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Most applications in optical metrology need a well calibrated camera. In particular, a calibrated camera includes a distortion mapping, parameters of which are determined in a final non-linear optimization over all camera parameters. In this article we present a closed form solution for the distortion parameters provided that all other camera parameters are known. We show that for radial, tangential, and thin prism distortions the determination of the parameters form a linear least squares problem. Therefore, a part of the camera calibration error function can be minimized by linear methods in closed form: We are able to decouple the calculation of the distortion parameters from the non-linear optimization. The number of parameters in the non-linear minimization are reduced. Several experimental results confirm the benefit of the approach.