Empirically CM gain and 100Hz noise are correlated (alog 44585) but the sense among us is that it's not residual frequency noise (at least via linear coupling), as no coherence was observed between DARM and signals like CM board output and POP9I etc.
To eliminate the possibility that 100Hz noise is the linear coupling of gain-limited residual frequency noise, we need to show the following.
- At least one of the relevant signals are not limited by the ADC noise and out of loop electronics noise.
- At least one of those signals that satisfy 1. above have no out-of-loop down-conversion to 100Hz, masking the true frequency noise in the readback (e.g. large high frequency out-of-band noise makes the amplifiers hit the slew rate limit or something). This is very, very unlikely, though.
This alog shows that the first point is true.
In the attached, left middle shows LSC-REFL_SERVO_CTRL_OUT_DQ when there was no light on REFL_A (green), and in low noise state before CM gain setting was made incorrect on Sunday (red) and with an incorrect CM setting (blue).
Both red and blue are more than an order of magnitude larger in-lock than the green trace, so apparently it's not limited by the ADC and read out electronics noise.
In the middle right is the CAL-DELTAL_EXTERNAL_DQ (without necessary calibration TF applied), just look at red/blue difference, blue is about a factor of 2 larger than red at 80Hz. If this is a linear frequency noise coupling it should be obvious in the coherence (left bottom) but there's really nothing to talk about while there's a clear difference in coherence at higher frequency.
In conclusion, the point 1. listed above is correct, yet there's no coherence for broadband 100Hz-ish noise, and therefore it's unlikely that this is linear frequency noise coupling.
Without addressing the point 2 (as it sounds unlikely), the next thing is to see if this is nonlinear coupling of the frequency noise. Injections would be useful, looking at demod signal of REFL_A_RF9_I would be useful, and changing CM gain somewhere in the chain would be useful.
FYI, in the above entry, CM gain difference between red and blue was 11dB or a factor of 3.5, and that was downstream of the REFL CM board (i.e. IMC REFL CM board IN2 gain). So at least red/blue difference of REFL_SERVO_CTRL_OUT as well as REFL_A_RF9_I_ERR make sense.
But comparing DARM red/blue doesn't make much sense as the coupling is also somehow related to the heating which is apparent from how the range degrades over time together with the frequency noise in DARM in kHz range when CM gain setting was wrong.
More explanations of the above.
Linear coupling to REFL sensing noise (shot noise etc.) imposed on the frequency noise was rejected right away because if that's the case CM gain change wouldn't make any impact whatsoever.
Since it changes with CM gain, and since we see no coherence anywhere, the true frequency noise is either somehow entirely gain-limited (not sensor limited) but all our signals are limited by ADC noise, which was rejected in the above, or it's sensor-limited at 100Hz but the gain-limited part of the noise (e.g. kHz or DC-ish frequency) is somehow down/up converted to 100Hz. In the latter case, it's an equivalent of additional REFL sensing noise and cannot be detected in-loop.