Summary: adding a digital offset to get a flat sensing function does not correspond to SRM detuning phase of 90, as modeled in FINESSE.

recap: I have modeled the SRCL DOF detuning due to mode mismatch. Nominally, we want the detuning phase of the SRM to be ø = 90˚ for resonant  sideband extraction conditions, where there are no optical spring effects. However, mode mismatches affect this phase, and consequently we can see optical spring effects showing up in the DARM sensing function.

On site, after locking we can add a digital offset to the SRM phase to flatten the sensing function, but then the question is “does the digital offset that flattens the DARM sensing function correspond to  ø = 90˚?”

And the answer is “no”, at least as modeled in FINESSE. 

I have added an offset to SRCL and looked at the corresponding sensing function, and it is clear that a ø = 90 is not necessarily a flat response (starting from 5 Hz), as the plot attached shows. 

In this case I’m looking at the RF readout (from DARM to AS45_Q), and where the average mismatch between all cavities is 0.01% (the start locking point is ø = 90.03˚). This also demonstrates that even a tiny mismatch can show optical spring effects.