Bayesian Estimation for White Light Interferometry

In this thesis, a new approach for the reconstruction of height maps from scanning white light interferometry is presented. This method unifies the conventional steps of preand postprocessing within Bayesian inference. An adept formulation of the prior allows for the exact computation of the height estimate, obviating the need for stochastic sampling or simulation methods. In conventional surface estimation for white light interferometry, a primary height map is calculated pixel-wise from the raw data, followed by a postprocessing step where outliers and other measurement artifacts are removed. Established and novel algorithms for both steps are discussed. The techniques of Bayesian inference for 2-D image processing, on which the novel surface estimation approach bases, are presented afterwards. For this new method, the localization of the fringe pattern is represented by the likelihood function, while the knowledge about the general surface properties goes into the prior probability of local height configurations. Both the 3-D data set and this prior are considered simultaneously in the estimation procedure, which analytically yields the optimum surface reconstruction as a mode of the marginal posterior probability. A method for quantitative comparison of height maps is developed and used to assess the performance of different postprocessing algorithms.