Because phase of MICH to DARM with engaging FF in klog#31704 is ~120deg. different from one in previous measurement (klog#31266), I tried to sort out of the situations to understand this difference.

Figure 1 shows the coupling from MICH to DARM. Though original transfer functions are from count at MICH feedback to DARM displacement, I converted them to from displacement equivalent value of MICH feedback to DARM displacement by using BS actuator response in klog#29974 for the easy understanding. Blue and green points represent TFs without and with FF measured in klog#31266, respectively. Blue curve seems to be well matched with theoretical coupling of differential phase at AS port coming from Michelson motion (I assumed arm Finesse is ~1400).

Red curve represents TF with FF measured today by Yokozawa-san. Green and red curves have ~120deg mismatch in phase around 50-100Hz. According to the FF gain, all MICHFF1 (MICH to DARM), MICHFF2 (MICH to PRCL), and PRCLFF1 (PRCL to DARM) were engaged in today's measurement (Fig.2). On the other hand, measurement in klog#31266 were done with engaging only MICHFF1 (Fig.3). So I thought that MICH to PRCL to DARM might be dominant in the past measurement. And then, I estimated TF of MICH to PRCL to DARM as a product of TF from MICH to PRCL and TF from PRCL to DARM in the case of the absence of MICHFF2 and PRCLFF1 (see also brown curve in Fig.1). But it couldn't explain the difference between the red and green curves. The performance of FF is enough for now. So it's not urgent issue. On the other hand, understanding one-by-one may help us to do the future activities such as optimization of FF, offline subtraction of residual of online FF, etc.

Transfer functions of MICH to PRCL which was used for estimating TF of MICH to PRCL to DARM above are shown in Fig.4. They were not measured today and only TFs measured in klog#31266 are shown in this plot. I also converted TF of count at MICH feedback to count at PRCL error point to one of displacement equivalent value of MICH feedback to displacement equivalent value of PRCL error signal by using the BS actuator response and PRCL optical gain, respectively. Strictly speaking, we should use K1:CAL-CS_PROC_PRCL_DISPLACEMENT instead of PRCL error signal for this purpose. But it should be enough because all measured data points with large coherence are larger enough than PRCL UGF. Blue and green points represent TFs without and with FF, respectively. When we actuate MICH length by BS, change in MICH length is coupled to PRCL lenght with a factor of 0.5. So the fact that gain of blue points (without MICH to PRCL FF) shows -6dB is reasonable.

TFs of PRCL to DARM are shown in Fig.5. Red curve is today's measurement with all 3 FFs by Yokozawa-san. Because the past measurement with a same configuration as green points are poor coherence, it's difficult to say there is significant difference between today's and past resutls. Blue points which was used to estimate TF of MICH to PRCL to DARM above represents the TF only with MICH to DARM FF. I have now no idea about what is the dominant pass of PRCL to DARM coupling. So I cannot show the any theoretical lines on this plot.

Fundamental noises for the current configuration was estimated (Attachment #1).
All the codes live in
/users/Commissioning/data/NoiseBudget/Spectra/2024/1121/Fundamentals

Thermal noise calculations:
 - Calculations are based on kagra_sensitivity.py but modified for O4 (kagra_O4_sensitivity.py).
 - Following parameters were used.
 TM temperature: 260 K (estimated from IM temperature)
 IM temperature: 260 K (measured)
 Sapphire blade spring frequency: 25 Hz (eyball fitted to align with the peaks)
 Sapphire blade spring loss: 3.6e-05 (see JGW-G1910180)
 Sapphire fiber loss: 1.0e-04 (see klog #26113)
 TM Q value: 1.0e+06 (see JGW-L2315445)

 - Sapphire parameters were extracted from arXiv:2005.0557. If temperature is below 100 K, default fitting equations are used.
    kappa20=(15700./15880)*((5*Tm**2.75)**(-4./5)+(10**10.25*Tm**(-3.8))**(-4./5))**(-5./4) #thermal conductivity
    Cth20=(0.69/0.80)*Tm**3.14/3.8/rhom  #specific heat per unit mass
    alpha20=(5.6/5.496)*Tm**2.99/10**12.15  #thermal linear expansion
 - For temperatures above 100 K, data in arXiv:2005.0557 was interpolated. See Attachemnt #2 for the data, fitting function, and interpolated curve.
 - Now kagra_O4_sensitivity.py can calculate thermal noise at any temperature.

Quantum noise calculations:
 - Calculations are based on kagra_sensitivity.py but modified for O4 (kagra_O4_sensitivity.py).
 - Following parameters were used.
 Power at BS: 19.60 W  (1.4 W input times PRG of 14; assuming all the power from IMC couples to the IFO)
 IFO to PD loss: 18 %  (Rough estimate; see below)
 - IFO to PD loss was estimated from the sum of the following losses
    OFI: 5% [JGW-G1809012, OFI wiki]
    OSTM: 0.89% [klog #30229]
    OMC: 5% [klog #30229]
    DC PD: 7% [From spec quantum efficiency of Excelitas C30665GH]
 - This is also consistent with klog #21397 with in the error bar.
 - Measured sensitivity is roughly 50% higher than the calculated shot noise at 1 kHz.

PD dark noise:
 - To see if shot noise calculations are correct, measured DC PD spectra are compared with dark noise measured in klog #31616 and shot noise calculated from K1:OMC-TRANS_DC_(A|B)_OUT_DQ, which is calibrated in mW.
 - See Attachment #3 for the spectra. Attachment #4 is the zoomed version.
 - A and B are unbalanced by 3%. A=7.4 mW B=7.6 mW.
 - Shot noise was calculated with P_shot = sqrt(2*h*nu*P_PD/eta) where eta=0.93 is the quantum efficiency.
 - Measured spectrum is 14% higher for A and 7% higher for B than shot+dark spectrum at 1 kHz.
 - Measured spectrum is 35% higher for A and 33% higher for B than shot noise at 1 kHz. This is not so consistent with 50% from quantum noise calculations.
 - If we believe in the DC PD power based calculations here, IFO to PD loss is estimated to be ~40%.
 - This sounds a bit too large, but there might be large misaglinment to OMC. If this is not the case, this could mean that there is error in K1:CAL-CS_PROC_DARM_DISPLACEMENT_DQ by ~20%, or there are some underlying additional noise that increases the noise at 1 kHz by ~20%, as indicated from AxB correlation measurements (klog #31577). Note that error in DC PD calibration into mW is not relevant for explaining the descrepancy.
 - See Attachment #5 for the dark noise contributions to DARM.

Next:
 - Check mode-matching of the beam into PRM.
 - Check OMC alignment.
 - Measure total optical loss from BS to PD using ITM single bounce.
 - Check DC PD A and B calbrations. The calibration factors in FM8 of K1:OMC-TRANS_DC_(A|B) seem to be the same, but A and B might be different, as indicated by 7.4 mW and 7.6 mW unbalance.
 - Check DARM calibration.

I measured TFs from PRMI ASC feedback signals (K1:ASC-{PRC2,MICH,INP2}_{P,Y}_OUT) to DARM (Fig.1,2,3,4,5,6) and TFs from PR3_OLDAMP_{P,Y}_OUT to DARM, PRCL, MICH (Fig.7,8).

I injected an white noise from each EXC channel in each filter bank so that the PRMI ASC feedback signal became ~10 times larger than the ones when there are no excitation. However, there seems to be very low coherence. So the WFS noises seem not to contribure the current DARM sensitivity. 

On the other hand, PR3 control noises, especially Pit have some coherence about DARM and MICH between 10-20 Hz. So PR3 PIT noise may be not so far from current MICH (or DARM?) sensitivity.

I will project them tomorrow.

I checked REFL51 and REFL135 dark offsets at several different timing (fig1:10/30, fig2:10/29, fig3:10/25).
Small jump can be seen in REFL51I signals but there seems no jump in the others.
Also, the jump is not so large compared to the drift.
So, it is likely that the dark offset change was due to the drift of the offset.

We measued TFs from PDA1_RF45_I_ERR and CARM_SERVO_MIXER_DAQ_OUT which are in-loop sensors for CARM to the DARM displacement (CAL-CS_PROC_DARM_DISPLACEMENT), and also measured the TF from PDA3_RF45_I_ERR, which is an out-loop sensor for CARM to the DARM displacement when we excited CARM from CARM_SERVO_EXC_A_CALI. Fig.1 shows the results. (Note that, the unit of the TF from MIXER_DAQ_OUT to DARM is m/V, the others' unit is m/cnt).

Then, we projected the current spectra of MIXER_DAQ_OUT as the in-loop sensor and PDA3_RF45_I_ERR as the out-loop sensor in DARM sensitivity by using each TF. Fig.2 shows each projection, magenta is the projection from MIXER_DAQ_OUT, green is from PDA3_RF45_I_ERR. According to the magenta line, the current in-loop CARM noise seems not to limit the current sensitivity. Unfortunately, the current PDA3 output in high frequency region seems to be dominate by the other noise due to the low input power to PDA3.

Next, we projected the sensing noises of MIXER_DAQ_OUT and PDA3_RF45_I_ERR. We picked up each raw sensing noise spectrum which were measured by Ushiba-san (see the detail in klog31636) in /users/Commissioning/data/CARM/2024/1114/SPE_CARM-20dB_CMS_sensingnoise.xml. Fig. 3 shows the projected sensing noises using each TF, the orange line is the sensing noise of MIXER_DAQ. Then, I tried to compensated roughly the input power difference between the orange and the magenta. The input power when the orange was measured was 2988 cnts, and the power when the magenta was measured was 846 cnts. So I assumed this orange sensing noise is only shot noise (honestly, orange line seems to have a shape so this assumption is overspeaking), and devided the orange line by (2988/846)^(1/2) ~ 3^(1/2). The black line is divied one. If the current sensing noise is only shot noise, the current CARM noise is limited by the sensing noise. 

>Even the OMC resonance peak happens to align with the peak of the lock loss blast, the energy deposited on OMC PDs (total of two PDs) for 10 W input will be
>10 * 19 W * 50 usec = 9.5 mJ

If we consider the speed of scan (5ms), OMC psses on the resonance 3 times within FWHM (15ms).
Even in that case, obtained energy of PD is less than 9.5mJ * 3 = 28.5 mJ, which satisfy the requirement (< 30mJ).

Too consistent, isn't it...?

The lock loss blast with a peak height of 19 W and FWHM of 15 msec gives integrated energy of roughly 19 W * 15 msec = 0.3 J.
Intra cavity power with 1 W input for each arm is Pcav = Pin * PRG * 4/T_ITM / 2 = 1 W * 15 * 4/0.4% / 2 = 7.5 kW.
This means that total energy stored in XY arms is Ecav*2 = Pcav * 2 * 2 * Larm / c = 0.3 J.
Amazingly consistent (see also JGW-T2416173).
To have less than 30 mJ at OMC PDs (total of two PDs) when the input power is 10 W, we need to reduce the OMC duty factor to less than 30 mJ / (0.3 J * 10) = 1%.
Continuously sweeping OMC with a triangular wave of peak-to-peak of 1 FSR gives (effective) duty factor of 1/Finesse = 1/800 = 0.125%.
So, sweep of 0.125 FSR peak-to-peak would be enough.
Using 100 Hz triangular wave, time to sweep the OMC resonance peak will be
1 / 100 Hz / 2 * (1/Finesse) / 0.125 = 50 usec
Even the OMC resonance peak happens to align with the peak of the lock loss blast, the energy deposited on OMC PDs (total of two PDs) for 10 W input will be
10 * 19 W * 50 usec = 9.5 mJ
This is smaller than the 30 mJ requirement. So, sweeping with 0.125 FSR peak-to-peak at 100 Hz will be good.

I changed the setpoint of the heater from 26.0° to 25.0° at 9:26 JST.

I checked the signals last night and confirmed that OMMT2T trans DC PD was not saturated when lockloss happened.
Figure 1-3 shows the signals when the lockloss happened in this morning.
The first peak power is about 19W and the second is about 4W (fig1).
FWHM of the first peak and second is about 15ms (fig2) and 5ms (fig3), respectively.

After achieving PRFPMI_RF_LOCKED, maximum power at AS is about 500mW (fig4), so if we set the power treshold at AS as 1W or something, the trigger seems to work only when lockloss happens.
In addition, speed of power increase from 1W to 19W is about 20ms (fig5).