I fixed the calculation for photothermal noise and compare it with the measured results. This time, they agree quite well.
I include **Thermo expansion** and **Thermo refractive **effects in **coatings **in to the calculation, and make sure that they are treated coherently. However I still use Farsi's calculation, not GWINC code (see below for why). Now the calculated TF shape agrees well with the measurement. However, the magnitude is still off by a factor of ~5. This can come from the calibration from power to Volt on the PD_trans_dc (from PSL:xx), the measurement data is taken from PSL:1021. The absorption I use for calculation is 5ppm, finesse is 7500. These numbers contribute to the magnitude of the calculated TF. I'll try to plot it with confidence interval to see if it will be close to the measured result or not.
**==why not GWINC?==**
Since GWINC code has a section(s) for thermo-optic noise (TO) calculation (following Evans 2008 paper), we should be able to modify it to produce the result for RIN induced noise in our case.__ However, there is one complication for this option.__ GWINC calculates (TO) by using the **[ Power spectral of temperature fluctuation on surface**] x **[dphi/dT]**.** [dphi/dT]** is derived from the coating structure and materials' properties. However, the temperature fluctuation on the surface is derived by fluctuation-dissipation theorem then averaged over a guassian beam profile(see Levin,2002). Hence, to use GWINC code to calculate our result, we need to calculate the pwr spectral density of the surface temperature which is heated up by gaussian beam profile, and averaged over gaussian beam as well. I'll try to do this later when I have more free time.
I reviewed Farsi calculation carefully They follow the sign for TE and TR in the coating(practically following Evans' paper),so I think it is valid as well. Even though Farsi calculates the effect from the first few layers which, as they claim, contribute most to TR, their argument agrees with the result provided by Evans' paper where they compare TR effect between ITM(8doublets), and ETM(19doublets) which are almost the same.
Plus, the effect from coating becomes comparable to that of substrate around 100 Hz and higher frequency. This means the contribution from substrate and coating must be calculated together, which is nicely done by Farsi as well. (This means you cannot just calculate the effect from a bare substrate, ie. from cerdonio, and add the effect from the coating on top of one another) Since we are going to use the calculation from substrate with coating from them, why not the coating calculation as well? |