GV Oct 6: This coupling is probably not correct - Finesse outputs TF magnitude in units of W/W, and not W/RIN. 

Since I was foiled (by lack of DAC) in my attempt to measure the coupling of laser intensity noise to MICH in the DRMI (no arms) configuration, I decided to try understanding the effect with a simulation.

For this purpose, I used my DRMI Finesse model - this had mirror positions tuned for locking and photodiode demod phases tuned to give a sensing matrix model that wasn't too far from an actual measurement (within factor of a few). So the model seems okay for a first pass at estimating this coupling.

Measuring transfer functions in Finesse is straightforward - use the fsig command to modulate some quantity (in this case the input beam intensity), and use the pd2 detector to demodulate the effect of this modulation at the port of interest (in this case AS55_Q).

**Note that to apply a modulation to an input beam (i.e. Laser) in Finesse, the keyword for the "type" argument given to fsig is "amp" and not "amplitude" as the manual would had me believe. In fact, there seem to be quite a few such caveats. The best way to figure this out is to go to the pykat installation directory, find the file components.py, and look for the fsig_name for the component of interest. It is also indicated in the same file, via the canFsig argument, if that property of the component can be modulated for transfer function measurements.  

Attachment #1 shows the result of such a sweep.

To estimate what the actual contribution to the displacement noise is, I used the DQ-ed MC transmission (recorded at 1024Hz) from the DRMI lock, computed the ASD using scipy.signal.welch, divided by the nominal MC transmission of ~15,000 counts to convert to RIN/rtHz. The RIN was then multiplied by the above calculated coupling function, and divided by the sensing matrix element for AS55_Q (in units of W/m) to give the curve shown in Attachment #2. If we believe the simulation, then Laser Intensity Noise shouldn't be the limiting noise between 10Hz-1kHz. 

I will of course measure the actual coupling and see how it lines up with Attachment #1 - would be a nice additional validation of the Finesse model. I will also try using the Finesse model to estimate some other coupling transfer functions (e.g. Laser Frequency Noise, Oscillator Noise).