AN OPTIMIZATION METHOD FOR THE RECONSTRUCCTION OF THE CRYSTALLINE GRIN

Abstract

In this paper, we present a method for obtaining the parameters characterizing the distribution of refractive index (GRIN) of a crystalline from measurements of the path of a light ray before and after passing through the isolated lens. The problem to be solved is addressed as an optimization one. We describe the procedure to calculate the ray path through the crystalline, based on the variational principle of Fermat, as a fundamental part of the method. To solve the optimization problem SIMPLEX (Nelder & Mead) and quasi-Newton (BFGS) methods are used, combined with the global search algorithm BASIN-HOPPING. To evaluate the method, the GRIN biparabolic model is used. We analyze the influence of the experimental uncertainties in the measurements of the ray paths and the number of measurements on the accuracy of the reconstruction. The results show that the method allows the GRIN reconstruction with acceptable accuracies (uncertainties below 10-2) for experimental uncertainties with standard deviation smaller than 10-3. Starting from 80, the number of rays measured had no considerable influence on the accuracy of the GRIN’s reconstruction. Using SIMPLEX and quasi-Newton algorithms comparable results are obtained, but the latter is more efficient.