Refracting, reflecting, and parabolic optical mechanisms

In superposition eyes the number of facets that contribute to the production of a single image depends on the type of optical mechanism involved. There are three general mechanisms, based on lenses (refracting superposition), mirrors (reflecting superposition), and lens-mirror combinations (parabolic superposition).

The refracting superposition mechanism was discovered by Austrian physiologist Sigmund Exner in the 1880s. He reasoned that the geometrical requirement for superposition was that each lens element should bend light in such a way that rays entering the element at a given angle to its axis would emerge at a similar angle on the same side of the axis. Exner realized that this was not the behaviour of a normal lens, which forms an image on the opposite side of the axis from the entering ray. He worked out that the only optical structures capable of producing the required ray paths were two-lens devices, specifically two-lens inverting telescopes. However, the lenslike elements of superposition eyes lack the necessary power in their outer and inner refracting surfaces to operate as telescopes. Exner solved this by postulating that the elements have a lens cylinder structure with a gradient of refractive index capable of bending light rays continuously within the structure. This is similar to the apposition lens cylinder elements in the Limulus eye (see above Apposition eyes); the difference is that the telescope lenses would be twice as long. The lens cylinder arrangement produces the equivalent of a pair of lenses, with the first lens producing a small image halfway down the structure and the second lens turning the image back into a parallel beam. In the process the ray direction is reversed. Thus, the emerging beam is on the same side of the axis as the entering beam—the condition for obtaining a superposition image from the whole array. In the 1970s, studies using an interference microscope, a device capable of exploring the refractive index distribution in sections of minute objects, showed that Exner’s brilliant idea was accurate in all important details.

There is one group of animals with eyes that fit the anatomical criteria for superposition but that have optical elements that are not lenses or lens cylinders. These are the long-bodied decapod crustaceans, such as shrimps, prawns, crayfish, and lobsters. The optical structures are peculiar in that they have a square rather than a circular cross section, and they are made of homogeneous low-refractive index jelly. For a period of 20 years—between 1955, when interference microscopy showed that the jelly structures lacked appropriate refracting properties, and 1975, when the true nature of these structures was discovered—there was much confusion about how these eyes might function. Working with crayfish eyes, German neurobiologist Klaus Vogt found that these unpromising jelly boxes were silvered with a multilayer reflector coating. A set of plane mirrors, aligned at right angles to the eye surface, change the direction of rays (in much the same way as len cylinders), thereby producing a single erect image by superposition. The square arrangement of the mirrors has particular significance. Rays entering the eye at an oblique angle encounter two surfaces of each mirror box rather than one surface. In this case, the pair of mirrors at right angles acts as a corner reflector. Corner reflectors reflect an incoming ray through 180 degrees, irrespective of the ray’s original direction. As a result, the reflectors behave as though they were a single plane mirror at right angles to the ray. This ensures that all parallel rays reach the same focal point and means that the eye as a whole has no single axis, which allows the eye to operate over a wide angle.

The third type of superposition eye, discovered in 1988 in the crab genus Macropipus by Swedish zoologist Dan-Eric Nilsson, has optical elements that use a combination of a single lens and a parabolic mirror. The lens focuses an image near the top of the clear zone (similar to an apposition eye), but oblique rays are intercepted by a parabolic mirror surface that lines the crystalline cone beneath the lens. The parabolic mirror unfocuses the light and redirects it back across the axis of the structure, producing an emerging ray path similar to that of a refracting or reflecting superposition eye.

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branchiopod: Responses to light

All three types of superposition eyes have adaptation mechanisms that restrict the amount of light reaching the retina in bright conditions. In most cases, light is restricted by the migration of dark pigment (held between the crystalline cones in the dark) into the clear zone; this cuts off the most oblique rays. However, as the pigment progresses inward, it cuts off more and more of the image-forming beam until only the central optical element supplies light to the rhabdom (located immediately below the central optical element). This effectively converts the superposition eye into an apposition eye, since in the dark-adapted condition up to a thousand facets may contribute to the image at any one point on the retina, potentially reducing the retinal illumination a thousandfold.

Optics of superposition eyes

Superposition optics requires that parallel rays from a large portion of the eye surface meet at a single point in the image. As a result, superposition eyes should have a simple spherical geometry, and, in fact, most superposition eyes in both insects and crustaceans are spherical. Some moth eyes do depart slightly from a spherical form, but it is in the euphausiid crustaceans (krill) from the mid-waters of the ocean that striking asymmetries are found. In many krill species the eyes are double. One part, with a small field of view, points upward, and a second part, with a wide field of view, points downward (similar to the apposition eyes of hyperiid amphipods). It is likely that the upper part is used to spot potential prey against the residual light from the sky, and the lower part scans the abyss for bioluminescent organisms. The most extraordinary double superposition eyes occur in the tropical mysid shrimp genus Dioptromysis, which has a normal-looking eye that contains a single enormous facet embedded in the back, with an equally large lens cylinder behind the facet. This single optical element supplies a fine-grain retina, which seems to act as the “fovea” of the eye as a whole. At certain times the eyes rotate so that the single facets are directed forward to view the scene ahead with higher resolution, much as one would use a pair of binoculars.