Possible optical functions of the central core in lenses of trilobite eyes: spherically corrected monofocality or bifocality

Abstract

The function of the central core in lenses of certain schizochroal-eyed trilobites is unknown. To understand the possible optical function(s) of this central core, we performed computational ray-tracing on the lens in the schizochroal compound eyes of a Silurian Dalmanites trilobite. We computed the intensity of light focused by the lens versus the distance from the lower lens surface along the optical axis as functions of the refractive indices n(lu) and n(cc) of the lower lens unit and the central core. We determined those values of n(lu) and n(cc) that ensure that the studied central-cored trilobite lens is monofocal, bifocal, or trifocal. The sharpness (as the measure of the correction for spherical aberration) of these focal points was quantitatively studied. We show here that one of the possible optical functions of the central core could be the correction for spherical aberration, independently of the number (1, 2, or 3) of focal points. Another possible optical function of the core could be to ensure bifocality of the lens. In this case the peripheral lens region could have a given focal length and the central lens region could possess a longer or shorter focal length, if the refractive index n(cc) of the core is smaller or larger than the refractive index n(lu) of the upper lens unit. Finally, trifocality of the lenses can be considered only as a theoretical option, but by no means an optically optimally functioning possibility.