Ray tracing through a schematic eye containing second-order (quadric) surfaces using 4 x 4 matrix notation.

Ray tracing is used in ophthalmology for evaluation of the optical properties of the eye. We demonstrate an algebraic method for tracing a bundle of rays through the optical system of an eye containing aspheric surfaces. Restricting to second-order surfaces (quadric surfaces) such as ellipsoids, paraboloids or hyperboloids, a surface is described by a 4 x 4 matrix. In this case, the normal vector can be derived analytically and the ray-surface intersection is calculated by solving a quadratic equation. We applied this straightforward matrix-based strategy to the spherical 4-surface Le Grand schematic eye, and the Le Grand eye modified by Kooijman containing four aspheric surfaces. We calculated the spot diagram for the focal plane as well as a pre- and post-focal plane for both model eyes, and found that the optical quality of the aspheric model characterized by the ray scatter in the spot diagram at the focal plane is much better than that of the spherical model. This calculation strategy may be helpful for evaluating the image distortion of decentred or tilted spherical or aspheric artificial intra-ocular lenses.