The optics of the spherical fish lens

Abstract

The optical design of the fish eye is particularly simple because immersion renders the cornea optically ineffective and the lens is nearly spherical in shape. Measurements have shown that an approximately parabolic gradient of refractive index exists within the lens. If full internal and external spherical symmetry of the lens applies, the geometrical-optical behaviour of the lens is then a function only of the refractive index of the surrounding medium, that of the lens core and cortex, and of the form of the index gradient. The theoretical optical performance of models of the spherical fish lens is calculated by means of the ray-tracing program Drishti as a basis for understanding the optical design of real fish and aquatic eyes. Models based on the gradients proposed by earlier workers are shown to be unable to predict reported spherical aberration and image quality. A model of the fish lens with a polynomial gradient is proposed that yields spherical aberration, image quality and chromatic aberration similar to that reported for the fish.