Delaying until 1am. Since SUS will not be done until midnightish and ISI is locked. These matlabs are running on opsws0.
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:
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:
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.
Mitchell, CPS racks were put together. Class A probes sorted. CPS sub assemblies started and nearly completed. Probes will be attached to their sub assemblies and staged on the ISI to be attached at a later date.
The IOC had apparently stopped running. I telneted into the procServ for it on h0epics and it automatically restarted. I burtrestored it.
9:00 Apollo craning LVEA
9:15 Gerardo EY for PCAL prep/inventory
9:15 Aaron EX to look at cabling
9:30 JeffB & Andres to HAM4/5 area for SUS work, out at 11:00
9:30 Keita to EY for ISCTY
9:45 Jodi to MidY
9:45 Betsy and Travis to EY for quad
10:00 Hanford Fire on-site
13:00 Karen to EY for cleaning, back 14:30
13:15 JeffB & Andres to HAM4/5
13:30 Jodi to MidY
13:30 Jonathan to MidY, back 14:00
14:45 Hanford Fire leaving
15:30 Vern to LVEA, out 15:45
15:30 Cyrus to MidY to return a PEM chassis
After TMSY work on monday I took some overnight measurements yesterday night to check for rubbing, and compared the results with model and TMSX data.
TF looks suspiciously different in the vertical degrees of freedom (VERT and ROLL) than TMSX and model, which indicates that there is probably still something blocking the table to move freely.
Per Keita's request, attached is a comparison between the TMSY last year in April and yesterday night
After lunch we went back to EY to find the mechanical grounding in the ETMy reaction chain. After a while we spotted a top mass MRB block (hanging part) brushing the tablecloth (structure part). Our pitch alignment earlier in the day caused the top mass to pitch into the structure. We could not adjust the structure out of the way* so we adjusted pitch to alleviate the brushing. The reaction chain pitch has a ~1.47mRad tolerance and we are still within this at ~860uRad. Quick low-coherence TFs looked promising so we are restarting the night run full suite Matlab TFs.
*We could not adjust the table cloth easily since 1) everything is suspended - ISI and HEPI included so it all bounces to the lightest touch, 2) the ACB is now mounted and difficult to maneuver around, and 3) the table cloth serves purpose for both chains simultaneously so adjusting it for one chain somewhat anti-adjusts it for the other chain - too risky at this point.
-Betsy, Travis
As a reference, I attached the results from the main and reaction chain transfer functions taken yesterday night, showing how the rubbing due to one of the vertical EQ stops affects the TF (2nd attachement).
Related: PUM P2P and Y2Y inversion filters:
https://alog.ligo-wa.caltech.edu/aLOG/index.php?callRep=10610
I injected into PUM drivealign P2P, through P2P inversion filter, and measured the TF from injection to the OL P (red thick) and Y (red thin dashed). Did the same thing to Y2Y to OL Y (blue thick) and P (blue thin dashed).
In a frequency band where I managed to get a high coherence (0.2Hz to 4Hz) P2P and Y2Y look pretty good. Also P2Y is good. However, Y2P (blue thin dashed) looks problematic between 1 and 2Hz (and maybe 0.4-0.6Hz).
I'll make a Y2P filter that eliminate this.
Apollo (Mark, Scotty), Greg Grabeel Taking advantage of the window in between the work on HAM 4 and HAM 5, Apollo installed the HWS viewports. Because of the hole pattern on the flange they are not able to be pointing directly down in regards to the scribe on the face, but they are fairly close. Hopefully close enough that the slotting on the light pipe will make up any difference.
Last night, we finally obtained successful transfer function data on both the main and reaction chains of the ETMy. As expected, the main chain looked clean (we'd taken sneak peeks prior). However, the reaction chain looked bad. So, we went out and found a tough-to-see earthquake stop touching the reaction chain top mass. This cleaned up the TFs. However, alleviating the stop made the reaction chain pitch change. Realigning the chain made the lower stage sensors fall out of range of course. After fixing all of these, we discovered the TF's had again gone to h*ll. I scrutinized the EQ stops, all flags, and all other potential spots for mechanical interference. Finding nothing in error, I gave up for lunch. TFs of the main chain are still clean so the interference must not be between the chains but to the structure, BOSEMs, or EQ stops. Will go hunting again after lunch.
We'll need to abort the spool replacement effort scheduled for this afternoon since we will continue to need the IAS equipment set up there until this QUAD satisfies both alignment and noise parameters. As usual, it is difficult to get a QUAD to satisfy both at the same time. I expect another round of TFs to be taken tonight since convincing ones self that the TFs look good is particularly difficult during low-coherence daytime measurements.
I committed an update to ^/trunk/Common/MatlabTools/SingleModel_Production that optionally corrects (for the single model only at this point) a long-standing known error with the B matrix in the Matlab state space for all models (single, double, triple, quad), whereby the coupling from structure pitch to optic longitudinal was zero.
The trouble is that the SS matrix elements have been derived for infinitely flexible wire. For realistic, stiff wire, the wire flexure correction would ideally be implemented with code like the following
where dblade, dpitch, dyaw1 and dyaw2 are the vertical and horizontal offsets to the wire attachment points, flex0 is the vertical component of the flexure length, and si0 and c0 are sine and cosine of the angle of the wire to the vertical. This amounts to insetting the ends of the wire by one flexure length at each end. However for historical reasons there is no dblade or analogous quantity defined in any of the Matlab models for the very top wire attachment, so that line has had to be left out. The A matrix turns out completely OK because it only depends on the shortening of the wire - the pendulum has effectively been hitched up by flex0 because dblade couldn't be increased, but it retains all the same pendulum resonances. However it has the effect of zeroing out the structure pitch to optic longitudinal coupling in the B matrix, because even with dblade=0, there's supposed to be a lever arm of flex0.
The impetus to fix this is that Fabrice has been doing a series of experiments with a seismometer mounted as an pendulum with the same structure as for HAUX/HTTS (two blades, two wires), and is seeing a coupling from pitch of the structure. Therefore it is of interest to have a debugged model with the proper pitch-to-longitudinal coupling for comparison purposes.
To implement the fix, I created a new Mathematica model with an explicit dblade parameter, ^/trunk/Common/MathematicaModels/TwoWireSimpleBladesED (ED=extra "d"), updated the Matlab-export code to match, and exported a new set of Matlab matrix elements symbexport1bladesEDfull.m. I then hacked ssmake1MBf.m to use these elements when pend.dblade is defined. The usual use case will be pend.dblade=0, but other values also work. The attached plot is generated by edplot.m and shows the P to L transfer function for the default case of the TwoWireSimpleBladesED model which has dblade=0.001 and flex0=0.0009687. The plot generated from the Matlab model is in blue, and is exactly overlain by comparison data exported from the equivalent Mathematica in red.
As might be hoped, the value at f=0 is -(dblade+flex0)= -0.0019687. The sign is negative because +pitch is right-handed around +y=left, i.e., nose down, so as pitch increases the effective flexure point moves backwards. See the attached diagram.
For now I'll manually post these but soon these will be posted by a robot.
model restarts logged for Tue 11/Mar/2014
2014_03_11 09:57 h1ioppemmy
2014_03_11 10:05 h1ioppemmy
2014_03_11 10:06 h1ioppemmy
2014_03_11 10:14 h1ioppemmy
2014_03_11 10:15 h1ioppemmy
2014_03_11 10:16 h1ioppemmy
2014_03_11 10:46 h1asc
2014_03_11 11:12 h1lsc
2014_03_11 13:25 h1ioppemmy
2014_03_11 13:26 h1ioppemmy
2014_03_11 13:27 h1ioppemmy
2014_03_11 13:27 h1pemmy
2014_03_11 21:37 h1lsc
2014_03_11 22:02 h1lsc
2014_03_11 22:06 h1lsc
2014_03_11 11:40 DAQ Restart
They weren't empty but they were wrong. The IPS raw signals only became useful Monday after we finished the final alignments after the Actuator connection. So if you care (likely not) about the ETM HEPI position before now (0955pdt) you'll have to look at the local coordinates. Now you can look at the cartesian values for positions. Remember, I zero'd (<50 counts, 655cts.0.001" or 38.8nm/ct) Monday. The raw IPS are all running under 300cts now (HEPI is still unlocked) but the ACB weight decreased slightly yesterday and I'm not surprised to see a little drift as well. The cartesian are all running under 10um or urad and most much less. The nominal position for control will be zero.
Yesterday we tacked both doors on HAM4 with four bolts. We did not complete a chamber closeout checklist: we are not going to pump down on this volume until after we revisit alignment of the SR2 there, i.e. we cannot pump down until going back in and completing the closeout.
I re-measured BS and PRM actuation transfer functions in PRY configuration after plant inversion done on Mar 5 (see alog #10559).
It seems like we succeeded in BS and PRM balancing within ~8 % and MICH to PRCL coupling is expected to be supressed by factor of ~4, compared with using only BS as an actuator.
For the sensing matrix measurment, the effect of residual MICH to PRCL coupling gives ~6 % error for MICH to REFL45Q element and ~16000 % error for MICH to REFL45I element.
[Motivation]
Before measuring the PRMI sensing matrix, we wanted to estimate how good output matrix diagonalization is.
[Method]
1. Lock PRY and measure open loop transfer function. Compare it with the model to derive optical gain.
2. Measure actuator transfer function of BS and PRM from ISCINF to REFLAIR_RF45_I_ERR in PRY (using the same template used in alog #10450). Calibrate these TFs into m/counts with the optical gain derived in step 1.
3. Closed loop correct TFs measured in step 2. TFs should look like 1/f^2 at 1-300 Hz (see comments on alog #10450). Since output matrix for MICH in PRMI are set to (BS,PRM)=(1,-0.5), these TFs should be equal (see alog #10559 and table below).
-table of actuation efficiency (optic motion to interferometer length change in m/m)-
PRY PRCL MICH
BS sqrt(2) 1/sqrt(2) sqrt(2)
PRM 1 1 0
4. Calculate expected actuator TFs for MICH to PRCL coupling using the measured TFs. BS ISCINF to PRC length change will be half as that of PRY. BS-0.5*PRM gives the residual MICH to PRCL coupling.
[Result]
1. OLTF_PRCL_1078572000.png: Openloop transfer function of PRY lock. By comparing with the model, this gives PRY optical gain of 1.8 W/m. So, the calibration factor for REFLAIR_RF45_I_ERR in PRY is 4.7e11 counts/m. Note that this calibration factor includes losses in the PD signal chain (e.g. loss from long cable). Also, note that PRM suspension model was 30 % off from the measurement (see #10482; measurement = 0.77 * SUS model). This correction factor is included in the model to derive the optical gain.
2. BSandPRMact_PRY.png: Measured actuator transfer functions for BS and PRM in PRY. x marks show raw measured TFs and dots show closed loop corrected ones. After closed loop correction, actuator TFs look like they follow 1/f^2. From the fit, BS actuator TF is 1.79e12 Hz^2/f^2 m/counts and PRM actuator TF is 1.93e12 Hz^2/f^2 m/counts for PRY. Considering the error bar from coherence and cavity build up fluctuation during the measurement, this 8% difference between BS and PRM is significant (error bars in TF magnitude are derived using the formula in alog #10506). We have done the balancing with the precision of ~10%, so this difference is reasonable.
3. BSandPRMact_MICH2PRCL.png: Estimated MICH to PRCL coupling from actuator diagonalization. Blue dots show BS ISCINF to PRC length change and red dots show BS and PRM combined actuator to PRC length change. Fitted lines show that MICH to PRCL coupling is expected to be supressed by factor of ~4 by actuator balancing. We can improve this supression ratio a little bit by changing the gain balancing between BS and PRM by 8%, but it's not easy to improve more and prove we did more.
[Is this enough?]
This means that our MICH actuator (BS - 0.5*PRM) changes MICH length by 1.79e12 Hz^2/f^2 m/counts and PRC length by 2.06e11 Hz^2/f^2 m/counts. According to Optickle simulation in LIGO-T1300328, sensing matrix for PRMI sideband is
PRCL MICH
REFL 45I 3.4e6 2.5e3
REFL 45Q 6.4e4 1.3e5 W/m
So, the estimated effect of residual MICH to PRCL coupling to the sensing matrix measurement is;
MICH to REFL45Q element: 6 % error (= 6.4e4/1.3e5/(1.79e12/2.06e11) )
MICH to REFL45I element: 16000 % error (= 3.4e6/2.5e3/(1.79e12/2.06e11) )
If we ignore MICH to REFL45I element, which is hard to measure anyway, I think this is acceptable.
[Next]
- Update gain balancing factor between PRM and BS from 1/16 to 1/14.7 (FM5 in H1:SUS-BS_M3_LOCK_L)
- Update IQ demod phase in H1:LSC-REFLAIR_A_RF45_PHASE_R to minimize PRCL to MICH coupling
- Measure sensing matrix in PRMI
After talking with Yuta, I took a look at our PRM M3 to M3 transfer functions, measured with the osems as actuators and sensors, and compared it with the model. We see a factor difference of ~20% (model=1.18*measurement). This would mean the calibration error comes from the actuation chain (both of us are using T1000061 as a reference for calibrating actuation).
I did the calibration of the error signal wrong. The calibration factor 4.7e11 counts/m was correct, but I multiplied this number to the measured data in the script, instead of dividing.
Correct figures are attached. Actuator calibration from the fitting is as follows
BS to PRY: 8.13e-12 Hz^2/f^2 m/counts (half of this is BS to PRCL in PRMI)
PRM to PRY: 8.79e-12 Hz^2/f^2 m/counts (same as PRM to PRCL)
BS-0.5*PRM to MICH: 8.13e-12 Hz^2/f^2 m/counts (same as BS to PRY)
BS-0.5*PRM to PRCL: 9.28e-13 Hz^2/f^2 m/counts
Discussion about MICH to PRCL supression ratio and sensing matrix measurement error from actuation off diagonal element remain unchanged.
Also, note that my definition of MICH is one-way length difference between BS to ITMX and BS to ITMY. PRCL is PRC one-way length.
[Data and script]
Data and script used lives in ~/yutamich/BSPRMact/ folder.
./PRMdrive_complete.xml (dtt of PRM actuation TF measurement)
./BSdrive_complete.xml (dtt of BS actuation TF measurement)
./PRYoltf_complete1.xml (dtt of PRY OLTF measurement)
./BSPRMact.py (script for plotting and calibrating data)
Assuming the frequency calibration of the network analyzer is accurate, we can compare the measured PRC length with the measured mode cleaner length. This was measured in alog 9679.
| Parameter | Value | Unit |
|---|---|---|
| FSRPRC | 2.600075 | MHz |
| LPRC | 57.6508 | m |
| FSRMC | 9.099173 | MHz |
| LMC | 16.473612 | m |
| FSRMC / 3.5 - FSRPRC | -306 | Hz |
| (1 - FSRMC / 3.5 FSRPRC) LPRC | 6.8 | mm |
Compared with the modeclaner, the power recycling cavity is about 7 mm too short. The other way around, the modecleaner is about 2 mm too long.
We hooked up the network analyzer to the timing comparator/frequency counter and set it to 40 MHz sharp at 0 dBm. The readback value was dead on, occasionally we would read 1 Hz higher. Conclusion: the frequency of the sweep is no more than 1 Hz off, even at 100 MHz.
I've redone the fits using both the magnitude and the phase. The fitting function is now the usual Fabry–Pérot reflectance function, with a complex magnitude to allow for global amplitude rescaling and global phase offset.
| Nominal FSR | Frequency (Hz) |
| −39.5 | −102 701 040 ± 200 |
| −39.5 | −102 700 900 ± 220 |
| −26.5 | −68 900 600 ± 180 |
| −12.5 | −32 500 080 ± 100 |
| 12.5 | 32 501 720 ± 110 |
| 26.5 | 68 903 940 ± 200 |
| 39.5 | 102 704 700 ± 200 |
The linear fit now gives an FSR of (2 600 073 ± 9) Hz. This is consistent with the previous fit, and anyway the total error is still dominated by some systematic, as seen by the fact that the residuals are excessively large.
Taking a systematic 400 Hz uncertainty on the residual for the 12.5 FSR measurement gives a systematic uncertainty of 32 Hz on the PRC FSR. Propagating foward gives (57.6508 ± 0.0007) m.
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?