[M.Takahashi, Nakagaki ]

Air Injection into EXC: Day 3

Air injection is ongoing.
Today, we introduced two air gas cylinders, and the current EXC pressure is 8.7× 10⁴ Pa.
We will continue on Monday (the 14th).

Cylinder 8:  9:39 – 10:55; pressure after injection: 7.7 × 10⁴ Pa
Cylinder 9: 10:58 – 12:13; pressure after injection: 8.7 × 10⁴ Pa

[Ushiba, Takahashi]

We checked the actual movable range of the IP in the Type-B suspensions. The transfer functions of the IP L were measured by changing the setpoint for L. The resonant frequencies of L depended on the setpoint and became higher with larger deviation. To keep the same (or lower) resonant frequencies, the movable range should be set to +4mm for SRM, +3mm for SR2, and +3mm for SR3.

The measured resonant frequencies are summarized below. The SR3 suspension touched a part (maybe the side stopper for the GAS filter) when the setpoint was set to 5000. The plots show the measured transfer functions in SRM, SR2, and SR3.

[Kimura, Nakagaki and M. Takahashi]
  At 9:43, we re-started air injection to EXC up to atmospheric pressure.
Pressurization continued until about 15:15. The inner presusure of EXC was 6.9 x 10^4 Pa, when pressurization was stopeed.
To reach this pressure, we used four high-pressure gas cylinders filled with 7 m³ of air.

[Fujimoto, Saito]

We did not acquire the beat signal data when injecting the sub-laser with P polarization because the peak shape was not clean. The shift between the resonance peaks for S and P polarization was observed for both PRX and PRY when using the main laser and setting the HWP at the detection port to S polarization, although the shift was small in PRY. We think this is because the BS has a low reflectivity for P polarization. Also, when injecting the sub-laser into PRX and aligning it using the RFPD DC signal, the maximum signal was about 3.9 times larger for S polarization than for P polarization. The signal was maximized for S polarization and minimized for P polarization. Therefore, we think that the eigenpolarizations are S and P polarization.
 

• First, with the main laser turned off, we adjusted the alignment of the sub-laser to SRY. Then, we turned on the main laser and adjusted the alignment to the RFPD. We then injected the sub-laser with S polarization and set the polarizer in front of the RFPD to S polarization. When we checked the beat signal, we could not observe the peaks separated by approximately 1 MHz that were observed in the previous measurement (klog:37466) (Photo 1). This may be due to the effect of higher-order modes. Even when we adjusted the sub-laser alignment to maximize the peak, higher-order modes sometimes appeared when checking the beat signal. Next, we changed the sub-laser to P polarization, readjusted the alignment, and tilted the polarizer by 45° to observe the beat signal. The peak shape was not clean due to higher-order modes (Photo 2). Since the peak shape was not clean, we did not acquire beat signal data from -1.6 GHz to 1.6 GHz.
   
• Next, to check whether a shift between the S- and P-polarized resonance peaks could be observed in SRY using the sub-laser, we set the polarization of the sub-laser to 45° and rotated the HWP at the detection port to S polarization. However, we did not observe any shift between the resonance peaks. We then used the main laser and rotated the HWP at the detection port to obtain a clean separation between the resonance peaks. When the HWP scale was set to 80, we observed the shift between the resonance peaks, as in the previous measurement (klog:37471) (Photo 3).
   
• Next, we locked the main laser to PRY and swept the PRM. We rotated the HWP at the detection port to minimize the P-polarized signal and set the HWP scale to 90. A small shift between the resonance peaks was observed (Photo 4). We think this is because the BS has a low reflectivity for P polarization.
   
• Next, we locked the main laser to PRX and swept the PRM. We rotated the HWP at the detection port to minimize the S-polarized light leaking into the P-polarized signal and set the HWP scale to 91. A shift between the resonance peaks was observed (Photo 5).
   
• Next, with the main laser turned off, we injected S-polarized sub-laser light into PRX and adjusted the alignment while monitoring the RFPD DC signal. The maximum signal was -106 counts (Photo 6). We then rotated the HWP to find the minimum count. When the HWP scale was 124 (P polarization), the count reached -32 (Photo 7). Therefore, we think that the eigenpolarizations are S and P polarization. The overall lower count values compared with the SRY measurement (klog:37471) are probably because the sub-laser has to be reflected by the BS when it is injected into PRX.

[Kimura and Nakagaki]
 We closed the gate valve called GVetmx between X-arm and EXA at 9:30.
 The vacuum pumping by TMP around the EXC was stopped in order to inject air into the EXC.
The pressure in the EXC at the time of the shutdown was ~10^-5 Pa.
 At 10:05, we started air injection to EYC up to atmospheric pressure.
Pressurization continued until about 16:00. The inner presusure of EXC was 2.8 x 10^4 Pa, when pressurization was stopeed.
To reach this pressure, we used three high-pressure gas cylinders filled with 7 m³ of air.
 The air injection operation is scheduled to resume on the morning of Sep. 11.
This may cause the temperature in the X-end chamber to change.
The injected air was G-2 grade pressurized air (klog25912) with a dew point of -80°C. 

We removed the mirror that had been placed inside the OMMT chamber (Photo 1), and also moved the optical setup on the optical table to the area near PR2 (Photos 2 and 3).

RAID rebuild
As Kanda-san reported, the RAID rebuild on hyades-1 is currently in progress and is expected to take several hours or longer. For this reason, the RAID management screen has been left open on hyades-1 (see Fig.1). Although it is unlikely that anyone will need to access it, please do not touch or use hyades-1 until the rebuild is complete.

KVM Cable Installation for Hyades
When hyades-1 was moved from the B1 rack to the N1 rack and eventually decommissioned, only one KVM cable for the Hyades servers remained in the B1 rack. As a result, the cable had to be switched between hyades-0 and hyades-2 as needed.

The KVM cable that had been used for the now-retired hyades-1 could have been reused for hyades-2. However, it appears that when hyades-2 was initially deployed, there were issues connecting it to k1fw1. As a result, hyades-1, which had been moved to the N1 rack, continued to be used for some time, and the KVM cable was moved to the N1 rack along with it. The current situation appears to be a remnant of that arrangement (see also klog#22520 and klog#23114).

Having to switch the KVM cable between hyades-0 and hyades-2 was inconvenient for investigations and maintenance work such as this one. Therefore, we installed an additional KVM cable so that both hyades-0 and hyades-2 can remain connected to the KVM console at all times.

I modified the VERTEX guardian (LOCK_PREP state) so that it doesn't change the ETMX guardian state during PRX/PRY.SRX/SRY lock acquisition.
It should be reverted after fiishing the vacuum work at EX.

[Fujimoto, Saito]

When injecting the sub-laser into SRY and aligning it using the RFPD DC signal, the maximum signal was about 3.7 times larger for P polarization than for S polarization. The signal was maximized for P polarization and minimized for S polarization.We also changed the polarization of the sub-laser and the polarization setting of the HWP at the detection port, but we did not observe the shift between the resonance peaks for S and P polarization that was observed in the previous measurement (klog:37445). However, when using the main laser and setting the HWP at the detection port to S polarization, a shift between the resonance peaks was observed. Since only the P-polarized signal showed a split into two peaks, and the maximum and minimum optical powers corresponded to P and S polarization, respectively, we think that the eigenpolarizations are S and P polarization.

Similarly, when injecting the sub-laser into SRX and aligning it using the RFPD DC signal, the maximum signal was about 5.9 times larger for S polarization than for P polarization. The signal was maximized for S polarization and minimized for P polarization. The shift between the resonance peaks was not clearly visible because the resonance peaks themselves were small. When using the main laser and setting the HWP at the detection port to S polarization, a small shift between the resonance peaks was observed. We think the different behavior from SRY is because the BS has a high transmission and a low reflectivity for P polarization.
 

• First, we calibrated the angular scales of the HWP and polarizer. We placed a PBS downstream of the HWP on the POS table and rotated the HWP to minimize the transmitted power through the PBS. The HWP scale was 82.2. Next, we placed a polarizer between the HWP and the PBS and rotated the polarizer to minimize the transmitted power through the PBS. The polarizer scale was 274.8. Then, we installed another HWP between the polarizer and the PBS and rotated the HWP to minimize the transmitted power through the PBS. The HWP scale was 90.8.
   
• Next, with the polarizer and ND filter in front of the RFPD removed, we injected P-polarized sub-laser light into SRY. We monitored the RFPD DC signal and adjusted the alignment, obtaining a maximum of -482 counts (Photo 1). We then changed the polarization to S polarization and obtained a maximum of -131 counts (Photo 2). When we rotated the HWP, the signal was maximized for P polarization and minimized for S polarization. Therefore, we think that the eigenpolarizations are S and P polarization. Next, we installed a mirror in front of the lens before the RFPD, and placed an HWP, a 150mm focal-length lens, a PBS, and two PDs to separately observe the P- and S-polarized components. We also checked the mode of the sub-laser at this point, and it was less clean than that of the main laser (Photo 3). We then injected S-polarized light and set the HWP at the detection port to S polarization. The S-polarized component had a higher optical power. When we rotated the HWP at the detection port so that the S- and P-polarized components had the same optical power, we did not observe the shift between the resonance peaks for S and P polarization that had been observed in the previous measurement (klog:37445) (Photo 4). Here, the yellow line corresponds to S polarization and the blue line corresponds to P polarization. We also rotated the HWP at the detection port to equalize the S- and P-polarized optical powers when the input polarization was P polarization or 45° polarization, but we did not observe any shift between the S- and P-polarized resonance peaks. In addition, even when the input polarization was set to 45° and the HWP at the detection port was set to S polarization, we did not observe any shift between the S- and P-polarized resonance peaks.
   
• Next, we injected S-polarized sub-laser light into SRX and adjusted the alignment while monitoring the RFPD DC signal. The maximum signal was -112 counts (Photo 5). We then changed the polarization to P polarization and obtained a maximum of -19 counts (Photo 6). When we rotated the HWP, the signal was maximized for S polarization and minimized for P polarization. Next, we injected S-polarized light and set the HWP at the detection port to S polarization. The S-polarized component had a higher optical power. When we rotated the HWP at the detection port so that the S- and P-polarized components had the same optical power, the resonance peaks themselves were too small to be clearly observed (Photo 7).
   
• Next, we injected the main laser into SRY, swept the SRM, and set the HWP at the detection port to S polarization. A shift between the resonance peaks for S and P polarization was observed (Photo 8). Since only the P-polarized signal showed a split into two peaks, we think that the eigenpolarizations are not rotated relative to the S/P axes, but are S and P polarization. We think that the P-polarized peak is caused by a small amount of P-polarized light that is already leaking into the signal. When we rotated the HWP at the detection port so that the S- and P-polarized components had the same optical power, the shapes of the S- and P-polarized peaks were slightly different (Photo 9).
   
• Next, we injected the main laser into SRX, swept the SRM, and set the HWP at the detection port to S polarization. A small shift between the resonance peaks for S and P polarization was observed (Photo 10). We think that the lower optical power of the P-polarized component is because the BS has a low reflectivity for P polarization. When we rotated the HWP at the detection port so that the S- and P-polarized components had the same optical power, the shapes of the S- and P-polarized peaks became consistent with each other (Photo 11).

The fitting results for SRY in klog:37466 are shown below.

The measurement data are saved in the following Dropbox folder:

All files/Dropbox KAGRA/Measurements/IFO/SRCL/SRCL_OMMT2_REFL_beat_signal_PZT_sweep/2026_09_07_SRY
 

• Fig. 1: Around 1.6 GHz, without a linear background. Using data from 1610.59 MHz to 1611.02 MHz, the fitted peak frequency was 1610.8297(27) MHz.
  Fig. 2: Around 1.6 GHz, with a linear background. Using data from 1610.59 MHz to 1611.02 MHz, the fitted peak frequency was 1610.893(13) MHz.

  Fig. 3: Around 800 MHz, without a linear background. Using data from 802.82 MHz to 803.27 MHz, the fitted peak frequency was 803.0799(23) MHz.
  Fig. 4: Around 800 MHz, with a linear background. Using data from 802.82 MHz to 803.27 MHz, the fitted peak frequency was 803.147(27) MHz.

  Fig. 5: Around -800 MHz, without a linear background. Using data from 800.72 MHz to 801.16 MHz, the fitted peak frequency was 800.9089(24) MHz.
  Fig. 6: Around -800 MHz, with a linear background. Using data from 800.72 MHz to 801.16 MHz, the fitted peak frequency was 800.839(13) MHz.

  Fig. 7: Around -1.6 GHz, without a linear background. Using data from 1592.3195 MHz to 1592.7295 MHz, the fitted peak frequency was 1592.4944(25) MHz.
  Fig. 8: Around -1.6 GHz, with a linear background. Using data from 1592.3195 MHz to 1592.7295 MHz, the fitted peak frequency was 1592.4459(93) MHz.

[Fujimoto, Saito]

We adjusted the HWP and polarizer for SRY to obtain a clean peak and acquired the beat signal data. After fitting the data, the deviation of the SRY length from the design value was found to be 2.332(93) cm. This result is consistent with the previous measurements reported in klog:37455: the deviations from the design value were 2.168(80) cm with the HWP scale at 14 and the polarizer scale at 295, and 2.319(71) cm with the HWP scale at 59 and the polarizer scale at 250. However, it is slightly different from the result obtained before moving the lens to improve the mode-matching ratio (klog:37250), where the deviation of the SRY length from the design value was 1.757(50) cm.

Using the SRX result from klog:37450 and the results from klog:37458, I calculated the SRC length and Schnupp asymmetry as follows:

SRC length: 66.61860(51) m
Schnupp asymmetry calculated from the SRC: 3.33775(102) m
Schnupp asymmetry from the weighted average: 3.33842(49) m

These results are consistent with the previous measurements reported in klog:37455 and klog:37458. With the HWP scale at 14 and the polarizer scale at 295, the SRC length was 66.61778(45) m, the Schnupp asymmetry calculated from the SRC was 3.339390(904) m, and the Schnupp asymmetry from the weighted average was 3.33884(48) m. With the HWP scale at 59 and the polarizer scale at 250, the corresponding values were 66.61853(41) m, 3.337880(825) m, and 3.33839(47) m, respectively. Comparing these results with the measurements before moving the lens to improve the mode-matching ratio (klog:37260), where the SRC length was 66.61409(70) m, the Schnupp asymmetry calculated from the SRC was 3.34023(139) m, and the Schnupp asymmetry from the weighted average was 3.33791(45) m, the SRC length and the Schnupp asymmetry calculated from the SRC are somewhat different. However, the Schnupp asymmetry obtained from the weighted average is consistent with the previous result.
 

• First, we set the HWP scale at the sub-laser to 82 (S polarization) and set the polarizer in front of the RFPD to S polarization. With the main laser turned off, we adjusted the alignment of the sub-laser to SRY. Next, we locked the main laser to SRY, adjusted the alignment to the RFPD, and checked the beat signal. However, as in the previous measurement (klog:37440), the peak was split. Therefore, we adjusted the alignment of the sub-laser to maximize the beat signal, and rotated the HWP and polarizer to maximize the beat signal as well. The HWP scale was then 124 (P polarization), and the polarizer scale was 2 (P polarization). However, the peak was split into three peaks.

  Next, we turned off the main laser and adjusted the alignment again using the sub-laser. When the polarizer in front of the RFPD was removed, the maximum signal was -16 counts for S-polarized injection and -52 counts for P-polarized injection, giving a difference of about a factor of three. The peak also appeared cleaner as a single peak for S polarization, whereas it was split into about three peaks for P polarization.

  Next, with the HWP scale at 82 (S polarization), we set the polarizer scale to 272 (S polarization). Peaks separated by approximately 1 MHz were observed (Photo 1). we then set the polarizer scale to 317, and one of the two peaks became larger (Photo 2). When I set the polarizer scale to 227, the other peak appeared to become larger (Photo 3). The three cases are plotted together in Fig. 1.
   

• Next, we acquired beat signal data around 1.6 GHz (Photo 4), 0.8 GHz (Photo 5), -0.8 GHz (Photo 6), and -1.6 GHz (Photo 7) with the HWP scale at 82 and the polarizer scale at 317, where the peak appeared the cleanest. I fitted the obtained SRY data both with and without a linear background. I will post the fitting results for the individual peaks later. From the peak frequencies obtained from the fits and their uncertainties, I calculated the minimum and maximum values within the uncertainty ranges. I then took the overall minimum and maximum values from the two fitting models, with and without a linear background, as the uncertainty range.
  Therefore, I used the following data to determine the SRY length:

  Minimum (MHz)    Maximum (MHz)
  1610.8271    1610.9060
  803.0776    803.1743
  -800.9112    -800.8258
  -1592.4969    -1592.4366

  I set the FSR index of the data around -1.6 GHz to 0. For each pair of nearby peak frequencies, I calculated the frequency difference and divided it by the design value of the FSR. I then rounded the resulting value to the nearest integer to determine the FSR index. I fitted the measured peak frequencies as a function of the FSR index using the linear function AN+B, where A and B are fitting parameters and N is the FSR index.
  The fitting results are shown below (Fig. 2):

  A: 2.307881(33) MHz
  B: -1592.467(27) MHz

  Since A corresponds to the FSR, I calculated the SRY length from the fitted value of A, obtaining:

  Fitted value: 64.94972(93) m
  Design value: 64.9264 m
  Difference from the design value (fitted value − design value): 2.332(93) cm

  This result is consistent with the previous measurements reported in klog:37455: the deviations from the design value were 2.168(80) cm with the HWP scale at 14 and the polarizer scale at 295, and 2.319(71) cm with the HWP scale at 59 and the polarizer scale at 250. However, it is slightly different from the result obtained before moving the lens to improve the mode-matching ratio (klog:37250), where the deviation of the SRY length from the design value was 1.757(50) cm.
   

• Using the SRX result from klog:37450 and the results from klog:37458, I calculated the SRC length and Schnupp asymmetry as follows:

  SRC
  Calculated value: 66.61860(51) m
  Design value: 66.5913 m
  Difference from the design value (calculated value − design value): 2.730(51) cm

  Schnupp asymmetry calculated from the SRC
  Calculated value: 3.33775(102) m
  Design value: 3.3298 m
  Difference from the design value (calculated value − design value): 0.795(102) cm

  Schnupp asymmetry
  Weighted average: 3.33842(49) m
  Design value: 3.3298 m
  Difference from the design value (weighted average − design value): 0.862(49) cm

  These results are consistent with the previous measurements reported in klog:37455 and klog:37458. With the HWP scale at 14 and the polarizer scale at 295, the SRC length was 66.61778(45) m, the Schnupp asymmetry calculated from the SRC was 3.339390(904) m, and the Schnupp asymmetry from the weighted average was 3.33884(48) m. With the HWP scale at 59 and the polarizer scale at 250, the corresponding values were 66.61853(41) m, 3.337880(825) m, and 3.33839(47) m, respectively. Compared with the measurements before moving the lens to improve the mode-matching ratio (klog:37260), where the SRC length was 66.61409(70) m, the Schnupp asymmetry calculated from the SRC was 3.34023(139) m, and the Schnupp asymmetry from the weighted average was 3.33791(45) m, the SRC length and the Schnupp asymmetry calculated from the SRC are somewhat different. However, the Schnupp asymmetry obtained from the weighted average is consistent with the previous result.

I offloaded the BF GAS with the FR.

I offloaded the F0 GAS with the FR.

The fitting results for PRX and PRY in klog:37458 are shown below.
The measurement data are saved in the following Dropbox folders:

All files/Dropbox KAGRA/Measurements/IFO/PRCL/PRCL_OMMT2_REFL_beat_signal_PZT_sweep/2026_09_04_PRX
All files/Dropbox KAGRA/Measurements/IFO/PRCL/PRCL_OMMT2_REFL_beat_signal_PZT_sweep/2026_09_04_PRY
 

• PRX
  Fig. 1: Around 1.6 GHz, without a linear background. Using the data from 1591.51 MHz to 1592.0 MHz, the fitted peak frequency was 1591.7750(12) MHz.
  Fig. 2: Around 1.6 GHz, with a linear background. Using the data from 1591.51 MHz to 1592.0 MHz, the fitted peak frequency was 1591.8014(56) MHz.

  Fig. 3: Around 800 MHz, without a linear background. Using the data from 807.62 MHz to 808.15 MHz, the fitted peak frequency was 807.8942(17) MHz.
  Fig. 4: Around 800 MHz, with a linear background. Using the data from 807.62 MHz to 808.15 MHz, the fitted peak frequency was 807.8842(49) MHz.

  Fig. 5: Around -800 MHz, without a linear background. Using the data from 821.12 MHz to 821.59 MHz, the fitted peak frequency was 821.3504(11) MHz.
  Fig. 6: Around -800 MHz, with a linear background. Using the data from 821.12 MHz to 821.59 MHz, the fitted peak frequency was 821.3352(35) MHz.

  Fig. 7: Around -1.6 GHz, without a linear background. Using the data from 1563.29 MHz to 1563.82 MHz, the fitted peak frequency was 1563.5494(14) MHz.
  Fig. 8: Around -1.6 GHz, with a linear background. Using the data from 1563.29 MHz to 1563.82 MHz, the fitted peak frequency was 1563.5525(32) MHz.
   

• PRY
  Fig. 9: Around 1.6 GHz, without a linear background. Using the data from 1599.85 MHz to 1600.57 MHz, the fitted peak frequency was 1600.1828(18) MHz.
  Fig. 10: Around 1.6 GHz, with a linear background. Using the data from 1599.85 MHz to 1600.57 MHz, the fitted peak frequency was 1600.1637(33) MHz.

  Fig. 11: Around 800 MHz, without a linear background. Using the data from 810.32 MHz to 810.95 MHz, the fitted peak frequency was 810.6120(14) MHz.
  Fig. 12: Around 800 MHz, with a linear background. Using the data from 810.32 MHz to 810.95 MHz, the fitted peak frequency was 810.5939(29) MHz.

  Fig. 13: Around -800 MHz, without a linear background. Using the data from 816.67 MHz to 817.23 MHz, the fitted peak frequency was 816.9934(28) MHz.
  Fig. 14: Around -800 MHz, with a linear background. Using the data from 816.67 MHz to 817.23 MHz, the fitted peak frequency was 817.0274(72) MHz.

  Fig. 15: Around -1.6 GHz, without a linear background. Using the data from 1596.96 MHz to 1597.66 MHz, the fitted peak frequency was 1597.3557(27) MHz.
  Fig. 16: Around -1.6 GHz, with a linear background. Using the data from 1596.96 MHz to 1597.66 MHz, the fitted peak frequency was 1597.4093(82) MHz.

[Fujimoto, Ye, Saito]

We adjusted the HWP and polarizer to obtain clean peaks and acquired beat signal data for PRX and PRY. After fitting the data, the deviations from the design values were 0.926(22) cm for PRX and 0.043(52) cm for PRY. Compared with the previous measurements before moving the lens to improve the mode-matching ratio (klog:37260), which gave deviations of 0.677(11) cm for PRX and -0.107(46) cm for PRY, both results are slightly different.

We also calculated the PRC length and the Schnupp asymmetry from the PRC. Using the Schnupp asymmetry calculated from the SRC in klog:37455, we then calculated the Schnupp asymmetry by taking a weighted average of the two values. The results were as follows:

PRC length: 66.59625(28) m
Schnupp asymmetry calculated from the PRC: 3.338630(565) m
Schnupp asymmetry from the weighted average:
3.33884(48) m when SRY was measured with the HWP scale at 14 and the polarizer scale at 295
3.33839(47) m when SRY was measured with the HWP scale at 59 and the polarizer scale at 250

Compared with the previous measurements before moving the lens to improve the mode-matching ratio (klog:37260), which gave a PRC length of 66.59425(24) m, a Schnupp asymmetry calculated from the PRC of 3.337640(473) m, and a Schnupp asymmetry from the weighted average of 3.33791(45) m, the PRC length is slightly different. However, there is no inconsistency between the Schnupp asymmetry calculated from the PRC and that calculated from the weighted average.
 

• To acquire the beat signal data for PRX, we first turned off the main laser and adjusted the alignment of the sub-laser. We then turned on the main laser and adjusted the alignment to the RFPD. When we checked the beat signal with the HWP scale at 82 and the polarizer scale at 50 using a spectrum analyzer, the peak was not clean (Photo 1). We therefore rotated the HWP and polarizer. The peak became clean when the HWP scale was set to 70 and the polarizer scale was set to 254. We then acquired data around 1.6 GHz (Photo 2), 0.8 GHz (Photo 3), -0.8 GHz (Photo 4), and -1.6 GHz (Photo 5).
   
• Similarly, for PRY, we first turned off the main laser and adjusted the alignment of the sub-laser. We then turned on the main laser and adjusted the alignment to the RFPD. We set the HWP scale to 16 and the polarizer scale to 117 to obtain clean peaks, and acquired data around 1.6 GHz (Photo 6), 0.8 GHz (Photo 7), -0.8 GHz (Photo 8), and -1.6 GHz (Photo 9).
   

• We then fitted the obtained PRX and PRY data with and without a linear background. I will post the fitting results for the individual peaks later. From the peak frequencies obtained from the fits and their uncertainties, we calculated the minimum and maximum values within the uncertainty ranges. We then took the overall minimum and maximum values from both fitting models, with and without a linear background, as the uncertainty range. The following data were therefore used to determine the PRX and PRY lengths.

  PRX
  Minimum (MHz)    Maximum (MHz)
  1591.7738    1591.8070
  807.8792    807.8958
  -821.3516    -821.3318
  -1563.5557    -1563.5479

  PRY
  Minimum (MHz)    Maximum (MHz)
  1600.1604    1600.1846
  810.5910    810.6133
  -817.0346    -816.9907
  -1597.4175    -1597.3530

  We set the FSR index of the data around -1.6 GHz to 0. For each pair of nearby peak frequencies, we calculated the frequency difference and divided it by the design value of the FSR. We then rounded the resulting value to the nearest integer to determine the FSR index. We fitted the measured peak frequencies as a function of the FSR index using the linear function AN+B, where A and B are fitting parameters and N is the FSR index.

  The fitting results were as follows.

  PRX (Fig. 1)
  A: 2.1957810(72) MHz
  B: -1563.5483(38) MHz

  PRY (Fig. 2)
  A: 2.308691(19) MHz
  B: -1597.363(21) MHz

  Since A corresponds to the FSR, we calculated the PRX and PRY lengths from the fitted values of A. The results were as follows.

  PRX
  Fitted length: 68.26556(22) m
  Design value: 68.2563 m
  Difference from the design value (fitted length − design value): 0.926(22) cm

  PRY
  Fitted length: 64.92693(52) m
  Design value: 64.9265 m
  Difference from the design value (fitted length − design value): 0.043(52) cm

  Compared with the previous measurements before moving the lens to improve the mode-matching ratio (klog:37260), which gave deviations of 0.677(11) cm for PRX and -0.107(46) cm for PRY, both results are slightly different.
   

• We also calculated the PRC length and the Schnupp asymmetry from the PRC. Using the Schnupp asymmetry calculated from the SRC in klog:37455, we calculated the Schnupp asymmetry from the weighted average as follows.

  PRC
  Calculated value: 66.59625(28) m
  Design value: 66.5914 m
  Difference from the design value (calculated value − design value): 0.485(28) cm

  Schnupp asymmetry calculated from the PRC
  Calculated value: 3.338630(565) m
  Design value: 3.3298 m
  Difference from the design value (calculated value − design value): 0.8830(565) cm

  Schnupp asymmetry
  When SRY was measured with the HWP scale at 14 and the polarizer scale at 295:
  Weighted average: 3.33884(48) m
  Design value: 3.3298 m
  Difference from the design value (weighted average − design value): 0.904(48) cm

  When SRY was measured with the HWP scale at 59 and the polarizer scale at 250:
  Weighted average: 3.33839(47) m
  Design value: 3.3298 m
  Difference from the design value (weighted average − design value): 0.859(47) cm

  Compared with the previous measurements before moving the lens to improve the mode-matching ratio (klog:37260), which gave a PRC length of 66.59425(24) m, a Schnupp asymmetry calculated from the PRC of 3.337640(473) m, and a Schnupp asymmetry from the weighted average of 3.33791(45) m, the PRC length is slightly different. However, there is no inconsistency between the Schnupp asymmetry calculated from the PRC and that calculated from the weighted average.