Inverse Optical Design and Its Applications

Abstract

We present a new method for determining the complete set of patient-specific ocular parameters, including surface curvatures, asphericities, refractive indices, tilts, decentrations, thicknesses, and index gradients. The data consist of the raw detector outputs of one or more Shack-Hartmann wavefront sensors (WFSs); unlike conventional wavefront sensing, we do not perform centroid estimation, wavefront reconstruction, or wavefront correction. Parameters in the eye model are estimated by maximizing the likelihood. Since a purely Gaussian noise model is used to emulate electronic noise, maximum-likelihood (ML) estimation reduces to nonlinear least-squares fitting between the data and the output of our optical design program. Bounds on the estimate variances are computed with the Fisher information matrix (FIM) for different configurations of the data-acquisition system, thus enabling system optimization. A global search algorithm called simulated annealing (SA) is used for the estimation step, due to multiple local extrema in the likelihood surface. The ML approach to parameter estimation is very time-consuming, so rapid processing techniques are implemented with the graphics processing unit (GPU).We are leveraging our general method of reverse-engineering optical systems in optical shop testing for various applications. For surface profilometry of aspheres, which involves the estimation of high-order aspheric coefficients, we generated a rapid ray-tracing algorithm that is well-suited to the GPU architecture. Additionally, reconstruction of the index distribution of GRIN lenses is performed using analytic solutions to the eikonal equation. Another application is parameterized wavefront estimation, in which the pupil phase distribution of an optical system is estimated from multiple irradiance patterns near focus. The speed and accuracy of the forward computations are emphasized, and our approach has been refined to handle large wavefront aberrations and nuisance parameters in the imaging system.