In gamma ray astronomy muon events have a distinct feature of casting ring-like images on the sensor plane, thus forming a well known signal class for Cherenkov telescopes. These ring-like images can then be used to deduce the optical point spread function (PSF) which is an important measure of the optical quality of the imaging-reflector. In this thesis the observed 'fuzziness' of muon rings is used as a measure to infer the PSF. However to have a good estimate for this 'fuzziness' parameter, the reconstruction of the ring center and ring radius itself needs to be accurate, so different methods of ring feature extraction are studied. To check for the accuracy of the methods a simulation and analysis is performed. Measuring the evolution of the PSF over time allows to identify its effects and take them into account for the reconstruction of gamma-rays postliminary. As a further benefit of the methods presented here no additional observations are needed to measure the PSF nor any human activity on site is required. The accuracy of the method, and the PSF of FACT vs. time are presented.