Matteo and Yuhang

As reported in elog2300, we optimized mode matching and mixer. We obtained a larger CCFC error signal after that. Then we used it to lock the filter cavity length for IR. Control loop information is summarized as follows:

1. Gain of CCFC loop: 50
2. Corner frequency of CCFC loop: 30Hz (one order low pass)
3. Error signal shape: figure 1
4. Open loop transfer function (only CCFC part): figure 2 (40mVpk-pk excitation used)
5. Error signal spectrum (loop on/off): figure 3.
6. Calibration for error signal: AOM speed (4000Hz/2.5s)(figure 4) divided by error signal slope around zero (75mV/43.7ms)(figure 1 and 5) divided by 2 (AOM scan green to IR) : 4000*43.7/2.5/75/2 = 466 Hz/V

We could see that the CCFC method stabilized length noise for IR below ~1kHz. The IR length noise reached 2.3Hz after closing the CCFC loop. Compared with the old case, we could see that the main difference in IR length noise is around 1kHz~10kHz. The reason for this difference is still unknown. But if the CCFC error signal can go back to the old case, the CCFC loop can reduce IR length noise to less than 1Hz.

By changing CCFC demodulation phase, CCFC error signal offset should change in a sinusoidal way. I checked this after the optimization of mixer. The result is in attached figure 1.

I checked the histogram of CCFC and CC1 error signal. This check is after the mixer optimization.

We could see that strange behavior of histogram reported in elog2302 disappeared.

Matteo and Yuhang

As reported in elog2289 and elog2302, the demodulated signal from mixer ZX05-1L-S+ has strange behaviors, such as not exactly sinusoidal or strange data distribution. We realized these issues but we didn't know what is the reason.

On 2020/22/07, we checked two quadrature-phase signals of CCFC error signal while CC1 phase is scanned more than 2pi. While checking, we found these two quadrature-phase signals were not the same. Attached figure 1 shows these two signals.From this figure, the quadrature-phase signal is quite similar with sinusoidal shape while the in-phase one is quite linear between each maximum and minimum. After observing this difference, we start to investigate what is the difference between these two channels.

Comparison of these two channels:

1. The RF signals come from the same PD, the LOs come from the same channel of DDS3

2. LO signal is splitted by ZMSCQ-2-90, RF signal is splitted by ZFDC-10-1-S+

3. They use the same mixer ZX05-1L-S+ and the same low pass filter SLP-1.9+

The splitting of LO makes one LO ~11dB smaller than the other one (The splitting of LO should give identical output. However, there is difference due to frequency issue.). The splitting of RF makes one RF ~10dB smaller than the other one. (RF signal is about -3dBm before splitting)

In the end, we found the problem comes from LO. We were using ~-6dBm LO, which is smaller than the datasheet requirement. However, in practice, this mixer needs even smaller LO (-12dBm LO is used now).

When CC1 is locked and the filter cavity is detuned, the CCFC error signal only shows an offset. This field should be identical with CC1 error signal if offset is not considered. Before the optimization of the mixer, we checked the histogram of this offset. From the attached figure, we could see that this histogram has some problems (no data located in the center). It could come from an oscillation of this signal.

We should recheck it after the optimization of the mixer. 

The filter cavity GR lock's OLTF may differ with the filter cavity GR+IR lock's OLTF at low frequency. Therefore, we start to investigate GR OLTF's low-frequency part.

In the attached figure, there are four measurements. Their legends are listed in the sequence of time on 2020/12/07. We could see that:

1. All measurement shows flat gain at low frequency, which is different from what we expect.

2. Morning and evening measurements' magnitude are quite different at low frequency. The reason for this difference is still unknown.

3. Measurement phases are different with/without SR560 (just passing through without gain/filters). We could see that the phase margin is better if SR560 is used.

Matteo and Yuhang

Based on Aritomi-san's code, I add the degradation from mode-matching to the CCFC error signal. The simulation result is in attached figure 1. From this simulation, worse mode-matching makes CCFC error signal degrade around resonance. But mode-matching doesn't affect the CCFC error signal's offset.

Based on this simulation, we sent BAB to the filter cavity and checked the mode-matching was about 0.75. We found the IR drift happened only in the yaw direction. After optimizing yaw, mode matching increased to about 0.9. When we checked the CCFC error signal's pk-pk value, we found some issues with this signal's demodulation. After optimizing the mixer, we saw an even better CCFC error signal. The comparison of CCFC error signals before and after optimization is in attached figure 2.

I compared the mm-optimized/mm-original CCFC error signal's minimum. In the simulation, the ratio is 0.64. While in measurement, it is 0.58.

We took a spare PSD and replaced the old one for PR Oplev. The spectrum of PSD was measured and shown in figure 1. We can see that the new PSD has higher noise than the reference. Apart from that, the new PSD also shows different peaks, which needs to be further examined.

TAMA PSD for PR pitch show excess noise again, the situation is shown in the figure 1.

I attached OLTF of CCFC and green lock. Note that I flipped the sign of measured data to match the measurement and theory. The measured phase is not consistent with theory.

In elog1727, I tuned CC PLL frequency from the fitting of CC separation frequency and CC PLL frequency, but the error of the fitting parameters is quite large with respect to optimal CC separation frequency 108 Hz. So this method is not precise to decide the correct detuning.

As written in elog2294, current CCFC error signal is not consistent with theoretical plot with optimal detuning, but instead it is similar to the theoretical plot with 25 Hz detuning.

If the current detuning is 25 Hz, we have to change the detuning by 29 Hz to obtain optimal detuning 54 Hz. Using the formula in elog1727, the CC PLL frequency has to be changed by 2*29 Hz/1.907605 =  30.41 Hz. Since the current CC PLL frequency is 6.99704303 MHz, optimal CC PLL frequency should be either 6.99707344 MHz or 6.99701262 MHz. I checked both cases by looking at CCFC error signal and found that 6.99701262 MHz is correct one (In DDS, 6.99701253 MHz was set). 

Here is the new CC PLL setting. I saved this setting as 20201126_dds3_CCFC.

Attached plot shows CCFC error signal with different CCFC demodulation phase. Amplitude of the CCFC error signal is normalized with 83mV which is the amplitude of CCFC error signal when CCSB are off resonance of FC and CC1 is scanned.

Now the shape of CCFC error signal is similar to theoretical plot. In addtion to that, zero crossing point of blue curve in second plot is around 58Hz which is almost optimal detuning.

CCFC error signal with 25 Hz detuning is very similar to the measurement.

Actually, the errors of the fitting parameters are -1907605 +/- 36859 and 13347486 +/- 257882. This error is quite large with respect to 108 Hz. We need to fine tune CC PLL frequency by looking at CCFC error signal.

By the way, optimal detuning should be 54 Hz. I attached CCFC error signal with optimal detuning. Normalized offset for I phase is 0.81 in the plot.

I checked that for optimal detuning (70Hz), the expected in-phase demodulation CCFC error signal should have normalized offset 0.91.

In this measurement, we got the in-phase demodulation CCFC error signal normalized offset to be about 0.69. I checked that for this normalized offset, the detuning set by PLL will be 43deg.

The calculation is in the attached figure.

By looking at the normalized offset-removed plots, it seems for different demodulation phase, they have the 'same' peak but just somtimes folded.

If we compare it with calculation, it seems the measured peak is a factor of 2 smaller than calculation.

It has been a long time that we found CCFC error signal measurement doesn't match well with calculation. Recently, we found that this might be due to an offset, as reported in elog2286.

The CCFC error signal is equation 14/15 in Aritomi paper, which can be written as proportational to sin(a_p-a_m+a0_m-2d_p). Please check details from arxiv:2004.01400.

Here a_p and a_m are the upper and lower sidebands phase change caused by the filter cavity. When the filter cavity has detuning much larger than linewidth (70Hz), a_p-a_m will be close to zero. a0_m is the lower sideband phase change caused by the filter cavity when carrier detuning is optimal. When we change the demodulation phase of CCFC, we add another term phi_d to the sine function.

Therefore, in the case that FC is locked and detuned to 1kHz (CC1 locked), the CCFC error signal will be sin(a0_m+phi_d). Since a0_m is a fixed number, we expect to measure a shifted sine wave when scanning phi_d (from 0 to 2pi). For each phi_d, we expect an 'offset' from zero. We got a 'shifted' sine wave from the experiment. The result of this measurement is in the first attached figure. There is also a sinusoidal plotted in this figure. We could see that the measurement matches with sinusoidal. The difference still needs to be investigated (one further check could be a measurement of error bar for each point, the other could be to plot a histogram of measured data)

To double-check this expected offset, we performed the filter cavity scan around resonance (CC1 locked, FC locked while AOM scanned). The CCFC error signal for different phi_d is in the attached figure2. If we subtract the measured offset from figure2, we got figure 3. Not surprisingly, all offsets of CCFC error signals were removed. Thus we know this offset agrees with the calculation.

Then the question comes: why we saw a different CCFC error signal in an experiment different from a calculation that is not caused by an offset problem?

If we compare figure 2 with the calculation, we could see that every time the CCSBs cross resonance of the filter cavity, the appeared peak seems to be not deep enough. So we guess the problem is related to how the filter cavity changes the CCSBs phase when they cross resonance.

This not ideal CCSBs phase change could be caused by mode mismatch/misalignment or PLL setting. More investigation is required.

Recently we are investigating HAMAMATSU PSD to be used for Oplev. This is due to the noise increase observed for BS Oplev spectrum, which was pointed out to be caused by PSD.

Last Friday, a similar problem was found also in PR Oplev. As shown in the attached figure 1 and 2, the PR Oplev noise has different noise increase at different time.

I also checked PR Oplev spectrum this Monday, the spectrum became normal as attached figure 3.

Oil under the rotary pump was there from the old days. I replaced the rotary pump to new dry pump (ACP15). The TMP with the dry pump is working now at the mid point.

DDS3 CH2 (14MHz) was split to used for both CC1 and CCFC demodulation so far. To change these demodulation phase independently, we used DDS3 CH3, which is usually used for CC2 demodulation, for CCFC demodulation. We changed CC1 and CCFC demodulation phase independently and checked CCFC error signal. We confirmed that changing CC1 demodulation phase is identical to changing CCFC demodulation phase for CCFC error signal.