Graded-index optics are matched to optical geometry in the superposition eyes of scarab beetles

Abstract

Detailed measurements were made of the gradients of refractive index (g.r.i.) and relevant optical properties of the lens components in the ventral superposition eyes of three crepuscular species of the dung-beetle genus Onitis (Scarabaeinae). Each ommatidial lens has two components, a corneal facet and a crystalline cone; in both of these, the gradients provide a significant proportion of the refractive power. The spatial relationship between the lenses and the retina (optical geometry) was also determined. A computer ray-trace model based on these data was used to analyse the optical properties of the lenses and of the eye as a whole. Ray traces were done in two and three dimensions. The ommatidial lenses in all three species are afocal g.r.i. telescopes of low angular magnification. Parallel incident rays emerge approximately parallel for all angles of incidence up to the maximum. The superposition image of a distant point source is a small patch of light about the size of a rhabdom. There are obvious differences in the lens properties of the three species, most significantly in the shape of the refractive-index gradients in the crystalline cone, in the extent of the g.r.i. region in the two lens components and in the front-surface curvature of the corneal facet lens. These give rise to different angular magnifications M of the ommatidial lenses, the values for the three species being 1.7, 1.3, 1.0. This variation in M is matched by a variation in optical geometry, most evident in the different clear-zone widths. As a result, the level of the best superposition image lies close to the retina in the model eyes of all three species. The angular magnification also sets the maximum aperture or pupil of the eye and hence the brightness of the image on the retina. The smaller M , the larger the aperture and the brighter the image. By adopting a suitable value for M and the appropriate eye geometry, an eye can set image brightness and hence sensitivity within a certain range. Differences in the eye design are related to when the beetles fly at dusk. Flight experiments comparing two of the species show that the species with the higher value for M and corresponding lower sensitivity, initiates and terminates its flight earlier in the dusk than the other species with 2.8 times the sensitivity.