I used the calibration of North and South NPRO control voltage to frequency change from CTN:1948.
Then using the following formula:
![\frac{\Delta T}{\Delta V} = \frac{S[\frac{Hz}{V}]}{-\alpha [\frac{1}{K}]\frac{c[\frac{m}{s}]}{\lambda [m]}}](https://latex.codecogs.com/gif.latex?%5Cfrac%7B%5CDelta%20T%7D%7B%5CDelta%20V%7D%20%3D%20%5Cfrac%7BS%5B%5Cfrac%7BHz%7D%7BV%7D%5D%7D%7B-%5Calpha%20%5B%5Cfrac%7B1%7D%7BK%7D%5D%5Cfrac%7Bc%5B%5Cfrac%7Bm%7D%7Bs%7D%5D%7D%7B%5Clambda%20%5Bm%5D%7D%7D)
where S is the calibration slope for NPRO from volts to the frequency
 is the coefficient of thermal expansion of fused silica, 
c is the speed of light 299792458 m/s
The offset was adjusted so that at t=0, the cavity temperatures is the same as the vacuum can in-loop temperature sensor reading at t=0.
This gave for the South Cavity -22.456 K/V and for the North Cavity -23.489 K/V
The South Cavity temperature changed 0.511 K, 0.539 K, and 0.565 K in the first step on the three days. Mean response to the first step is 0.538 K.
The North Cavity temperature changed 0.520 K, 0.574 K, and 0.639 K in the first step on the three days. Mean response to the first step is 0.578 K.
The South Cavity temperature changed -0.878 K, -0.860 K, and -0.863 K in the second step on the three days. Mean response to the second step is -0.867 K.
The North Cavity temperature changed -0.903 K, -0.933 K, and -0.910 K in the second step on the three days. Mean response to the second step is -0.915 K.
Code and Data
Edit Fri Sep 6 12:01:49 2019 anchal in RED above.
Found out that there is a bored hole in the spacer so the laser doesn't travel in fused silica actually. So the refractive index used above is wrong.
Updated calculations and plots for the same. |