Inverse optical design of the human eye using likelihood methods and wavefront sensing

We are developing a method for estimating patient-specific ocular parameters, including surface curvatures, conic constants, tilts, decentrations, thicknesses, refractive indices, and index gradients. The data consist of the raw detector outputs from one or more Shack-Hartmann wavefront sensors, and the parameters in the eye model are estimated by maximizing the likelihood. A Gaussian noise model is used to emulate electronic noise, so maximum likelihood reduces to nonlinear least-squares fitting between the data and the output of our optical design program. The Fisher information matrix for the Gaussian model was explored to compute bounds on the variance of the estimates for different system configurations. In this preliminary study, an accurate estimate of a chosen subset of ocular parameters was obtained using a custom search algorithm and a nearby starting point to avoid local minima in the complex likelihood surface.