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“instead of being lens cylinders with high refractive indices and a radial gradient, the [optical structures of shrimps and their relatives] were square structures of low refractive index, made of more or less homogeneous jelly…[Klaus Vogt in 1975] found that the jelly blobs were silvered, and they were not lenses at all, but mirror boxes (Fig. 8.13b)…it now appears that this reflecting system is the rule throughout the long-bodies [sic] decopod crustaceans–the shrimps, prawns, lobsters, crayfish, and the anomuran squat lobsters…In essence the reflecting superposition mechanism is extremely simple. In 1975 Vogt wrote: ‘Rays from an object point entering through different facets are superimposed not by refracting systems as in other superposition eyes, but by a radial arrangement of orthogonal reflecting planes which are formed by the sides of the crystalline cones and the purine layers surrounding them.’ As Fig. 8.14 shows, the mirrors direct light to a common focus. Mirrors are inverters, just like the telescopes in refracting superposition eyes (Fig. 8.3b), and so the ray-bending that the two kinds of optical element perform is almost identical. However, problems start to arise when one tries to work out what will happen to rays that are not in the idealized central plane shown in Fig. 8.14b. In general, rays in oblique planes will not encounter just one side of each mirror box, but two. What happens to such rays? Do they, like the singly reflected rays in Fig. 8.14, all reach a common focus?

“It turns out that the square arrangement of the facet array (almost unique to the decapod crustaceans) is crucial here. The principle is that of the ‘corner reflector’ [like those mirrors found in corners of stores]…A ray reflected from the two mirrors must be rotated through a total of two right angles, which means that it will return parallel to its original direction, no matter what angle the ray initially makes with the mirror pair. In other words, apart from a slight lateral displacement of the reflected ray, a corner mirror behaves as though it were a single mirror, but one that is always at right angles to the incoming ray. This property turns out to be very useful, for example in radar reflectors for ships and buoys, and it is also the property that makes reflecting superposition possible…

“Various other features of these eyes are important for their function. The mirror boxes must be the right depth, two to three times the width, so that most rays are reflected from two of the faces, but not more. Rays that pass straight through are intercepted by the unsilvered ‘tail’ of the mirror boxes, and Vogt (1980) showed that its refractive index decreases in such a way that appropriate critical angle reflexion continues to occur through the clear zone. Finally, there is the weak lens in the cornea of the crayfish. This lens ‘pre-focuses’ the light that enters the mirror box, thus given a narrower beam at the retina. All these features provide an image generally comparable in quality to that produced by refracting superposition optics (Bryceson and McIntyre), although it does seem that rays which make too many or too few reflections contribute to measurable stray light (glare) in the image of on the retina.” (Land and Nilsson 2002:172-174)