Application of radial basis functions for the surface reconstruction using deflectometry

Deflectometric methods have been employed for the topography measurement of specular surfaces, and when it comes to the final stage different approaches have been investigated to interpolate through the global shape to obtain a smooth object within an optimised local precision. To this end radial basis functions have been incorporated resulting an integration approach using Hermite-Birkhoff interpolation. In this paper we have focused on the effect of the width of the radial basis functions and a so called Expectation Maximization approach is followed to optimise the results which are then compared using Zemax simulations. As the results show this method will help improving the errors of the shape reconstruction by choosing a proper width for the basis function which are being used.