I fixed the code for photothermal effect (following Farsi), the calculation for substrate effect agrees with Cerdonio at low frequency. And both calculations (Cerdonio/ Farsi) agree if the coating thickness is zero.

 I found a mistake in my code for photothermal noise calculation and fixed it. Now the result agrees well with that of Cerdonio's. However, the effect from thermal expansion of coating may be wrong. I try using the parameters in their setup and have not come up with the similar plot they have. So, I'll have to check my calculation again.

 fig1: comparison between Cerdonio's and Farsi's calculation. The effect from coating(red) may be still incorrect.

Note: I use Riemann sum for the integral in both calculation. The step size has to be small enough for both calculations, otherwise the results won't match up nicely.