A wide-angle gradient index optical model of the crystalline lens and eye of the octopus

Cephalopods and fish have had no common ancestor since the Cambrian, and their eyes are a classic example of convergent evolution. The octopus has no cornea, and immerson renders the trout cornea optically ineffective. As a result, the nearly spherical lens is responsible for all refraction in these eyes. In spite of the fact that the octopus lens consists of two joined parts, while the trout lens consists of one part, we show here that their optical properties are very similar. An index gradient bends rays within these lenses, adding power and correcting spherical aberration. High spherical symmetry in both lenses strongly reduces other monochromatic aberrations and yields a wide field of vision, advantageous in attack and evasion. The octopus Mattheissen's ratio, 2.83, an inverse measure of light-gathering power, lies above the trout value of 2.38 but within the range of values reported for fish. Strong uncorrected longitudinal chromatic aberration is nearly identical in both animals as a result of similar lens protein optical properties, and will limit resolution. We discuss how animal lifestyle requirements and lens material properties influence the design of these eyes.