I calculated the photothermal noise following the method from Farsi etal 2012 paper. The results is plotted below. I think I did something wrong, by looking at the low frequency part, the results from Cerdonio and Farsi do not agree. I'm still checking on it.

==Cerdonio  vs Farsi==

Cerdonio calculated the displacement noise due to thermal expansion of substrate induced by shot noise. This can be modified to estimate the noise due to absorption of RIN (see PSL:). Farsi extended the calculation to take thermal expansion and thermo refractive effect from coating into account. Since our measurement does not match up with Cerdonio's calculation that well.  I check if the mismatch comes from coating expansion or not. (I did not expect much, since the spotsize is 291 um, and the coating thickness is ~4um. Heat diffusion length ( ~ sqrt(k/2piCf ) )tells us that the effect from coating will be ~ 1000 Hz and above)

==result==

There are a few things that make me uncertain about my calculation code:

1. The effect from substrate is going up with wrong slope while it should match the calculation from Cerdonio at low frequency because the thermal diffusion length is much longer than the coating thickness and most of the effect comes from substrate only.
2. With our parameters the effect from coating is not significant until ~ a few kHz while it is dominating around 100 Hz for their setup.Their spot size on the mirror is~ 100um, so I expect that for our setup, the effect from the coating should kick in before 1kHz.

I'll double check my calculation again.