Theoretical Eye Model with Aspherics*

Abstract

A model for the human eye is proposed, similar to Gullstrand’s well-known 4-radius model, however with the front surface of the cornea and the back surface of the crystalline lens taken to be rotationally symmetric aspherics. Whereas for the cornea a polynomial is used based on experimental data of Bonnet, a second-order parabola was tentatively adopted for the back surface of the lens. This model results in slight spherical undercorrection, in agreement with experimental findings. On the other hand, the sine condition is not well satisfied, probably due to neglect of the shell structure of the lens. By ray tracing, astigmatism and coma as well as the meridional and sagittal focal lengths were computed up to a visual angle of 90°. Calculations were also made for the same model preceded by a plano-concave contact lens (Goldmann 3-mirror contact glass), showing that this combination results in considerably reduced astigmatism.