Jeff's recent tests with the REFL WFS in a single-bounce optical configuration (LHO:63474) allow us to compare how RM motion shows up in the WFS signals in and out of lock.
First page: REFL WFS dc and 9 MHz signals taken with the interferometer unlocked and the beam bouncing off PRM, dc centering loops engaged; I infer about 7 mW total on each of the WFSs. RM motion is evident in the WFS dc signals from about 6 to 20 Hz, which is nothing new. The motion is also weakly evident in the 9 MHz WFS pitch signals. The most straightforward way that I can think of to make such a signal in the 9 MHz channels is through RFAM. In this scenario, the relative dc pitch signal δPdc/Pdc should be equal to the relative rf pitch signal δPrf/Prf. We already have the spectrum of δPdc/Pdc via H1:ASC-REFL_{A,B}_DC_PIT_OUT_DQ, and we have the spectrum of δPrf via H1:ASC-REFL_{A,B}_RF9_{I,Q}_PIT_OUT_DQ, which I calibrated into watts [0].
From the above it is possible to infer the 9 MHz RFAM Prf, which I find to be about 1 µW [1]. Using Pdc = 7 mW and a modulation depth Γ = 0.22 rad, the RFAM can also be interpreted as a sideband imbalance of ΔΓ = 0.1 mrad (from Prf = Pdc ΔΓ), or as an imbalance of optical power between the upper and lower 9 MHz sidebands in the TEM00 mode (about 0.2%, from ΔP9/P9 = 4ΔΓ/Γ).
Second page: same as the first page, but now taken in full lock, and I infer about 15 mW total power on each WFS. In the recent full lock, the appearance of RM motion in the WFS dc channels is about the same as in the single-bounce test, but now the RM motion shows up about 100 times stronger in the 9 MHz WFS channels compared to the single-bounce configuration. It is unlikely that the noise is being impressed on the signal from somewhere else, since the RMs only produce beam motion at the LSC REFL and ASC REFL diodes, and even the LSC REFL diodes don't show as high a coherence with RM pitch as the REFL WFSs do. The other option is that this huge increase in signal is due to an increase in the gain that transduces RM motion to WFS rf signal, as could be caused by a large increase in effective RFAM in full lock.
Staying with the hypothesis that this is due to RFAM, it now implies Prf = 0.1 mW, or effectively a 10 mrad modulation imbalance, or equivalently an imbalance of TEM00 ±9 MHz sideband power of about 20%. This could be due to the differential action of the interferometer on the spatial mode structure of the upper and lower 9 MHz sideband fields.
Interestingly, WFS B RF9 I is almost totally insensitive to RM motion, unlike the other three WFS 9 MHz pitch channels. Perhaps that is just an accident of the digital phase rotation.
Third page: same as second page, but now taken from full lock near the end of O3b. The appearance of RM motion in the WFS rf channels is not as bad as the recent lock. Looking in particular at WFS B RF9 I&Q, one can see that the signal below 5 Hz is roughly the same in amplitude as the recent lock, but the RM motion above 6 Hz is more than 10× less. Again, the RM-induced beam spot motion on the diodes as inferred from the WFS dc channels is more or less the same. This is consistent with the notion that the appearance of HAM1-induced beam motion on the WFS rf channels is mediated by some variable optical gain (e.g., HOM-induced sideband imbalance) distinct from the optical gain of the angular signals coming from the main interferometer.
In the larger context of reducing noise in these WFSs near and above 10 Hz, we expect about 10 dB of broadband noise reduction by locking down the RM blades (LLO:59677). If the above sideband imbalance picture is correct, it suggests that further noise reduction in the REFL WFSs near and above 10 Hz is possible, potentially reaching shot-noise-limited performance, by paying attention to the HOM content of the reflected field. One obvious test is to try to adjust the HOM content of the reflected beam with the TCS. Another test, perhaps, is to intentionally introduce RFAM onto the input beam and see if it is possible to change the coupling.
[0] For the 9 MHz calibration I used the numbers Elenna tabulated (LHO:62976), but with 15 dB of whitening gain rather than 21 dB.
[1] More specifically, the RFAM for WFS A I&Q is 1.3 µW & 0.6 µW, and for WFS B I&Q it is 1.2 µW & 0.5 µW — and actually to estimate these I used a slightly different time stretch when Jeff was injecting extra table motion, since this raises the motion above the WFS shot noise more clearly.
Lisa asked if it was possible to see the coupling change as the HOM content of the beam is changed. The first page of the attachment is from a lock stretch where Georgia turned on CO2 Y heating (LHO:62759). It clearly shows a change in optical power (carrier and sidebands) in the power recyling cavity and the REFL beam, but there is not a discernible change in the coupling from HAM1 Z motion into WFS RF9 around 7.5 Hz, where the coherence between these two signals is high (>0.9). I also show coupling from PR3 motion to WFS RF9 motion at 0.75 Hz, where the coherence is high (again >0.9).
I then looked at the same signals from a recent lock stretch in what I suppose is the nominal inteferometer configuration (second page of attachment). There is a disturbing oscillation with a ~30 minute period, which Georgia and Craig say is probably from ADS. The surprising (?) thing is that here the HAM1 Z coupling into WFS RF9 motion is modulated by more than a factor of 2 as the interferometer is driven around by the ADS, while the coupling of PR3 motion into WFS RF9 stays the same.
Not sure what this all means yet, but it is clear that (1) the coupling of HAM1 motion into the WFS is modulated by the configuration of the optical field in the interferometer, and (2) this coupling is apparently different from the coupling of interferometer optic motion (e.g., PR3) into the WFS. At the same time, it seems a straightforward HOM modification test (e.g., turning on central heating) already shows a null result for modulating the HAM1Z to REFL WFS coupling.