  Low internal friction coatings are key components of advanced technologies
such as optical atomic clocks and high-finesse optical cavity and often lie at
the forefront of the most advanced experiments in Physics. Notably, increasing
the sensitivity of gravitational-wave detectors depends in a very large part on
developing new coatings, which entails developing more suitable methods and
models to investigate their loss angle. In fact, the most sensitive region of
the 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 which
describe only ideal physical properties have been adopted, wondering about the
use of one or more loss angles to describe the mechanical properties of
coatings. Here we show the presence of a systematic error ascribed to
inhomogeneity of the sample at its edges in measuring the coating loss angle.
We present a model for disk-shaped resonators, largely used in loss angle
measurements, and we compare the theory with measurements showing how this
systematic error impacts on the accuracy with which the loss model parameters
are known.
