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Low internal friction coatings are key components of advanced technologiessuch as optical atomic clocks and high-finesse optical cavity and often lie atthe forefront of the most advanced experiments in Physics. Notably, increasingthe sensitivity of gravitational-wave detectors depends in a very large part ondeveloping new coatings, which entails developing more suitable methods andmodels to investigate their loss angle. In fact, the most sensitive region ofthe detection band in such detectors is limited by the coating thermal noise,which is related to the loss angle of the coating. Until now, models whichdescribe only ideal physical properties have been adopted, wondering about theuse of one or more loss angles to describe the mechanical properties ofcoatings. Here we show the presence of a systematic error ascribed toinhomogeneity of the sample at its edges in measuring the coating loss angle.We present a model for disk-shaped resonators, largely used in loss anglemeasurements, and we compare the theory with measurements showing how thissystematic error impacts on the accuracy with which the loss model parametersare known.

A Systematic Error in the Internal Friction Measurement of Coatings for Gravitational Waves Detectors