Dimensional limits for arthropod eyes with superposition optics.

An essential feature of the superposition type of compound eye is the presence of a wide zone, which is transparent and devoid of pigment and interposed between the distal array of dioptric elements and the proximally placed photoreceptive layer. Parallel rays, collected by many lenses, must (through reflection or refraction) cross this transparent clear-zone in such a way that they become focused on one receptor. Superposition depends mostly on diameter and curvature of the cornea, size and shape of the crystalline cone, lens cylinder properties of cornea and cone, dimensions of the receptor cells, and width of the clear-zone. We examined the role of the latter by geometrical, geometric-optical, and anatomical measurements and concluded that a minimal size exists, below which effective superposition can no longer occur. For an eye of a given size, it is not possible to increase the width of the clear-zone cz=dcz/R1 and decrease R2 (i.e., the radius of curvature of the distal retinal surface) and/or c=dc/R1 without reaching a limit. In the equations 'cz' is the width of the clear-zone dcz relative to the radius R1 of the eye and c is the length of the cornea-cone unit relative to R1. Our results provide one explanation as to why apposition eyes exist in very small scarabaeid beetles, when generally the taxon Scarabaeoidea is characterized by the presence of superposition eyes. The results may also provide the answer for the puzzle why juveniles or the young of species, in which the adults possess superposition (=clear-zone) eyes, frequently bear eyes that do not contain a clear zone, but resemble apposition eyes. The eyes of the young and immature specimens may simply be too small to permit superposition to occur.