Geometric optical optimization of the corneal lens of Notonecta glauca

The optimal shape of the corneal lens of the water bug backswimmer (Notonecta glauca) and the optimal shape and position of the thin transition layer between the distal and proximal units of its cornea are theoretically determined. Using a geometric optical method, first the shape of a geometric interface between the lens units is determined, which eliminates the longitudinal spherical aberration. This interface is investigated for differently formed thick lenses when the medium in contact with the entrance surface of the lens is water or air. The optimal transition layer for the amphibious backswimmer is that, the boundaries of which are the theoretical interfaces for water and air, and the refractive index varies continuously in it. The optimal shape of the corneal lens is determined, with the disadvantageous lenses, with respect to the possible minimal spherical aberration and amount of reflected light from the transition layer, being rejected. The optimal position of the transition layer in the cornea can be obtained from the minimization of the amount of diffracted light on the marginal connection of the layers. The optimal corneal lens for backswimmer has ellipsoid boundary surfaces; the optimal transition layer in it is thin bell-shaped, at the marginal connection of which there is no dimple, the maximum of the layer is on the margin of the cornea. The shape of the theoretically optimal corneal lens, the shape and position of the theoretically optimal transition layer agree well with those of Notonecta glauca. The question posed, the geometric optical method used and the results presented are of general importance, and not only with respect to vision in the bug Notonecta, but also in the fossil trilobites, or in the wave guide theories which have been employed in similar modelling problems, in design of system of lenses without spherical aberration, for example.