I've been working on analyzing the data from the DRMI locks last week.

Here are the results of the sensing measurement.

Details:

1. The sensing measurement is done by using the existing sensing matrix infrastructure to drive the actuators for the various DoFs at specific frequencies (notches at these frequencies are turned on in the control loops during the measurement).
2. All the analysis is done offline - I just note down the times at which the sensing lines are turned on and then download the data later. The amplitudes of the oscillators are chosen by looking at the LSC PD error signal spectra "live" in DTT, and by increasing the amplitude until the peak height is ~10x above the nominal level around that frequency. This analysis was done on ~600seconds of data.
3. The actual sensing elements in the various PDs are calculated as follows:
   • Calculate the Fourier coefficients at the excitation frequency using the definition of the complex DFT in both the LSC PD signal and the actuator signal (both are in counts). Windowing is "Tukey", and FFT length used is 1 second.
   • Take their ratio
   • Convert to suitable units (in this case V/m) knowing (i) The actuator discriminant in cts/m and (ii) the cts/V ADC calibration factor. Any whitening gain on the PD is taken into account as well.
   • If required, we can convert this to W/m as well, knowing (i) the PD responsivity and (ii) the demodulation chain gain.
   • Most of this stuff has been scripted by EricQ and is maintained in the pynoisesub git repo.

The plotting utility is a work in progress - I've basically adapted EricQs scripts and added a few features like plotting the uncertainties in magnitude and phase of the calculated sensing elements. Possible further stuff to implement:

• Only plot those elements which have good coherence in the measurement data. At present, the scripts check the coherence and prompt the user if there is poor coherence in a particular channel, but no vetos are done.
• The uncertainty calculation is done rather naively now - it is just the standard deviation in the fourier coefficient determined from various bins. I am told that Bendat and Piersol has the required math. It would be good to also incorporate the uncertainties in the actuator calibration. These are calculated using the python uncertainties package for now.
• Print a summary of the parameters used in the calculation, as well as sensing elements + uncertainty in cts/m, V/m and W/m, on a separate page.
• Some aesthetics can be improved - I've had some trouble getting the tick intervals to cooperate so I left it as is for the moment.

Also, the value I've used for the BS actuator calibration is not a measured one - rather, I estimated what it will be by scaling the old value by the same ratio which the ITMs have changed by post de-whitening board mods. The ITM actuator coefficients were recently  measured here. I will re-do the BS calibrations over the weekend.

Noise budgeting to follow - it looks like I didn't set the AS55 demod phase to the previously determined optimal value of -82degrees, I had left it at -42 degrees. To be fixed for the next round of locking.