A question is if the optical gain for differential signals created inside the CITF is different from the DARM optical gain as a function of SR alignment. The 56MHz optical gain which involves being recycled by SR is not affected by the SR misaligment, because the ~1.5urad SR misalignment is small compared to the ~12m length of the CITF, and the CITF is marginally stable. Is it the same for differential perturbations created by the BS?

Figure 1 shows a lock acqusition, with SR aligned at the beginning (pole at 400Hz) and then 10 minutes later misaligned (pole at 200Hz)

Figure 2 shows three times, 21:10 UTC with SR still aligned (purple), 21:20 UTC with SR misaligned (red), 21:30 UTC with SR aligned (blue)

Figure 3 zooms on the BS drum mode (1872Hz VIR-0476A-16 https://tds.virgo-gw.eu/?content=3&r=12696). It is decreasing over the 10 minutes of SR misalignment, but then in the following 10 minutes is decreases again by the same fraction in h(t). Hence this decrease is not a change in optical gain, but just the drum mode damping. Meanwhile on B1 the first step is clearly larger, as the optical gain at high frequency changes due to the SR misalignment. So it seems the optical gain evolves the same way as the DARM gain. And there is no strange effect that the SR recycling work differently for perturbations created in the CITF and perturbations created in the arms.

There are noise projections and measurements done proving in a model dependent way that the CO2 DAS laser is not limiting the sensitivity (VIR-0911A-19, VIR-0199A-24).

Another proof that is model independent comes from the tuning of the TCS done in October last year starting from the TCS switched off: https://logbook.virgo-gw.eu/virgo/?r=62282 . Only the NI CO2 is a potential source of noise, as this is the one with a high power put on the CP to compensate the cold lens on the CP. The lock acquisition was done with 0.1W on the NI CP, and then two steps were performed in lock to increase the power to 0.4W.

Figure 1 shows the two steps done at 18:23 UTC and 20:28 UTC.

Figure 2 shows that there was no impact on the BNS range. If the CO2 laser was a noise source the impact on the sensitivity would be immediate and the noise level would be proportional to the CO2 laser power.

The noise fitting done a few days after that measurement had shown that the sensitivity was limited by the mystery noise at that time https://logbook.virgo-gw.eu/virgo/?r=62301. See figure 3. So if the CO2 laser was the origin of mystery noise (through RIN coupling, jitter coupling, or any other way). Then we should have seen increase in steps of the noise level in the sensitivity, which was not the case.

The fact that the noise is independent from the optical gain when changed by DARM offest, while it is dependent from the optical gain when changed by SR alignment, could be intuitively done from the fact that the noise is generated in the central area. Infact by alignment of SR the equivalent reflectivity  of input mirror is changed: so the behaviour of a phase signal generated in the arm or in the central area could be different?

The rigid mounting of the CP into a metal structure highlighted by Enrico and Antonino raises the question of what is the thermal noise of the CP, as the rigid mounting (VIR–0128A–12, section 10.3.3) is likely increasing the loss angle orders of magnitude above the loss angle of fused silica (1e-8).

An example of thermal noise computation in transmission of an optic was done 15 years ago for GEO: LIGO-T0900209. One of the noise listed there is transmissive substrate brownian noise which depends on the loss angle. For the GEO beam splitter the optical length noise is 2e-20 m/rtHz at 100Hz. Neglecting the differences in the geometry, for Virgo this is attenuated by a factor 5e-3 as the beam splitter is outside the Fabry-Perot arm cavities, and after dividing by the 3km arm length correspond to a strain noise of 3e-26 1/rtHz that is negligible.

However if the loss angle of the CP is not 1e-8 but 1e-3 due to the friction with the metalic frame that holds it, then the noise level in terms of strain becomes 1e-23 1/rtHz at 100Hz, comparable to the level of the 1/f^0.66 mystery noise.

A large caveat is that at first glance the coupling mechanism is not compatible with measurements. Plan wave simulations (Optickle) show that the BS to h(t) coupling is independent of the SR reflectivity. The CP optical length noise should couple the same way as the beam splitter position noise, and changing SR reflectivity changes the DARM optical gain in a similar way as misaligning SR. Experimentally we see the noise change in h(t) as a function of SR alignment, while in this scenario of optical length noise in the short Michelson this doesn't happen according to plane wave simulations. But it is possible that changing SR reflectivity is not a good approximation of the effect of misaligning SR. It would interesting to check with Finesse simulations, how the BS to h(t) coupling changes with SR misalignment.

Nonetheless, It would be interesting to evaluate what is the expected CP thermal noise when the mounting frame is taken into account, and think if it is feasible to measure experimentally the quality factor of one of its bulk modes, for example the drum mode. As even if doesn't explain the mystery 1/f^0.66 noise, it could be a source of additional noise that hides just beneath it.

The unmodelled noise limiting Virgo in the bucket is still unexplained despite several physical mechanisms have been proposed and some ruled out [see wiki].

A possible candidate for mystery noise may be the coupling of the polarization fluctuations of the beam generated in the central interferometer with the (difference of) birefringence of the compensation plates.

The reason for this is that the compensation plates are mounted in a different way with respect to the mirrors and can have stress generated either by the supports on which they are placed or by the lateral screws by which they are tightened.

It is also doubtful whether the machining of the compensation plate, starting from the bulk, has left inner mechanical stress.

Indeed, as regards the compensation plates (to our knowledge), a constraint on birefringence apparently was not requested before the assembly  (see for example VIR-0075A-15, VIR-0153A-16, VIR-0380A-14).

The actual amount of residual stress should be simulated from the mounting conditions to evaluate the birefringence. In the bulk of the mirrors, the required value was of the order of dn < 10-7. This limit was reached (and also well surpassed) by the bulks. In the case of a mirror subjected to stress, the value can be higher, even ten times or more, so even if the compensation plates are thinner than the mirror bulk, their effect could be dominant. In this way the difference in polarization angle of the two plates could be up to Psi_0 = 10-2 rad. (Notice that this gives a contribution to contrast defect of 10-4 which is compatible with the requirement made on the mirror bulk)

Another point to evaluate is the birefringence fluctuations for a mirror subjected to stress. In literature, this is very difficult to find (at least for us) and what we found are polarization fluctuations of the order of 10-9 rad/\sqrt(Hz) with a slope of approximately 1\/sqrt(f), but on very different optical substrates. Recent measurements in Virgo give the upper limit dpsi < 10-9 rad/\sqrt(Hz) in the fluctuation of beam polarization in B5 [see wiki]

The way this noise enters the sensitivity is better evaluated not by considering the phase noise of the recombining beams but the power noise at the dark port. Such a calculation shows that this noise depends on the optical gain.

The noise can be calculated as \tilde(P)/Prc = (1/4)Psi_0 \tilde(Psi).  where Psi_0  is the angle at the beam splitter recombination, Prc the recycled power, and \tilde(Psi) is its fluctuation.

If we assume as value of Psi_0 and \tilde(Psi) the upper values given above, the resulting noise is compatible with the present sensitivity.

Better investigations are needed.

As discussed in VIR-0200A-24, the beam splitter amplifies the angle measurement of polarization noise by a factor sqrt(40) instead of 40. As the polarization angle is between electromagnetic fields and not powers. Hence the upper limit on polarization noise in LN3 are actualy  ~8e-10 rad/rtHz.

Comparing the Hrec specta for the two periods, the change in sensitivity is due to a small (3÷4%) change in the level of broadband noise, corresponding to the ~3.5% change in optical gain; plus the enhancement of some spectral lines, e.g. at 111 Hz, 120 Hz, 122.5 Hz, 133 Hz etc. See first picture.

Indeed the Hrec BRMS in 110÷133 Hz changed by about 10%, and the DARM BRMS in 110÷120 Hz changed by about 8% between 16:10 UTC and 16:30 UTC, see first and last plots in the second picture. But the Hrec and DARM BRMS  around 220 Hz, where no spectral lines were enhanced, did not change significantly, see traces in red.

The B1s photodiode has been replaced by one that doesn't have a large electronic noise on Feb 20.

Figure 1 shows that the new electronic noise level is at 2e-8 mW/rtHz.

Figure 2 shows the B1s photodiode in LN3. This can be compared to the previous analysis done a month ago: https://logbook.virgo-gw.eu/virgo/?r=63036.

With the lower sensing noise the noise that has a shape of a pole at ~500Hz becomes more clearly visible on B1s. It is coherent with B5 (and B4), and one can use B5 to subtract it. The result is the red line on the figure. Trying to fit the remaining noise with just a noise of the 1/f^0.66 plus some frequency independent noise (shot noise + electronic noise) yields the cyan line, which doesn't follow well the measured noise.

A better fit can be achieved by adding to the 1/f^0.66 noise a noise shaped as a ~500Hz pole, which would assume that the the ~500Hz pole noise is not well subtracted and that there is a second component of it at 7e-8 mW/rtHz that is not coherent with the one visible on B5. Another way to achieve a good fit is to use a 1/f^0.5 noise instead of the 1/f^0.66 noise, note that a 1/f^0.5 slope is not compatible with the measured mystery noise slope. https://logbook.virgo-gw.eu/virgo/?r=63220.

Figure 3 compares the current situation (purple) with the one before the RAMS servo active loop was closed. The noise on B1s at 100Hz has reduced by a factor ~5 since then thanks to the RAMS servo. The OOTL monitoring of the 56MHz RAMS has reduced by a factor 20, so in principle the 56MHz RAM is factor below what we measured on B1s right now. This is also consisten with the ~5% coherence between B1s and 56MHz OOTL RAMS signal. This conclusion assumes that OOTL RAMS is indeed an out-of-loop signal.

So there is an excess noise optical on B1s, and it doesn't seem to be easily explained by RAMS or pure mystery 1/f^0.66 noise, nor by the ~500H pole noise.

The measurement with quarter wave plate instead of a half wave plate (P-polarization fluctuations in quadrature with the S-polarized local oscillator instead of in phase) are essentially the same.

Figure 1 corresponds to the single bounce propagating along the B5 beam path. The upper limit on the polarization fluctuation of the input beam is 8e-8mW/rtHz / 19mW / 2 = 2.1e-9 rad/rtHz.

Figure 2 corresponds to a LN3 configuration. The upper limit on the polarization fluctuation of the beam in the north Michelson arm is 4.5e-8 mW/rtHz / 5.3mW / 2 / 40 = 1.1e-10 rad/rtHz.

This is a quick analysis of the B5 polarization measurements with the half-wave-plate installed.

Figure 1 shows data with the B1p beam in single bounce propagating through the B5 beam path. The power on the B5 PDs was expected to be equal, this is not the case. The ratio of powers is 0.6 which is a bit unexpected. It could be due to the B5 beam path that is not in the horizontal plane and might be rotating the polarization axis of the beam. This is also not consistent with the fluctuations of power on the photodiode in the audio channel were the ratio is ~0.8. Using that 0.8 ratio to create the difference between B5P and B5 in dataDisplay. The difference spectrum has a noise floor at 8e-8mW/rtHz, and one can notice that the difference is working as the PSTAB line at ~235Hz is a factor few lower than in the individual photodiodes. This noise floor is consistent with shot noise of ~19mW (sum of the two photodiodes).

Following the equation in VIR-0032A-24 with phi=pi and alpha=pi/8. The ratio of the power difference to the power sum should be equal to twice the polarization fluctuation, hence the upper limit on the polarization fluctuation of the input beam is 8e-8mW/rtHz / 19mW / 2 = 2.1e-9 rad/rtHz. This is a factor 3 improvement over the previous measurement.

Figure 2 shows data in LN3. The B5 photodiode are limited by the excess noise that has a pole at 500Hz shape that is visible B2, B4, B5, but the same B5P - 0.8*B5 difference as in single bounce is able to remove it and the result has a noise floor of ~4.4e-8 mW/rtHz, The shot noise of the 4.5mW beam is expected to be 3.9e-8 mW/rtHz, once adding to it the photodiode electronic noise floor of ~2e-8 mW/rtHz (see figure 3) the noise floor is well explained by shot noise + PD electronic noise. The polarization fluctuations in the arms are amplified by a factor 40 by the BS AR coating polarizing reflectivity. So the upper limit on the polarization fluctuation of the beam in the north Michelson arm is 4.4e-8 mW/rtHz / 4.5mW / 2 / 40 = 1.2e-10 rad/rtHz. A factor 10 improvement over the previous upper limit. Note that this measures polarization fluctuations that are in phase with the S-polarization beam, the quarter wave plate needs to be installed to perferom the measurement of the fluctuations that are in quadrature of the S-polarized beam.

Figure 1 During the DAS tuning yesterday there was at one point that made the B1p DC clearly worse by about 10%. The peak of the transient was between 16:00 and 16:20 UTC. The range also got worse by 3 Mpc, but this was not due to the CMRF which had uncorrelated fluctuations. There are fluctuations in optical gain associated with this transient, but they are only 3%, not enough to explain the change in range.

Figure 2 and 3 show the simplified noise budget for a time of higher and lower B1p DC power. It assumes a fixed level of mystery noise in mW/rtHz, and adjust the conversion into h(t) based on the maesured optical gain and pole frequency. When the B1p power is higher at 16:10 UTC the measured sensitivity moves further up compared to that noise budget. This could be due to the increase of the mystery noise in units of mW/rtHz, or the increase of some other broadband noise.

Figure 4, 5 and 6 show respecively camera images before, after and during the transient. On B1p it is hard to see a significant change, but on B1s (OMC reflection), there is a high order (10 or more) diagonal mode that becomes more visible when the B1p power is higher. This could be related to the increase in noise either through clipping or if it happens to be the order 23 mode. To check if it is a residual transmission of the order 23 mode one would need to increase the B1 camera gain to maximum (to saturate the TEM00 mode), and then do a similar step of DAS to see if something appears on the B1 camera.

/users/mwas/detchar/toySensitivity_20240219/toySensitivity.m

The table mentioned in the text was missing...

Though not explicitly mentioned, the computation for the optical gain included the effect of double cavity pole frequency: In particular the Hrec BRMS noise was rescaled in Fig2 and FIg7÷11 according to OG/(1-(f/DCP)^2), where OG is Hrec_ORgain_meancavities and DCP is Hrec_ORpole_meancavities.

In attachment the BRMS noise in Hrec and rescaled to B1 power for two different frequency intervals (110÷133 Hz and 110÷120 Hz). The rescaled noise levels in B1 power are similar, though the noise levels in Hrec are not, the difference being due to the slightly different DARM response between 100 Hz and 200 Hz. 

The attached table contains the data shown in the various plots; the columns are respectively: 

1) GPS time

2) contrast defect (B1p power)

3) Hrec BRMS in 110÷133 Hz

4) DCP frequency

5) low-frequency optical gain

6) SSFS coupling to DARM

7) BRMS noise on B1 power in 110÷133 Hz

8) same as 7) but with contribution from SSFS coupling subtracted

About the impact of SR misalignment on SSFS coupling, this is evident in FIg3. With SR aligned the SSFS coupling is usually larger. However, rescaling Hrec noise for the optical gain does not remove the contribution of SSFS noise; and subtracting the (usually small) residual contribution from SSFS coupling after rescaling seems correct: there are data with high optical gain and high SSFS coupling (e.g. during the Etalon tuning on 29/12), and data with low optical gain and low SSFS coupling, see again Fig3.

This is clear in the attached plots FIg1a÷FIg11a, which are the same as in the previous entry, with two different colours to show data with DCP frequency above 300 Hz (red) and below 300 Hz (blue). 

The Pearson correlation coefficient r from data in the plots is:

r=-0.47 for Hrec BRMS noise and optical gain

r=0.53 for Hrec BRMS noise and contrast defect

r=0.56 for SSFS coupling and contrast defect

r=0.28 for B1 power BRMS noise and contrast defect

r=0.07 for B1 power BRMS noise and contrast defect, after subtracting SSFS coupling contribution from B1 power BRMS

How does this analysis take into account the difference between LN2 and LN3? My impression is that this is not taken into account.

Some of the effects of the transition of LN2 to LN3 are:

• Looking at the optical gain at 60Hz (from Hrec) is not a good representation of the optical gain at 110-130Hz at which the analysis is done. One should take into account the change in DCP frequency from 400Hz to 200Hz, which changes the gain at 120Hz by 10%
• The correlation between SSFS and the noise in h(t)/B1 can be in large part due to the LN2 to LN3 transition. As in LN2 the loop to zero the SSFS is open, while in LN3 it is closed. So subtracting the SSFS correlation with the h(t)/B1 noise can be in some part double counting the effect of changing the optical gain with SR misaligned.

Summary:

1) Hrec noise in the bucket scales inversely with optical gain; the noise in W/sqrt(Hz) is independent on optical gain;

2) the coupling of frequency noise in DARM is correlated with contrast defect;

3) when subtracting the (usually small) contribution from SSFS, Hrec noise in the bucket is basically independent on contrast defect.  
 

The attached plots contain all data from December and January at 12 W input power; each point is an average over 100 s.

- Hrec noise is the BRMS of Hrec in the band 110÷133 Hz

- optical gain is Hrec_ORgain_meancavities

- noise on B1 is the noise in power units, i.e. Hrec BRMS multiplied by the optical gain in W/m and by the arms lenght in m.

- SSFS coupling (or CMRF) is the magnitude of the 227 Hz line in DARM

- contrast defect is LSC_B1p_DC

Fig1: Hrec noise vs optical gain clearly shows inverse scaling;

Fig2: noise on B1 vs optical gain is basically constant, although it sligtly increases for small values of the optical gain;

Fig3: CMRF vs optical gain also shows some inverse scaling;

Fig4: contrast defect vs optical gain clearly shows inverse scaling;

Fig5: contrast defect vs CMRF shows clear linear correlation: poor contrast defect usually implies poor CMRF; this might be partly due to the BS CMRF loop not working in LN2;

Fig6:  Hrec noise vs contrast defect; a linear correlation is clearly visible. 

Fig7: noise on B1 vs contrast defect: some linear correlation is also visible, though smaller than on Hrec.

Fig8: noise on B1 after subtracting the contribution of SSFS coupling, as computed from Fig7

Fig9: noise on B1 vs contrast defect shows some linear correlation

Fig10: after subtracting the contribution from SSFS coupling, noise on B1 is independend on contrast defect

Fig11: after subtracting the contribution from SSFS coupling, the smal residyual dependence of noise on B1 from optical gain (Fig2) disappears too

In conclusion, HOMs might affect the CMRF for frequency noise, but have no effect on the mystery noise. Frequency noise is not contributing significantly with good CMRF, but CMRF fluctuations produce not negligible contribution.

Didier has processed h(t) with individual B1 photodiodes. This allows to cross correlate the two photodiodes to remove shot noise and see more clearly what is underneath. Unfortunately there are the ~25min glitches which spoil the results, I have tried to work around this by adding by hand gating, with a mixed result.

Figure 1 and Figure 2 show the result one where the gating worked better than in the other case. The cross-correlated spectrum is higher than the normal one at low frequency, because the cross-correlated uses gating, while the normal one can use the median-mean average spectrum that is not affected by glitches. What is interesting is that starting from 60Hz up to 800Hz the correlated noise spectrum floor follows very well the expectation of mystery noise plus coating thermal noise. This means that the actual slope of the mystery noise is very close to the -0.66 slope currently used.

Figure 3 shows the cross-correlated spectrum in pink, the noise budget with -0.66 slope in light blue and with -0.75 slope in dark blue. The -0.75 is a much worse fit at high frequency when constrained to have the same level at 100Hz.

This confirms that the mystery noise slope is -0.66, with error bars that slope is in between -0.65 and -0.70. This measured can still be biased by other noises, as the analysis above assumes that other noises are negligible in the 80Hz-800Hz band.

This also shows that squeezing has the potential of improving the sensitivity at all frequencies above 60Hz. But in practice this will be very difficult due to the high losses in the intentionally misaligned SRC cavity.

/users/mwas/calib/Hoft_PD1vsPD2_20240205/hPD1vsPD2.m

The CO2 projector couplings where studied and measured in initial Virgo (VIR-0615B-09). They were not negligible at that time, but If I understand well the CO2 laser was shining directly on the HR face of the mirror at that time, and not on the CP. With the CO2 intensity stabilization, the RIN was ~1e-7 1/rtHz.

The CO2 projector acts now on the CP, which is inside the marginally stable recycling cavities. One consequence of the marginally stable nature, is that spot size on the input mirror changes rapidly with the effective curvature of the input mirrors. I am finding that beam spot radius changes by ~5% (from 48mm to 51mm) when changing the radius of curvature by 0.1m. We have a large DAS correction on the NI CP to remove the cold lens (a few tens of meters?). So a 1e-7 1/rtHz CO2 RIN could correspond to 5e-7 1/rtHz fluctuations in the beam spot radius, and be a source of RIN created inside the interferometer that could be many orders of magnitude larger than the noise expected from the PSTAB performance. In reality the fluctuations will be a few order of magnitude smaller, as at 100Hz the fluctuation in laser power are much faster than the response time of the mirror curvature.

It should be simple to confirm experimentally that the CO2 intensity noise is not a problem. For example by turning off the NI DAS CO2 intensity stabilization loop, or adding a line into that intensity stabilization loop to make the CO2 intensity noise larger.

Input power was increased from 12W to 15W on Jan 23. A question is if it had an impact on the mystery 1/sqrt(f) noise, in particular if it made it higher.

Figure 1 compares the sensitivity a few days after the power increase (yellow) and before (red). There is no difference in the 80Hz-130Hz frequency band. At high frequency sensitivity is clearly better by ~10%, which is roughly the improvement that is expected from the input power increase as sqrt(15/12) = 1.12. Also many of the lines (157Hz, 196Hz, 310Hz) got reduced, but that could be just a coincidence. Compared to the situation from the Christmas engineering run (blue), the noise is clearly worse, by ~8%.

Figure 2 shows the spectrum for all the days since the middle of the Christmas run, with 1h of data each time, using a media-mean average spectrum to avoid the spectrum being spoiled by 25min glitches. The sensitivity clearly got worse in a systematic way, but it is hard to say from that figure when it happened.

Figure 3 is the same as figure 2, but with only a few of the times shown. During the run, just after the OMC replacement, and couple of other times after that. There is no clear trend that I can see, and in the last few weeks the level has been moving up and down by a few percent.

/users/mwas/detchar/hCompare_20240116/hHighRes.m

A question at the weekly meeting was if the improvement in mystery noise betwen Oct 25 and Oct 26 was due to a change in contrast defect. The mystery noise had decreased by ~30% while the optical gain had increased only by ~5%.

Figure 1 shows that there was no change in B1p power between the two times considered.

Figure 2 and 3 show that there was a change in B1p shape. The B1p central spot change from being a double spot to being a single larger and rounder spot. And the very higher order (>4) modes power looks reduced, with less cyan colored fringes, To try to learn more from this images we are missing a way to analyze the B1p modal decomposition based on the camera and phase camera image shape.

Figure 4 on the B1p phase camera the beam size on the image is too small, making it harder to learn anything from it.

At the beginning of the TCS tuning in October we had seen strong changes in the mystery noise level. Looking back at these data, the changes cannot be explained by only optical gain improvement.

Figure 1 and 2 correspond to a reanalysis of these data, and it includes the measurement by Hrec optical gain and double cavity pole at that time. Trying to fit the gap between a simplified noise budget and the measured sensitivity with mystery noise shows that on Oct 25 the noise level on B1 was ~8e-11 W/rtHz, and on Oct 26 it was ~6e-11 W/rtHz (and now we have ~4e-11 W/rtHz). So in addition to increasing optical gain, TCS tuning seem to decrease the level of mystery noise on B1. Between those two times the optical gain had only increased by 5%. In between there was several adjustments of the DAS and PR CHRoCC.

This conclusion remains as usual uncertain, as it relies of filling the gap in the noise budget, so assumes that there is no other significant noise changing in the mean time.

/users/mwas/detchar/toySensitivity_20231231/toySensitivity.m

One limitation of the previous analysis is that it mostly compares data with SR aligned at 25W and data with SR misaligned at 12W of input power, although previous analysis have pointed out that the level of mystery noise in W/rtHz does not depend on SR alignment (VIR-1164A-23). The main reason is that at 12W of input we have no data with SR aligned and good CMRF. I took some time today during the RH step transient to try to get some data with SR aligned and reasonable CMRF.

Figure 1 shows these measurements with the first 5 minutes with BS and OMC misaligned in TY to improve the CMRF and the last 5 minutes with everything aligned in a normal configuration. For more details see notes at the end of this entry.

Figure 2 shows the SSFS noise projection during this time where coupling was reduced. It was still far from perfect, but the projection is a factor 3 below the sensitivity curve, and the usual 4e-11 W/rtHz of mystery noise at 100Hz explains well the gap between the noise budget and the measured sensitivity with SR aligned.

Figure 3 shows again the analysis of B1 with the effect of the DARM loop removed, and shot noise and coating thermal noise incoherently subtracted from the spectrum. In the thick line is highlighted this measurement with SR aligned, compared to other measurements with SR misaligned earlier in December. With SR aligned the noise is clearly not higher, and at the same level as the more recent SR misaligned data. This seems to confirm that the level of mystery noise in W/rtHz on B1 does not depend on SR alignment.

Measurement details

10:15-10:24 trying BS TX SET changes to imporve CMRF in LN2 (SR
aligned), in the past BS TY SET changes had no effect. There doesn't
seem to be a clear effect on CMRF using TX either.

10:27 Turning of OMC AA drift control
changing TX set point
10:30-10:31 CMRF improved by a factor 2, with OMC TX misalingment, but 3% loss in optical gain
10:32 turning back on OMC AA TX drift control
changing TY set point

continued with several combinatino of OMC AA TX or TY open with a set point, and a set point on BS TX/Ty

Best result seems to be for BS TY set of 3e-4, and an OMC AA TY offset of ~2 urad
11:06 (5min) taking data in that state
putting back standard configuration with OMC AA enabled and BS TX/TY set at zero
11:14 (5min) taking data in that state

On Fiodor's request, we conducted some cross-check simulations to understand the behavior of the optical gain of DARM as a function of the angle of the SRM.

We begin with a brief description of our interpretation of the effect of SRM tilt on the transfer function "DARM motion -> DARM sensor (B1)," conveniently referred to as DARM TF. In Fig.1, the DARM TF is shown for three different optical configurations:
1) DRMI - Dual Recycled Michelson Interferometer, the currently used scheme.
2) PRMI - Power Recycled Michelson Interferometer. In this case, the SRM has been removed from the model.
3) SRM fully misaligned - This configuration is a functional equivalent of when the SRM is placed in the "parking" position, i.e., it is widely misaligned. In this configuration, the light reflected by the SRM is lost. Therefore, this configuration was emulated by setting the mirror losses to the mirror reflectivity value (L=0.6), reflectivity to zero (R=0), and leaving transmissivity unchanged (T=0.4).
The optical gains are all normalized to the DC gain (at 10 Hz) of the DRMI curve. 

When the SRM is operated in Resonant Sidebands Extraction conditions, the SRM-Arm optics can be treated as a single cavity with lower finesse than that of the individual arm cavities. Lower finesse corresponds to a broader bandwidth, and for this reason, in Fig.1, the optical pole frequency of the DARM TF is higher for the DRMI curve compared to the PRMI curve. Regarding the optical gain, this is inversely proportional to bandwidth. Therefore, a wider bandwidth corresponds to reduced optical gain. For this reason, the optical gain is higher in the case of PRMI compared to DRMI.

It is interesting to note what happens in the "SRM fully misaligned" case. In this case, the DARM TF is identical to that of PRMI, with the optical gain reduced by a factor R. For clarity:
G2 = R  G1
where G1 is the optical gain in the PRMI case, and G2 is the optical gain in the "SRM fully misaligned" case. This is expected as the signal 'reflected' from the SRM is lost in this configuration. Anyway, the important point here is that the DARM TF for the case of complete misalignment is analogous to that of a PRMI.

For smaller angles than the "parking" one, our interpretation is that the system is in an intermediate configuration between "SRM fully misaligned"  and DRMI. Tilting the SRM decreases the equivalent reflectivity of the SRM and increases equivalent losses. Therefore, as the SRM angle increases, the "signal recycling" effect is increasingly lost, and the DARM TF tends towards that of the "SRM fully misaligned” case (which is identical to a PRMI-like response).

This interpretation seems to be compatible with experimental observations and the results of our simulations. We calculated the DC optical gain of the DARM TF with Finesse varying the SRM angle; the result is shown in Fig2, where we display the DC gain as a function of the SRM angle. The DC gain is calculated at a frequency of 10Hz. The result appears to be compatible with experimental data.


The purpose of the simulation was to investigate the behavior of the DC gain of the DARM TF as a function of the misalignment of the SRM. In the past, the behavior of the DCP in relation to misalignment had been studied. The results can be found here: https://logbook.virgo-gw.eu/virgo/?r=55862

- The Finesse model used is the common Kat file for Virgo, which is available at: https://git.ligo.org/finesse/finesse-virgo/-/blob/main/src/finesse_virgo/katscript/00_virgo_common_file.kat
- Experimental data is referenced to GPS time: 1386088818

Figure 1 shows a basic noise budget when SR is misaligned to optimize the sensitivity curve. It includes only 4 noise sources

• Coating thermal noise, as implemented right now in the simulink noise budget, based on coating thermal noise measurement at MIT
• Mystery noise, assuming 4.4e-11 (100/F)^0.66 W/rtHz noise on B1 and the optical gain & pole frequency measured by hrec
• Shot noise, based on the measure difference between two B1 PDs of ~4.2e-11 W/rtHz and the optical gain & pole frequency measured by hrec
• Low frequency noise, an arbitrary curve to fit the reminder of the noise, it has a 1/f^4 slope.

Of course this is not all the noises that we have, so there is a gap of 8Mpc remaining between the measured 47Mpc during that 1h long average and the sum of 55Mpc. The spectrum is computed using a median-mean-average method, so that it is not polluted by the ~25min occurence glitches.

Reducing either shot noise or the mystery noise by factor sqrt(2) while keeping everything the same improves the total by ~5Mpc to 60Mpc.

/users/mwas/detchar/B1compare_20231221/toySensitivity.m

There are confusing results on how the mystery noise level has changed with the input power reduction. Looking at fits of the missing noise in the noise budget, and taking into account the DARM response transfer function, the noise on B1 corresponding to the mystery noise was 12e-11 W/rtHz @ 100Hz with 25W input power, but only 4e-11 W/rtHz at 12W input power once the thermal tuning was done VIR-1164A-23. Naively one would expect a factor 1.8 reduction from the input power reduction (and matching change in B1 power set point to keep the same DARM offset in meters), instead we measure a factor 3 reduction. However this estimation relies on a lot of modelling. So here I try to make a somewhat more direct analysis.

FIgure 1 selects the best range for each 4 day period and shows directly the B1 spectrum at that time. Looking at the region around 90Hz, the spectrum decreased by a factor ~1.8 when reducing the input power. Which seems consistent with just a change of input power. But B1 is affected by the shape of the DARM open loop transfer function (OLTF). At first order it shouldn't change that much, as the DARM UGF is actively controled

Figure 2 and 3, however there have been some changes in the estimated DARM OLTF, especially in the phase.

FIgure 4 this has a large impact on the impact of the DARM loop on the B1 noise (which is 1/(1-OLTF))

Figure 5 shows B1 corrected for that effect, the ratio at ~90Hz in that case is a bit larger a factor 2.1.

Figure 6 subtracts from B1 the other important noise sources in this frequency range (shot noise, based on B1 PD1-PD2 difference, and coating thermal noise, based on theory times the DARM response function measured by Hrec). In that case the ratio between before and after the input power decrease is 2.5, not quite the factor 3 derived from comparing different noise budgets but getting close to it.

So in addition to the expected factor 1.8 decrease due to the change of power, there seem to be an actual decrease in the noisy field that beats with the local oscillator, leading to an additional factor ~1.35 decrease in the mystery noise level on B1 (and h(t)).

Unfortunately this analysis shows that the result depends strongly on taking into account small difference in the DARM OLTF and evaluating the other noise source in addition to the mystery noise. This analysis tend to confirm the result from the noise budget that the mystery noise decrease further that just one would expect from the change in input power (and change in DARM optical gain), but it is difficult to be very confident of that conclusion.

/users/mwas/detchar/B1compare_20231221/B1compare.m