Figure 1 shows the spectrum for the 56MHz TEM00, both USB and LSB, normalized to be units of RIN, and with the contribution of shot noise and PD electronic noise quadratically subtracted. The spectrum looks the same for both sidebands, and there was no significant change during the 2.5 hours separating the repeated measurement of the USB, which is a sign that the alignment has not drifted in the meantime, the beam jitter peaks are small in all cases. The requirement (VIR-1225B-19) for the RAM servo is 2.5e-8 V/V/rtHz at 100Hz, which should correspond to RIN of the sideband of 5e-8 1/rtHz. So probably RAM is a significant part of that spectrum, but this would need to be checked further, as the RAM servo was better than the requirements from what I remember.

Figure 2 shows the coherence with B1s, it is substantial at ~30%. It means that the sidebands are a major contributor to the dark fringe fluctuations in the 100Hz and 500Hz. The coherence for the red trace is smaller as there is a loud glitch on B1s dominating the spectrum during that measurement. 

There is no broadband coherence of the sideband with h(t).

Figure 3 shows the series of measurements with the first measurement being the 56MHz USB, and the last measurement being also the 56MHz USB

Figure 4 shows the spectrum of the higher order modes from 2 to 10, with two measurements for the mode order 9 (vertical and horizontal peaks). The PD electronic noise is 1e-8 mW/rtHz, and for the peaks with low power, the spectrum at 1kHz is very close to that limit. There is about a factor 10 difference in power between the brightest mode (order 3) and the  dimmest (order 10). The B1 photodiodes have a lower dynamic (~5mW), which would be sufficient as the brightest mode has 1mW in this scan, and have a lower electronic noise at 6.5e-9, so that could be a simple solution to gain a factor sqrt(2) in SNR for these measurements.

Figure 5 shows the same normalized in units of RIN and with the shot noise and electronic noise quadratically subtracted. In these units the noise level is more similar between the modes, the beam jitter peak height varies by one order of magnitude between different modes. There could be a similar level (within a factor 2) of noise that has a power-law shape around 100Hz, with a slope between 1/f and 1/f^{2/3}. That level of noise is a factor 2 higher than what is measured with the 56MHz sideband, so it is not intrinsinc to the measurement process, but HOM may be more affected than a TEM00 mode by beam jitter.

Figure 6 shows that none of those mode is coherent with B1s down to 0.1% level, which is surprising. It tells us that the EDB OMC is adding new information that is not accessible using only B1s, but it is unclear what that information means. There is coherence in the 20-30Hz band where the SRCL and MICH lines are in LN2 and at ~156Hz where the mechanical mode of SIB1 is.

Figure 7 shows the coherence with h(t), there is no broadband coherence to the 0.1% measurement noise level.

Figure 8 and 9 shows mode 3 and 5 which have the powerlaw slope the most clear, as they have high power and low amplitude for the beam jitter peaks

Figure 10 and 11 shows mode 2 and 4 which have a significant lower noise than modes 3 and 5

/users/mwas/OMC/RINanalysis_20250703/

Today I have locked the EDB OMC again on HOM in LN2. This time without realigning the OMC after the first initial realignment. There is no coherence with any of the HOM that I have tried. 

Initially the EDB picomotor process could not be reached. I must have forgotten to switch off the server last week, and it lost connection on Sunday. Piernicola and Bernardo turned on and off the picomotor manualy, which restarted the connection.

aligned EDB OMC on 56MHz USB, first to maximize the power, then ~50
picomotorse in horizontal to reduce the jitter peaks

16:47 UTC (5min) - locked on 56MHz USB

when going through carrier TEM00 there is ~0.1 mW on it. The 6MHz TEM00 are much smaller, around 0.02mW.

Adjusted demodulation phase to put all the signal in the i quadrature, this must have increased the gain by factor 3 or 4 (and the calibration)

17:09 UTC (5min) - locked on carrier TEM00 (very noisy and low power), not sure if the locked actualy worked or just stabilized in temperature around the mode

Reduced the gain by factor 2 (and calibration of error signal, still
probably wrong by factor 2) as the loop was oscillating when locking
on TEM00 56MHz LSB

17:19 UTC (5min) - locked on 56MHz LSB

order 1 mode of 56MHz sideband has about 0.05mW of power, 10 times less than the TEM00

17:30 UTC (5min) locked on carrier order 2 mode, mostly horizontal

17:40 UTC (5min) locked on carrier order 3 mode, 1-vertical, 2-horizontal

17:50 UTC (5min) locked on carrier order 4 mode, 4-vertical, 0-horizontal

17:59 UTC (5min) locked on carrier order 5 mode, 0-vertical, 5-horizontal

18:07 UTC (5min) locked on carrier order 6 mode, 1-vertical, 5-horizontal

18:16 UTC (5min) locked on carrier order 7 mode, 1-vertical, 6-horizontal

18:26 UTC (5min) locked on carrier order 8 mode, 1 vertical, 7 horizontal

18:35 UTC (5min) locked on carrier order 9 mode, 9 vertical, 0 horizontal

18:46 UTC (5min) locked on carrier order 9 mode, 1 vertical, 8 horizontal

18:56 UTC (5min) locked on carrier order 10 mode, 0 vertical, 10 horizontal

19:06 UTC (5min) locked on 56MHz USB TEM00, alignment is still good
 

A month ago after the WE replacement the fitted level of 1/f^{2/3} was 30%-40% higher than back in March: https://logbook.virgo-gw.eu/virgo/?r=66647

Figure 1 shows the simplified noise budget for last night. The fitted noise level for the 1/f^{2/3} is only 10% higher in units of mW/rtHz than back in March, however we have seen a year or two ago that the 1/f^{2/3} noise level in strain units doesn't depend on the input power, https://logbook.virgo-gw.eu/virgo/?r=63111 . Which probably means that it doesn't depend on the power in the arms. Given that the power in the arms increased by 10%, the DARM optical gain (W/m) has in practice increased by 10%, and to keep the same noise in strain units the noise level in mW/rtHz has to increase by 10%. 

In any case, a 10% difference is within the error bar of trying to fit the noise by eye in the noise budget. So the only thing we can be sure of is the excess of 1/f^{2/3} noise seen in April/May is no longer present.

/users/mwas/detchar/toySensitivity_20250611/toySensitivity.m

On May 16 we have turned off both the NE and WE RH at the same time with the interferometer locked https://logbook.virgo-gw.eu/virgo/?r=66809

Figure 1. The interferometer remained operational for a surprisingly long time. The RH switch-off was at 15:20 UTC, and the interferometer stay locked, and relocked successful twice over the following 7 hours until ~22:30 UTC. The power in the arms decreased by 15% and stabilized around 20h, this is likely due to a degradation of the mode matching between the input beam and the interferometer. Note that the B2 power also decreases, this is expected as the PR direct reflectivity is smaller than the reflected field from the interferometer, so with less light getting into the interferometer the destructive interference between the two becomes better, lowering the B2 power. Surprisingly the B1p power decrease by up to 25% (around 17h).  The DARM optical gain also decreased by 15% and reached a steady state around 20h, but then in the following lock it dropped by another 10%.

The last lock was significantly different from the previous, in additional to the drop in DARM optical gain, the SSFS noise coupling change signs, which made the BS TY loop slowly diverge, and the height of the DARM line on B1s decreased by a factor ~5. The SDB1 alignment to align the OMC also jumped by ~20urad in TY.

Figure 2 shows the noise budget at 20:00 UTC. The sensitivity is lower, as the DARM optical gain has reduced, but taking into account that change in gain the projection of 1/f^{2/3} noise and shot noise explains well the sensitivity curve.

Figure 3 shows the noise budget at 22:00 UTC. The sensitivity becomes better than what can be explained by the standard noise budget. It could be explained by lowering the 1/f^{2/3} noise contribution by 20%. At high frequency the SSFS noise contribution is large as the BS TY loop is not cancelling the coupling anymore.

Overall this tell us that 1/f^{2/3} noise doesn't come from a fine tuning of some HOM resonance in the arm cavity, as the EM radius of curvature sweep would have moved it away from that fine tuning.

The improvement in the apparent 1/f^{2/3} noise in the last lock is interesting, but it doesn't give any clear conclusion. The actual sensitivity doens't improve, it is just that it degrades less than what one would expect from the decrease in DARM optical gain, it could be that for example both the noise and the DARM signal are less transmitted by the OMC, due to poorer mode matching between the OMC and the interferometer, as the OMC jumped to a different alignment configuration. The OMC alignment always changes when SR is misaligned, but in that last lock it went into the opposite direction than normally during the LN2->LN3 transition.

/users/mwas/detchar/toySensitivity_20250516/toySensitivity.m

I have some of the EDB OMC scans that were done in LN3 in the past few weeks. In the figures below in blue is a scan with the beam centered on WE before the tuning of the RH, and in red and green with the beam off-center, while in black is a scan of the SDB1 OMC with SR manually misaligned by a comparable amount to the LN3 configuration. For the EDB OMC the expectation is that 5% of the beam power reaches the photodiode, so in principle it needs to be multiplied by 20 to have the power at the level of the SDB1 OMC reflection, in practice I have multiplied it by a factor 100 instead to have comparable heights of the peaks in the scan. It is unclear why this is the case, it could be the EDB OMC alignment which is bad, and lowers all of the peaks in a similar way, but I find that doubtful. More likely there are mistakes in the estimation of the transmission to the EDB OMC and/or to B1 PD3 in transmission of the SDB1 OMC.

Figure 1 shows the full scan, the height of the peaks roughly agree between all cases for most of them. Note that for the EDB OMC some of the scan data is missing or incorrect at the beginning or end of the frequency range.

Figure 2 zooming in the 56MHz TEM00 (-56MHz and +56MHz and their order 1 modes (+16MHz and +128MHz) look higher in the EDB scans. I don't have a good explanation for that.

Figure 3 zooms around the carrier TEM00, what is surprising is that ther is one, as normally that should be all transmitted by the SDB1 OMC , and nothing should reach the EDB OMC. It is puzzling. It could be the 6MHz sideband if the reconstruction of the frequency from the scan is wrong, but in that case it is still surprising why the peak is much larger than in the reference scan of the SDB1 OMC (black line).

/users/mwas/OMC/EDB_OMC_scan_20250424/EDB_OMC_SCAN.m

This is the analysis of the OMC scans done last week. The lines in blue, black and magenta correspond to SR misaligned, and the lines in red, green and yellow to SR aligned. The first two lines (red and blue) are for the WE mirror with the large point absorber, and the rest is measurements from October 2024 and provides a reference. Overall there is no sigificant difference compared to last year. 

A possible exception is mode of order 5, which is large (50-80mW) for both SR aligned and misaligned last week compared to the aligned case (10-20mW), while last year it was large only for SR aligned, and less clearly the same is true for the mode order 6 and 7. But this is not reliable, as looking at the scan with the downgoing temperature of the OMC the modes for SR aligned are not high, and are at similar level as last year, the SR misaligned case is not well controlled as the SR misalignment is added by hand and drifting.

Figure 1, zoom on order 1 mode, it is higher when SR is misaligned

Figure 2, zoom on order 2 mode, no significant difference

Figure 3, zoom on order 3 mode, it is higher when SR is aligned

Figure 4, zoom on order 4 mode, it is higher when SR is aligned

Figure 5, zoom on order 5 mode, it is higher when SR is aligned, and also for SR misaligned only for last week scan

Figure 6,  zoom on order 6 mode, it is higher when SR is aligned, and also for SR misaligned only for last week scan

Figure 7, zoom on order 7 mode

Figure 8, zoom on order 8 mode

Figure 9, zoom on order 9 mode

Figure 10, zoom on order 10 mode

Figure 11, zoom on order 11 mode, the 56MHz upper sideband TEM00 is visible around -50MHz

Figure 12, zoom on order 00 mode, the 56MHz upper sideband order mode is visible around +20MHz for the SR misaligned scans

Figure 13 shows the up-going and down-going scan with SR misaligned, and the highlighted modes order 5 and 6

Figure 14 for completeness shows the up-going and down-going scan last week with SR aligned.

/users/mwas/OMC/OMC_scan_demod_20250516/OMC_SCAN.m

In order to compare with previous measurements before the WE replacement (https://logbook.virgo-gw.eu/virgo/?r=65254) I have made this morning scans of the OMC with SR aligned and misaligned (initially planned for yesterday evening). The data analysis and comparison with previous scans of the SDB1 OMC and the EDB OMC remains to be done.

Figure 1 One thing that I have noticed is that when misaligning SR in CARM NULL 1F around 07:40 UTC, the power on B4 (carrier recycling gain) has increased. Which would mean that the effect of the point absorber, even with the beam off-center on WE depends on signal recycling, and with signal recycling misaligned the losses due to the point absorber are smaller.

Measurements times

06:06 UTC - OMC scan start in CARM NULL 1F (20min after lock)
unlock near the end of the scan

relock, SR_TY steady around -225.0 wihle SR/BS TX moving (due to the
mis-centering on WE), starting to add offset on SR_TY while the other
transients are ongoing. But SR TY moved -225.4 just before that, so using that as a reference of aligned SR to add ~2urad of misalignment to.

7:25 UTC, SR_TY_SET = 0.3
7:28 UTC, SR_TY_SET = 0.5
7:30 UTC, SR_TY_SET = 0.15 to stabilize at SR TY = -224

7:33 UTC - OMC scan start with SR misaligned
7:40-7:44 increase SR_TY_SET to 0.25 and then reverted to 0.2 to recover DCP around 190Hz and lower B1p power
Overshoots to DCP of ~150Hz, continously adjusting the SR TY offset to try to stay around 190Hz.

08:04 restoring SR alignment

Only to have the comparison between the OG in the  various configurations:

- 'Old WE'; 'new WE before cleaning';'new WE before cleaning Y offset';'new WE after cleaning'; 'new WE after cleaning Y offset'

Comparing the sensitivity before and after WE mirror cleaning, see attachment with different curves:

a) red before cleaning, no shift on WE mirror

b) blue before cleaning, shift on WE mirror: optical gain is about 20% better than in a)

c) purple after cleaning, no shift on WE mirror: optical gain is about 5÷6% better than in a)

d) green after cleaning, shift on WE mirror: optical gain is similar as in b)

A quick conclusion is that:

1) the broadband ~1/f^2 noise between 50 and 70 Hz, that was present before cleaning and did not depend on optical gain, is not present anymore

2) the 3 Hz comb, that was present before cleaning and whose ampltude did not depend on optical gain, is not present anymore

3) the broadband (1/f^2/3?) noise between 100 Hz and 200 Hz is scaling with the optical gain; with similar optical gain, it's roughly the same before and after cleaning.

Figure 1. I have locked the EDB OMC on the order 3 mode which in the scans appears to be the most powerful, more powerful by a factor ~2 than the other HOM.

14:12 UTC (15min) OMC locked on order 3 mode, nominal 0.001V modulation depth
14:29 UTC (15min) OMC locked on order 3 mode, 0.1V modulation depth
The ITF unlocked

During the unlock I have added a demodulation of the EDB_B1t photodiode at twice the modulation frequency of the SDB1 OMC. It might be useful in understanding the EDB OMC alignment relative to the SDB1 OMC alignment.

Figure 2 shows the transmission spectrum and OMC error signal for the two modulation depth. There is no coherence with h(t) for either of those. The photodiode noise shows an interesting looking slope between 70Hz and 200Hz.

Figure 3 shows the two spectra from today, and two spectra from last week with the OMC locked on the order 2 mode. All scaled to be in terms of RIN (normalized by the transmitted power) and with the estimated level of shot noise and electronic noise removed. All have a similar level of noise at 100Hz, not exactly the same slope, and the slope is somewhere in between 1/f^0.66 and 1/f.

Figure 1 shows the simplified noise budget when the beam is on WE center. To match the measured noise I had to increase the amplitude of the 1/f^4 noise, and increase the 1/f^{2/3} noise level by 40%. The difference in DARM optical gain is automatically taken into account by the noise budget.

Figure 2 shows the simplifed noise budget when the beam is offset by 6mm in Y on WE. To match the measured noise I had to increase the amplitude of the 1/f^4 noise further, which is understandable as angular noise couplings are higher with a beam off-centered on the mirror. The 1/f^{2/3} noise level in mW is the same, and the only things that changes it is the increase in optical gain when the beam is miscentered on WE.

Figure 3 shows for illustration the same data as figure 1 (beam on WE center) using the noise parameters from Feb/Mar 2025.

Figure 4 shows a sanity check a simplified noise budget from March with the same parameters as figure 3.

/users/mwas/detchar/toySensitivity_20250429/toySensitivity.m

As usual

The latest measurements of 1/f^{2/3} between SR aligned and misaligned seems to confirm that the level of noise depends on the recycling by SR https://logbook.virgo-gw.eu/virgo/?r=66178. This would mean that the noise could be carried over by a higher order mode, and be higher when SR is aligned, as then the higher order mode amplitude is higher due to signal recycling.

If we consider order 2 modes there are two degrees of freedom:

• One has been explored by changing differentially the radius of curvature of the end mirrors. This had shown that there was no change in noise level when changing the power of the order 2 mode by a factor ~5, see for example section 2.1 of https://git.ligo.org/virgo/commissioning/mystery_one_over_f_two_thirds_noise . Changing the end mirrors radius of curvature changes the radius of the beam on the input mirrors, but it doesn't change the curvature of the beam on the input mirrors, as it has to remain parallel to the input mirror curvature.
• The changes in curvature of the input mirror have never been explored to my knowledge. Changing the lenses in the compensation plates has a similar effect, it changes the wavefront curvature of the beam, but outside of the cavity instead of inside. This equivalent when looking from the point of view of the destructive interference at the beam splitter, that is not perfect and send some higher order modes toward SR.

Analytical computations of the field reflected from a mismatch with the arms have been done a few years ago https://tds.virgo-gw.eu/?r=21578, (VIR-0117A-23). In slide 6 one can see that a difference in end mirror radius of curvature creates an order 2 mode that is in phase with the carrier, while on slide 16 that a difference in CP lenses creates an order 2 mode that is in quadrature with the carrier. The mode that is in quadrature with the carrier at the input of the arms is in the quadrature used for the local oscillator for measuring DARM. So differential CP lenses create a static order 2 mode that is in the right quadrature to transport noise to the dark port.

On Feb 7 2024,  https://logbook.virgo-gw.eu/virgo/?r=63200, there were two steps of the DAS correction on NI and WI, following the increase of input power from 15W to 18W. There were difference in 1/f^{2/3} noise level observed during that time, VIR-0159A-24.

Figure 1 shows the noise level after the change in DAS power while figure 2 is during the night before the change in DAS power (but already at 18W of input power). The fit of the 1/f^{2/3} noise requires a 20% improvement in noise level. This improvement is in addition to any changes in double cavity pole frequency and DARM optical gain. In both cases the detector is in LN3, and the frequency noise projection is sufficiently low to be negligible.

/users/mwas/detchar/toySensitivity_20240207/toySensitivity.m

We have collected some data with SR aligned both this Tuesday and last Tuesday which is an opportunity to look again at how the 1/f^{2/3} depends on SR aligment

Figure 1 shows for reference a noise budget in standard condition with SR misaligned

Figure 2 is last week on Feb 4 with SR aligned. To match the observed noise curve I have increased the level of 1/f^{2/3} noise by a factor 1.6 compared to the SR misaligned case. This is in addition to the 1.38 change in level due to change in optical gain.

Figure 3 is today on Feb 11 with SR aligned. Again to match the observed noise curve the 1/f^{2/3} noise level is increased by a factor 1.6 compared to the SR misaligned case. In this case the SSFS noise is slightly lower as the EOM passive RF filtering was put in place this morning https://logbook.virgo-gw.eu/virgo/?r=66176

This is a similar conclusion from measurements from November 2024 https://logbook.virgo-gw.eu/virgo/?r=65488, but this time the frequency noise has been lower, likely thanks to the BS TX being in full bandwidth, good weather and the additional reduction due to the EOM RF filtering. And the measured factor remains comparable to the 1.7 factor that can be estimated from SR recycling gain for HOM.

/users/mwas/detchar/toySensitivity_20250211/toySensitivity.m

Reposting an entry from Friday that went back into the drafts.

Figure 1. The tilt of the two CPs was restored to have roughly the same position as before, with the ghost beams far from the B1 beam on the B1/B5 diaphragm. I have deliberately chosen a slightly different position.

Putting the CP ghost beams as close as possible to the B1 beam while remaining on the B1/B5 diaphragm on SDB1 following instructions in https://logbook.virgo-gw.eu/virgo/?r=65427

Figure 1. Starting point, only WI CP ghost beam is visible, as the other ghost beam is on the silicium part of the beam dump which scatters much less

16:49 UTC - starting changing NI and WI CP TY tilt
17:08 UTC - finished the changes

Figure 2. End point of the alignment of the two CPs

There is a significant difference between the two pictures in terms of where are bright patches of light on different parts of SDB1. For example the bright patch on the side of the close loop picomotor of MMT_M2 disappears. This is not just a transient, as the starting point picture looks very similar to the end point picture from end of October. So the position of these light patches is stable over long time scale, but changed completely by changes in CP tilt of ~1mrad.

17:44 UTC - starting moving beam on WE mirror using MIR_Y_SET in order to check the 120Hz bump on B8 DC.

The mis-centered states by 3mm in either direction are not stable, with the interferometer progressively getting in a worse state once the transition on the end mirrors is over. At one point it caused an unlock.

During the relock checked in CARM NULL 1F that adding offsets in MIR_Y_SET doesn't seem to be creating issues, and the 120Hz is visible in that state too.

I will post some figures tomorrow, there seem to be an impact of the beam spot position on the arm cavity mirrors on the 120Hz bump on B8 DC and in h(t).

When trying to simulate a DARM optical response transfer function in Optickle (plane wave simulation), an SR with 42% reflection and 12% losses reproduces the case of SR misaligned, while an SR with 60% reflection and 2% losses reproduces the SR aligned configuration.

The gain of a field added inside a cavity with losses is 1/(1 - sqrt(R)*sqrt(1-L)), which with the numbers above is equal to 4.29 for the SR aligned case and 2.55 for the SR misaligned case, which has a ratio of 1.7. So for an optical field resonating inside the SRC one would expect the field amplitude to decrease by a factor 1.7 when misaligning SR, this would be consistent with corresponding noise created by that field decreasing also by a factor 1.7, as the 1/f^{2/3} noise seems well explained by a noisy field beating against the DC read-out local oscillator.

Figure 1. Assuming that the noisy 1/f^{2/3} field is recycled by SR we speculate how it depends on the reflectivity of SR. The lines assume that the field is recycled by SR, and then attenuated by the SR transmission, and the DARM response transfer function was computed in optickle with 87kW in the arms for all the cases and 6.3mW of carrier TEM00 on the dark fringe. The SR aligned and misaligned configuration match the fit of 1/f^{2/3} verifying that there is no obvious mistake in the computation. SR with 70% transmission (that has same DCP as current SR misaligned configuration) would yield the same level of 1/f^{2/3} noise. And the no SR configuration matches the fit of "flat" noise in O3, with the big caveat that in O3 the noise level depedent on the DARM offset which is not the case of the 1/f^{2/3} noise. For the configuration without SR I assume no field amplification and that 100% of the field is transmitted by the SR lens.

Figure 1. Shows data during the SSFS noise injection, 10min of data includes several injection at different frequency bands together. The yellow line is the h(t) spectrum before noise subtraction performed by Hrec, red is after noise subtraction made by Hrec, and blue line is the total noise projection inicluding SSFS noise. It fits well

Figure 2. Shows the transfer function used to make the SSFS noise projection it is linear (not quadratic) sum of a frequency independent compentent and a 1/f component. The two components have opposite sign so below 200Hz the 1/f component cancels some of the frequency independent contribution. This is necessary to obtain a good fit with the measurement.

Figure 3 and 4 show the simplified noise budget on data in the 3 minutes preceeding the SSFS noise injection. The difference between the two curves is the method of computing the spectrum. Figure 3 uses the standard pwelch method while Figure 4 uses the median-mean spectrum computation method used in GW data analysis that reduces the impact of glitches, such as the 25 min glitches. The latter allows to see that the fit is reasonably good down to 50Hz. Note that the 1/f^{2/3} need to be scaled to be higher by a factor 1.8 than when SR is misaligned in order to match the total measured noise

Figure 5 shows the simplified noise budget for the previous lock, where 10 minutes of data is available, using the same SSFS noise transfer. In this case also a factor 1.8 of increase in 1/f^{2/3} noise compared to the SR aligned case is needed.

Figure 6 shows for reference a simplified noise budget from the night following these measurements. The SSFS noise coupling transfer function is fitted to measurement from Oct 28, and match frequency noise lines at 227Hz and the bump at 2.5kHz. In this case the 1/f component adds coherent with the frequency independent one. In any case for the SR misaligned case the frequency noise coupling is small, so the exact details of the noise projection do not matter as the contribution is negligible to the total noise.

/users/mwas/detchar/toySensitivity_20241107/toySensitivity.m

Did not manage to make any clear measurement with SR aligned, but managed to do one SSFS noise injection with SR aligned (to be analyzed).

Figure 1 shows trend of data during the shift

Figure 2 shows the fit of noise during the first SR aligned time with the LSC lines switched off and high frequency noise coupling. The 1/f^{2/3} required to fit the measurement is again factor 1.5 higher than when SR is misaligned.

Relock to LN2

Tried to do the steps of LN3 listed in /virgoDev/AEI_SQZ/changeDCP.py
and the adjusting BS TY to reduce the frequency noise coupling but that made the control less stable with more alignment
fluctuations, and eventually causing an unlock.

Relock to LN2.

Adjusting BS TX and TY to try to reduce frequency noise coupling, but again had issues with low frequency fluctuations causing an unlock.

Relock to LN2
Unlocked after 3 minutes while taking reference data

Relock to LN2

20:15 UTC - running the SSFS noise injection script

20:41 UTC - started taking reference time, but dark fringe started to fluctuate after a few minutes. Tried to go to LN3 to make it darker, but unlocked before SR had the time to misaligne.
 

/users/mwas/detchar/toySensitivity_20241107/toySensitivity.m

A decrease in total strain noise by a factor 1.35 when the optical gain increase by a factor 1.35 can be explained by fixed 1/f^{2/3} noise only if the 1/f^{2/3} noise is dominant for both the SR aligned and SR misaligned configuration. This is clearly not the case for the SR misaligned configuration where quantum shot noise is a factor 1.5 below the total noise. Hence the scaling of total noise is not linear with the 1/f^{2/3} noise contribution, and to have 1.35 decrease in total noise the 1/f^{2/3} noise needs to decrease by a large factor than just the decrease in total noise.

Laser intensity noise may or may not be a significant contribution. But the figure shown don't information on that, one would need to make a figure with the actual noise projection of laser intensity noise. An increase in coupling of a negligible noise can still result in a higher but still neglible contribution. The figure with the high coupling of PSTAB noise correspond also to a higher coupling of frequency noise by a factor ~5, and seems to be dominated by the frequency noise coupling increase. Frequency noise has been already taken into account in the analysis.

The effect can be likely explained by residual intensity noise.

- First plot in attachment: the Pstab coupling was changing significantly during the test. The sensitivity with SR aligned (high DCP) changed according to the Pstab coupling.

- Second plot: comparing data with SR aligned and low Pstab coupling (10:00 UTC) and data with SR misigned (12:00 UTC): the change in sensitivity at 100 Hz is only a factor ~1.35, which can be simply explained by the corresponding change in optical gain

- Third plot: comparing data with SR aligned and low Pstab coupling (10:00 UTC) and data with SR aligned and high Pstab coupling (10:14 UTC); the impact of increased coupling of common intensity noise is clearly visible.

In conclusion: there is no evidence from such data set that SR angle changes the noise level in W/rt(Hz)

Reanalyzing these data about sensitivity with SR aligned and misaligned from a year ago, Nov 1 2023, based on the current understanding of the mystery noise and frequency noise coupling, and the effects of SR misalignment. At that time the input power was 12W, and the TCS tuning was in progress following the reduction of input power from 25W to 12W that occured a few weeks before.

Figure 1 shows data from the night before when the CMRF was bad because the BS TY loop to minimize the frequency noise coupling was not working properly https://logbook.virgo-gw.eu/virgo/?r=62340. It shows that frequency noise can be reasonably well projected using the quadratic sum of the I and Q quadratures of the SSFS error signal, and modeling the coupling as the quadratic sum of a frequency independent coupling and a 1/f coupling between frequency noise and the power on B1. The relative weight of the 1/f and frequency independent coupling was adjusted to match the SSFS line at 227.1Hz and the coupling of the frequency noise bump at ~2.5kHz.

Figure 2 shows data with SR misaligned (175Hz DCP, 1.71e9 W/m optical gain). The frequency noise coupling is relatively small, and actually the projection is higher than it should be at the 227.1Hz line by a factor 1.5. The noise in the sensitivity is well explain by a 1/f^0.66 noise with a level of 4e-11 W/rtHz at 100Hz.

Figure 3 shows data with SR aligned (360Hz DCP, 1.32e9 W/m optical gain). The frequency coupling is larger, and matching the measured level of frequency at 2.5kHz with a frequency independent term make the projection at 227.1Hz a factor 2 too large. Despite this overprojction of frequency noise there is a gap between the measured sensitivity and the noise budget. The increase of optical gain by a factor 1.3 is not able to explain the increase in noise.

Figure 4 shows the same data with SR aligned, and to match the sensitivity with the noise budget one needs to increase the 1/f^0.66 noise level by a factor 1.6 to 6.4e-11 W/rtHz. This is the same increase as needed to explain the analysis of sensitivity with SR aligned and misaligned tested last month https://logbook.virgo-gw.eu/virgo/?r=65129

Conclusion: SR alignment changes the level of 1/f^0.66 mystery noise more than by just the change in DARM optical gain. There is also a reduction in noise in terms of W/rtHz when SR is misaligned by a factor about 1.6. This needs to be confirmed again, by doing a measurement of sensitivity with SR aligned and a noise injection of SSFS with SR aligned and misaligned to check the frequency noise projection shape in both cases more precisely than just based on two lines separated by a factor 10 in frequency.

/users/mwas/detchar/toySensitivity_20231101/toySensitivity.m

A bit more analysis concerning the OMC scans, the first (blue) and last (black) measurement are with SR aligned. And with SR misaligned (green and red)

Figure 1. Shows highlighted the 56MHz sideband TEM00 and order 1 mode, both for lower and upper sideband. In addition the order 1 (~74MHz) and order 2 (~142MHz) of the carrier are shown. What is clear is that with SR misaligned the power of the 56MHz order 1 mode increase by a factor at least 5, which sounds reasonable. This explains the appearance of a peak around 20MHz in the FSR.

Figure 2 Shows the carrier modes from 1 to 12 from left to right. The peaks at ~45MHz that disappear with SR misaligned is the order 12 mode of the carrier. The HOM powers look reduced in power by at least a factor 2, and up to a factor 10 (for mode 4). The order 2 modes look all with similar power.

We can actually have 4 measurement of the order mode power in a single scan, two crossed when the OMC temperature is increasing and two when it is decreasing. This is not the case for the first (blue) measurement, as the interferometer unlocked during the down going scan.

Figure 3 shows all the measurents, there is lots of scatter with a single configuration having factor ~2 changes. So the order 2 mode is constant versus SR misalignement, but the error bars of that statement are that is constant within an error band of a factor 2.

/users/mwas/OMC/OMC_scan_demod_20241003/OMC_SCAN.m

Did several scans in CARM NULL 1F with SR aligned, and SR misaligned in TY to have the DCP ~200Hz.

Figure 1 shows the four scans made today (in two different locks). The two scans with SR aligned are in black and blue, and with SR misaligned are in green and red. Most of the HOM decrease in power with SR misaligned, as expected. An exception is the order 2 mode which remains roughly at constant power. There is also some modes between 0MHz and 50MHz in this figure which either change in power by a factor 10 or move in frequency. I don't know what these are, I will need to look in the data more carefully.

Details

Unlocking and relocking to CARM NULL 1F
16h11m20 UTC - OMC scan started (CARM_NULL_SCAN_ON)
unlocked when the temperature scan was going back down

Relocked to CARM NULL 1F
Adding an offset in SR TY
-233.5 urad - starting steady state
0.6 offset in SR_TY_SET to make a transition in alignment over a few minutes
-232 urad - ending steady state, maintained with SR_TY_SET ~ 0.15
17h04m33 UTC - OMC scan started
17:26 UTC - stopping scan (CARM_NULL_SCAN_OFF)

Adding -16.0 MICH_SET to balance 56MHz sibeand on B1p

17h33m19 UTC - OMC scan started
17:54 UTC - stopping scan

Realigning SR and adjusting MICH offset to balance 56MHz sidebandon B1p

18h05m14 UTC - OMC scan started

In this entry  it was shown that MICH and DARM optical response change in the same way at low frequency (using the calibration lines at 70 Hz) when going from the configuration SR aligned to the configuration with SR misaligned.

I checked that this is true also at higher frequency, using the calibration lines around 360 Hz (BS at 361.5 Hz, WE at 363.5 Hz and NE at 365.5 Hz): the ratio between the 2 configurations is 0.77 for both BS and NE/WE lines. Note that for the lines ~70 Hz the ratio is 1.54 for both BS and NE/WE (see entry). The ratio is different at 70 Hz and at 360 Hz as the TF changes shape between SR aligned and SR misaligned, as we know.

The fact that the ratio is the same for BS and for NE/WE at these 2 different frequencies shows that the TF changes most probably in the same way for MICH and DARM.