The Optics of the Compound

No anatomic description of CEs is complete without a consideration of how light reaches the photosensory rhabdoms of the retinula cells. The outer surface of the CE is covered with transparent cuticle subdivided into many hexagonally packed corneal convex lenslets, each over an ommatidium. The cornea is from 30 to 50 |im thick, and serves to protect the soft visual cells beneath it. Directly under each corneal lenslet, there is a crystalline conical lens that acts as a "light funnel" to channel light energy down the center of the ommatidium to the retinula cell rhab-doms. The purpose of this conical lens is to concentrate photon energy on the transducer region of each retinula cell. The conical lens arises from four specialized

FIGURE 5.1-10 Low-magnification light micrograph of silver-stained, coronal section through a Romalea OL. Note the many different layers of neurons in the medulla (M), and in the lobula (L) neuropile, the large neuron cell bodies outside the neuropile, and the tracts running between neuropile masses. (T) trachea, (H) hemolymph channel. (From Northrop, R.B. and E.F. Guignon, J. Insect Physiol., 16: 691, 1970. With permission.)

FIGURE 5.1-10 Low-magnification light micrograph of silver-stained, coronal section through a Romalea OL. Note the many different layers of neurons in the medulla (M), and in the lobula (L) neuropile, the large neuron cell bodies outside the neuropile, and the tracts running between neuropile masses. (T) trachea, (H) hemolymph channel. (From Northrop, R.B. and E.F. Guignon, J. Insect Physiol., 16: 691, 1970. With permission.)

Semper cells lying under the cornea. In the CEs of primitive arthropods (e.g., Machilis), the cone is formed directly from the Semper cells, or by special structures secreted by them. In many CEs, the cone is shielded on the sides by pigment cells (Mazokhin-Porshnyakov, 1969). (Figure 5.1-2 above illustrates schematically the anatomic variations of cone lens design between arthropod species.) The rhabdom region of retinula cells is known to have a higher refractive index than do the surrounding cells. This means that light entering the rhabdoms from the cone is trapped in them (a fiber-optic effect), contributing to the efficiency of the transduc-tion process.

A retinula cell of a CE ommatidium can be characterized by a directional sensitivity function (DSF), s(0, It will be seen in the next section that, in general, the narrower the DSF, the higher the resolution of the CE. The DSF is a normalized function; i.e., s(0, 0) = 1. Also, s(0m/2, 0) = 0.5. To measure a DSF, the back of the insect's head is removed, and a glass micropipette microelectrode with a very small tip is inserted into a retinula cell with minimum physical disturbance. A movable, bright point-source of white light is suspended on a semicircular track centered over the eye. The amplitude of the retinula cell depolarization is recorded as a function of the angular position of the light, which is flashed on and off. When the light is centered over the ommatidium under study (generally near a line perpendicular to

FIGURE 5.1-11 Scheme of basic neural connections in the OL of an Aeschna (dragonfly) larva. Key: I, lamina ganglionaris; II, medulla; III, lobula; HX and BX, external and internal chiasmata, respectively; OT, optic tract. (The medulla actually has more than three anatomical layers.) Types of neurons: 1, fibers from retinula cells (swelling is not soma); 2 and 4, small and large lamina monopolar cells; 3, recurrent monopolar cell; bipolar interneurons 12, 14, 15, 16, and 17 connect individual ganglion layers directly to the brain. Other interneurons interconnect ganglia; some apparently provide centrifugal feedback. (From Mazokhin-Porsh-nyakov, G.A., Insect Vision, Plenum Press, New York, 1969. With permission.)

FIGURE 5.1-11 Scheme of basic neural connections in the OL of an Aeschna (dragonfly) larva. Key: I, lamina ganglionaris; II, medulla; III, lobula; HX and BX, external and internal chiasmata, respectively; OT, optic tract. (The medulla actually has more than three anatomical layers.) Types of neurons: 1, fibers from retinula cells (swelling is not soma); 2 and 4, small and large lamina monopolar cells; 3, recurrent monopolar cell; bipolar interneurons 12, 14, 15, 16, and 17 connect individual ganglion layers directly to the brain. Other interneurons interconnect ganglia; some apparently provide centrifugal feedback. (From Mazokhin-Porsh-nyakov, G.A., Insect Vision, Plenum Press, New York, 1969. With permission.)

FIGURE 5.1-12 (A) Schematic structure of the OL of the fly Calliphora vomitoria, based on the pioneering neuroanatomical work of Cajal and Sanchez, 1915. (Compare this to the author's light micrograph, Figure 5.1-11a and b.) Key: BM, basement membrane; OK, retinula cell axons (nonspiking); other symbols as in Figure 5.1-12. Note that three, distinct afferent tracts are shown. (B) Schematic of the optic ganglia of the butterfly Celerio euphorbiae. Same notation is used. Note that fibers from the retinula cells are organized into bundles, between which are found hemolymph channels and tracheae. (From Mazokhin-Porshnyakov, G.A., Insect Vision, Plenum Press, New York, 1969. With permission.)

FIGURE 5.1-12 (A) Schematic structure of the OL of the fly Calliphora vomitoria, based on the pioneering neuroanatomical work of Cajal and Sanchez, 1915. (Compare this to the author's light micrograph, Figure 5.1-11a and b.) Key: BM, basement membrane; OK, retinula cell axons (nonspiking); other symbols as in Figure 5.1-12. Note that three, distinct afferent tracts are shown. (B) Schematic of the optic ganglia of the butterfly Celerio euphorbiae. Same notation is used. Note that fibers from the retinula cells are organized into bundles, between which are found hemolymph channels and tracheae. (From Mazokhin-Porshnyakov, G.A., Insect Vision, Plenum Press, New York, 1969. With permission.)

FIGURE 5.1-13 Comparison between the intracellulary recorded potentials of LMCs and their associated retinula cells in the dragonfly Hemicordula tau. Stimulus is a 500 ms flash from a point source of white light. Light intensity is attenuated by neutral density filters. (Thus -4.3 means the source is attenuated by 4.3 log10 units.) Horizontal bars are all 500 ms; vertical bars are all 10 mV. Note the retinula cells depolarize while the LMCs hyperpolarize; neither types spike. (From Laughlin, S.B., in The Compound Eye and Vision in Insects, G.A. Horridge, Ed., Clarendon Press, Oxford, 1975. With permission of Oxford University Press.)

FIGURE 5.1-14 Graphs of response/intensity for retinula cells and LMCs of the dragonfly Hemicordula tau. —o—, magnitude of the peak response of LMCs to flashes. —•—, plateau magnitude response of LMCs. —A—, retinula cell response. Note that retinula cell responses are log-linear over about two decades of intensity. Curiously, at high intensities, the plateau magnitude response of the LMCs decreases. (From Laughlin, S.B., in The Compound Eye and Vision in Insects, G.A. Horridge, Ed., Clarendon Press, Oxford, 1975. With permission of Oxford University Press.)

FIGURE 5.1-14 Graphs of response/intensity for retinula cells and LMCs of the dragonfly Hemicordula tau. —o—, magnitude of the peak response of LMCs to flashes. —•—, plateau magnitude response of LMCs. —A—, retinula cell response. Note that retinula cell responses are log-linear over about two decades of intensity. Curiously, at high intensities, the plateau magnitude response of the LMCs decreases. (From Laughlin, S.B., in The Compound Eye and Vision in Insects, G.A. Horridge, Ed., Clarendon Press, Oxford, 1975. With permission of Oxford University Press.)

a tangent plane touching the corneal facet of the ommatidium under study), a maximum response is noted. As the light source is traversed away from the maximum axis, the response falls off to zero. The shape of the DSF curve depends on the state of light adaptation of the CE, and on absolute intensity of the light, so this must be standardized. Recall that the retinula cell depolarization responds in a logarithmic manner to light intensity (see Equation 5.1-1). The DSF in a light-adapted (LA) eye is narrower than that of a dark-adapted (DA) eye because of pigment shielding in the LA ommatidia. Figure 5.1-15 shows a large difference in the DSFs of the eye of the cockroach Periplaneta americana for a LA vs. a DA eye. Circles are electrophysiological data; solid curves are fits by a mathematical model for the DSFs. Another set of DSFs for DA and LA locust retinula cells is shown in Figure 5.1-16. These investigators found that the locust DSFs were in fact slightly elliptical in two-dimensional shape, rather than circular. They found that the mean 8m/2 for the intensity DSF for an LA locust retinula cell was about 1.7°. The DSF peak was pointy, which means that trying to model it with a Gaussian function is not as accurate as a Hill hyperbolic function, e.g., s(x) = 1/(1 + (x/8m/2)2).

Wilson (1975) (cited in Northrop, 1975) measured DSFs in LA locust eyes, and found mean 8m/2 = 0.73° in the horizontal plane and 8m/2 = 0.685° in the vertical plane for ten animals. That Wilson's 8m/2 values were significantly smaller is probably due to extreme light adaptation and careful microelectrode technique. As will be seen, Wilson's smaller 8m/2 values make it easier to make a model for anomalous resolution in the CEs of locusts.

FIGURE 5.1-15 Normalized, percent angular sensitivity as a function of the angle 0 of light incident upon a facet of the eye of the cockroach Periplaneta americana. Solid curves represent theoretical calculations. Circles are from electrophysiological measurements. DA, dark-adapted eye; LA, light-adapted eye. Note the large increase in 0m/2 for the dark-adapted eye. (From Snyder, A.W., in The Compound Eye and Vision in Insects, G.A. Horridge, Ed., Clarendon Press, 1975. With permission of Oxford University Press.)

FIGURE 5.1-15 Normalized, percent angular sensitivity as a function of the angle 0 of light incident upon a facet of the eye of the cockroach Periplaneta americana. Solid curves represent theoretical calculations. Circles are from electrophysiological measurements. DA, dark-adapted eye; LA, light-adapted eye. Note the large increase in 0m/2 for the dark-adapted eye. (From Snyder, A.W., in The Compound Eye and Vision in Insects, G.A. Horridge, Ed., Clarendon Press, 1975. With permission of Oxford University Press.)

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Locust Compound Eye

FIGURE 5.1-16 The averaged DSFs for 50 dark-adapted and 50 light-adapted locust reti-nula cells. Vertical scale, linear % sensitivity; horizontal scale, linear angle between point source and ommatidial center axis. Note that the dark-adapted eye trades off resolution for sensitivity; it has about double the 0m/2 as the light-adapted eye. These DSFs have sharp peaks. (From Tunstall, J. and Horridge, G.A., Z. Veral. Physiol., 55: 167, 1967. With permission from Springer-Verlag.)

FIGURE 5.1-16 The averaged DSFs for 50 dark-adapted and 50 light-adapted locust reti-nula cells. Vertical scale, linear % sensitivity; horizontal scale, linear angle between point source and ommatidial center axis. Note that the dark-adapted eye trades off resolution for sensitivity; it has about double the 0m/2 as the light-adapted eye. These DSFs have sharp peaks. (From Tunstall, J. and Horridge, G.A., Z. Veral. Physiol., 55: 167, 1967. With permission from Springer-Verlag.)

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