Figure 1, the 157Hz bump decrease in the first hour of each lock, Figure 2 during the shift yesterday it did not decrease because the MICH SET loop was intentionally disable for an hour, and then MICH SET adjusted quickly by hand. 

Figure 3 confirms that RIN coupling due to a MICH offset is the dominant coupling path fo the 157Hz bump. Blue was with a large RIN coupling to DARM, red  and yellow are with the coupling intentionally increased by adding a MICH offset in the wrong direction, and green purple and green are with the MICH offset adjusted to minimize the RIN coupling (at 1.5kHz).

Figure 4. As seen benfore when the PRCL offset is adjusted to minimize the frequency to amplitude conversion on B2 (blue and red lines), the B2 Audio spectrum is much cleaner, especially at high frequency.

Figure 5 and 6 what is surprising is that looking at the B2 quadrants. In the vertical direction the coupling of frequency noise (227Hz line) decrease in the vertical direction by a factor few, but in the horizontal direction there is no significant change. Does that mean that the coupling has a significant contribution of HOM? Note that this is true only for B2 QD1, on B2 QD2 the line at 227Hz is not visible in neither the H nor V direction, at any of the times. And on both quadrant the sum channel sees the line clearly and decreases by a factor 10 when adjusting the PRCL offset.

/users/mwas/ISC/RINanalysis_20240506/analyseRIN.m

Shift started with a couple of unlocks.

17:56 UTC turned off MICH SET loop (putting MICH_SET_CAL to zero)

MICH set loop had not converged, so PSTAB was not yet at zero.

18:00 UTC (5min) PRCL set = 8.0 to zero the frequency to amplitude conversion on B2.

18:06 UTC (5min) PRCL set = 8.0, MICH set = -5.0, to increase PSTAB to DARM coupling

18:13 UTC (5min) PRCL set = 0.0, MICH set = -5.0

18:23 UTC (5min) PRCL set = 0.0, MICH set = 12.0 to zero the PSTAB to DARM coupling

18:29 putting back MICH SET loop (cali at -100000)

Figure 1. I have noticed any changes in the sensitivity during this test, appart from the 157Hz bump getting smaller when changing the MICH set to zero the PSTAB to DARM coupling. To be checked more carrefully if MICH set is really the cause.

Figure 2. Summarizes the change in PRCL and MICH offset. A PRCL offset of 8 changes the PSTAB to DARM coupling by about the same amount as a change of MICH offset of 5.

https://git.ligo.org/virgo/commissioning/commissioning-tasks/-/issues/52

In 2017 the PRC was measured to have a wrong length by 3-4mm: https://logbook.virgo-gw.eu/virgo/?r=36884

I have checked in Optickle that mistuning the sideband frequency by a 2 kHz (which should be equivalent to a 4mm cavity length change), the sideband behavior becomes asymetric with PRCL offset. WIth the sideband power increasing by 1-2% in one direction and decreasing by 1-2% in the other direction, when changing the PRCL offset by ~0.2nm. This is similar to the measurements done last Friday, but it disagrees with the PRCL calibration done a year ago: https://logbook.virgo-gw.eu/virgo/?r=36884. That calibration would say that the PRCL offset was changed by 1.5nm, which would make the sideband power change by a few tens of percent. Maybe that calibration is no longer valid, as some normalizing factors could have been changed when chaning PRCL error signal from 8MHz to 6MHz sideband, or when installing the RAMS on the 6MHz.

Figure 1 shows in red the normal situation, in blue with the frequency to amplitude noise coupling divided by ~2 by adding the PRCL offset and in purple by adding the PRCL offset which zeros the coupling. The power fluctuation on B2 at ~1.5Hz improve by a factor 10 when reducing the coupling, on B4 there is also an improvement by a factor ~3, while on B4 12MHz the situation becomes worse, with fluctuations increasing by a factor 2. That would make sense if we improve the resonance condition for the carrier and degrade for the 6MHz sideband.

Figure 2 are the same times but with colors not in the same order. It includes also the B7 and B8 powers, and while on B8 the improvement is monotonic when improving the frequency to amplitude noise conversion, on B7 it is not the case. Is that a consequence of one arm being 3cm shorter than the other?

Lets assume that the PRC length is wrong by ~3mm, there are several options to resolve this:

1. Move PR by 3mm, which then requires retuning the input beam mode matching as it will change the input beam mode matching by one or a few percent
2. Change the sideband frequency by ~2kHz, but that would require moving the IMC end mirror by ~5cm to follow, so it is not a viable option
3. Move the input mirror by 3mm and maybe  also the end mirrors to keep the arm length the same. It might be the easiest to do and is the most reversible. It will also change the SRC length, but we have no measurements whether the SRC length is right or wrong, and it should be less critical because of the low finesse of the SRC.

Doing a PRCL offset scan to minimize the frequency to amplitude coupling at the input of the interferometer: https://git.ligo.org/virgo/commissioning/commissioning-tasks/-/issues/12

Starting after the calibration measurements between 16:00 and 16:15 UTC. The steps are done at a speed of ~1 unit of PRCL per 20 second.

16:22 UTC (5min) PRCL_SET = 1.0
16:28 UTC (5min) PRCL_SET = 2.0
16:35 UTC (5min) PRCL_SET = 4.0
16:42 UTC (5min) PRCL_SET = 6.0
16:51 UTC (5min) PRCL_SET = 0.0
17:00 UTC (5min) PRCL_SET = 6.5
17:07 UTC (5min) PRCL_SET = 6.2
17:16 UTC (5min) PRCL_SET = 12 - interupted by unlock just after 17:18:40 UTC

just after reaching LN3

18:10 UTC (5min) PRCL_SET = -6.0
18:17 UTC (5min) PRCL_SET = 0.0

Figure 1 summarizes the scan done up to the unlock, PRCL_SET ~ 6 correspond to zeroing the frequency to amplitude conversion by the interferometer as seen on B2. It also shows that adding the offset in PRCL reduces the 6MHz gain as seen on B4 12MHz by 2%.

Figure 2 compares the time with the frequency noise coupling to minimized (blue) to the normal situation (purple). The B2 noise is 10 times lower between 1Hz and 3Hz, and it is also lower above 1kHz where the frequency noise is dominant. In between B2 is dominated by the pole at ~500Hz noise, subtracting it using B5 or B4 could reveal more clearly the improvement in coupling of frequency noise to B2 at other frequencies. There is no wideband impact on the h(t) noise.

Figure 3, 4, 5 show that the frequency noise lines (227Hz, 1111Hz and 3345Hz) are a factor ~30 lower on B2, and about a factor 2 lower in h(t).

Figure 6  my impression is that the coupling of frequency noise to h(t) becomes lower because for SSFS_LF the I and Q quadratures become more overlapped, so the BS TY minimizes both at the same time, and for SSFS_LINE the I and Q quadratures (that are very correlated), become of equal magnitude but opposite sign.

I wonder what it means that the frequency to amplitude noise coupling is zeroed, while the sideband gain decreases. Does it mean that the sidebands are not well tuned to the length of PRCL, and we need to choose to have carrier well resonant or sidebands well resonant?

Figure 7 the coupling of frequency noise to B2 has been quite stable since the beginning of the run

Figure 8 shows the PRCL offset scan done just after the unlock. This scan went with the same magnitude but in the wrong direction for the frequency to B2 noise coupling, and this time it increased the B4 12MHz mag signal by ~1.3%. So it points towards the current working point being in between being good for sideband gain and being good for the frequency to amplitude coupling at the interferometer input. That would intuitively make sense if the sideband frequency doesn't match the PRCL length, and the RF error signal that is the between sideband and carrier finds a working point in between being good for the carrier and for the sideband.

Lately, some of the unlocks at CARM null 1f were occurring during the engagement of the first control filter of CARM slow loop (RFC 6 MHz error signal). Systematically, the engagement is characterized by an oscillation at 430 mHz (see Fig.1), which sometimes leads to the unlocks.

By looking at the model this could be explained by a loop instability due to low loop gain, in which the open loop has a 0dB crossing in a region where there is no phase margin left, which causes the arise of the aforementioned oscillation (see Fig.2, blue plot).

The issue has been easily cured by increasing the loop gain (addittionally the filter has been slightly modified by adding a missing integrator). However, in the sequence of the used filter, we switch from a very robust filter (CARM slow syn, blue fig.2) to a less robust filter with much roll-off (CARM slow test2, red fig.2) with completely different shape. This doesn't make much sense, so the situation can be improved and made less critical by changing the first filter with one with shape similar to the final one, but with less boost, in order to have less kicks during the engagement.

The west arm has been measured to be ~3cm shorter than the north arm (VIR-1085A-21). This causes the 56MHz TEM00 to resonate at different frequencies in the north and west arm. A question is if it causes issues with noise couplings.

Figure 1 shows the fitted coupling of CARM to DARM at a time of good sensitivity.

Figure 2 is the corresponding noise budget.

A 3cm length asymmetry over 3km length arm creates a 1e-5 coupling of CARM to DARM. This makes sense intuitively, and is confirmed by optickle simulations. So that asymmetry is comparable to what is measured once BS and SR are misaligned in LN3. Before misalignments the measured CARM to DARM coupling can easily be a factor 10 higher.

So the ~3cm arm length difference is not a major contribution to SSFS noise coupling. The other simple noise coupling is due to the BS AR coating, which creates a 3e-6 CARM to DARM coupling, the two could cancel each other if the west arm was ~1cm longer than the north arm. Something to keep in mind for the far future that we could use the difference in arm length to fine tune CARM to DARM couplings if we ever get to a situation where the coupling starts to be smaller than 1e-5.

A few notes about lock acquisition and automation during the afternoon shift:

• at 14:18:40 UTC the FmodErr tuning via MC_Z was triggered (Figure 1): the calibration is mistuned (but undercompensating, so it is safe); given the INJ stability and the coming works for tomorrow on the INJ side we did not change it, but it will verified tomorrow during the recovery if possible;
• the work on SIB2_DEMOD_RFC_B2PD2_Clock, preparatory for this afternoon's shift, did not change demodulation phases significantly: the RFC one did not change at all, and the B2_6MHz one only changed by 3 mrad (the PD2 one); however, this was was observed in the previous lock being already off by ~0.12 rad, so it was tuned; a fine tuning was also done on the same phase in the DRMI stage of the lock acquisition (30 mrad);
• by looking at the B2 phases, I noticed that the B2_PD2_56MHz one looked mistuned, at least by looking at _I and _Q in time domain; this is used for phase noise subtractions, and it will be checked with experts; to be noted that, if mistuned, it is not because of today's work, but probably it was not checked during the last recovery;
• we had an unlock possibly linked to the BS engagement in full bandwidth at 19:01:37 UTC, at the end of the ACQUIRE_LOW_NOISE_1 state (Figure 2): despite only TX is using the blended signal with B4_QD2_6MHz (which earlier today was found having issues), the TY one was the one DOF drifting more; for the time being we disengaged the full bandwidth loop from the automation;
• we had a few unlocks due to the INJ system in different moments of the lock acquisition: GPSs are 18:23:38 UTC, 19:23:04 UTC, 19:54:07 UTC; towards the end of the shift they became much more frequent;
• we had a weird unlock at 20:19:50 UTC: the ITF unlocked at CARM_NULL_1F when the requested state was an earlier one (REDUCING_CARM_OFFSET_3_OF_3); why it happened and why such request was made is unclear to us (FIgure 3, logfile);
• a few other automation topics:
  • we reduced the waiting time in CARM_NULL_1F from 15 to 10 minutes;
  • we checked the path of the OMC scan directly via ITF_LOCK (states CARM_NULL_SCAN_{ON,OFF}); these are working, but once in CARM_NULL_SCAN_OFF one should wait for the OMC to stabilize before moving on with the lock acquisition; in the future a timer will be added in order to do this automatically; some care will be given in order to avoid the two timers to sum up and make the lock acquisition even more tedious;
  • we implemented the automated turning on/off of the IRIG-B monitoring once in DOWN/LOW_NOISE_2 respectively; we already tested at 20:30:11 UTC ITF_LOCK re-enabling it once in DOWN, and it was successful; we also added its disengagement at the end of ACQUIRE_LOW_NOISE_2, still to be tested.

We left the ITF trying to relock in LOW_NOISE_2, with the failsafe on.

Summary

• PRCL and SSFS offsets have the same effect on the coupling of SSFS and PRCL noise onto B2 Audio
• There is demodulation phase noise on the SSFS Q signal when there is an SSFS I offset, and it is consistent with a simple product of the offset and the phase noise
• The mixed sensing of SSFS improves PRCL noise. To be tested if it improves laser frequency noise and sensitivity.

Details

We have explored PRCL and SSFS offsets, While waiting for the thermal stabilization before doing an OMC scan to characterize the current thermal working point, . The PRCL offset scan was done before the OMC, and the SSFS offset scan was done after the OMC.

These are the times of the SSFS

16:08 starting adding an SSFS offset by steps of a factor 3. At 3e-3
starts to have an effect on the coupling of SSFS to B2 Audio.
16:15 (1min) offset of 3e-3
16:16:20 (1min) offset of 6e-3
16:18 (1min) offset of 12e-3
16:20:30 (1min) offset of 24e-3
16:24:00 (1min) offset of 50e-3

unlock when doing a 100s ramp to 100e-3 offse

Figure 1 shows the B2 audio spectrum for 3e-3 offset (red), 12e-3 offset (green), 24e-3 offset (purple) and 50e-3 offset (blue)

The step from 24e-3 to 50e-3 has additional noise that is clearly not linear with the offset. While the frequency noise lines are still linear with the offset.  The additonal noise at 24e-3 between 100Hz and 1kHz, maybe already part of that additional noise that is no longer proportional to the offset.

Figure 2 comparing the PRCL offset scan and the SSFS offset scan. The two error signals (B2 demodulated at PRCL line frequency and at SSFS line frequency) have the same dependence for both scans. So the PRCL and SSFS offset look like the same degree of freedom. At least from the B2 audio perspective.

Figure 3 compares two different offsets (3e-3 in blue and 12e-3 in purple). With the large offset there start to be noise visible on unnorm Q, it is coherent with B4 112MHz phi. So this is demodulation phase noise.

Figure 4, shows that at 16:18 the offset on unnorm I is double the one on Q. Also 0.012*3e-5*6/112 = 2e-8, so the noise we see on unnorm Q is at the expected level from demodulation phase noise. And on unnorm I (SSFS error signal), we must have the same issue (but a factor 2 smaller as the Q offset is a factor 2 smaller). This should help in validating a projection on the phase noise on the SSFS (and sensitivity curve)

After Alain put the changes for the SSFS mixed sensing, we have tried several weights for the addition of B2 8MHz into the SSFS signal to remove the 2MHz laser noise.
17:35 (1min) reference period
17:39:10 (1min) 1e-4 FF weight
17:40:50 (1min) 1e-3 FF weight
17:42:20 (1min) 3e-3 FF weight
17:47:00 (1min) 1e-2 FF weight
17:48:40 (2min) 3e-2 FF weight (increases SSFS unnorm Q, and decrease B2 PD2 6Mhz I)
17:50:40 (1min) -1e-2 FF weight unlock

Figure 5 compared the 3e-2 weight (blue) to the reference period (purple). B2 6MHz I (PRCL) is lower with the FF on, and this is usually a reasonable out-of-loop sensor of frequency noise. With the FF on, also PRCL is less coherent with B2 4MHz (another signal that should be a good sensor of the 2MHz laser noise). On the other hand it is adding noise into the SSFS quadrature, I am not sure if it is reasonable or not.
 

Analysing a bit more some of the B2 8MHz FF data

Figure 1. Shows the test with 0dBm modulation depth on the 8MHz. In blue is OMC aligned, in red OMC misaligned, and in yellow is OMC misaligned and 8MHz modulation depth increase from -6dBm to 0 dBm. There is no appreciable increase in noise seen in h(t) with the higher modulation depth, so it was not an effective sensor for the noise we try to subtract, which could be the explanation why no improvement could be achieved.

Figure 2 Shows the test with 9dBm modulation depth. In blue is OMC misaligned, in red is 8MHz modulation depth increase from -6dBm to 9dBm. In yellow is feed-forward with a gain of 1e-2 and in purple with a gain of 3e-2. The FF makes the sensitivity worse for several peaks (~700Hz, ~2kHz, ~3.2kHz), and better in between them. The wavy structure is probably due to the delay in the feed-forward, with the sign changing every 1.2kHz. This would mean the delay in the feed-forward is 800us, instead of the expected 250us, which makes it much more difficult to be effective. It is uncertain if the improvement in sensitivity are due to the FF removing the spurious 2MHz noise, or due to the FF changing the SSFS gain. My impression is that it is the latter, as the change is highest at high frequency, where the SSFS gain is the lowest. Note that during this test there was no high pass on the FF, so it was also adding an offset on the SSFS which could have an important effect on othe coupling.

Figure 3 shows again the test with 0dBm modulation depth (where the impact was not sufficient to be visible on h(t)), but this time looking at PRCL instead of DARM.  In blue is reference, in red and green is 8MHz modulation depth increased from -6dBm to 0dBm without FF, in yellow/cyan/purple is FF with different signs and amplitude. The FF is waving due to the delay, but it seems to be able to reduce the level of noise even at 100Hz (if the sign is correct). Yellow (gain of 2e-2) could be the right gain and sign.

In conclusion. There is clearly the delay which makes the analysis more complicated. At 9dBm of 8MHz modulation one would need to pay more attention to the diagonalzation, as the FF affects significantly the SSFS gain. Looking at PRCL gives some hope that the FF might work.

Conclusions

• PRCL->SSFS works with a gain of 2e-3 on SSFS_phi.LSC_err.PRCL_err
• The feed-forward appears not necessary as in normal conditions the feed-forward correction will be a factor 100 below the SSFS sensing noise
• Did not manage to get a B2 8MHz feed-forward that reduces frequency noise as seen on DARM with misaligned OMC. But could have an impact on the frequency noise seen on PRCL (and in some cases increase the noise seen on DARM)

Feed-forward measurements

08:42:30 (3min) SSFS noise injection (100-150Hz)

08:48:20 (3min) PRCL noise injection

PRCL->SSFS FF at 1e-3 gain

08:54:20 (3min) PRCL noise injection

PRCL->SSFS FF at 3e-3 gain

08:59:30 PRCL->SSFS FF at -3e-3 gain

09:02:20 PRCL->SSFS FF at -1e-3 gain

09:04:20 PRCL->SSFS FF at -3e-3 gain

misaligned SDB1 in TY by ~5 urad adding an offset in the RF B1s quadrant signal

09:21 (2min) reference time

09:28 (2min) PRCL noise injection wide band 

09:33:30 (2min) PRCL noise injection wide band higher amplitude

09:36:10 (1min) PRCL->SSFS FF at -1e-3 gain

09:37:50 (2min) PRCL->SSFS FF at 1e-3 gain

09:40:00 (3min) PRCL->SSFS FF at 2e-3 gain

09:43:20 (2min) PRCL->SSFS FF at -2e-3 gain

09:45:30 (2min) PRCL->SSFS FF at 0 gain

09:49:30 (3min) PRCL->SSFS FF at 2e-3 gain

09:53:00 (2min) PRCL->SSFS FF at 0 gain

09:55:30 PRCL noise injection off

Figure 1 shows that the feed forward with 2e-3 gain (blue curve)
improve the sensitivity compared to no FF (purple curve) (in this
configuration where we inject PRCL noise and have the OMC misaligned
by 5urad in TY to make the CMRF worse).

What is slightly surprising is that this feed forward makes the B2 PD2
audio spectrum worse, but maybe it only means that frequency noise
doesn't cancel PRCL noise as seen on B2.

Figure 2 shows in red during the feed-forward and PRCL noise
injection, and in blue without feedforward or noise injection. The FF
correction visible in SSFS_Err_I_unnorm is at similar level to the
signal at 3kHz. So the FF in this condition is comparable to the SSFS
sensing noise. But in normal condition PRCL correction is 100 times
smaller, so in normal condition (no PRCL noise injection), it doesn't
look like the PRCL FF to SSFS will improve anything, as it will be 100
below the SSFS sensing noise.

10:06:30 (3min) 8MHz modulation depth at 9dBm

10:12 (1min) B2 8MHz FF with gain 1e-5

10:14 (1min) B2 8MHz FF with gain 1e-4

10:15:20 (1min) B2 8MHz FF with gain 1e-3

10:16:50 (1min) B2 8MHz FF with gain 1e-2

10:18:30 (1min) B2 8MHz FF with gain 3e-2 - seems to be making things
worse, and creates a peak at 700Hz. Maybe sign is wrong.

Tried to add a delay compensation in the FF filter. ITF unlocked when
turning back the FF on with this feed-forward.

Relocked after a while, with some Metatron data reading issues in the
middle. Added a high pass filter at 10Hz to the FF in the meantime, as the feed-forward was adding an offset into the SSFS.

12:42 (2min) reference time. 8MHz modulation depth at 9dBm and OMC misaligned in TY by ~5urad

12:45:00 (1min) B2 8MHz FF with gain -1e-2

12:48:00 (3min) B2 8MHz FF with gain -2e-2

Another lock

13:43 (2min) reference time
13:50 (2min) OMC misaligned

13:56 (2min) 8MHz modulation depth increased from -6dBm to 0dBm

13:58:40 (2min) B2 8MHz FF with gain  2e-2

14:01:20 (2min) B2 8MHz FF with gain  -2e-2

14:03:40 (2min) B2 8MHz FF with gain  0e-2

14:08:20 (2min) B2 8MHz FF with gain  4e-2

14:12:10 (2min) B2 8MHz FF with gain  -4e-2

14:15:40 (2min) B2 8MHz FF with gain  1e-2

turned B2 8MHz phase by 90deg

14:22:30 (2min) B2 8MHz FF with gain  1e-2

14:25:50 (2min) B2 8MHz FF with gain  -1e-2

14:28:10 (2min) B2 8MHz FF with gain  -2e-2

14:30:20 (2min) B2 8MHz FF with gain  -0.5e-2

14:32:30 (2min) B2 8MHz FF with gain  2e-2

14:34:40 (2min) B2 8MHz FF with gain  0e-2
 

PRCL and SSFS offset

Added a B2 PD2 Blended demodulation at SSFS and PRCL line frequency (for studies of offsets) and tuned their phase in CARM NULL 1F.

FIgure 3 shows an example of the time serie in CARM NULL 1F after phase tuning. These might be good monitors of SSFS and PRCL working point offsets, to be tested.

Figure 1 shows the B2 spectrum and SSFS error & quadrature. In purple is last night. In red is last year with PRCL offset of zero, and in blue is last year with a PRCL of ~2 AU. Last year the B4 PD with the notch at 6MHz was in loop for the SSFS, hence the sensing noise of the SSFS was 10 times higher. But B2 audio spectrum was much lower than now, and only adding a large PRCL offset was making it higher than what we have now. This would confirm that we are working with a large PRCL and/or SSFS offset.

Figure 2 shows the B2 spectrum for most days in April and May. There was a change where the background increased by a factor 2 and the sensitivity to frequency noise (the bumps at ~3kHz) by a factor 10. It occured at the end of April or beginning of May.

Conclusions

• Adding a PRCL offset can turn B2 Audio into a good out of loop sensor of laser frequency noise
• We might have an offset since beginning of May on PRCL or SSFS, but apparently it did not have a large impact on the sensitivity.

There is evidence that B2 audio channel sees laser frequency noise. This is surprising to me, and could mean we have an offset on a common degree of freedom (either PRCL or SSFS/CARM). The offset would be measurable by demodulating B2 audio at a laser frequency dither line or a PR length dither line.

The last test of PRCL offset I could find is from October 2022.

Figure 1 show B2 audio demodulated at the 1111Hz laser frequency line. It clearly shows the steps in PRCL offset, note that the starting point doesn't correspond to zero.

Figure 2 shows B2 audio demodulated at the 64.4Hz PRCL line. It clearly shows the steps in PRCL offset, and start from zero.

Figure 3 show B2 audio demodulated at the 1111Hz last night. It is clearly away from zero, and what is more surprising it has a large value, that back in october corresponded to a ~1AU offset on PRCL.

Figure 3 show B2 audio demodulated at the 64.4Hz last night. It is clearly away from zero, and what is more surprising it has a large value, that back in october corresponded to a ~1AU offset on PRCL.

It would be interesting to these demodulations of B2 online, and adjust the offset of PRCL to zero the 64.4Hz demodulation, and the offset of the SSFS to zero the 1111Hz line demodulation. It could be also interesting to check B4, especially for the SSFS degree of freedom.

Code

/users/mwas/ISC/B2demod_20230717/B2_demod.m

Yesterday's study of 6MHz vs 8MHz noise coupling seems to confirm that the issue is laser noise at 2MHz being shifted by the modulation (6MHz modulation shifts to 8MHz and pollutes the 8MHz error signal, while the 8MHz modulation shifts the noise to 6MHz and pollutes the 6MHz error signals). Looking through past data it seems that this additional noise could be subtracted from the SSFS using already existing signals.

Figure 1 shows data from April when the 8MHz modulation depth was still large, in purple in normal condition and in blue with a misalignment of BS and/or OMC causing the CMRF to be worse. One can notice several thing on that figure.

1. RFC PD1 8MHz Q is coherent with B2 PD2 6MHz I. B2 PD2 6MHz I was out-of-loop at that time, and should be a good out of loop sensor of laser frequency noise. The RFC PD1 8MHz Q spectrum shows the pole at ~500Hz shape that is characteristic of the noise that is spoiling the SSFS. So this would show that RFC 8MHz Q could be a good sensor to subtract the noise polluting the SSFS sensing.
2. On the blue curve (when CMRF is worse), the coherence of B2 PD2 6MHz I with DARM and the coherence of RFC 8MHz Q with DARM increases. This would confirm that what we see is indeed noise polluting the SSFS sensing (and the due to imperfect CMRF it pollutes DARM)

Figure 2 compared the same data from April (in purple), to data in June (in blue). In June the 8MHz modulation depth was significantly reduced, and B2 PD2 6MHz I was used in loop for PRCL control.

1. The 8MHz modulation is lower, so the coherence between RFC  PD1 8MHz Q and B2 PD2 6MHz I is lower, as the laser frequency noise is less polluted by the conversion of 2Mhz noise into 6MHz noise by the 8MHz modulation.
2. The coherence of B2 8MHz I with RFC PD1 8MHz Q becomes very large. So because the B2 8MHz I doesn't see a signal anymore (a signal from the beat of the carrier light with the 8MHz sideband), it becomes a good sensor of the spurious noise (the beam of the 2MHz laser noise with the 6MHz sideband).
3. The spectrum of RFC PD1 8MHz Q doesn't change much. So in both cases we don't see there the beat of the 8MHz with the carrier, but the beat of the 2MHz laser noise with the 6MHz sideband.
4. The ratio of the B2 8MHz I spectrum between 100Hz and 3kHz has a factor 4, while for RFC PD1 8MHz Q it is only a factor 2. So B2 8MHz I has a better SNR to measure the spurious noise, while RFC 8MHz Q is quickly limited by the photodiode sensing noise.

My conclusion from this is that B2 8MHz I could be fed forward to the SSFS error signal to remove the spurious noise from the SSFS sensing, as long as the 8MHz modulation depth is small. RFC 8MHz Q could also be used as feed forward, it would work for any 8MHz modulation depth, but has a poor SNR, so would reduce the noise by at most a factor 2. A potential alternative would be to use a B2 4MHz demodulation, to look at the conversion of the 2MHz by the 6MHz sideband into the opposite direction (-2MHz instead of +2MHz). This would have the advantage of having a high SNR, without the limitation that the 8MHz modulation depth needs to be low to prevent the appearance of a laser frequency signal.

With the current architecture the delay of B2 8MHz I sent to the SSFS would have a delay of ~250us, which would limit the efficiency of a subtraction.

Figure 3 shows the impact of on subtraction of a 250us delay, at 100Hz the subtraction could be at most a factor 5, the subtraction would stop working at 700Hz and at 2kHz it would actually increase the noise by a factor 2.

There is a solution for that problem too, by doing a mix of the B4 6MHz I signal and B2 8MHz I directly in the DSP for the SSFS. The delay would then be small and the same for both photodiodes, so it would not limit the subtraction. However it assumes that there is no frequency dependency needed for the subtraction and just a simple linear combination of the two PD signals will work well at all frequencies.

Note that the reason why the 2MHz laser noise is shifted by the modulation remains open, as it requires a non linearity in the system. Potential explanations could be:

1. EOM phase modulation is inherently non linear. We should be able to compute the expected coupling and compare it with the measurement that were done by injecting a line in the fiber EOM at 2MHz + 2kHz
2. The IMC has a different optimal working point for each frequency. And at 2MHz is not at the top of the resonance, but on the side of it. So adjusting Fmoderr, or adjusting an offset in the IMC length lock could reduce the non-linearity causing the 2mhzn ois econvertion (maybe at the price of making other couplings worse, for instance the frequency to amplitude noise conversion in the audio-band).

I found similar results (and conclusion), see the attached pdf.

Taking the reflectivity of the currently installed NI [IM02, VIR-0543A-14], and one of the spare input mirror [IM03,  VIR-0326A-23], one can check if etalon tuning can compensate for the difference in HR side reflectivity, using for example the formula in VIR-0929A-19.

Figure 1 shows the result, and the etalon effect in NI and in one of the spare is not able to to bring the two mirrors to the same reflectivity, whatever choice of phase of etalon in each mirror. The maximum of the red curve is about 200pm below the minimum of the blue curve. This is a large different, comparable to a random tuning of etalon with the current mirrors. It means that WI mirror cannot be replaced by the spare, without also replacing the NI mirror.

There is a proposal to use B4 6MHz Q (quadrature of SSFS) instead of B4 56MHz I for the control of MICH. The advantage is that this would remove phase noise from MICH (as the quadrature would be zero, instead of the large SRCL offset), and it would remove potential phase noise from the SSFS loop (which right now has a large offset in quadrature).

Figure 1 shows the spectra during a MICH noise injection. The transfer function between the two photodiodes is flat above 5Hz. The signal is 3 times smaller in B4 6MHz Q than in B4 56MHz I, but part of that should be recovered as the B4 6MHz phase is not well tuned, and half the signal is in the other quadrature. Right now the sensing noise of B4 6MHz Q looks high, because fo the demodulation amplitude noise, but that would disappear once the signal is in loop at zero.

A first step to check that B4 6MHz Q is indeed usable, would be to put an offset in the current MICH signal to bring the DC value of B4 6MHz Q around zero, and check that this doesn't create serious issues somewhere else. And then the hand-over might be easy as around the MICH UGF the two signals have a flat transfer function, and not much phase change (about 10 deg over 20Hz).

We currently lock SR with an offset on the longitudinal RF photodiode to keep SR in the tuned position, as a consequence a large amount of demodulation noises is introduced into the sensitivity curve. Keeping the RF PD signal to zero would resolve this issue, but would mean we operate an interferometer with detuned SR in a not controlled way. An issue with that is weather the LSC noise subtraction would still work, or would the needed subtractions change as the SR detuning is drifting.

Figure 1 compared two Optickle simulations of the Advanced Virgo optical response (DARM->B1 transfer function), one with 0 detuning of SR, and one with 10nm of SR detuning.

Figure 2 shows the feed forward needed from MICH to DARM to compensate for the MICH actuation. It is computed as the ratio of the two transfer functions: MICH->B1 / DARM->B1. The two transfer functions look identitical, so as first order there would be no changes needed in the MICH to DARM feedforwards, if they are implemented at the mirror correction level.

Figure 3 shows the relative difference between the two lines on figure 2. It is smaller than 1e-4.

Figure 4 shows the difference in SR to DARM coupling for 0nm and 10nm offset. In this case there is a very large difference, but only above 100Hz, so maybe it doesn't matter much, as above 100Hz the SR control loop should not be reinjecting that much SR length sensing noise.

Riccardo Maggiore has made some nice simulation of the impact of DARM offset and SRCL offset on the B1 power. Simulations were done with 135kW stored in the arms, which is the best estimate of the present situation corresponding to 675mW on the SNEB/SWEB benches.

Figure 1 shows that the B1 power fluctuations of ~10mW from a week ago correspond to DARM lock precision of +/-2.5pm. Note that the OMC was not well aligned at that time. So it is likely that the power fluctuation on B1 were actually larger, so a poorer DARM lock precision. Since then the DARM lock precision has been improved by more than a factor 10. The design for the DC readout is to have a DARM offset of approximately 1.5pm.

FIgure 2 shows that an SRCL offset has no significant impact on the B1 power

Figure 3 shows that the SRCL offset still has no impact on B1 power even when a DARM offset is present. So an SRCL offset will not be biasing our estimation of the DARM offset.

The last test for the lock of CARM with the signal SIB2_RFC_8MHz_I was done on August 1st 2019; those tests were done with a very rough filter, unconditionally stable but with very poor performance, just to have a starting point.

A trend of the meaningful channels is in Figure 1; of all the tests and configurations explored, probably two stretches of data can be useful before the next shift:

• GPS = 1248692748 (DUR = 300 s): CARM loop closed with "high" gain in LOW_NOISE_1;
• GPS = 1248700638 (DUR = 300 s): CARM loop closed with "low" gain in LOW_NOISE_3.

Just to have a comparison, I replicated in Figure 2 the first plot of the original entry with these data stretches.

Figure 1. Shows the RFC error signal spectrum from Sep 7 in blue, and in red it shows roughly what it would need to be to compliant with the OMC requirement on the absolute laser frequency stability. The red curve is obtain from the blue just by using a 1/F shaped loop (pure integrator) with a unity gain at 2Hz.

Figure 2 shows the perspective from the OMC error signal point of view.

• In dark blue is the OMC error signal, note that error signal has a large sensing noise as the OMC length dither was reduced by a factor 10 just before O3 as a precaution against non linear noise couplings
• In red is the RMS of that error signal, it is at 1.3e-11 m, while the requirement for O4 and for the Advanced Virgo design is 6e-13m
• In yellow is the scaled RFC error signal multiplied by frequency. It needs to be multiplied by F, as the OMC tries to follow the CARM motion, and has a filter with roughly a 1/F shape at 0.1-1Hz frequencies. With that transformation the RFC error signal matches roughly what the OMC is seeing.
• In purple is the corresponding RMS, which is dominated by the bump at ~30mHz, but with also some contribution from the lines between 0.1Hz and 1Hz.
• Green is same as yellow, but with a filter with 1/F shape and unity gain at 2Hz applied
• In light blue is the corresponding RMS, the different lines have a similar order magnitude contribution, and add up to a 5.3e-13m RMS

Note that slow CARM loop implemented in January 2017, was compliant and leading to an OMC length RMS of 4e-13m. But this was a computed not a measured quantity, so it assumes all the calibration factors to convert from RFC error signal to OMC error signal are correct.

Script in /users/mwas/OMC/OMCspecCARM_20191016

The theoretical offset on CARM of 6.5e-13m corresponds to an offset on the laser frequency of 61mHz. It could be one reason why fmoderr needs to be retuned in dark fringe once the interferometer is locked, but probably not the only one as the fmoderr tuning is always different, and this theoretical offset should always be the same.

The lower and upper 56MHz sidebands are unbalanced in the interferometer. Before the power increase there was about 10% difference in the power of the two sidebands TEM00 modes

In order to explore the impact of this I have made a simulation in Optickle, based on the Optickle simulation that reproduce the intereferometer in the noise budget. To obtain misbalance sidebands, I put the IMC in the simulation with a length wrong by 1mm, and the lock point offset. In this case the upper 56MHz is on resonance, the carrier is slightly off resonance, and the lower 56MHz is very much misbalance. In total it reduced the carrier power in the arms by 10%, and the upper sideband has double the power of the lower sideband. This is not a good model of what actually happens in the interferometer, as it doesn't only introduce a power unbalance between the sidebands, but also changes their relative phase, as one sideband is on resonance, and the other is offset.

Figure 1 and 2 show the signals on B4 56M I and Q for the case with perfectly balanced sidebands for a scan of respectively the BS position and the CARM length.

Figure 3 and 4 show the same with a misbalance of the two sidebands. The two signals become correlated, so a sideband unbalance will cause the optimal demodulation phase for MICH/SSFS to change.

Figure 5 (perfect) and 6 (sideband misbalance) show a zoom for BS position scan. For the perfect case, there is no offset in the error signal (zero of error signal correspond to 0 position for the BS). But for the misbalance case, there is an offset 2e-12m when the error signal crosses 0. However that offset is small, and we need in any case an offset on MICH and/or DARM for the dark fringe, so this shouldn't matter.

Figure 7 (perfect) and 8 (sideband misbalance) show a zoom fro the CARM position scan. What is surprising is that there is an offset 6.5e-13 m present in both cases. This corresponds to a slight detuning of the arms, with 0.5% power loss compared to the case if the laser frequency is perfectly matched with the arm lengths. I am not sure what it means, but it could be worth exploring what is the impact on the intereferometer of adding an offset into the SSFS error signal to check whether the zero of the SSFS error signal is actually the best working point for the interferometer.