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.
|
|
PRP |
PRY |
BSP |
BSY |
|
AA_EP |
1 |
|
1 |
|
|
AA_EY |
|
1 |
|
1 |
|
AA_IP |
1 |
|
1 |
|
|
AA_IY |
1 |
1 |
1 |
1 |
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.
