I figured out why folks befor eme had to use a different definition of effective coating coefficent of thermal expansion (CTE) as a simple weighted average of individual CTE of each layer instead of weighted average of modified CTE due to presence of substrate. The reason is that the modification factor is incorporated in another parameter gamma_1 and gama_2 in Farsi et al. Eq, A43. So they had to use a different definition of effective coating CTE since Farsi et al. treat it differently. That's my guess anyway since thermo-optic cancellation was demonstrated experimentally.
Following points are in relation to previously used noisebudget.ipynb file.
Following points are in relation to the new code at https://git.ligo.org/cit-ctnlab/ctn_noisebudget/tree/master/noisebudget/ObjectOriented.
The new noise budget code is ready. However, there are few discrepancies which still need to be sorted.
The code could be found at https://git.ligo.org/cit-ctnlab/ctn_noisebudget/tree/master/noisebudget/ObjectOriented
Please look into How_to_use_noiseBudget_module.ipynb for a detailed description of all calculations and code structure and how to use this code.
In the previous code, while doing calculations for Thermoelastic contribution to Photothermal noise, the code used a weighted average of coefficients of thermal expansion (CTE) of each layer weighted by their thickness. However, in the same code, while doing calculations for thermoelastic contribution to coating thermo-optic noise, the effective CTE of the coating is calculated using Evans et al. Eq. (A1) and Eq. (A2). These two values actually differ by about a factor of 4.
Currently, I have used the same effective CTE for coating (the one from Evans et al) and hence in new code, prediction of photothermal noise is higher. Every other parameter in the calculations matches between old and new code. But there is a problem with this too. The coating thermoelastic and coating thermorefractive contributions to photothermal noise are no more canceling each other out as was happening before.
So either there is an explanation to previous codes choice of using different effective CTE for coating, or something else is wrong in my code. I need more time to look into this. Suggestions are welcome.
The effective coating CTR in the previous code was 7.9e-5 1/K and in the new code, it is 8.2e-5 1/K. Since this value is calculated after a lot of steps, it might be round off error as initial values are slightly off. I need to check this calculation as well to make sure everything is right. Problem is that it is hard to understand how it is done in the previous code as it used matrices for doing complex value calculations. In new code, I just used ucomplex class and followed the paper's calculations. I need more time to look into this too. Suggestions are welcome.