Pictures: link

[Saito, Tanaka, Fujimoto]

Abstract

We performed a PRX length measurement using the beat signal between the main laser and the auxiliary laser in OMC REFL.
As a cross-check of the data analysis, I analyzed the data independently from Saito-kun. In this entry, I show my results.
Please refer to Saito-kun’s klog entry (klog #37185) for the details of the measurement.

From my analysis, the measured PRX length is consistent with the design value within the measurement uncertainty of 1.3 cm, and this is consistent with Saito-kun's result:

• L_PRX_design = 68.2560 m
• L_PRX_measured = 68.267(13) m
• Difference between measurement and design: (1.1±1.3) cm

Details for analysis

Design values for PRX

The design values for PRX are as follows:

• L_PRX_design = 68.2560 m
• FSR_PRX_design = 2.19609 MHz

Measured beat frequency

We measured the beat frequencies between the main laser and the auxiliary laser when the auxiliary laser was resonant in PRX at four different frequency regions: around -160 MHz, -140 MHz, +140 MHz, and +160 MHz.

For the +140 MHz and +160 MHz cases, we measured the frequency range where the maximum could not be clearly distinguished, and estimated the center values and error bars from that range.

For the -140 MHz and -160 MHz cases, due to time constraints, we did not perform this range measurement. Instead, we used the frequencies that seemed to correspond to the maxima as the measured points. For their error bars, we used the uncertainty obtained from the +140 MHz measurement, which was 0.064 MHz.

The results are summarized in the table below:

Fitting results

I plotted the beat frequency as a function of the FSR index and fitted the data with a linear function, a*x+b, where x is the FSR index.

Fig. 1 shows the measured data points and the fitted line.

The fitting model and the obtained parameters are as follows:

• Model: a*x+b
• Results:
  • a = 2.19575(40) MHz
  • b = -160.376(47) MHz

Results for the FSR and PRX length

The fitted parameter (a) directly gives the FSR of PRX.
The PRX length calculated from this FSR is as follows:

• FSR_PRX_measured = 2.19575(40) MHz
• L_PRX_measured = 68.267(13) m
• L_PRX_design = 68.2560 m
• Difference between measurement and design:
  L_PRX_measured - L_PRX_design = (1.1±1.3) cm

Therefore, within the measurement uncertainty of 1.3 cm, the measured PRX cavity length is consistent with the design value.

[Tanaka, Fujimoto, Saito]

To observe the beat signal with the RFPD installed at OMC REFL, the vertical axis of the spectrum analyzer was set to a linear scale, and the number of frame averages was increased to make the peak height and frequency easier to identify. During the observation, the beat frequency occasionally shifted toward lower frequencies, sometimes as often as once every few seconds. The No. 3 sub-laser used in this experiment (as identified in the JGW DOC documentation) is known to exhibit frequency-noise events that increase its RMS frequency noise approximately once every 5 s to 2 min, and the occurrence rate closely matched that of the observed beat-frequency shifts. Therefore, these frequency shifts are considered to originate from the frequency noise of the sub-laser. The beat-signal amplitude also fluctuated, which is believed to be caused by fluctuations of PRX. Accordingly, when the beat signal was stable, the LO frequency was varied, and the minimum and maximum frequencies at which the beat-signal amplitude reached its maximum were measured around 160 MHz, 140 MHz, −160 MHz, and −140 MHz. Fitting these measurements yielded a PRX length of 68.27 ± 0.01 m, compared with the design value of 68.2563 m.
 

• The sub-laser was injected into PRX, the PLL was engaged, and the beat signal was observed with the RFPD installed at OMC REFL. The objective was to determine the minimum and maximum frequencies at which the beat-signal amplitude reached its maximum. For this purpose, the vertical axis of the spectrum analyzer was set to a linear scale, and the number of frame averages was increased to improve the visibility of the peak height and frequency. By varying the PLL LO frequency, both the resonance point (Fig. 1) and the anti-resonance point (Fig. 2) were observed. At the anti-resonance point, however, the beat-signal peak appeared to split into two peaks.
   
• During the measurements, the beat frequency occasionally shifted toward lower frequencies, sometimes as often as once every few seconds. The beat signal in the PLL path exhibited the same frequency shift. Initially, fluctuations of the Moku:Lab LO signal were suspected, so the LO source was switched from the Moku:Lab to the function generator that had originally been used. However, no change was observed. Fluctuations of the main laser were also considered, and an additional control loop was applied to suppress them, but this likewise produced no improvement. On the other hand, the No. 3 sub-laser used in this experiment (as described in the JGW DOC documentation) is known to exhibit frequency-noise events that increase its RMS frequency noise approximately once every 5 s to 2 min, and the occurrence rate closely matched that of the observed beat-frequency shifts. Therefore, the observed frequency shifts are considered to originate from the frequency noise of the sub-laser. The beat-signal amplitude also fluctuated, which is believed to be caused by fluctuations of PRX.
   

• Therefore, when the beat signal was stable, the LO frequency was varied, and the minimum and maximum frequencies at which the beat-signal amplitude reached its maximum were measured around 160 MHz, 140 MHz, −160 MHz, and −140 MHz. Negative frequencies correspond to the case where the sub-laser frequency is lower than the main-laser frequency. The measured values are listed below.

  Minimum    Maximum
  162.363 MHz    162.442 MHz
  140.366 MHz    140.494 MHz
  −140.683 MHz    −140.555 MHz (assuming ±0.064 MHz around −140.619 MHz)
  −160.435 MHz    −160.307 MHz (assuming ±0.064 MHz around −160.371 MHz)

  The midpoint between the minimum and maximum frequencies was then calculated for each measurement. Each midpoint was divided by the FSR calculated from the PRX design length of 68.2563 m. The resulting values were rounded to the nearest integers, and the measured frequencies were fitted with the linear function AN+B, where A and B are fitting parameters and N is the corresponding integer. The fitting results are shown in Fig. 3 and are summarized below:

  A = 2.1957 ± 0.0004 MHz
  B = −0.08 ± 0.03 MHz

  Since A corresponds to the FSR, the PRX length calculated from the fitted FSR is

  Fitted PRX length: 68.27 ± 0.01 m
  Design value: 68.2563 m

With Jinshui Tian, Yuli Liang

We are preparing for the installation of the Ncal system. As part of this preparation, we checked the installation area and confirmed the tools, space, and cable routing needed for the pylon and Ncal installation work.

The following items were checked at the site:

• We placed the full-scale drawing of the pylon at the planned installation location. No serious issue was found. We also measured the distance to nearby structures, and the closest clearance was about 3 cm.
• We confirmed that a lifter, Bishamon, is available at the Xend.
• We checked the possible location for hanging a chain block. The floor of the mezzanine level was inspected for this purpose.
• We confirmed that the parts of the gantry crane exist at the site. However, we probably will not use it for the actual installation work.
• We took site photos of the possible routes for the signal cables and power cables.

The site photos will be shared later.

[Fujimoto, Kenta, Saito, YamaT]

We laid cables on the AS table to connect Moku to the DGS network.

Only one UTP cable had been laid from the OMC fire alarm rack to the k1ctr6@OMC and laying a new cable from the OMC fire alarm rack requires an aerial work platform and schedule coordination with technical staffs. So I installed a new unmanaged switch in the workstation cart and split the DGS LAN to k1ctr@OMC and Moku@AS-table as shown in attached figures.

This implementation is not suitable for permanent equipment. So it will be removed after finishing recent PRCL/SRCL works. If DGS wired LAN will be permanently required around AS table, make a request in advance so we can coordinate schedules with technical staffs for laying a new cable between the OMC fire alarm rack and the AS table.

I offloaded the BF GAS with the FR.

[Joshua, Tanaka, Disha, Fujimoto, Saito]

To perform the measurement proposed in klog:37169 using the beat signal at the OMC REFL, a new RFPD was installed at OMC REFL. After injecting the sub-laser into PRX and engaging the PLL, the beat signal was successfully observed with the newly installed RFPD. The amplitude and frequency of the beat signal both fluctuated, making it difficult to finely adjust the LO frequency to maximize the beat signal. However, since both the resonance and anti-resonance points were successfully identified, we plan to reduce the effect of these fluctuations by increasing the number of averaging frames on the spectrum analyzer. The beat frequency will then be determined by measuring the minimum and maximum frequencies at which the beat-signal amplitude begins to decrease.

• The reflected beam from the BS in front of the OMC REFL camera had previously been dumped, so this beam was utilized for the measurement. First, the beam dump was removed, and the beam power was measured to be approximately 3 mW using a power meter. A mirror, a lens with a focal length of 50 mm, an OD = 0.5 ND filter, and an RFPD were then installed (Fig. 1). The lens was inserted to focus the beam onto the RFPD, while the ND filter was used because the maximum allowable input power to the RFPD is 1 mW. The optical power measured immediately before the RFPD was approximately 0.95 mW. The alignment was then adjusted to maximize the DC output of the RFPD.
   
• Next, the sub-laser was injected into PRX, the PLL was engaged, and the beat signal was observed using the RFPD installed at OMC REFL. The beat signal was successfully detected. However, it was difficult to finely adjust the LO frequency used for the PLL to maximize the beat signal because both its amplitude and frequency fluctuated. Therefore, the LO frequency was swept by ±3 MHz around 160.4 MHz at a rate of 10 mHz. Under these conditions, both the resonance point (Fig. 2) and the anti-resonance point (Fig. 3) were observed. The spacing between adjacent resonance points was approximately 2.2 MHz. Based on these results, we plan to increase the number of averaging frames on the spectrum analyzer to suppress the influence of the fluctuations and determine the beat frequency by measuring the minimum and maximum frequencies at which the beat-signal amplitude begins to decrease.

Not " EYC P-55", "IYC P-55" is correct. 

[Tanaka, Hirose, Fujimoto, Saito]

As the PLL UGF was increased, the beat signal became progressively broader. It is therefore likely that the reason why no fringes were observed on the OMC REFL PD at a UGF of 10 kHz in the previous experiment (klog:37170) was that the broadened beat signal prevented the PLL from accurately detecting changes in the frequency difference between the LO and the beat signal, resulting in insufficient modulation of the PZT. Next, an offset was added to the error signal while operating at a UGF of 1 kHz, where the temporal fluctuation of the beat frequency was relatively small. However, the change in the beat frequency was nonlinear with respect to the applied offset, and it was difficult to measure the frequency shift accurately because the beat frequency continuously fluctuated by several MHz.
 

• First, since different behavior was observed between PLL operation at UGFs of 10 kHz and 1 kHz in the previous experiment (klog:37170), the dependence of the beat signal on the UGF was investigated to determine the most suitable UGF for evaluating the frequency shift caused by adding an offset to the error signal. The measured UGFs and FWHM of the beat signal were as follows:

  UGF: 100 Hz (SR560 gain = 20), FWHM: 75 kHz (Fig. 1)
  UGF: 1 kHz (SR560 gain = 200), FWHM: 536 kHz (Fig. 2)
  UGF: 10 kHz (SR560 gain = 2000), FWHM: 1.9 MHz (Fig. 3)

  These results show that the beat signal became broader as the UGF increased, presumably because the control noise was being fed back through the PLL. Therefore, it is likely that the absence of fringes on the OMC REFL PD at a UGF of 10 kHz in the previous experiment (klog:37170) was caused by the broadened beat signal, which prevented the PLL from accurately sensing changes in the frequency difference between the LO and the beat signal, resulting in insufficient PZT modulation.
   

• Next, an offset was applied to the error signal while operating at a UGF of 1 kHz, where the temporal fluctuation of the beat frequency was relatively small, although occasional frequency excursions of several MHz were still observed. When a 10 mV offset was applied, no measurable change in the beat frequency was observed during stable periods. Increasing the offset to 100 mV produced a frequency shift of approximately 0.1 MHz during stable periods. When the offset was increased to 200 mV, the beat frequency shifted by approximately 10 MHz, while fluctuating by about 5 MHz around this value. Finally, applying a 300 mV offset produced a frequency shift of approximately 70 MHz, accompanied by even larger fluctuations. These results indicate that the beat-frequency shift is nonlinear with respect to the applied error-signal offset. Moreover, because the beat frequency continuously fluctuated by several MHz, accurately quantifying the frequency shift was difficult.

[Fujimoto, Komori]

Abstract:

We discuss this estimation more concretely and quantitatively.
We should be able to measure the PRC and SRC lengths with a resolution of 0.1%, corresponding to an error of 6–7 cm.
Whether we can reach the 0.01% level, corresponding to 6–7 mm, will depend on how we determine the beat frequency.

Details:

The designed value of the SRY length, for instance, is 64.926 m, and the FSR of the SRY cavity is 2.3088 MHz.
On the other hand, using the method described in the original post, we should be able to measure the beat frequency with a resolution comparable to the cavity linewidth, which is approximately 0.2 MHz.
If we lock the beat frequency at 100 times the FSR, approximately 230 MHz, and measure it with a resolution of 0.2 MHz, the relative error of the measurement is 0.1%.
Therefore, the FSR can be estimated with the same relative error.

Let us simulate a realistic situation.
Suppose that we measure the beat frequency to be 221.3 ± 0.2 MHz.
The possible solutions are 95 × (2.330 ± 0.002) MHz and 96 × (2.305 ± 0.002) MHz, corresponding to absolute lengths of 65.03 ± 0.06 m and 64.33 ± 0.06 m, respectively.
Since the designed value is 64.926 m, and we can probably assume that the deviation from the designed value is less than 60 cm, we can select the solution of 65.03 ± 0.06 m.

However, an error of 6 cm is too large.
We have to measure the beat frequency with a relative error of 0.01% in order to estimate the absolute length with a resolution below 1 cm.

In addition to the method described in the original post, we propose another method to determine the beat frequency with the auxiliary laser frequency locked.
By dithering the auxiliary laser frequency at an audio frequency, for example 1 kHz and tuning the offset, we can minimize the peak height in the noise spectrum measured by the OMC REFL PD.
This method may be better than the original proposal because, generally speaking, minimizing a peak in a noise spectrum is easier than maximizing it.

The error of this method will be determined by RMS of the residual displacement of the SRC length.
If the RMS displacement with the SRC locked is less than 10% of the cavity linewidth, corresponding to 0.02 MHz, we should be able to achieve a relative error of 0.01% in the absolute length estimation.

[Kimura and Yasui]
 On July 6, as part of maintenance work on the cryogenic cooling units, we set up two valve units for the radiation shield cryo-coolers (IYC P-53 and EYC P-55).
 The remaining tasks are filling the system with G-1 class helium gas up to 15 bar and performing leak tests on all connections.

[Tanaka, Fujimoto, Saito]

The cutoff frequency of the high-pass filter in the SR560 used for the OMC REFL PD signal was reduced from 300 Hz to 30 Hz, allowing frequency sweeps to be performed at a slower rate. When the PLL UGF was increased to 10 kHz and the LO frequency was modulated to scan PRX, no fringes were observed on the OMC REFL PD. However, both the feedback signal and the beat signal appeared to be modulated properly. Therefore, the reason why no fringes were observed on the OMC REFL PD at a UGF of 10 kHz remains unclear. An alternative approach was also tested by scanning PRX through the addition of an offset signal to the error signal. As in the case of LO frequency modulation, no fringes were observed on the OMC REFL PD when the UGF was increased to 10 kHz. In addition, the feedback signal became distorted and no longer followed the waveform of the injected signal.
 

• First, after reducing the OMC REFL intensity noise for PRX and PRY (klog:37150), it was noticed that the cutoff frequency of the high-pass filter in the SR560 used for the OMC REFL PD had not been updated. Therefore, it was changed from 300 Hz to 30 Hz, allowing the frequency sweep to be performed more slowly.
   
• Next, with the PLL UGF set to approximately 1 kHz, the LO frequency was frequency-modulated with a sensitivity of ±15 MHz/V. An 800 mVpp, 300 Hz sinusoidal waveform generated by a function generator was used as the external modulation signal. Under these conditions, PRX was scanned and fringes were successfully observed on the OMC REFL PD. However, when the UGF was increased to approximately 10 kHz by increasing the gain of the SR560 used in the PLL, the fringes disappeared. The UGF was then returned to approximately 1 kHz, and the frequency of the external modulation signal was increased above 300 Hz. As the modulation frequency increased, the number of peaks observed on the OMC REFL PD also increased. Conversely, when the UGF was reduced below 1 kHz by decreasing the SR560 gain, the number of peaks observed on the OMC REFL PD decreased. Furthermore, even when the external modulation frequency was increased above 300 Hz with the UGF maintained at approximately 10 kHz, no fringes were observed on the OMC REFL PD. Nevertheless, the feedback signal at a UGF of 10 kHz showed the same modulation behavior as that at a UGF of 1 kHz, and the beat signal observed with the spectrum analyzer also appeared to vary as expected. Therefore, it remains unclear why no fringes can be observed on the OMC REFL PD when the UGF is increased to approximately 10 kHz.
   
• Finally, an attempt was made to scan PRX by adding an offset signal directly to the error signal. As shown in Fig. 1, a 20 Hz, 300 mVpp sinusoidal signal was added to the error signal. In Fig. 1, the red trace represents the error signal, while the blue trace represents the injected signal. As in the case of LO frequency modulation, increasing the UGF from approximately 1 kHz to approximately 10 kHz caused the fringes to disappear from the OMC REFL PD. In addition, the feedback signal became distorted and no longer matched the waveform of the injected signal (Fig. 2). The degree of distortion varied with time and occasionally became more pronounced. Furthermore, while measuring the open-loop transfer function, the feedback signal was found to become distorted whenever a low-frequency excitation signal was injected.

Here, I would like to propose a possible method for the PRCL/SRCL length measurement without sweeping the LO frequency.

The procedure is as follows:

0. Place an RFPD in OMC REFL.
1. Lock the main laser to SRY.
2. Lock the PLL of the auxiliary laser and the main laser.
3. Manually adjust the LO frequency and bring the auxiliary laser to resonance in SRY. In this step, the resonance can be checked using the beat signal observed with the RFPD in OMC REFL.
4. Measure the beat frequency in POS or OMC REFL and calculate the FSR by dividing it by an appropriate integer.

The SNR of this method can be roughly estimated as follows.
On the RFPD currently placed on the POS table, the powers and SNR are:

- Main laser: ~30/2 uW
- Auxiliary laser: ~1 mW
- SNR, defined as the ratio between the noise floor and the peak height: ~40 dB

On the other hand, the expected powers in OMC REFL are:

- Main laser: ~10 mW
- Auxiliary laser: ~20 uW

Therefore, if we reduce the main laser power incident on the RFPD placed in OMC REFL to 1 mW, the SNR will become worse than that on the POS table by a factor of about sqrt(10). However, the beat signal is still expected to be clearly visible.

In addition, in this measurement, we may be able to reduce the error in estimating the FSR by using a large LO frequency offset and bringing the auxiliary laser to a resonance far from the carrier resonance.

[Takahashi.M, Sawada.H, Nakagaki]

We ran cables in preparation for monitoring the status of the gate valve between PR3 and PRM.
 

The OMMT-GV interlock has been set to monitoring mode.

Monitoring start time: 15:30 (JST)
Automatic close threshold: 9.9e-04
Vacuum pressure at start of monitoring
 SRMGV : 2.5e-05
 OMMTGV : 3.8e-05