First- and Third-Order Optical Theory of Gradient Index Materials, with Application to Contact Lenses

Purpose. To investigate the feasibility of using gradient index media in contact lenses, we developed simple methods which we used to derive the power and aberrations associated with the contact lenses. Methods. In one method, we assume that the height of a ray does not change as it passes through the lens. We describe a second method in which the ray is assumed to follow a parabolic path as it passes through the lens. We use sophisticated third-order theory and finite raytracing for comparison with these methods. Results. The methods are compared for contact lenses with parabolic radial gradient index media. Without the gradient index, these lenses would have zero power. The formula for power which assumes no change in ray height gives errors of approximally 0.8 and 1.5% for lenses of thickness 0.18 and 0.36 mm. However, the formula for third-order spherical aberration which uses the same assumption gives poor estimations. The method for calculating power using the parabolic ray path is very accurate. The sophisticated third-order aberration theory was reasonably accurate out to 2.5 mm ray height. The contact lenses with the gradient index media have much smaller aberration in air than do conventional contact lenses of the same powers, with the sign of the aberration being reversed. Conclusion. Our simple procedures give good estimations of powers of contact lenses with gradient index media. The approximate method, which assumes that the height of a ray does not change as it passes through the lens, should not be used for finding the spherical aberration of such a lens. Contact lenses with gradient index media have potential for minimizing spherical aberration