Sorry for the confusion. this is probably my mistake. I likely forgot to load the calibration filter.

Based on what I remember, the unloaded part is most likely TM_LOCL_L part.
I’m sure I had confirmed the other filters were loaded, so TM_LOCL_L is the most plausible one that was missed.

Also, I think that the current parameters have already been updated using the results from klog#36236.

[Tanaka, Komori, Dan]

We adjuseted the ASC OUTMTRX for {D,C}{HARD,SOFT} to reduce the couplings.

(After some trial with different methods to estimated the appropriate values) we evaluate the values with the following method:

1. Requested LSC, ASC to be down
2. Keep the suspension to be LOCK_AQUISITION state
3. Turned OFF MN MNOLDAMP of all type A suspension by turning ON FM8=null filter of them.
4. Cut the path of TM by change the gain of TM LOCK from 1 to 0 for all type A suspensions.
5. Injected a sin (freq = 0.05Hz) into K1:ASC-DHARD_P_SM_EXC and measured TM oplev signals.

We used the measured values to calculate the OUTMTRX values and updated them and measure it again to confirm that the oplev values gave almost same values.
(We have NOT confirmed that the couplings are redueced.)

Attached figures are the measured TF from K1:ASC-DHARD_P_SM_EXC to oplevs and the OUTMTRX after the adjustment.

We confirmed that the IFO can reach PRFPMI_RF_LOCKED state at the end with the new OUTMTRX values.

[Komori, Dan]

We adjusted the DHARD P filter "HBtest" to increase the UGF of the DHARD P loop.

We

• adjusted the notch filter freq (it was at 7.5Hz but we moved it to 7.35Hz based on the TF meas data.)
• added another notch filter at 9.2Hz (after the work, we found it is near by the freq of PRM ADS, which was ON during the meas. So it might be not nessesary.)

After these change, we could raise the gain of DHARD P loop to -3.5 which gave the 2Hz  UGF.

Meas file: /users/Commissioning/data/ASC/2026/0202/DHARD_P_newact_OLTF.xml

I'm not sure which one is the latest calibration, but anyway I found unloaded calibration filters as shown in Fig.1 (CFC bit in STATE_WORD is raised).
According to an differences in current and unloaded filters, there is ~30% mismatch in the gain of the actuation path.

In general, a mismatch in one of the actuation or sensing paths are much enhanced around UGF because it induces also a phase mismatch around UGF. It is not surprising if ~50-60% errors occur around UGF. By the way, a too large phase mismatch can make difficult to any kind of correlation analysis around UGF because the noise components which should be enhanced as the sum of the sensing and actuation paths can be canceled out and ones which should be canceled out can be enhanced.

I haven't checked it's really unloaded filter issue or just a wrong detection by the front-end model. Anyway, after the calibration measurements, we need to ensure not only the parameter updates but also filter loading, SDF clearing, and so on.

Result on 2025-04-10: https://klog.icrr.u-tokyo.ac.jp/osl/?r=33406

Result on 2025-11-25: https://klog.icrr.u-tokyo.ac.jp/osl/?r=35672

Result on 2026-01-30: https://klog.icrr.u-tokyo.ac.jp/osl/?r=36255

supplemental plots

I analyzed the (BL-)white noise acoustic injection in the PSL room.

I assumed the coupling is linear and applied the Coupling Function model.

The current sensitivity is limited by the PSL room sound at 200-600 Hz.

I continued the trial of high bandwidth ASC.

## Frequency dependent MN actuator balance

First of all, I tried to take a balance of Type-A MN balance. In the original low-band width ASCs case, we used TM and MN stage as the actuator. A cross over frequency between their stage was 0.1Hz. At that time, we took the actuator balance by using TM and each MN actuator effeiceincy was tuned respectively so that the cross-over frequency became 0.1 Hz (klog). On the other hand, in the high-band width ASC case, we will use only MN stage as the actuator, So, I confimed the the MN actuator efficiecy by measuring the frequency responce of TM oplev when MN was excited.

This TF measurement setup is as below

• Type A suspension guardian state: Lock acquisition
• Turn off both P and Y TM oplev DC controls by engaging null filters in FM9 of {I, E} TM{X, Y}_MN_OLDAMP_{P, Y}
• Excitation signal was injected from DHARD_P_SM_EXC. This time, OUTMTRX was not changed.
• Only gain filters in MN_LOCK filters were engaged, that is, I turned off FM4, FM9 and FM10 in this time.
• TM_LOCK gains were set 0 so that the excitation did not feed back to TM stages.

Fig.1 shows the results of each frequency responce of each TM oplev when each MN was excited. Each DC gain seems to be almost the same, but each gain above 1 Hz seems to be different due to the resonance frequecy's difference (especially ITMY).  Since MN stages were used as the actuator below 0.1 Hz previously, it maybe ok that the just each DC gain was aligned. However, this time, we want to enhance the bandwidth up to several Hz. it may be necessary to adjusted the gain in both DC region and several Hz region. So I attempted a frequency dependent MN actuator balance by implementing frequency dependent gain filter in each MN_LOCK filterbank. This time, I adjusted other 3 Type As' responces based on the ETMX responce,

I summrized the each gain value at 0.14 Hz as a representative DC gain and at 3 Hz as a representative higher freq. region and the difference from ETMX.

As for ITMX, I just adjusted the overall gain by implementing -3.45 (=(3.6+3.3)/2) dB in FM2 of MN_LOCK. As for ITMY and ETMY, I made the filters like fig.2 so that the both gains at 0.1 Hz and 3 Hz were almost the same as the ETMX. In this time, I did not take into account the gain around the 0.8 - 1 Hz. Such filters were labeled "test", and implemented in FM2 of ETMY_MN_LOCK and in FM6 of ITMY_MN_LOCK respectively.

After the implementation, I measured the responces again. Fig. 3 shows the results. the frequency dependent balance seems to work well.

## DHARD and CHARD P

I engaged DHARD P control with new filter. Also, I used the same filter as DHARD for CHARD P control. Fig. 4 and 5 show the OLTFs of DHARD and CHARD, respectively. Their UGFs are set to 1.5 Hz.

Fig.6 shows the spectra of ASC error signals. As for DHARD P, RMS after balancing seems to become bigger than the one before balancing, but it is still lower than the one of old filter.

## Note

I found that there is still couplings. fig. 7 shows the timeseris of the error -feed back of ASC during CHARD _P OLTF measurement. Although CHARD_P was excited, DHARD_P error signals. 

[Kenta, Michimura]

We found that the PRG measurements done yesterday (klog #36242) was bogus since the misalignments of ITMs where not sufficient.
By applying sufficient amount of ITM misalignments, PRG for carrier PRX and PRY, BS T and R, ITM reflectivity for s-pol and ITM p-pol conversion ratios are found to be the following:

Carrier PRG for PRX from POP_DC and AS_DC       0.341+/-0.006
Carrier PRG for PRY from POP_DC and AS_DC       0.330+/-0.009
ITM reflectivity ratio X/Y for s-pol from AS_DC and POS_SPOL   1.039+/-0.005
BS T/R ratio for s-pol from POP_SPOL    0.998+/-0.012
BS T for s-pol  0.4995+/-0.0030
BS R for s-pol  0.5005+/-0.0030
BS T/R ratio for p-pol from POP_PPOL and POS_PPOL       4.025+/-0.031
BS T for p-pol  0.8010+/-0.0012
BS R for p-pol  0.1990+/-0.0012
ITM p-pol conversion ratio X/Y from POP_PPOL and POS_PPOL       0.663+/-0.005

They are all consistent with our expectations. Asymmetry in ITM reflectivities for s-pol is probably due to birefringence asymmetry, and measured PRG suggests that losses in PRC is ~10% for PRX and ~15% for PRY.

We have also successfully estimated the PRG for sidebands in PRX, PRY and PRFPMI, and average PRC length as follows.

Sideband PRG for PRX           0.0730+/-0.0013
Sideband PRG for PRY           0.0599+/-0.0011
Sideband PRG for PRFPMI   7.30+/-0.11
Average PRC length      66.525+/-0.006 m

The measured PRCL is shorter from the design (66.591 m) by 6.6(6) cm.
If we are to keep the current f2 modulation frequency (44.9946924104 MHz), PRCL needs to be shortened by 10.3(6) cm.
Pretty low sideband PRG for PRFPMI suggest 13.4(2)% losses in PRC, consistent with PRX and PRY.
 

POP and POS PD checks:
 - We confirmed that SPOL and PPOL PDs at POP and POS are not swapped by blocking the beams in front of these PDs.
 - We found two beams in front of POS_SPOL PD even with ITMX in aligned state and ITMY in MISALIGNED state. We found that one of them was actually from ITMY, and was hitting on the PD.
 - We confirmed that by misaligning both ITMX and ITMY with MISALIGNED_BF, all the relevant PDs listed below will be zero.
 - The measurements done yesterday can be explained by X measurements seeing both beams and Y measurements seeing only Y beam.
 - With eyeballs, we confirmed that the beam is hitting on the SPOL PDs (for PPOL, it was dark and hard to see).
 - POP_SPOL PD had gain of 10 dB, while POP_PPOL, POS_SPOL and POS_PPOL PDs had 40 dB.

Data used:
 - The raw data for PRX/PRY carrier (attachment #1) and sidebands (attachment #2) are attached. For the sideband lock, the data for PRFPMI 5W we took on Jan 27 is also plotted for comparison.
 - The summary table for the carrier/sideband lock and ITM single bounce is as follows:
                                ITMX single        ITMY single          PRX carrier             PRY carrier         PRX sideband        PRY sideband
K1:LSC-AS_PDA1_DC_OUT_DQ        0.03009+/-0.00014  0.02871+/-0.00017    0.0944+/-0.0014         0.0889+/-0.0015     0.01553+/-0.00009   0.01507+/-0.00009
K1:LSC-POP_PDA1_DC_OUT_DQ       0.00313+/-0.00008  0.00273+/-0.00007    0.01079+/-0.00015       0.0089+/-0.0004     0.00178+/-0.00009   0.00135+/-0.00009
K1:LSC-POP_SPOL_DC_OUT_DQ       2.252+/-0.029      2.18+/-0.04          7.45+/-0.25             7.24+/-0.24         1.148+/-0.027       1.243+/-0.025
K1:LSC-POP_PPOL_DC_OUT_DQ       16.66+/-0.07       6.25+/-0.04          98+/-8                  18.5+/-1.4          11.66+/-0.09        3.52+/-0.05
K1:LSC-POS_SPOL_DC_OUT_DQ       672.2+/-2.4        653.2+/-2.4          (2.02+/-0.05)e+03       (1.94+/-0.07)e+03   356.5+/-1.5         353.2+/-1.5
K1:LSC-POS_PPOL_DC_OUT_DQ       16.08+/-0.07       97.6+/-0.4           103+/-6                 295+/-19            11.01+/-0.10        53.6+/-0.5
K1:LSC-POP_PDA2_RF90_I_ERR_DQ   (3+/-4)e-05        (-3.9+/-3.5)e-05     -0.00676+/-0.00014      -0.00578+/-0.00034  0.00701+/-0.00006   0.00606+/-0.00012
K1:LSC-POP_PDA2_RF90_Q_ERR_DQ   (3+/-4)e-05        (3.3+/-2.6)e-05      -0.00956+/-0.00019      -0.00760+/-0.00028  0.00987+/-0.00008   0.00788+/-0.00007
POP90 sqrt(I^2+Q^2)             (4+/-4)e-05        (5.1+/-3.2)e-05      0.01171+/-0.00017       0.00955+/-0.00030   0.01210+/-0.00007   0.00994+/-0.00009

 - X and Y are consistent, except for POP_PPOL and POS_PPOL, probably due to the amount of birefringence difference in ITMX and ITMY. p-pol from ITMX and ITMY can be seen more at POP and POS, respectively, due to high BS p-pol transmission.
 - For POP90, Y measurements are higher by 22(2)%. This is due to f2 not matching with PRCL. Even with the sideband lock, 2*f2 might not be on resonance if f2 is detuned for PRCL. When PRX length and PRY length are equally detuned, we won't see the POP90 difference. Since X gives larger POP90, PRX length is less detuned for f2. See following discussions.

Carrier power recycling gain estimates:
 - Power recycling gain can be estimated from taking the power ratio (PR locked)/(ITM single bounce) and multiplying it by PRM power transmission TPRM.
 - Below are the results. Although there are variations, PRX and PRY seems to be consistent. PRG estimated using PRX POP_PPOL_DC and POS_PPOL_DC is higher. This can be explained because BS is not very lossy for p-pol. To derive the PRG given above, average of measured PRG using POP_DC and AS_DC are used.

Carrier PRG for PRX from POP_PDA1_DC    0.357+/-0.011
Carrier PRG for PRX from AS_PDA1_DC     0.325+/-0.005
Carrier PRG for PRX from POP_SPOL_DC    0.342+/-0.012
Carrier PRG for PRX from POP_PPOL_DC    0.61+/-0.05
Carrier PRG for PRX from POS_SPOL_DC    0.310+/-0.008
Carrier PRG for PRX from POS_PPOL_DC    0.67+/-0.04
Carrier PRG for PRY from POP_PDA1_DC    0.339+/-0.017
Carrier PRG for PRY from AS_PDA1_DC     0.321+/-0.006
Carrier PRG for PRY from POP_SPOL_DC    0.344+/-0.013
Carrier PRG for PRY from POP_PPOL_DC    0.306+/-0.023
Carrier PRG for PRY from POS_SPOL_DC    0.307+/-0.011
Carrier PRG for PRY from POS_PPOL_DC    0.313+/-0.021

Beam splitter ratio estimates and X/Y assymetry estimates:
 - Using the same method described in klog #36242, the parameters given above are derived.
 - It seems like BS T and R measurements done in klog #29284 had ~2% systematic errors.
 - With these parameters, estimated carrier PRG for s-pol without additional losses be the following. To explain the measured PRG, losses in PRC are estimated to be ~10% for PRX and ~15% for PRY. This ratio is consistent with the measured ITM p-pol conversion ratio (0.663).
PRX PRG for s-pol with no loss 0.373+/-0.004
PRY PRG for s-pol with no loss 0.374+/-0.004

Sideband power recycling gain and f2 detuning:
 - Sideband power recycling gain measued with POP90 can be estimated by

Gprsb = Gprcr / (1+(2*Fpr*delt/FSRprc)**2)

where Gprcr is the power recycling gain for carrier, Fpr is the PRX/Y finesse, delt is the f2 frequency detuing and FSRprc is PRC (average) FSR. Ideally, delt is the same for PRX and PRY by FSRprc*Las/2/Lprc, where Las is the Schupp asymmetry. This is an approximation for Las/Lprc << 1 (which is not so true for KAGRA due to large Las). However, in reality, there is a slight difference due to f2 detuning from PRC FSR (~2.25 MHz) times 20. This can be estimated by taking the ratio of Gprsb for PRX/PRY estimated from the POP90 ratio during PRX and PRY sideband lock.

 - Using the measured Schnupp assymetry (3.36(1) m from klog #14560) and designed PRCL 66.591 m, this detuning can be estimated as

Estimated f2 detuning of PRC    0.070+/-0.004 MHz

 - With this value, sideband PRG in PRX and PRY can be estimated as follows:

Sideband PRG for PRX    0.0730+/-0.0013
Sideband PRG for PRY    0.0599+/-0.0011

 - Also, from f2 detuning and the current f2 value of 8*5.6243365513 MHz, average PRCL can be estimated as follows. This is consistent with the design within 6.6(6) cm.

Average PRC length      66.525+/-0.006 m

 - Then, using the estimated sideband PRGs for PRX and PRY, POP90 can be calibrated into sideband PRGs. The calibration factor for sqrt(I^2+Q^2)/Pin will be 5.64(8), and sideband PRG for PRFPMI is 7.30(11). See attachment #3.
 - Pretty low PRG suggest 13.4(2)% losses in PRC, which is consistent with PRX and PRY measurements. This is similar to the scenario shown in klog #36238. Note that this loss includes the effect from f2 detuning.

Discussions:
  - Measured f2 detuning suggests that, if we are going to keep the current f2 modulation frequency (44.9946924104 MHz), PRCL needs to be shortened by 10.3(6) cm. We can also shorten the IMC length by similar amount and retune f2. Presice amount depends on how well current f2 is aligned with IMC FSR. 
  - The reason why we have higher carrier PRG from TRX (currently ~13.6) and TRY (currently ~12.8) could be from p-pol. Since BS T:R=8:2 for BS, the most of the s-pol is in between PR-ITMX cavity, rather than PR-ITMY cavity. This hypothesis can be tested by measuring carrier PRG using SPOL/PPOL PDs at arm transmission (we need to remove or adjust HWP for this).
  - During PRFPMI, carrier PRG gives the total of losses in PRC and arm cavity, and they are degenerate. Since ITM reflectivity is also chaning (klog #36238), it would be nice if we can occasionally measure the arm cavity round-trip losses from REFL power locked/unlocked,  together with the finesse measurements. Or any ideas for measuring both independently during PRFPMI?

Next:
 - Measure finesse with the current situation to check carrier PRG in PRFPMI, and to estimate current ITM reflectivity and arm round-trip loss. Measure carrier PRG in PRFPMI using SPOL/PPOL PDs at the arm tranmission to see if PRG assymetry measured with TRX/TRY is from polarization issues. Carrier PRG in PRFPMI can also be estimated from POP (and SPOL, PPOL PDs there).
 - Measure IMC FSR again to see if current f2 is aligned with IMC FSR.
 - Decide if macroscopic PRC length tuning (or IMC length tuning) is necessary before RSE commissioning.

I restored the script of ASC_LOCK. IFO will be left OBSERVATIO _WITHOUT _LINES. 

Michimura, Tanaka

Fig.1 shows the spectra and culmutive RMSs, red is the error signal with new filter when gain = -2, and blue is the one with the old filter.

Thanks to enhance the control bandwidth from 0.3 Hz to ~1.5 Hz, RMS from 100 Hz to 0.2 Hz become approximately 1/3 lower even though there is gain peaking around 2 Hz.

On the other hand, the noise floor above 10 Hz  seems to become larger due to the 1-10 Hz lead filter implemetation. It is necessary to implement the roll off filter. 

[Tanaka, Komori, Sugioka, Dan]

Background (Issue found in the previous day’s work)

During the ASC high-band work on the previous day, Komori-san found a critical issue: the suspension MN LOCK P filter bank (FB) contains an integrator. Because of this, the phase is already significantly rotated around ~1 Hz. When TM LOCK P is turned off, the MN side cannot properly take over the control above ~0.1 Hz, resulting in an unstable configuration.

In the origianl configuration,

• above ~0.1 Hz the MN contribution is small,
• and the TM loops mainly maintain the control in that band.

In the current attempt to realize a high-band configuration where MN also controls above ~0.1 Hz, the MN LOCK filtering needed to be modified.

Plan for today

• In the suspension MN LOCK P filter bank (FB), introduce a new high-band filter FM4 = HBtest to replace (fig 001):
  • FM9 = int
  • FM10 = LP1
• Combine it with the newly prepared K1ASC-DHARD_P filter (FM6) to test whether the system can be locked with the signal and only with MN stage. (fig 002)
• We do not hand the control back to the TM loops. Instead, we adjust the DHARD-side gain while measuring OLTF to confirm stability and related behavior.

Preparation

• Disable TM act path for all four TMs: set TM LOCK P gain from 1 to 0.
• For three Type-A suspensions (all except ETMX), switch K1:VIS-{}_HIERSWITCH_P to OFF so that signals can reach the MN without going through the TM path. (ETMX was already OFF.) (fig 005)
• In MN LOCK P filter bank:
  • turn OFF FM9 and FM10,
  • turn ON FM4 = HBtest (fig 001).
  • This filter is designed so that the magnitude becomes flat around ~1 Hz, and the phase is advanced in that region.

Temporary modifications to ASC_LOCK GRD (fig 003)

For this test, we temporarily modified parts of the ASC_LOCK GRD.

• For the Type-A suspension MN LOCK filter switching:
  • Original: turn ON FM9
  • Test setting: turn ON FM4 = HBtest
• We also adjusted the behavior around INCREASE_SOFTHARD_GAIN so that:
  • SOFTs are closed with gain staying at -1,
  • HARDs stop at gain -0.2,
  since we want to manually increase DHARD-side gain during the OLTF measurements.

Procedure

1. Request ENGAGE_WFSDC on LCK_LOCK. (This also auto-requests ASC_LOCK to ENGAGE_WFSDC.)
2. Request INCREASE_HARDSOFT_GAIN on ASC_LOCK:
   • SOFT sides stay at gain -1
   • HARD sides stop at gain -0.2
3. Set DHARD P gain to 0 to open the loop once.
4. Switch DHARD P filter bank from the original set (FM1 × FM2 × FM4 × FM5 × FM7 × FM8) to the new filter FM6.
5. Increase DHARD P gain step-by-step: -0.5 → -1 → -2.
6. Measure OLTF at each gain state.

Results (fig 004)

• By increasing DHARD P gain to -1 and -2, we were able to push the UGF to around ~1.5 Hz.
• Measurement file: /users/Commissioning/data/ASC/2026/0129/DHARD_P_new_filter_OLTF.xml

Findings

1. If K1:VIS-{}_HIERSWITCH_P remains ON, turning off TM LOCK P stops signals from reaching MN, so MN-dominant control cannot work as intended. We switched it OFF for all Type-A suspensions except ETMX (which was already OFF).
2. Since this test targeted only the P path, the MN LOCK filters must be configured as:
   • P: FM4 (HBtest)
   • Y: FM9 (usual)
   We updated ASC_LOCK.py accordingly.

Remaining issues

• Gain peaking is large.
• We expected stronger low-frequency suppression due to the integrator inside MN LOCK P FM4, but it was not as large as expected.
• This may indicate insufficient DoF separation and/or residual coupling? Further investigation will be necessary.

I also  analized the white noise shaker injection at positition 2 (EXC : K1:PEM-EXCITATION_EY0_RACK_2_EXC, K1:PEM-PORTABLE_EYC_RACK_EY0_ADC0_DSUB26_OUT_DQ).

Some  very small excess in the DARM were found at 115, 250, 300, 660,  780, 855 Hz.

I analized the white noise shaker injection at positition 1 (EXC : K1:PEM-EXCITATION_EY0_RACK_1_EXC, K1:PEM-PORTABLE_EYC_RACK_EY0_ADC0_DSUB25_OUT_DQ).

There were no significant excess in the DARM.

I assumed the coupling from ACC -> QPDs are liner and applied the Coupling Function model.

[Tanaka, Dan, Sugioka, Komori]

Abstract:

We have started a trial to increase the ASC bandwidth in order to reduce power fluctuations inside the arm cavities, which can mitigate non-stationary and non-linear noises in the interferometer.
The first target is the DHARD pitch loop, for which we aim to increase the unity gain frequency (UGF) up to a few hertz, although this has not been succeeded yet.

Details:

We have been observing non-stationary noise and likely non-linear noise around 100 Hz in KAGRA, which must be addressed to achieve better sensitivity.
One possible cause is the large fluctuation of the arm transmission power, exceeding 1%, whereas it is typically 0.01–0.1% in LIGO.
In addition, the ASC bandwidth of the arm cavities in LIGO is 4–5 Hz, while that in KAGRA is only around 0.5 Hz.
Since the ASC control noise coupled into DARM is much smaller than the current sensitivity, we can increase the ASC bandwidth to significantly reduce the transmission power fluctuations.

The first target is DHARD pitch.
The pitch resonant frequencies of the MN, IM, and TM are 0.8 Hz, 45 Hz, and 7.5 Hz, respectively.
Therefore, within an ASC bandwidth of a few hertz, these three masses can be regarded as a single effective pendulum, making it relatively straightforward to increase the UGF.

As a first step, we designed a new filter for higher-bandwidth operation using a simple phase compensation filter.
Another important concept of the new ASC scheme is that the feedback is applied only to the MN, and not to the TM, in order to avoid noise contamination.
The expected openloop transfer functions are plotted in Fig. 1, where the blue and red curves correspond to the current and targeted designs, respectively.
Although the loop has not yet been fully optimized, the new design achieves a UGF of approximately 2 Hz.

We implemented this new filter through the following steps:

• Reducing the {D, C}{HARD, SOFT} gains from −1 to 0.3 to decrease the ASC UGF from 0.3–0.5 Hz to around 0.1 Hz, ensuring that the UGF is below the crossover frequency between the MN and TM (0.1 Hz).

• Turning off the TM LOCK filter and configuring the ASC to actuate only on the MN.

• Turning off the DHARD pitch control, replacing the old filter with the newly designed one, and re-enabling the control.

We successfully closed the DHARD pitch loop with the new filter and measured the openloop transfer function, shown by the red dots in Fig. 2, which can be compared with the conventional loop shown by the blue dots.
However, the achieved UGF is still low, and an oscillation at 0.8 Hz appeared when we increased the gain further.

We will investigate the origin of this instability in more detail.
In addition, the coupling between DHARD and CHARD appears to be significant, so improving the decoupling between these degrees of freedom is another important task.

[Kenta, Michimura]

Power recycling gains were measured in PRX and PRY configurations.
The power recycling gains were rougly 0.3 for both PRX and PRY, but the power measured at POP is rougly two times higher for PRX case, compared with PRY.
This natively suggests that the BS T:R ~ 0.6:0.4, which in turn does not explain the measured PRG.
Birefringence effects could be contributing, but seems hard to explain the whole story.

Background:
 - The motivation was to calibrate the POP90 signal into actual power recycling gain for sidebands to aid optical loss measurements (klog #36231).
 - We also wanted to measure BS transmision and reflectivity in-situ to compare the result with klog #29284.

Locking and data taking:
 - We first zero-ed the relevant PD offsets by closing the shutters.
 - Locked PRX or PRY using K1:LSC-REFL_PDA2_RF135_I_ERR on carrier or sidebands by changing the sign.
 - Confirmed the alignment and error signal offsets to maximize the power recycling gain.
 - Took data for at least 100 seconds.
 - We also took the same data with ITM single bounce configurations, PRM mis-aligned to estimate the power recycling gain.

Data used:
 - The raw data for PRX/PRY carrier (attachment #1) and sidebands (attachment #2) are attached. For the sideband lock, the data for PRFPMI 5W we took last night is also plotted for comparison.
 - The summary table for the carrier lock and ITM single bounce is as follows:
                                ITMX single             ITMY single             PRX carrier             PRY carrier
K1:LSC-AS_PDA1_DC_OUT_DQ        0.03021+/-0.00013       0.02899+/-0.00023       0.087+/-0.006           0.082+/-0.005
K1:LSC-POP_PDA1_DC_OUT_DQ       0.00613+/-0.00010       0.00273+/-0.00012       0.0193+/-0.0004         0.00900+/-0.00027
K1:LSC-POP_SPOL_DC_OUT_DQ       4.845+/-0.031           2.357+/-0.027           14.8+/-0.5              7.20+/-0.23
K1:LSC-POP_PPOL_DC_OUT_DQ       23.29+/-0.07            8.95+/-0.20             161+/-14                30.5+/-1.5
K1:LSC-POS_SPOL_DC_OUT_DQ       1306+/-4                653.4+/-2.6             (3.86+/-0.13)e+03       (1.92+/-0.05)e+03
K1:LSC-POS_PPOL_DC_OUT_DQ       111.60+/-0.33           97.2+/-0.4              465+/-25                297+/-7
 - As you can see, somehow X is always roughly two times higher, except for AS_DC and POS_PPOL.
 - Although POS_SPOL should be essentially the same as AS_DC, the behaviour is very different. It actually seems like POS_SPOL and POP_PPOL are swapped. But for now, we assume that they are not swapped.
 - Increase from single bounce to PRX/PRY are roughly a factor of 3, except for POP_PPOL in PRX case (in red).

Carrier power recycling gain estimates:
 - Power recycling gain can be estimated from taking the power ratio (PR locked)/(ITM single bounce) and multiplying it by PRM power transmission TPRM.
 - Below are the results. Although there are variations, PRX and PRY seems to be consistent. They are smaller than naive estimates from measured BS T and R (klog #36231).

Carrier PRG for PRX from POP_PDA1_DC    0.326+/-0.008
Carrier PRG for PRX from AS_PDA1_DC     0.298+/-0.019
Carrier PRG for PRX from POP_SPOL_DC    0.316+/-0.011
Carrier PRG for PRX from POP_PPOL_DC    0.72+/-0.06
Carrier PRG for PRX from POS_SPOL_DC    0.306+/-0.011
Carrier PRG for PRX from POS_PPOL_DC    0.431+/-0.023
Carrier PRG for PRX from all    0.399+/-0.012
Carrier PRG for PRY from POP_PDA1_DC    0.342+/-0.018
Carrier PRG for PRY from AS_PDA1_DC     0.293+/-0.019
Carrier PRG for PRY from POP_SPOL_DC    0.316+/-0.011
Carrier PRG for PRY from POP_PPOL_DC    0.352+/-0.019
Carrier PRG for PRY from POS_SPOL_DC    0.304+/-0.008
Carrier PRG for PRY from POS_PPOL_DC    0.317+/-0.008
Carrier PRG for PRY from all    0.321+/-0.006

Beam splitter ratio estimates and X/Y assymetry estimates:
 - POP being different between X and Y, but not for AS suggests BS T and R assymetry.
 - First, by taking the ratio (ITMX single)/(ITMY single) for AS_DC, ITM reflectivity ratio for s-pol can be estimated as follows.

ITM reflectivity ratio X/Y for s-pol from AS_PDA1_DC    1.042+/-0.009
                                                                                                                                                                                                                           
 - This is not conistent with PhysRevApplied.14.014021, which gives 1.000352+/-0.000028. But not very important.
 - By taking the ratio (ITMX single)/(ITMY single) for POP_SPOL, (TBS_s/RBS_s)**2*RITMX_s/RITMY_s can be estimated. Using the ITM reflectivity ratio above, BS T and R for s-pol are:

BS T/R ratio for s-pol from POP_SPOL    1.405+/-0.011
BS T for s-pol  0.5841+/-0.0019
BS R for s-pol  0.4159+/-0.0019

 - This is also not consistent with klog #29284, and not consistent with PRG measurements for PRX and PRY being almost the same, as it naively gives the following PRG. Another possibility for explaining X having more power could be clipping only in BS-ITMY or something similar, but this is also not compatible with PRG measurements. Clipping between BS-POP only for Y due to uglier beam or something like that? (See, also the background in klog #30823).

PRX PRG for s-pol 0.518+/-0.004
PRY PRG for s-pol 0.2816+/-0.0017

 - By taking the ratio of the ratio (ITMX single)/(ITMY single) for POP_PPOL and POS_PPOL, (TBS_p/RBS_p)**2*(TBS_s/RBS_s) can be estimated. Then, by using the estimated BS T/R for s-pol above, T/R for p-pol can be estimated as follows:

BS T/R ratio for p-pol from POP_PPOL and POS_PPOL       1.271+/-0.016
BS T for p-pol  0.5596+/-0.0031
BS R for p-pol  0.4404+/-0.0031

 - This is also not consistent with klog #29284. This could be due to POS_SPOL and POS_PPOL swap.
 - Finally, by taking the product of the ratio (ITMX single)/(ITMY single) for POP_PPOL and POS_PPOL, (RITMX_p/RITMY_p)**2*(TBS_s/RBS_s) can be estimated, where RITMi_p is the p-pol conversion factor on ITM reflection. Then, by using the estimated BS T/R for s-pol above, this p-pol conversion factor can be estimated as:

ITM p-pol conversion ratio X/Y from POP_PPOL and POS_PPOL       1.459+/-0.018

 - This is actually reasonable, compared with simulations and previous measurements (PhysRevD.110.082007).

Sideband power recycling gain:
 - To estimate the power recycling gain for the sideband lock, we have plotted sqrt(I^2+Q^2)/Pin, where I is K1:LSC-POP_PDA2_RF90_I_ERR_DQ, Q is K1:LSC-POP_PDA2_RF90_Q_ERR_DQ, and Pin is K1:LAS-POW_IMC_DC_INMON. The quadrant sum was necessary to make sure to catch all the signal. See attachment #3.
 - Simply multiplying this by 15 would give PRG of 0.3 for PRX. For PRY, the power is somehow half, as usual. Since this is a lock for sidebands, Schnupp asymmetry or PRCL not consistent with current f2 frequency are not relevant.
 - If we believe in this calibration, sideband PRG for PRFPMI is 19. This could well be the case, if losses in PRC for sidebands are ~4% (see klog #36238 and klog #36233).
 - Actually, I and Q were almost the same for PRX and PRY case, but the most of the signal were in I for PRFPMI case. See attachment #2.
                                                                                                                                                                                                                           
Next:
 - Check if POS_SPOL and POS_PPOL are not swapped.
 - Check if polarization monitor PDs are aligned.
 - Check the beam shape for ITMX and ITMY single bounce.
 - Make a polarization monitor MEDM screen

Abstract

Details

In the previous study, I assumed that the losses in PRC (TPRC) are the same for carrier and sidebands.
If this is different due to, e.g., Michelson Schnupp asymmetry and Lawrence effect, estimated PRC losses for sidebands will be different.
To demonstrate this, I have plotted the case where initial PRC loss for sidebands being 10% (roughly the same as single bounce loss to p-pol due to ITM birefringence; JGW-G1910369) and PRC loss for carrier being 0.2 of that for sidebands (this gives initial loss of 2% for carrier, to get the consistent arm cavity round-trip loss with klog #30823).
In this scenario, Tarm was estimated using A-0.2*B.

This also well explains the measured arm cavity finesse drop and power recycling gain drop.
Increase in the optical loss inside the PRC will be 10% to 23% (can be anything), and increase in the ITM transmission stays to be ~500ppm.
Estimate of the increase in the ITM transmission is robust since we cannot attribute the main cause of the finesse drop to round-trip loss increase (see klog #36231).

This senario may be the most plausible scenario.

Next:
 - Calibrate POP90 with expected sideband power recycling gain for PRX (or PRY). For PRX or PRY, expected sideband PRGs are dominated by losses from BS, and are the following.

Gprx=(tp/(1-rp*tBSs*tBSs))**2
Gpry=(tp/(1-rp*rBSs*rBSs))**2
PRX sideband PRG 0.400 +/- 0.004
PRY sideband PRG 0.344 +/- 0.003

Here, I used the following measured BS transmission and reflectivity (klog #29284).

tBSs**2=51.9 +/- 0.2 (stat.) +/- 0.2 (sys.) # for s-pol
rBSs**2=47.7 +/- 0.2 (stat.) +/- 0.2 (sys.) # for s-pol

I summarized the height adjustment of GAS filters in the Type-A towers during the warming up since Dec. 8th. The plots show the sum of changed setpoints.

Arm cavity round-trip loss and changes in ITM reflectivity were estimated using measured power recycling gains and arm cavity finesse.
Increase in the optical loss inside the PRC from 2% to 10%, and increase in the ITM transmission by ~500ppm can explain both power recycling gain and finesse measurements.
These suggest that power recycling gain reductions are mainly from PRC loss increase, and arm cavity finesse reductions are mainly from ITM transmission increase.
Arm cavity round-trip loss (including ETM transmission) stays almost unchanged within ~20ppm.

Assumptions:
  - Nominal mirror transmissions are the ones summarized in klog #36231, but losses inside the PRC (including ITM AR losses), ITM HR transmission and arm round-trip loss changes over time.
  - Losses in PRC (TPRC) are the same for carrier and sidebands. NOTE that this could be wrong due to, e.g., Lawrence effect.

What we did:
  - Used the same data set as klog #36231.

  - This time, sideband power recycling gain was estimated using K1:LSC-POP_PDA2_RF90_I_ERR_DQ, divided by K1:LAS-POW_IMC_DC_INMON to normalize for the input power changes (see left bottom plot). Overall factor was calibrated by calculating the nominal sideband PRG at the beginning of the data using the following equations. TPRCorig is the nominal losses in PRC, and was eyeball fitted to be 2% to have the arm cavity round-trip loss result consistent with klog #30823 (see right middle plot).
tp=sqrt(T['PRM'])
rp=sqrt(1-T['PRM'])
ranti=sqrt(1-TPRCorig)
PRGsideband=(tp/(1-rp*ranti))**2

  - Using the power recycling gain for sideband and carrier,  A=Tarm+TPRC (see red and blue dots in right bottom plot) and B=Tanti+TPRC (see yellow dots in right bottom plot) were estimated, where Tanti is the loss from the arm for sidebands, TPRC is the losses in PRC, and Tarm is the loss from the arm for carrier. Since estimated Tanti+TPRC is huge compared with TITM, it is safe to assume that B is mostly from TPRC.

  - Therefore, A-B gives Tarm (see cyan and magenta dots in right bottom plot). Note that in this calculation, we are assuming that TPRC is the same between carrier and sideband. Changes in A B (EDITED ON Jan 28) is actually mostly from TPRC, and Tarm is roughly constant over time. This means that the arm cavity round-trip loss is roughly constant over time.
 
  - Using the following simultaneous equations, TRTL and Tarm can be measured, where TRTL is the arm cavity round-trip loss. Results are plotted as cyan and magenta crosses and stars in right middle plot.

A-B = Tarm = TRTL*4/TITM
Finesse = 2*pi/(TITM+TRTL)

Discussion:
  - Assumption that TPRC is 2% initially is just a rough guess (+/- 0.5% or so to make TRTL consistent with klog #30823), and it does not change the overall trend very much. If POP90 is properly calibrated, this will not be necessary.
  - Huge increase in the PRC loss TPRC to 10% is a mystery. TPRC includes ITM AR losses and the Michelson fringe conditions.
  - If TPRC is smaller for carrier than that for sidebands due to, e.g., Lawrence effect, TRTL increases and changes for TITM reduces. This is also a plausible senario.

Next:
  - Redo this calculation once the fitting for the finesse measurements are fixed by Oshino-san.
  - Investigate the cause of huge increase in the PRC loss (AR frosting? Resonant condition changes for p-pol? Birefringence changes? Michelson contrast changes?)
  - See if ITM reflectivity changes are consistent with lce layers (see, also, klog #34903)
  - Calibrate POP90 using modulation depths and power at the PD so that we don't need to guess nominal losses in PRC.