[Tanaka, Fujimoto, Saito]

The high-voltage amplifier tested in klog:37154 was inserted between the SR560 used in the PLL and the PZT of the sub-laser. By setting the SR560 gain to 1000 and the cutoff frequency of the Moku:Lab integrator to 1 kHz, and by adding a 10 kHz low-pass filter in Moku:Lab, the UGF increased to approximately 10 kHz. The 10 kHz low-pass filter was introduced because oscillations at around 85 kHz were observed in the error signal. However, under these conditions, no fringes could be observed on the OMC REFL PD during a PRX scan. Reducing the gain of the SR560 allowed the fringes to reappear, so the SR560 gain was changed to 200 and the cutoff frequency of the Moku:Lab integrator was reduced to 100 Hz. The LO frequency was then frequency-modulated with a sensitivity of ±30 MHz/V. As the external modulation signal, an 80 Hz, 800 mVpp sinusoidal waveform generated by a function generator was applied, and a PRX scan was performed to acquire data. Owing to an earthquake, it was not possible to obtain the current open-loop transfer function or data using a triangular-wave modulation signal, so these measurements will be carried out next time.

• First, the high-voltage amplifier tested in klog:37154 was inserted between the SR560 used in the PLL and the PZT of the sub-laser. Before introducing the amplifier, the SR560 gain had been set to 2000. Since the amplifier provided an additional gain of 10, the SR560 gain was reduced to 200, and it was confirmed that PLL operation was still possible. To increase the UGF beyond the previous value of approximately 1 kHz, the gain of the SR560 was gradually increased. However, oscillations appeared in the error signal at around 85 kHz. Therefore, a 10 kHz low-pass filter was added using Moku:Lab. With the SR560 gain set to 1000 and the cutoff frequency of the Moku:Lab integrator set to 1 kHz, the open-loop transfer function was measured, yielding a UGF of approximately 10 kHz (Fig. 1). An attempt was then made to perform a PRX scan, but no fringes were visible in the OMC REFL PD signal. When the gain of the SR560 was reduced, fringes became visible again in the OMC REFL PD signal. Therefore, the SR560 gain was set to 200 and the cutoff frequency of the Moku integrator was set to 100 Hz.
• Because the high-voltage amplifier enabled the PZT to be driven over a larger range, the frequency modulation sensitivity was increased to ±30 MHz/V. To drive the PZT as slowly as possible while maintaining a clean fringe shape, an 80 Hz, 800 mVpp sinusoidal waveform generated by a function generator was used as the external signal for frequency modulation. Data for both the OMC REFL PD signal and the external modulation signal were then acquired (Fig. 2).
   
• Due to an earthquake, it was not possible to obtain the current open-loop transfer function or the data corresponding to the case where a triangular-wave signal was used for frequency modulation. These measurements are planned for the next session.

Test of alignment-recording setup before installing a new laser source in Pcal-Y

With Misato Onishi and Seiya Matsuo.

We performed a test of the setup to record the current Pcal-Y alignment before installing a new laser source in the Pcal-Y Tx module.

We are planning to install an additional laser source inside the Pcal-Y Tx module. Since this work may change the present optical alignment by accident, we would like to record the alignment outside the vacuum chamber during the installation work as a backup reference.

Our current plan is to extract the two Pcal-Y beams from the Tx module, propagate them along the tunnel toward ETMY, and record their positions using irises. Today, we assembled a jig to extract the beams from inside the Tx module.

However, it took longer than expected to extract both beams from the Tx module at the same time. At the moment, one of the beams is slightly blocked by another structure. It should be possible to solve this by further adjusting the positions of the optical components, but we had to stop the work today due to time limitations.

We plan to continue this work next week.

Tanaka, YamaT

This noon, Large earthquake occured in Hirara, Okinawa. On the other hands, ITMX guardian seems to keep the LOCK_ACQUISITION state even though ITMX control seemed not to work due to this earthquake (fig.1).

We found that the SUS_KICKED threshold (=100), which is judged whether the suspension is kicked from RMS of MN_OLDAMP error, seems to be high (fig.2). So current Type A cannot escape to the emergency state in this threshold.

Then we decided to lower the threshold from 100 to 40. We hope this threshold works well.

[Ushiba, Komori, Fujimoto, Saito]

As in the SRC scan (klog:37151), the LO frequency was frequency-modulated with a coefficient of ±15 MHz/V. As the external signal for the frequency modulation, 300 Hz, 800 mVpp triangular and sinusoidal waveforms generated by a function generator were applied, and scans of PRX and PRY were performed to acquire data. These data will be used to determine the lengths of PRX and PRY.
 

• First, only the sub-laser light was injected into PRX, and the sub-laser PZT was driven with an 8 Vpp triangular wave at 170 Hz. Fringes were observed on the OMC REFL PD, and the alignment was adjusted to maximize the fringe amplitude (Fig. 1). Next, the main laser was turned on, and the alignment of the PLL path was optimized to maximize the beat signal, resulting in a beat amplitude of approximately 5 dBm.
   
• The measurement then proceeded to the PRX scan. As in the SRC scan (klog:37151), the LO frequency was frequency-modulated with a coefficient of ±15 MHz/V. A function generator was used to provide external modulation signals consisting of 300 Hz, 800 mVpp triangular and sinusoidal waveforms. The OMC REFL PD signal was recorded using "K1:IOP-OMC0_MADC0_TP_CH12", while the external modulation signal was monitored using "K1:IOP-LSC0_MADC0_TP_CH22". Data from these two channels were acquired simultaneously (Fig. 2). The measurements then moved on to the PRY scan. As in the PRX measurement, data were acquired using both triangular-wave and sinusoidal-wave external modulation signals. These data will be analyzed to determine the lengths of PRX and PRY.

[Saito, Komori, Ushiba, Miyoki, Fujimoto]

Abstract

We borrowed a high-voltage amplifier from Miyoki-san and tested it for use in the PLL for the PRCL/SRCL length measurements.
The measured results are as follows:

- Gain: 20 dB
- Phase delay: ~1 deg at 10 kHz, and ~45 deg at 509 kHz
- Input-referred noise: ~1.4e-8 V/rtHz at 1 kHz

Tomorrow, we plan to implement this amplifier in the PLL control in order to extend the range of the PLL scan and  increase the UGF.

Details

The current PLL scan range in the PRCL/SRCL length measurement is limited by the output range of the SR560, which is ±5 V. This corresponds to a scan range of about ±10 MHz.
Therefore, in order to extend the PLL scan range, we decided to introduce a high-voltage amplifier made by Miyoki-san, which is the same type as the one used for the EOM in the CARM control.

Instruments

We borrowed a high-voltage amplifier (PA-85), shown in Fig. 1, and its power supply, shown in Fig. 2.
The gain is fixed at 20 dB, and there is no offset. A banana-plug-to-Hirose-4-pin cable is used for the power supply connection.
Since the PZT input range of the Mephisto is ±65 V, we will set the supply voltage to about ±60 V when using this amplifier.

Transfer function

Fig. 3 shows the transfer function measured with Moku:Lab. The results are as follows:

• Gain: 20 dB
• Phase delay: ~1 deg at 10 kHz, and ~45 deg at 509 kHz

The phase delay is quite small for a high-voltage amplifier. Therefore, we expect that a UGF of 10 kHz can be achieved even with this amplifier.

Input-referred noise

In Figs. 4 and 5, red lines show the output noise measured with Moku:Lab and the black lines correnspond to the Moku: Lab ADC noise.

Taking into account the ADC noise of Moku:Lab, the input-referred noise of the high-voltage amplifier is estimated to be as follows:

• ~7e-9 V/rtHz at 10 kHz–100 kHz
• ~1.4e-8 V/rtHz at 1 kHz

In the actual control system, this amplifier will be connected after the SR560, whose gain is expected to be 300–3000. Therefore, the input-referred noise levels above are considered to be negligibly small.

Plan for tomorrow

Tomorrow, we will implement this amplifier in the PLL control and optimize the OLTF by increasing the UGF, adjusting the integrator, and making other necessary changes.
In addition, since this amplifier will extend the PLL range, we plan to perform the PRCL/SRCL length measurements with a larger scan amplitude.

[Komori, Smith, Fujimoto, Saito]

When the OMC REFL PD signal was observed without injecting the sub-laser light, the fringe amplitude was approximately 4 counts. After injecting the sub-laser light, the fringe amplitude increased to approximately 180 counts, corresponding to an SNR of about 45. As in the previous measurement (klog:37138), the LO frequency was frequency-modulated with a coefficient of ±15 MHz/V. As the external signal for the frequency modulation, a 300 Hz, 800 mVpp triangular or sinusoidal waveform generated by a function generator was applied, and scans of SRX and SRY were performed to acquire data. In addition, to obtain data with a higher sampling frequency, the channel "K1:IOP-OMC0_MADC0_TP_CH12" was used to monitor the OMC REFL PD signal, and the channel "K1:IOP-LSC0_MADC0_TP_CH22" was used to monitor the external signal used for frequency modulation. An attempt was made to determine the lengths of SRX and SRY from these data using curve fitting. However, the fitting procedure developed previously (klog:37145) depended strongly on the initial fitting parameters and did not produce reliable results. Therefore, the fitting method will be improved so that stable fitting can be achieved.
 

• First, the OMC REFL PD signal was observed without injecting the sub-laser light, and the fringe amplitude was found to be approximately 4 counts. Next, the sub-laser light was injected and the sub-laser PZT was driven, resulting in a fringe amplitude of approximately 180 counts. Therefore, the SNR was approximately 45. Since the signal amplitude was sufficiently large, attention was shifted to the PLL system. The beat signal amplitude was approximately 5 dBm, which was considered sufficient, and measurements proceeded to scanning SRX.
   
• As in the previous measurement (klog:37138), the LO frequency was frequency-modulated with a coefficient of ±15 MHz/V. A 300 Hz, 800 mVpp triangular waveform generated by a function generator was applied as the external signal for the frequency modulation. In addition, to obtain data with a higher sampling frequency, the channel "K1:IOP-OMC0_MADC0_TP_CH12" was used to monitor the OMC REFL PD signal, and the channel "K1:IOP-LSC0_MADC0_TP_CH22" was used to monitor the external signal for frequency modulation. The signals from these two channels were recorded, and after changing the external modulation signal from a triangular wave to a sinusoidal wave, another set of data was acquired.
   
• After acquiring the SRX scan data, measurements proceeded to SRY scanning. As in the SRX measurements, data were acquired both when the external signal for frequency modulation was a triangular waveform and when it was a sinusoidal waveform (Fig. 1). An attempt was then made to determine the lengths of SRX and SRY from these data using curve fitting. However, the fitting method developed previously (klog:37145) depended strongly on the initial fitting parameters and did not provide satisfactory results. Therefore, the fitting procedure will be improved to achieve more reliable and stable fitting results.

[Saito, Yokozawa, Smith, Komori, Fujimoto]

Abstract

We succeeded in reducing the OMC REFL intensity noise for PRX and PRY to a level comparable to that obtained in the SRY, by tuning the PRCL OLTF and suppressing the control noise.
As the next step, we plan to perform the PRX/PRY length measurements using the OLTF tuned in this work.

Details

In the SRY length measurement, we were able to reduce the main laser intensity noise observed with the OMC REFL PD by locking the OMC to the carrier and suppressing the control noise from the SRCL control. This significantly improved the SNR of the length measurement.

Therefore, as preparation for the next PRX/PRY length measurements, we tuned the PRCL OLTF so that the OMC REFL intensity noise for PRX and PRY becomes comparable to the level achieved in the SRY/SRX cases.

Tuning of the PRCL OLTF

First, we requested PRX_1F_LOCKED in the VERTEX guardian to lock PRX. At this point, excluding the simple gain filters, the filters used for the control were as follows, and no roll-off filter was applied:

- UGF20: z3p300, gain = 94.6
- DC8: 8 Hz integrator

We then created and applied the following filter in the PRCL1 filter bank:

- tmp260701:
  - gain = 1.2
  - z1p8 (to change the cutoff frequency of the 8 Hz integrator to 1 Hz)
  - ELP80

By adding tmp260701, the OLTF became UGF ~17 Hz, PM ~36 deg, roll-off at 80 Hz, and an integrator cutoff at 1 Hz, which is almost same as the one used for SRY.
The measured PRCL OLTF is shown in Fig. 1.

Measured OMC REFL intensity noise with PRX/PRY

Using the OLTF described above, we measured the main laser intensity noise with the OMC REFL PD.
During the measurement, the ISS was turned on, and the OMC control was operated with gain = 3 and dither amplitude =1000, which realizes UGF of 30 Hz.

The red trace in Fig. 2 shows the intensity noise measured with the OMC REFL PD for PRX. It reaches a level comparable to the SRY intensity noise measured yesterday, shown by the black trace, above 10 Hz.

Fig. 3 shows the result for PRY. A similar noise level was also obtained in this case.

One point to note is the peak around 2–3 Hz. Since this peak was not observed in the SRY/SRX cases, it may be related to the motion of the Type-Bp suspensions. However, since its contribution to the RMS seems to be small, we decided to leave it as it is for now.

Plan for tomorrow

Tomorrow, we plan to perform the PRX/PRY length measurements using the OLTF tuned in this work.

However, since we have not resonated the auxiliary laser in PRX or PRY before, we will first check whether we can make the auxiliary laser resonate in the same way as in the SRY case, and whether we can lock the PLL.

The SRY scan data acquired in the previous experiment (klog:37138) were divided into segments according to the time intervals between changes in the slope of the triangular waveform used for frequency modulation, and each segment was fitted individually. When the same initial values for the fitting parameters were used for all segments, some of the fits failed to converge properly. However, these problematic cases could be fitted successfully by changing the initial parameter values, suggesting that individual initial values should be assigned for each data segment. Using identical initial values for all segments, the resulting SRY length was found to be 64.94 ± 0.02 m.
 

• First, the OMC REFL PD signal data acquired in the previous experiment (klog:37138) were normalized. The signal used for frequency modulation was converted from counts to frequency using the conversion factors of 610 μV/count and 15 MHz/V. Next, the data were divided according to the intervals between changes in the slope of the triangular waveform used for frequency modulation, and each segment was fitted using scipy.optimize.curve_fit. The fitting function was

  Φ=4πL(f+f_offset)/c
  P_t=A/(1+B(sin(Φ/2))^2)

  where f is the modulated frequency and c is the speed of light. The fitting parameters were L, f_offset, A, and B. The initial values of the fitting parameters were set as follows:

  L=65 m (the expected SRY length),
  f_offset=282 THz (the laser frequency),
  A = the maximum value of the OMC REFL PD signal within the fitting interval,
  B=6.48, corresponding to 4×finesse/π^2 for an assumed SRY finesse of 4.

  In addition, near the times at which the slope of the triangular modulation waveform changed, the frequency derived from the recorded data might differ from the actual frequency variation. Therefore, for each interval between successive slope changes, the first one-sixth and the last one-sixth of the data were excluded from the fitting procedure. The fit corresponding to the smallest uncertainty in the SRY length is shown in Fig. 1, while the fit corresponding to the largest uncertainty is shown in Fig. 2. The fit in Fig. 1 appears satisfactory, whereas the fit in Fig. 2 appears poor. Although the fit in Fig. 2 can be improved by changing the initial parameter values, doing so causes some other datasets to fit poorly. Therefore, it is likely necessary to choose the initial parameter values individually for each dataset. The SRY lengths obtained from all fits are shown in Fig. 3. Here, up sweep refers to the intervals in which the slope of the triangular modulation waveform was positive, while down sweep refers to the intervals in which the slope was negative. The mean values and standard errors calculated from all fitted SRY lengths are:

  Up sweep: 64.89±0.03 m
  Down sweep: 64.99±0.02 m
  →Overall: 64.94±0.02 m

[Fujimoto, Yokozawa, Smith, Saito, Komori]

Abstract:

We successfully reduced the intensity noise on the OMC REFL PD.
The noise sources were found to be control noise from the SRY length and OMC length control loops, as well as residual 9 Hz noise in the OMC length due to insufficient gain.

Details:

As a continuation of the work reported in klog:37137, we investigated the origin of the intensity noise measured on the OMC REFL PD.

First, we measured the noise with the MCE feedback, as described in klog:37137.
We found that we had already tried this configuration previously (brown vs. red line in klog:37137), and that using only frequency feedback without mass feedback gives better performance.

Next, we tried to reduce the intensity noise by locking the OMC and allowing the carrier intensity noise to escape to the OMC transmission port, as proposed in klog:37139.
Although the intensity noise was reduced at high frequencies, the noise bump around 100 Hz did not change.
This suggests that the noise originates from intensity fluctuations of the RF sidebands.

The next step was to identify the origin of the RF sideband intensity noise.
In principle, the coupling from SRC length noise to intensity noise should be quadratic, but asymmetry can introduce linear coupling.

We turned on the whitening filter of the RF PD currently used to measure the SRY length signal (POP17-I), since sensing noise can introduce additional noise through the feedback control.
However, this did not change the noise, which means that the sensing noise is not dominated by ADC noise, but by other sources such as PD dark noise.

The hypothesis that sensing noise causes control noise in the SRY length loop seemed to be correct, because the shape of the noise spectrum reflects the transfer function of the SRCL filter, including the phase compensation and roll-off elliptic filters, as shown by the green line in Fig. 1.
When we changed the cutoff frequency of the elliptic filter from 300 Hz to 100 Hz, we immediately obtained an improved spectrum without the OMC locked, shown in orange, and a further improved spectrum with the OMC locked, shown in blue.

We also observed a 9 Hz peak, which is known to be a problematic resonance around the OMC, along with many peaks at high frequencies.
We successfully reduced these peaks by increasing the UGF of the OMC length control from 7 Hz to 30 Hz, as shown in brown.

In addition, we adjusted the filters to use a lower gain in order to further reduce the control noise.
We also found that the control noise of the OMC length loop was another dominant noise source around 100 Hz, so we reduced the filter gain while maintaining the same UGF by increasing the dither amplitude.

Finally, we obtained the lowest noise spectrum, shown in red, which is close to the dark noise level, shown in purple.
For reference, the coherence between the OMC REFL signal and the ISS/SRCL noise is shown in Fig. 2.

Using this configuration, we will perform the cavity scan with a better SNR.

• Recovery procedure was simplified thanks to the new status bit served by pylon-camera-server.
• A new function to record current gain/exposure as the default values (see Fig.1). Please record them if you want to keep these values after rebooting camera process (e.g. in the case of server maintenance).

With Takaba-san
We checked the items for the Ncal installation at X-end. It seems that the parts needed to set up and fix the pylons are available. The details are summarized below.

• Around the sill plate (for laser hazard area) area:
  • M10 bolts: 8 × 2
  • M10 nuts: 8 × 2
  • M16 bolts: 12 × 2
  • M16 washers: 12 × 2
  • M10 spring washers: 8
  • Pylons: 2
• Behind EXA, under the pipe:
  • Laser sensor sets: 2
  • Magnetic fluid seals: 2
  • Stractures for bearing?: 1
  • Belt: 1
  • O-rings: 3?
  • Rotor shafts: 2
  • Motors: 2
  • Small vacuum chambers: 2
  • Pylons: 2

In the recent SRY length measurements, the intensity noise of the main laser observed with the OMC REFL PD has been limiting the improvement of the SNR.

I came up with an idea to lock the OMC to the main laser during the measurement.
With this configuration, the main laser, which is the source of the intensity noise, will be transmitted through the OMC, while the auxiliary laser, whose frequency is shifted from the main laser, will be reflected by the OMC. Therefore, this method may improve the SNR.

I would like to discuss this method at tomorrow morning' meeting.

[Fujimoto, Komori]

Abstract:

We will try to reduce the intensity noise on the OMC REFL PD in order to perform cavity scans with a better signal-to-noise ratio.
We measured the intensity noise of the injected light and confirmed that it is sufficiently small.

Details:

As reported in klog:37124, we are suffering from intensity noise on the OMC REFL PD, which degrades the signal-to-noise ratio of the cavity scan.
Figure 1 shows the recently measured intensity noise, where the red and orange lines represent the best-case measurements with good alignment and intensity stabilization turned on.
If we can reduce this noise, we will be able to estimate the FSR more precisely.

First of all, we suspected that the intensity stabilization might have degraded because its performance had not been checked for some time.
Figure 2 shows the intensity noise measured by the out-of-loop PD with the ISS turned off and on, shown in red and blue, respectively.
This result indicates that the ISS is working properly, and that the other noise sources should be investigated as possible origins of the intensity noise on the OMC REFL PD.

Other noise candidates are as follows:

• Frequency noise
  Currently, the IMC is locked using a combination of frequency feedback and MCE mass feedback.
  We do not know the crossover frequency at the moment, but if it is too high, the frequency noise may not be sufficiently suppressed.
• Suspension noise
  Some suspensions related to the SRY cavity may be noisy enough to imprint displacement and angular motion onto the intensity noise.
• Beam clipping
  Beam clipping may occur at the OMC REFL PD.

[Smith, Fujimoto, Saito]

The cutoff frequency of the high-pass filter in the SR560 used for the OMC REFL PD signal was set to 300 Hz. As in the previous experiment (klog:37130), the PLL was locked using the SR560 configured as a first-order low-pass filter with a cutoff frequency of 1 Hz and a gain of 2000, together with an additional integrator with a cutoff frequency of 100 Hz implemented in Moku:Lab. The LO frequency was frequency-modulated with a sensitivity of ±10 MHz/V. When a 300 Hz, 800 mVpp sinusoidal or triangular signal generated by a function generator was used as the external modulation signal, SRY flashes were successfully observed. Furthermore, data for an SRY scan were acquired using a frequency modulation sensitivity of ±15 MHz/V. The FSR and the length of the SRY will be determined from these data.
 

• Since the main-laser noise was smaller when the cutoff frequency of the SR560 high-pass filter used for the OMC REFL PD signal was set to 300 Hz than when it was set to 100 Hz, the cutoff frequency was set to 300 Hz.
   
• Next, only the sub-laser beam was injected, and the alignment was adjusted to maximize the fringe amplitude. The main-laser beam was then injected as well. The alignment of the PLL path was also optimized to maximize the beat signal amplitude.
   
• As in the previous experiment (klog:37130), the PLL was locked using the SR560 configured as a first-order low-pass filter with a cutoff frequency of 1 Hz and a gain of 2000, together with an additional integrator with a cutoff frequency of 100 Hz implemented in Moku:Lab. A 1 Vpp sinusoidal signal generated by the Moku:Lab function generator was used as the LO signal. The LO frequency was adjusted to approximately match the beat frequency and then finely tuned so that the feedback signal was close to 0 V. The LO frequency was then frequency-modulated with a sensitivity of ±10 MHz/V. When a 300 Hz, 800 mVpp sinusoidal signal generated by a function generator was used as the external modulation signal, the result shown in Fig. 1 was obtained. The upper plot shows the OMC REFL PD signal, while the lower plot shows the external modulation signal used for the frequency modulation. When the external signal was changed to a triangular waveform, the result shown in Fig. 2 was obtained. In both Fig. 1 and Fig. 2, the sub-laser PZT was swept over a range of ±4 MHz, and approximately seven peaks were observed during one period of the external modulation signal. Since the FSR is approximately 2.2 MHz, these peaks are believed to correspond to SRY flashes. Increasing the frequency of the external modulation signal resulted in cleaner peak shapes, but the number of observed peaks decreased. Therefore, a modulation frequency of approximately 300 Hz appears to be optimal.
   
• Finally, an SRY scan was performed using a frequency modulation sensitivity of ±15 MHz/V, and the OMC REFL PD signal together with the external modulation signal were recorded. The FSR and the corresponding SRY length will be determined from these data.

I found a frequency counter with the frequency range up to 200MHz in NAOJ.

It will be shipped to Kamioka tomorrow.

[Smith, Hirose, Fujimoto, Saito]

The 20 dB attenuator placed before the SR560 input was removed, and the SR560 gain was increased to 2000. In addition, a Moku:Lab was inserted before the SR560, and an integrator with a cutoff frequency of 100 Hz was added. Measurement of the open-loop transfer function showed that the UGF was approximately 2 kHz. With the cutoff frequency of the high-pass filter in the SR560 used for the OMC REFL PD signal set to 300 Hz, SRY flashes were observed when the LO frequency was modulated by ±2 MHz at a modulation rate of 300 Hz. Furthermore, SRY flashes were also observed when the cutoff frequency of the SR560 high-pass filter was changed to 100 Hz and the modulation rate was reduced to 100 Hz. However, the noise level was higher than in the 300 Hz cutoff-frequency case.
 

• First, as in the previous experiment (klog:37123), the PLL was locked using only the SR560 by configuring it as a first-order low-pass filter with a cutoff frequency of 1 Hz and a gain of 200. The open-loop transfer function was then measured, yielding a UGF of approximately 2.5 Hz (Fig. 1). The reason why the UGF decreased compared with the previous result (klog:37123) is unclear. Next, the 20 dB attenuator before the SR560 input was removed, and the SR560 gain was increased to 2000. Measurement of the open-loop transfer function under these conditions showed a UGF of approximately 2 kHz. The corresponding open-loop transfer function is shown by the light orange trace in Fig. 2. Subsequently, a Moku:Lab was inserted before the SR560, and an integrator with a cutoff frequency of 100 Hz was added. The measured open-loop transfer function again showed a UGF of approximately 2 kHz. The corresponding transfer function is shown by the orange trace in Fig. 2.
   
• Next, while attempting to scan the SRY, it was noticed that the DC signal from the OMC REFL PD was approximately -300 counts. When the light incident on the PD was blocked using a sensor card, the signal returned to approximately 0 counts (Fig. 3). The reason for the offset of approximately -300 counts remains unknown.
   
• Next, a 1 Vpp sinusoidal signal generated by the Moku:Lab function generator was used to modulate the LO frequency. The LO frequency was first set equal to the beat frequency and then frequency-modulated by ±2 MHz at a modulation rate of 300 Hz. Under these conditions, with the cutoff frequency of the SR560 high-pass filter used for the OMC REFL PD signal set to 300 Hz, four peaks were observed within one 300 Hz modulation cycle (Fig. 4). Since the FSR of the cavity is approximately 2.2 MHz, these peaks are believed to correspond to SRY flashes. Furthermore, when the modulation rate was reduced to 100 Hz and the cutoff frequency of the SR560 high-pass filter was also reduced to 100 Hz, four peaks were again observed within one 100 Hz modulation cycle (Fig. 5). However, the noise level was higher than in the case with the 300 Hz cutoff frequency.

Measured TFs from the IP actuator to the ACCs (or FLDACCs) showed increasing gain toward DC below 70mHz for L and 50mHz for T as reported in klog. It is due to the cradle effect. It is difficult to correct the gain using general servo filters. We are considering whether feedforwarding can reduce the gain at low frequencies. I tried to create ACC L signals compensated by the low-passed signals offline. Plot 1 shows the used low-pass filter. Plot 2 shows time-domain data of LVDT, ACC, and low-passed ACC signals. The IP L was excited with the IP actuator during 300~1500sec. Plot 3 shows the ratio of the LVDT TF and the ACC TF. The gain with compensated signals was smaller than the original, but the phase difference was larger.