[Kenta, YamaT]
 

Abstract

Finally, we found that optical gain estimation by Michelson fringes was not done in proper configuration and corrected actuator efficiency is consistent with O4a value within ~3%.
Although not directly related to inconsistency in this time, I found cause of the inconsistency between FSM and Pcal in O4a comes from the handling of the laser norm scale.
As for the latter issue, I'm waiting for a cross-check by someone.
 

Details

When MICH is locked by guardian, guardian engages FM1 (for compensating whitening gain), FM5 (for compensating whitening filter) and FM8 (for gain of MICH lock). During an OLTF measurement, these filters were surely engaged as shown in Fig.1. On the other hand, FM1, FM5 and FM9 (for gain of PRMI lock) were engaged during a Michelson fringe measurement as shown in Fig.2. So these two measurements were done in different configurations.

Checking FM8 (MICH gain) and FM9 (PRMI gain) by the foton file, MICH and PRMI gain is 17.578 and 0.41315015, respectively (see also Fig.3). So in order to estimate actuator efficiency, difference in these two gains must be taken into account and it can be done easily and accurately because this is just a digital gain. Though Michelson fringes were measured with PRMI gain (= 0.41315015), correct gain was MICH gain (=17.578). So RFPD signal should be corrected by a factor of ~42.546 (= 17.578 / 0.41315015). In other words, estimated optical gain should be also corrected by a factor of 42.546 as follows (see also Fig.4 and Fig.5).
Correct: 4.986e+8 +/- 9.3e+6
Incorrect: 1.172e+7 +/- 2.2e+5
As discussed below, this corrected value also contains a mistake as ~10-20%.

OLTF measurement was done in proper configuration. So we don't need to apply any correction for OLTF measurements. I did OLTF fitting again with corrected optical gain, then actuator efficiency was estimated as 5.10e-11 +/-1.0e-12 which was consistent with ~3% in the previous measurement ("23/04/26 FSM" in the table of klog#25024).


By the way, I checked bugs in my scripts in order to investigate inconsistency in the estimated actuator efficiency between this time and O4a and found that this ellipse fitting code compute the "optical gain" from displacement to K1:LSC-POP_PDA1_RF17_Q_ERR_DQ not to K1:LSC-MICH_IN1. On the other hand, actuator efficiency estimation treated "optical gain" as from displacement to K1:LSC-MICH_IN1. This mistake doesn't affect to the comparison between the estimated values in this time and past because both this time and past are affected as same level (fortunately short Michelson measurements are always done with 1.1-1.2W output from IMC.). On the other hand, this fact affected to the comparison between the calibration by pcal and Michelson fringes as a factor of 1.1-1.2.

In fact, laser power during the measurement in klog#24969 is ~1.16. So optical gain and actuator efficiency should be corrected as a factor of 1/1.16 and 1.16, respectively. Finally estimated actuator efficiencies by FSM on '23/4/26 must be corrected as 5.238e-11 +/- 0.074e-11 to 6.076e-11 +/- 0.086e-11. Almost all inconsistency on the comparison between Pcal and FSM in klog#24969 can be explained. I want to wait cross check by someone to conclude this issue.

Note that: Fortunately (again), DARM, PRCL, and MICH calibrated signals were provided based on the pcal calibration, so these signals in O4a were not also affected.