Abstract

- I estimated the optical gains of PRX (3f, 1f) and actuator efficiencies of PRs.
- Actuator efficiency of PRM is 10.7% smaller than one in O4a (need to ask validity to VIS folks).
- Because there was no past measurement of PR2 and PR3, I couldn't compare them.
- Actuator efficiency of PRM and PR2 is almost same in the unit of mirror displacement.
- Actuator efficiency of PR3 is 13.8% smaller than others (need to ask validity to VIS folks).
- Optical gain of 3f and 1f is +5.7dB and -0.3dB different from the results in 2022, respectively.
- Because they couldn't explained only by the effect of phasing as +2.9dB (3f) and +1.6dB (1f), so we still need to continue the investigation about remaining +2.8dB (3f) and -1.9dB (1f).
 

Details

1. Actuator efficiency ratio of PRs and ITMX
I measured four transfer functions from ITMX (K1:VIS-ITMX_TM_CAL_EXC), PR2 (K1:VIS-PR2_TM_CAL_EXC), PR3 (K1:VIS-PR3_TM_CAL_EXC), and PRM (K1:VIS-PRM_TM_CAL_EXC) to the PRCL error point (K1:LSC-PRCL1_IN1). As I explained in the section 3 of klog#29974, A ratio of these transfer functions corresponds to a ratio of actuator efficiencies.

Raw measurement data are shown in Fig.1 (ITMX), Fig.2 (PR2), Fig.3 (PR3), and Fig.4 (PRM) and these are save in /users/Commissioning/data/PRCL/2024/0624. Though transfer functions from PRs could be measured well, coherence of TF measurement from ITMX is slightly low. This is because the actuator efficiency of ITMX is ~200 times smaller than one of PRM according to O4a results in klog#25024. In fact, the injection was done with ~30000 counts at DAC. If we want a same level of coherence as the TF measurement from PRs, ~43000ct is required according to the estimation. Of course DAC limit is 32767ct, so if we want to improve this measurement, longer integration time is required. Another solutions are to do same measurements with PRY or PRMI. In these configurations, we can use BS instead of ITMX as the standard of the calibration.

Overplots and ratio of these transfer functions are shown in Fig.5-6 (ITMX vs. PR2), Fig.7-8 (ITMX vs. PR3), and Fig.9-10 (ITMX vs. PRM) and estimated ratio of actuator efficiencies are as follows.
PR2/ITMX = -513.0 +/- 5.0
PR3/ITMX = -439.8 +/- 4.2
PRM/ITMX = -255.2 +/- 2.7

From these results, actuator efficiency ratio of PRs are also computed as follows.
PR2/PRM = 2.010 +/- 0.029
PR3/PRM = 1.724 +/- 0.025
If the actuator efficiency of PRs in the unit of mirror displacement is completely same, actuator efficiency of PR2 and PR3 in the unit of PR cavity length is larger than one of PRM as a factor of 1 + cos(\theta), where \theta is open angle of PRM-PR2-PR3 beam. According to klog#29334, open angle is ~0.02rad. So the actuator efficiencies of PR2 and PR3 are twice (= 1 + 0.9998...) larger than one of PRM. I'm not sure the individual difference of each coil-magnet. So I cannot conclude that a factor of 1.724 of PR3/PRM which corresponds to ~13.8% difference in the efficiency to mirror displacement is reasonable or not now.

2. Actuator efficiency of PRs
Now we have already known the actuator efficiency of ITMX_TM as
H_itmxtm = -2.914e-12 +/- 0.032e-12 * (1Hz/f)^2 [m/ct]
in the measurement with MICH reported in klog#29974 (Because +MICH direction and +PRCL direction is opposite for ITMX, polarity is reversed here.), so absolute actuator efficiency of PRs can be estimated as
H_pr2tm = -1.495e-09 +/- 0.022e-9 * (1Hz/f)^2 [m/ct]
H_pr3tm = -1.282e-09 +/- 0.019e-9 * (1Hz/f)^2 [m/ct]
H_prmtm = -7.44e-10 +/- 0.11e-10 * (1Hz/f)^2 [m/ct].

Actuator efficiency of PRM is 10.7% (-0.98dB) smaller than the results in O4a. Validity of this value should be confirmed after asking concrete repair work of PRM to VIS folks. There is no reference of PR2 and PR3 because they didn't measure before O4a.

3. Optical gain of PRX
Actuator efficiency is available from previous section, I also estimated the optical gain of PRX with 3f and 1f. Measured OLTFs are shown in Fig.11 (3f) and Fig.12 (1f). Comparison plots of measured TFs and model function with PRM efficiency and digital filters at the measurement time are also shown in Fig.13-14 (3f) and Fig.15-16. In 3f lock, we can see the slight tilt in the residual plot of phase. So there may be missing phase or time delay. Finally, obtained optical gains are as follows.
H_prx3f = 1.347e9 +/- 0.021e9 (=182.6dB) [ct/m]
H_prx1f = 6.92e8 +/- 0.11e8 (=176.8dB) [ct/m]

4. Comparison with 2022
In the thread of klog#29999, difference in the open loop gain between measurements in 2022 and 2024 is being discussed. As the one of the check of this issue, I also computed optical gains in 2022. When we adopt using the actuator efficiency of PRM on '23/04/26 (before O4a) optical gains of 3f (Fig.17-18) and 1f (Fig.19-20) are
H_prx3f_2022 = 7.005e-1 +/- 0.077e-1 [ct/m]
H_prx1f_2022 = 7.132e-1 +/- 0.080e-1 [ct/m].
After the measurement in 2022, we changed a calibration factor in PD filterbank from ct/m to ct/nm in order to avoid numerical rounding error on diaggui. So we need to revise these efficiencies as a factor of 1e9 in order to compare the value in 2024. Then we obtained as
H_prx3f_2022' = 7.005e8 +/- 0.077e8 (=176.9dB) [ct/m]
H_prx1f_2022' = 7.132e8 +/- 0.080e8 (=177.1dB) [ct/m].

So difference in the optical gains are +5.7dB (3f) and -0.3dB (1f). According to the discussion in klog#29999, optical gain should be increased as +2.9dB (3f) and +1.6dB (1f) by phasing. So we are still missing +2.8dB for 3f and -1.9dB for 1f. Ushiba-kun pointed out that the HWP status of the REFL (only affect 3f) may have changed. So next step is probably checking the DC power on REFL PD at the measurement time in 2022 and 2024.