Elli and Stefan showed in aLOG 20827 that the signals measured by AS 36 WFS for SRM and BS alignment appeared to be strongly dependent on the power circulating in the interferometer. This was apparently not seen to be the case in L1. As a result, I've been looking at the AS 36 sensing with a Finesse model (L1300231), to see if this variability is reproducible in simulation, and also to see what other IFO variables can affect this variability.
In the past when looking for differences between L1 and H1 length sensing (for the SRC in particular), the mode matching of the SRC has come up as a likely candidate. This is mainly because of the relatively large uncertainties in the SR3 mirror RoC combined with the strong dependence of the SRC mode on the SR3 RoC. I thought this would therefore be a good place to start when looking at the alignment sensors at the AS port. I don't expect the SR3 RoC to be very dependent on IFO power, but having a larger SR3 RoC offset (or one in a particular direction) may increase the dependence of the AS WFS signals on the ITM thermal lenses (which are the main IFO variables we typically expect to change with IFO power). This might therefore explain why H1 sees a bigger change in the ASC signals than L1 as the IFOs heat up.
My first step was to observe the change in AS 36 WFS signals as a function of SR3 RoC. The results for the two DOFs shown in aLOG 20827 (MICH = BS, SRC2 = SRM) are shown in the attached plots. I did not spend much time adjusting Gouy phases or demod phases at the WFS in order to match the experiment, but I did make sure that the Gouy phase difference between WFSA and WFSB was 90deg at the nominal SR3 RoC. In the attached plots we can see that the AS 36 WFS signals are definitely changing with SR3 RoC, in some cases even changing sign (e.g. SRM Yaw to ASA36I/Q and SRM Pitch to ASA36I/Q). It's difficult at this stage to compare very closely with the experimental data shown in aLOG 20827, but at least we can say that from model it's not unexpected that these ASC sensing matrix elements are changing with some IFO mode mismatches. The same plots are available for all alignment DOFs, but that's 22 in total so I'm sparing you all the ones which weren't measured during IFO warm up.
The next step will be to look at the dependence of the same ASC matrix elements on common ITM thermal lens values, for a few different SR3 RoC offsets. This is where we might be able to see something that explains the difference between L1 and H1 in this respect. (Of course, there may be other effects which contribute here, such as differential ITM lensing, spot position offsets on the WFS, drifting of uncontrolled DOFs when the IFO heats up... but we have to start somewhere).
Can you add a plot of the amplitude and phase of 36MHz signal that is common to all four quadrants when there's no misalignment?
As requested, here are plots of the 36MHz signal that is common to all quadrants at the ASWFSA and ASWFSB locations in the simulation. I also checked whether the "sidebands on sidebands" from the series modulation at the EOM had any influence on the signal that shows up here: apparently it does not make a difference beyond the ~100ppm level.
At Daniel's suggestion, I adjusted the overall WFS phases so that the 36MHz bias signal shows up only in the I-phase channels. This was done just by adding the phase shown in the plots in the previous comment to both I and Q detectors in the simulation. I've attached the ASWFS sensing matrix elements for MICH (BS) and SRC2 (SRM) again here with the new demod phase basis.
**EDIT** When I reran the code to output the sensitivities to WFS spot position (see below) I also output the MICH (BS) and SRC2 (SRM) DOFs again, as well as all the other ASC DOFs. Motivated by some discussion with Keita about why PIT and YAW looked so different, I checked again how different they were. In the outputs from the re-run, PIT and YAW don't look so different now (see attached files with "phased" suffix, now also including SRC1 (SR2) actuation). The PIT plots are the same as previously, but the YAW plots are different to previous and now agree better with PIT plots.
I suspect that the reason for the earlier difference had something to do with the demod phases not having been adjusted from default for YAW signals, but I wasn't yet able to recreate the error. Another possibility is that I just uploaded old plots with the same names by mistake.
To clarify the point of adjusting the WFS demod phases like this, I also added four new alignment DOFs corresponding to spot position on WFSA and WFSB, in ptich and yaw directions. This was done by dithering a steering mirror in the path just before each WFS, and double demodulating at the 36MHz frequency (in I and Q) and then at the dither frequency. The attached plots show what you would expect to see: In each DOF the sensitivity to spot position is all in the I quadrature (first-order sensitivity to spot position due to the 36MHz bias). Naturally, WFSA spot position doesn't show up at WFSB and vice versa, and yaw position doesn't show up in the WFS pitch signal and vice versa.
For completeness, the yaxis is in units of W/rad tilt of the steering mirror that is being dithered. For WFSA the steering mirror is 0.1m from the WFSA location, and for WFSB the steering mirror is 0.2878m from the WFSB location. We can convert the axes to W/mm spot position or similar from this information, or into W/beam_radius using the fact that the beam spot sizes are at 567µm at WFSA and 146µm at WFSB.
As shown above the 36MHz WFS are sensitive in one quadrature to spot position, due to the constant presence of a 36MHz signal at the WFS. This fact, combined with the possibility of poor spot centering on the WFS due to the effects of "junk" carrier light, is a potential cause of badness in the 36MHz AS WFS loops. Daniel and Keita were interested to know if the spot centering could be improved by using some kind of RF QPD that balances either the 18MHz (or 90MHz) RF signals between quadrants to effectively center the 9MHz (or 45MHz) sideband field, instead of the time averaged sum of all fields (DC centering) that is sensitive to junk carrier light. In Daniel's words, you can think of this as kind of an "RF optical lever".
This brought up the question of which sideband field's spot postion at the WFS changes most when either the BS, SR2 or SRM are actuated.
To answer that question, I:
- Added 18MHz and 90MHz "WFS" to the Finesse model.
- Phased these new "WFS" so that all the 18MHz or 90MHz "sum" signals show up in the I-phase (see first two plots).
- Plotted the new "WFS" responses to BS, SR2 and SRM pitch and yaw (normalized by their "sum" signal), as a function of SR3 RoC (see the rest of the plots).
Some observations from the plots:
- 90MHz "WFS" show much more response to SRC1 (SR2) and SRC2 (SRM) tilts than 18MHz "WFS". This is somewhat intuitive, because the 45MHz sidebands are resonant in the SRC and the SRC eigenmode may be more sensitive to SR alignments than a beam traced through "single bounce" style.
- The 90MHz response to SRM/SR2 tilt remain very much in the I phase, with almost no signal in the Q-phase.
- 18MHz "WFS" show more response to MICH (BS) than the 90MHz "WFS". This is problably because a BS tilt causes a large coupling of 9MHz HG10/01 mode from the PRC to the SRC relative to the amount of 9MHz HG00 mode already in the SRC (due to high Michelson reflectivity + SRC non-resonance for 9MHz HG00). Since I normalize to the total sideband power, this looks like a bigger response in 18MHz than 90MHz.
- The 18MHz response to BS tilt is mostly in the Q phase. I'm not sure exactly how to interpret this, but my naive guess is that it's related to the BS tilt being a "differential" mode tilt for the X and Y arms of the small Michelson.
I looked again at some of the 2f WFS signals, this time with a linear sweep over alignment offsets rather than a dither transfer function. I attached the results here, with detectors being phased to have the constant signal always in I quadrature. As noted before by Daniel, AS18Q looks like a good signal for MICH sensing, as it is pretty insensitive to beam spot position on the WFS. Since I was looking at larger alignment offsets, I included higher-order modes up to order 6 in the calculation, and all length DOFs were locked. This was for zero SR3 RoC offset, so mode matching is optimal.