Stefan, Yuta, Kiwamu
We have measured the length sensing matrix in the sideband locked PRMI. The data is now under analysis and will be posted later.
Also since we now know that the in-vac REFL is functional (see alog 10661), we switched the PRMI sensors from the in-air one to the in-vac one. This is a permanent change and in fact, it is already reflected in the guardian.
Preparations (adjustment of PD gains and demod phases):
After we locked the PRMI with the sidebands resonant, we re-adjusted the demod phases such that the PRCL signal is maximized in all the in-phase paths. This was done by inserting a new notch at 100 Hz both in MICH and PRCL filters and exciting PRM with an amplitude of 30000 cnts at the output side of the LSC. We used dtt to check the demod phases. The new settings are now:
- REFL_A_RF9 = 84.9 deg
- REFL_A_RF45 = 19.2 deg
- REFLAIR_A_RF9 = 90 deg
- REFLAIR_A_RF45 = 144.6 deg
- REFLAIR_B_RF27 = 91.8 deg
- REFLAIR_B_RF135 = 76.3 deg
We didn't phase the POP detectors this time as we were focusing on the REFL detectors. Also, we changed the PD gain in the digital system to make all of them identical to REFLAIR_45. This was meant to make the calibration easier. The new gain settings are now:
- REFL_A_RF9_I(Q)_GAIN = 0.252
- REFL_A_RF45_I(Q)_GAIN = 0.275
- REFLAIR_A_RF9_I(Q)_GAIN = 1.040
- REFLAIR_A_RF45_I(Q)_GAIN = 1 (because this was chosen to be the reference for everyone else)
- REFLAIR_B_RF27_I(Q)_GAIN = 0.210
- REFLAIR_B_RF135_I(Q)_GAIN = 1 (we didn't do it on this guy for some reason)
At this point, we could see all the I-phase signals beautifully overlaid on each other in the spectrum.
The measurement:
We then moved on to the measurement of the LSC sensing matrix. We continued shaking PRM with the same amplitude of 30000 cnts. We left the notches in at 100Hz to avoid surpression from the LSC control loops. Since we wanted to quickly get a result, we decided to use dtt instead of the online lockins. Monitoring the DAC of BS, PRM and PR2 suspensions we didn't observe a saturation during the measurement. Good. All the 1f detectors had a whitening gain of 0 dB while REFL_RF27 and REFL_RF135 had a whitening gain of 27 dB and 21 dB respectively. We set the bandwidth of the FFT to be 0.1 Hz and averaged it by 10 times. Note that the PRCL loops should have a UGF of about 35-ish Hz and the MICH loop should have a UGF of about 10-ish Hz. So the excitation is above the UGFs.
As for the MICH sensing matrix measurement, we tried three different excitations -- (1) excitation on the diagonalized combination of PRM and BS at 100 Hz, (2) excitation on only BS at 100 Hz, and (3) excitation on ITMs at 18 Hz. The third configuration was not really successful in a sense that we didn't see a big excitation. Also we didn't spend a long time to study the optimum excitation on ITMs this time.
In the first and second excitation configurations, we injected an excitation with an amplitude of 300 cnts above of which the BS saturated at its DAC. Since the excitation was puny, we narrowed dtt's bandwidth down to 0.01 Hz this made the coherence somewhat better.
A permanent change -- in-vac locking:
We did nothing special to switch the sensor from the in-air to in-vac. We simply set the LSC gains right. Currently REFL_A_RF45_I is for PRCL and REFL_A_RF45_Q. for MICH. We then confirmed that the in-vac detector grabbed the PRMI fringe without a problem. Also we noticed that the in-vac Q-signal contained less noise by a factor of 5-ish (actually I forgot the exact number, sorry) above 30 Hz and therefore the BS DAC should be happier now.
Additionally, we confirmed that we could still transition to the 3f diodes smoothly by the guardian.
PRMI sensing matrix elements measured are as follows;
===PRM actuation===
== Raw data
REFL_A_RF9_I 1.57e-03 +/- 2.27e-05 counts/counts (err: 1.4 %)
REFL_A_RF9_Q -2.21e-06 +/- 4.34e-07 counts/counts (err: 19.7 %)
REFL_A_RF45_I 1.58e-03 +/- 2.14e-05 counts/counts (err: 1.3 %)
REFL_A_RF45_Q 7.43e-06 +/- 1.98e-06 counts/counts (err: 26.7 %)
REFLAIR_A_RF9_I 1.60e-03 +/- 2.22e-05 counts/counts (err: 1.4 %)
REFLAIR_A_RF9_Q 2.95e-06 +/- 4.30e-07 counts/counts (err: 14.6 %)
REFLAIR_A_RF45_I 1.60e-03 +/- 2.09e-05 counts/counts (err: 1.3 %)
REFLAIR_A_RF45_Q 1.30e-05 +/- 1.80e-06 counts/counts (err: 13.9 %)
REFLAIR_B_RF27_I 1.58e-03 +/- 2.22e-05 counts/counts (err: 1.4 %)
REFLAIR_B_RF27_Q -4.41e-06 +/- 5.33e-07 counts/counts (err: 12.1 %)
REFLAIR_B_RF135_I 1.02e-03 +/- 2.57e-05 counts/counts (err: 2.5 %)
REFLAIR_B_RF135_Q -6.73e-06 +/- 1.05e-05 counts/counts (err: 155.7 %)
== Calibrated data (calibration error is not included in the error shown below)
REFL_A_RF9_I 1.51e+06 +/- 2.18e+04 W/m (err: 1.4 %)
REFL_A_RF9_Q -2.12e+03 +/- 4.17e+02 W/m (err: 19.7 %)
REFL_A_RF45_I 5.44e+05 +/- 7.34e+03 W/m (err: 1.3 %)
REFL_A_RF45_Q 2.55e+03 +/- 6.81e+02 W/m (err: 26.7 %)
REFLAIR_A_RF9_I 1.41e+06 +/- 1.97e+04 W/m (err: 1.4 %)
REFLAIR_A_RF9_Q 2.61e+03 +/- 3.81e+02 W/m (err: 14.6 %)
REFLAIR_A_RF45_I 4.75e+05 +/- 6.22e+03 W/m (err: 1.3 %)
REFLAIR_A_RF45_Q 3.86e+03 +/- 5.37e+02 W/m (err: 13.9 %)
REFLAIR_B_RF27_I 7.72e+03 +/- 1.09e+02 W/m (err: 1.4 %)
REFLAIR_B_RF27_Q -2.15e+01 +/- 2.60e+00 W/m (err: 12.1 %)
REFLAIR_B_RF135_I 1.78e+02 +/- 4.47e+00 W/m (err: 2.5 %)
REFLAIR_B_RF135_Q -1.17e+00 +/- 1.82e+00 W/m (err: 155.7 %)
===BS-0.5*PRM actuation===
== Raw data
REFL_A_RF9_I 4.69e-05 +/- 9.95e-07 counts/counts (err: 2.1 %)
REFL_A_RF9_Q -1.62e-05 +/- 2.12e-07 counts/counts (err: 1.3 %)
REFL_A_RF45_I 4.68e-05 +/- 1.08e-06 counts/counts (err: 2.3 %)
REFL_A_RF45_Q -8.04e-05 +/- 5.47e-07 counts/counts (err: 0.7 %)
REFLAIR_A_RF9_I 4.73e-05 +/- 1.40e-06 counts/counts (err: 3.0 %)
REFLAIR_A_RF9_Q -1.60e-05 +/- 6.25e-07 counts/counts (err: 3.9 %)
REFLAIR_A_RF45_I 4.66e-05 +/- 1.57e-06 counts/counts (err: 3.4 %)
REFLAIR_A_RF45_Q -8.04e-05 +/- 9.60e-07 counts/counts (err: 1.2 %)
REFLAIR_B_RF27_I 3.10e-05 +/- 6.23e-06 counts/counts (err: 20.1 %)
REFLAIR_B_RF27_Q -3.30e-05 +/- 9.95e-06 counts/counts (err: 30.2 %)
REFLAIR_B_RF135_I -3.56e-04 +/- 4.16e-04 counts/counts (err: 116.6 %)
REFLAIR_B_RF135_Q 1.16e-03 +/- 2.22e-04 counts/counts (err: 19.1 %)
== Calibrated data (calibration error is not included in the error shown below)
REFL_A_RF9_I 4.87e+04 +/- 1.03e+03 W/m (err: 2.1 %)
REFL_A_RF9_Q -1.68e+04 +/- 2.20e+02 W/m (err: 1.3 %)
REFL_A_RF45_I 1.74e+04 +/- 4.02e+02 W/m (err: 2.3 %)
REFL_A_RF45_Q -2.99e+04 +/- 2.03e+02 W/m (err: 0.7 %)
REFLAIR_A_RF9_I 4.53e+04 +/- 1.34e+03 W/m (err: 3.0 %)
REFLAIR_A_RF9_Q -1.53e+04 +/- 5.98e+02 W/m (err: 3.9 %)
REFLAIR_A_RF45_I 1.50e+04 +/- 5.05e+02 W/m (err: 3.4 %)
REFLAIR_A_RF45_Q -2.59e+04 +/- 3.09e+02 W/m (err: 1.2 %)
REFLAIR_B_RF27_I 1.64e+02 +/- 3.29e+01 W/m (err: 20.1 %)
REFLAIR_B_RF27_Q -1.74e+02 +/- 5.25e+01 W/m (err: 30.2 %)
REFLAIR_B_RF135_I -6.69e+01 +/- 7.80e+01 W/m (err: 116.6 %)
REFLAIR_B_RF135_Q 2.18e+02 +/- 4.16e+01 W/m (err: 19.1 %)
===BS only actuation===
== Raw data
REFL_A_RF9_I 8.01e-04 +/- 5.85e-06 counts/counts (err: 0.7 %)
REFL_A_RF9_Q -1.54e-05 +/- 2.82e-07 counts/counts (err: 1.8 %)
REFL_A_RF45_I 8.05e-04 +/- 5.85e-06 counts/counts (err: 0.7 %)
REFL_A_RF45_Q -6.80e-05 +/- 1.06e-06 counts/counts (err: 1.6 %)
REFLAIR_A_RF9_I 8.12e-04 +/- 6.26e-06 counts/counts (err: 0.8 %)
REFLAIR_A_RF9_Q -1.21e-05 +/- 5.48e-07 counts/counts (err: 4.5 %)
REFLAIR_A_RF45_I 8.13e-04 +/- 6.26e-06 counts/counts (err: 0.8 %)
REFLAIR_A_RF45_Q -6.52e-05 +/- 1.24e-06 counts/counts (err: 1.9 %)
REFLAIR_B_RF27_I 8.09e-04 +/- 1.04e-05 counts/counts (err: 1.3 %)
REFLAIR_B_RF27_Q -1.63e-05 +/- 6.16e-06 counts/counts (err: 37.7 %)
REFLAIR_B_RF135_I 4.21e-04 +/- 2.67e-04 counts/counts (err: 63.3 %)
REFLAIR_B_RF135_Q -5.33e-04 +/- 2.51e-04 counts/counts (err: 47.2 %)
== Calibrated data (calibration error is not included in the error shown below)
REFL_A_RF9_I 1.18e+06 +/- 8.60e+03 W/m (err: 0.7 %)
REFL_A_RF9_Q -2.26e+04 +/- 4.14e+02 W/m (err: 1.8 %)
REFL_A_RF45_I 4.23e+05 +/- 3.08e+03 W/m (err: 0.7 %)
REFL_A_RF45_Q -3.57e+04 +/- 5.54e+02 W/m (err: 1.6 %)
REFLAIR_A_RF9_I 1.10e+06 +/- 8.48e+03 W/m (err: 0.8 %)
REFLAIR_A_RF9_Q -1.64e+04 +/- 7.42e+02 W/m (err: 4.5 %)
REFLAIR_A_RF45_I 3.70e+05 +/- 2.85e+03 W/m (err: 0.8 %)
REFLAIR_A_RF45_Q -2.96e+04 +/- 5.64e+02 W/m (err: 1.9 %)
REFLAIR_B_RF27_I 6.04e+03 +/- 7.79e+01 W/m (err: 1.3 %)
REFLAIR_B_RF27_Q -1.22e+02 +/- 4.60e+01 W/m (err: 37.7 %)
REFLAIR_B_RF135_I 1.12e+02 +/- 7.09e+01 W/m (err: 63.3 %)
REFLAIR_B_RF135_Q -1.41e+02 +/- 6.68e+01 W/m (err: 47.2 %)
Errors shown are statistical errors for this measurement (using coherence, number of averaging and the formula in alog #10506) and calibration errors are not included. The sensor calibration and the actuator calibration has roughly ~10% error (see for example, alog #9630 and #10213).
For the sensor calibration (counts/W),numbers in H1PRMI awiki was used. For the actuator calbiration (m/counts), numbers in alog #10724 (see comments) was used. "m" in these units are either cavity one-way length change, or MIchelson one-way length difference between X and Y. However, "BS only" ones are calibrated in BS motion (since BS changes MICH by sqrt(2) and PRCL by 1/sqrt(2) ). 'W" in these units are the amplitude of modulated laser power (before demodulation).
PRM to I signals in counts/counts look alike since we adjusted the PD filter gains to be that way. PRM to Q signals are significantly smaller than I as a result of demodulation phase adjustment.
BS-0.5*PRM actuation is supposed to be pure MICH actuation, but since it is not true perfectly, both I signals and Q signals show up.
[Data and script]
Raw data and the script to calbirate data lives in
/opt/rtcds/userapps/release/lsc/h1/scripts/sensmat../sensemat_20140312_PRCL_part3.xml(dtt of PRM actuation)./sensemat_20140312_MICH_100Hz_part1.xml(dtt of BS-0.5*PRM actuation)./sensemat_20140312_MICH_100Hz_part2.xml(dtt of BS only actuation)./sensmat_20140312_PRCL.txt(magnitude, phase, and coherence data for each PD extracted manually from dtt)./sensmat_20140312_MICH.txt(magnitude, phase, and coherence data for each PD extracted manually from dtt)./calibPRMsensmat.py(script for calibration, putting signs and errors to the data)The formula from Bendat is correct for simple cases, but, as you might guess, its not right in the case where you have finite overlap between FFT segments. Otherwise, you could choose a 90% overlap and get much less calculated uncertainty for the same total length of data, than what you get with the DTT default of 50%. (i.e. two overlapping data segments have a finite correlation)
For the usual DTT parameters of 50% overlap + Hann window, the effective number of averages is:
Nave_equiv = 1.89 * (T_total / T_fft)
(cf. Chapter 10 of http://books.google.com/books/about/Noise_and_Vibration_Analysis.html?id=-1DSxrlhL5sC )
I see the point that we have to include the overlap into the formula for error estimation.
But if the overlap is 50%, (T_total/T_fft) will be (Nave+1)/2. So, Nave_equiv = 1.89 * (T_total / T_fft) = 0.945 * (Nave +1). This means that Nave_equiv will be more than Nave when Nave < 18. This this true?