Model-based Reconstruction of Freeform Surfaces with Radial Basis Functions

Optical elements with freeform surfaces open new degrees of freedom in the design of optical systems. Reliable measurement of shape is challenging, specially in case of strongly curved ones. A realization of deflectometry, Experimental Ray Tracing, has proven to measure those surfaces with high accuracy. A crucial step is integration of measured gradients from sampled and noisy data. A model based method for surface reconstruction based on Radial Basis Functions (RBF) using non-linear optimization is presented and compared to a new machine learning based RBF-Network approach.