based on measurements made in the field (Barlow et al., 1982). The sand (optical density of 0.33 log units attenuation) reflects twice as much light as the carapace (0.66 log units) and half as much as the water column (0 log units). B: White dots indicate the direction of view of ommatidia in the center of the eye viewing the scene. Optic axes of each ommatidium diverge by 6 deg, intercepting the scene at the white circles. Distortion resulting from the curvature of the eye is ignored. The field of view of each ommatidium is approximated by a Gaussian function with width of 6 deg at half-maximum sensitivity centered on the optic axis (Barlow et al., 1980). We limited the field of view of each ommatidium by setting its sensitivity to zero for all regions beyond 7.1 deg from the optic axis of the ommatidium. At 7.1 deg, sensitivity is 6% of maximum. C: The Limulus-tyt view of the scene in A. Field of view of each ommatidium was convolved with the light distribution in scene A. Grey levels within each hexagon give the light intensities passing through each lens facet. The optical transformation severely blurs the scene.
CJ,
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The Limulus-eye view of the world low, 1969; Laughlin, 1981) or degradation through angular motion, finite diameter of the rhabdom, and neural convergence (Snyder, 1977). It will be interesting to learn how the visual system uses this rudimentary information.
lumination. Investigative Ophthalmology and Visual Science (Suppl.) 29, 350. BARLOW, R.B., J R . , BOLANOWSKI, S.J. & BRACHMAN, M.L. (1977). Ef-
ferent optic nerve fibers mediate circadian rhythms in the Limulus eye. Science 197, 86-89. BARLOW, R.B., J R . , CHAMBERLAIN, S.C. & LEVINSON, J.Z. (1980). Lim-
The aperture: a reliable and novel technique for assessing A
