  Increasing requirements in the sensitivity of interferometric measurements is
a common feature of several research fields, from gravitational wave detection
to quantum optics. This motivates refined studies of high reflectivity mirrors
and of noise sources that are tightly related to their structure. In this work
we present an experimental characterization of photothermal and
thermo-refractive effects in high reflectivity mirrors, i.e., of the variations
in the position of their effective reflection plane due to weak residual power
absorption. The measurements are performed by modulating the impinging power in
the range 10 Hz $\div$ 100 kHz. The experimental results are compared with an
expressly derived theoretical model in order to fully understand the phenomena
and exploit them to extract useful effective thermo-mechanical parameters of
the coating. The measurements are extended at cryogenic temperature, where most
high sensitivity experiments are performed (or planned in future versions) and
where characterizations of dielectric film coatings are still poor.
