I calculate the spotsize on mirrors of different cavity length.
The setup for FSS experiment can be modified to measure coating thermal noise, (providing we can push down to coating noise limit).
The possible setup will have two cavities with different length. The short one will be more sensitive to coating than the long one.
(I'm not sure yet why should we have two short cavities.)
I used R=0.5 m mirrors in the calculation, since that what we have. the length starts from 1 cm to 20 cm.
Results from shorter length might be added later.
The blue plot shows the spotsize on the mirror for symmetric cavity,
the red and green plots show the spotsize on flat and curve mirror for curveflat cavity.
From [ref1], the minimum spot size that the adiabatic approximation still holds (with 1% accuracy) is
R_heat/ w ~0.01
R_heat is sqrt(k / Cf ), so for SiO2, k = 1.38 W/mK, C = 1.6 J / Km^3 R_heat is ~10 um at 10Hz,
Thus, the minimum spotsize is ~ 1 mm. The cavity length can go down to 5 mm.
