To understand the noise contribution from PR/BS to the AA signal, we did several measurements and calculations. They are reported in elog2266 and elog2270. However, the sum of contribution was not done in the way of quadrature sum. So the results shown in elog2266 and elog2270 are not correct. Besides, elog 2270 used TFs which were measured without excitation. This should be replaced with TFs which are measured with excitation. This is due to that excitation can make the measurement of TF have more coherence. So we follow the same way of calculation with elog2270, except for the TFs and the noise sum method.

The measurement of TFs was done by exciting PR pitch, PR yaw, BS pitch, and BS yaw one by one. We call the measured TF with the style of TF_PRP_IP, which stands for the transfer function from PR pitch to INPUT pitch.

The quadrature sum of noise projection to INPUT pitch follows the equation:  IP = PRP*TF_PRP_IP + PRY*TF_PRY_IP +BSP*TF_BSP_IP +BSY*TF_BSY_IP. Here mirrors angular motion use name-style PRP to stand for PR pitch motion.

The results of noise projection and measurement is attached. Note that the data of PR/BS oplev signals and AA signals are directly from DGS. So the value itself doesn't correspond to a meaningful unit.

From this result, PR and BS angular motion are not the limiting noise of AA signals, except for INPUT pitch.

At the beginning of AA implementation, we checked balance (between each segment of QPD), demodulation phase (this is equavilent demodulation phase set in DGS, which can rotate the input I/Q signals by a matrix. In our case, we rotate signals to I phase.) and rotation angle (this is the quavilent rotation of QPD). All of these were done without the lock of AA loop. And we found some change from day by day.

Since now we have AA locked. I checked them again and optimized accordingly. The old work gave already quite good gain/phase/angle values. For example, in the first two attached figures, we can see the balance situation of QPD1 and 2. The balance is already quite good. Since we could get exact values from figrue 1 and 2. I calculated the required gain to balance them. After applying these gain, the balance situation is shown in the attached figure 3 and 4. We can see that the balance becomes much better. But if this will change again from day by day should be examined later.

(Old gain is 1 for each segments.) New gain is shown in the following table

After that, I also optimized the demodulation phase. The result is shown in the attached figure 5 and 6.We could see that only negligible signals go to Q phase. This should also be checked again later.

New phase is shown in the following table

Then, the rotation angle was also optimized. The optimization result is shown in the attached figure 7 and 8. However, we could see that pitch to yaw coupling has become already around 15% in WFS1/2. This should also be checked later if they will change or not.

Old rotation angles are all zero. New angles are shown in the following table

In the end, a new matrix was developed to close AA loop. The loop filters/gains are the same with the old case. A comparison of diagonalized signals are shown in the attached figure 9. It can be seen that they don't have large difference.

By measuring the transfer function from PR/BS p/y motion to Input/End diagonalized signals, we could calibrate PR/BS p/y motion to Input/End diagonalized signals. As a result, we could know how much PR and BS angular motion are contributing to the diagonalized AA signals (Input/End diagonalized signals).

Some measurement situation: The transfer function measurement was done without excitation. PR/BS local control was closed. 

Reconstruction method: Let's take reconstruction of Input_p as an example. Input_p = PR_p*TF + PR_y*TF + BS_p*TF + BS_y*TF. This means that we sum PR/BS p/y motion's contribution to AA diagonalized signal. (Here PR_p/y and BS_p/y signal is directly the oplev signal without any modification. The Input_p signal is also directly from DGS system)

The results are shown in attached figures. We could see that AA diagonalized signals are almost totally limited by PR/BS angular motions.

I measured SHG cavity scan to check finesse of SHG (Pic. 1,2). The fitting result doesn't match the measured data very well possibly due to the non symmetric peak shape. From the fitting, I obtained SHG finesse of 43, but this is not consistent with design value of 72. 

Takahashi-san, Tanioka

We installed a quadrupole mass spectrometer (Q-mass) to the cryostat as shown in the attached picture.
I will try to take data from next Monday.

After the AA loop could be closed with high UGF, the locking noise was not checked again. So I did this check today.

The PR and BS local control was closed all the time. Then I measured locking noise when AA loop is closed or open. The result is shown in the attached figure.

The locking noise level is much higher than the one reported in elog2231, which has lower AA UGF.

If we compare the shape of the locking noise spectrum, it is very similar with the diagonalized AA_INPUT_PIT.

The transfer function from PR/BS motion to AA diagonalized signal was measured and reported in elog2265. We were thinking to use this TF and PR/BS motion to reconstruct the AA diagonalized signal. Then we would like to compare this reconstructed signal with the measured AA diagonalized signal. We want to do this comparison because we found the AA diagonalized signal is higher than the corresponding INPUT/END oplev signal. This was reported in elog2245, which was strange for us because AA singal is usually less noisy.

Therefore, we measured the TF from PR/BS p/y to AA diagonalized signals when excitation was sent to PR/BS. As reported in elog2265, the coherence is only large enough between around 10 to 40Hz(the spectrum below 10Hz is not considered because the higher AA noise is mainly found above 10Hz). This was later figured out that, as shown in the attached figure 1, the excitation send to PR/BS make their motion higher than PSD noise level above 10Hz. In the usual case (no excitation), as shown in the attached figure 2, the spectrum above 10Hz is bascially PSD electronic noise.

Therefore, to calibrate PR/BS motion to AA diagonalized signal, I took one point above the PSD noise level while avoiding peaks or large deviation. After that, I assume the spectrum has 1/f2 slope because the measured AA diagonalized signal has also 1/f2 slope. And I got the attached figure 3 as the spectrum of PR/BS p/y motion above 10Hz.

To combine TF and PR/BS motion, I checked the coherence of TF. Since we have p/y coupling in AA, we found the PR/BS motion has the following coupling contribution for AA diangonalized signal.

Here '1' means PR/BS motion will contribute to AA. For example, AA_EY (reconstructed) = PRY*TF(PRY to AA_EY) + BSY*TF(BSY to AA_EY)

In this way, I got the reconstructed AA signal as shown in the attached last four figures. (measured AA signal is also shown for comparison). Note that the spectrum above 30Hz is not compared because there was no coherence.

The reconstruction fit well for END mirror. But the reconstruction is higher than the measurement for INPUT mirror.

Since we want to know if the AA diagonalized signals are dominated by PR/BS motion. So we want to use a transfer function to calibrate PR/BS motion into AA diagonalized signals. There is excitation sent to PR/BS p/y when the measurement is done. The excitation is as following:

The measurement of transfer functions are attached as four figures. It is shown in them that there were some coherence between 10~20Hz. We could multiplify this spectrum with PR and BS oplev signal and compare it with the diagonalized AA signal.

After the discussion with Eleonora and Matteo, I modified the filters for AA. For old and new filters, the comparison of AA diagonalized signal is shown in the attached figure. (Blue is the old case, red is the new case)

The new filter configuration is as following:

It was reported that PR/BS local brings noise to AA. However, after the replacement of BS PSD, the AA diagonalized signal shows no difference when PR/BS local control is on or off.

The comparison of the old case (blue curve: local control increase noise around tens of Hz) and the new case (red curve: local control doesn't increase noise) is shown in the attached figrue.

To buy or make a new PSD, the gain of PSD is an important and necessary information. Therefore, I measured it as following.

The wavelength of the used laser is 635nm. I set this wavelength for the laser power meter. Then I checked the 635nm laser power used in PR chamber. It was 0.28mW.

Then I measured the PR PSD sum voltage with oscilloscope, which is 11.4V.

Therefore,the high gain PSD should have gain of 40.7 V/mW.

I forgot to measure the size of PSD, but it seems to be 1 inch. I will confirm.

As reported in elog 2258, the BS PSD showed large noise last Friday. I checked also today, the noise is still present. So we decide to replace it. As also mentioned in elog 2258, we have only a spare low-gain PSD. So we decide to use SR560 to amplify its output.

The only two SR560 could be used are the one used for CCSB lock and the one used for FC length control (feedback to END mirror). So I temporary took them and used to amplify the low-gain PSD. As shown in the first attached figure, there is a comparison of the PSD. It shows that resistors have a ratio of 100,000:500. Therefore, I set the gain of 200 for the two SR560 for PSD's pitch and yaw.

Then I compare the spectrum of this PSD with the old high-gain PSD. This is shown in the attached figure 2. It is clear that the gain of 200 is too much. I adjusted it to 50 and then, as shown in the attached figure 3, old and new spectrums match around several Hz. It is also shown in this figure that the noise floor of new PSD above 10Hz is generally smaller.

Then I checked the local control of BS also works well.

Since we have p/y coupling in AA diagonalized matrix. To remove this coupling, the pitch and yaw singal cannot be separated as before.

I modified the k1fds simulink file and now there is possibility to mix yaw to pitch or mix pitch to yaw. In this way, the pitch yaw coupling could be removed.

The new matix window is shown in the attached figure.

The oplev p/y sensing coupling was optimized long time ago. SInce recently we compare AA diagonalized signal with oplev signal. We decide to check again the oplev p/y coupling again.

The PR and INPUT have not obvious p/y coupling as shown in the attached figure 1 and 2. But there is coupling for end mirror (as shown in the attached figure 3), which was removed by putting PSD rotation angle to be zero (as shown in the attached figure 4).

Long time ago, we had issue of BS PSD pitch which shows large noise at high frequency (see elog1642). Today, we found BS PSD pitch noisy again. And this time, the spectrum is as shown in the attached figure 1, which is even worse.

To make sure it is the problem of PSD, I replaced it with another PSD, which has smaller gain. Then the spectrum is as shown in the attached figure 2. As we can see, the pitch spectrum is fine. Therefore, the old BS PSD really has some problems.

I also discussed with Eleonora, she suggested me to buy/make a new one.

The problem is solved by using directly a long ethernet cable between computer and picomotor box.

Today, when I align filter cavity, I found the output of Input pitch is very large. As shown in the first attached figure, the H3 coil has an output of 30,000. This is reaching the maximum of coil.

So I tried to offload this value with picomotor. However, there is an error coming out when I use labview to move picomotor. The error is shown in the attached figure 1. To fix this problem, I did following check:

1. We tried to move PR picomotor, which worked. Therefore, the Labview should work well. And the network connection of the old PC should be also fine.
2. We checked the ethernet cable connection to the picomotor box. But the cable is connected to a high cable (as shown in the attached figure 2). So it is not very easy to check if the cable is correct or not. But anyway, this cable is connected.
3. We also tried to plug in and out the power cable for picomotor box, which didn't solve the problem.
4. We checked also the IP address of picomotor box, which is consistent with the one used in Labview.

However, the picomotor still didn't work. I have already sent Takahashi-san an email to ask how to solve this problem.

The measurement is the same with the last comparison of AA/oplev except for that the PR/BS local control is off.

But even in this case, the AA signal is still higher than oplev signal.

This coherence check was done between PR/BS oplev singal and AA diagonalized signal. Note that there is no excitation sent to PR/BS, but the PR/BS local control loop was closed.

Note: blue curves are PR/BS local control open, red curves are PR/BS local control closed.

We could see a strong coherence between PR pitch/yaw oplev signal and AA.

Therefore, the PR local control seems to be introducing noise in pitch/yaw from 10 to several tens of Hz.

This coherence check was done between PR/BS oplev singal and AA diagonalized signal. Note that there is no excitation sent to PR/BS, the PR/BS local control loop was open.

It can be seen that there is almost no coherence above 10Hz. I think this is also reasonable, because PR/BS motion at high frequency should be similar.