J. Kissel, E. Hall

See Evan's entry here: LHO aLOG 18770.

We still need to double check it, and I'm sure we've made a mistake or two, but we think we've installed as much as we can based on the results of the DARM Open Loop Gain transfer functions we have compared against a model (see LHO aLOG 18769) and of the actuation coefficient measurements (see LHO aLOG 18767)

For lack of better quantitative understanding of the DARM OLGTFs we have, we should still consider this calibration at an accuracy of 50% and 20 [deg]. (At least it's better than the factor of two promised :-/ ).

Note that we have NOT yet updated the inverse actuation function in the hardware injection path. Sorry -- but that'll have to wait until the morning.

We've still got plenty more to do and understand, but thanks to all who have helped over the past 1.5 weeks. You help has been invaluable, and much appreciated!!

P.S. IF NEED BE -- one can revert to the old CAL-CS calibration by switching back to ETMX, then reverting to the former sensing function via the filter archive.

J. Kissel, K. Izumi, E. Hall

We've put together a model of the new DARM loop after (a) all of our core CDS electronics been replaced (DAC, AI filters, AA filters, I/O chassis power supplies you name it), (b) a low-noise, low voltage driver on our ETMY, and (c) reshaping of the hierarchical control scheme to account for the new driver's lack of drive strength. 

The message -- we've still got some work to do to get back to the level of understanding we had of the frequency dependence before the above mentioned changes. As such, we have to inflate the frequency dependent uncertainty in the run back to 50% in magnitude and 20 [deg] in phase. Indeed, because the frequency dependence of residual between model and measurement is so large, it's difficult-at-best to make a statement about the optical gain (overall sensing function scaling factor), even though we have so accurately and precisely measured the actuation scale factors (LHO aLOG 18767).

For the time being, we'll use an optical gain of 1.31e6 [ct/m] in the sensing path, having scaled the model to match the OLGTF measurement at the UGF (for the first two measurements shown). Further, we'll stick with a DARM coupled cavity pole frequency of 355 [Hz], since it had been so for the few lock stretches we'd gotten before all the electronics hubbub.

--------
Details:
The model lives in 
/ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/PreER7/H1/Scripts/DARMOLGTFs/H1DARMOLGTFmodel_ER7.m, 
the parameters with which to match the three measurements are in the functions
H1DARMparams_1116854228.m (for 2015-05-28 measurement)
H1DARMparams_1116990382.m (for 2015-05-30 measurement)
H1DARMparams_1117124229.m (for 2015-05-31 measurement)

Since the first 2015-05-28 measurement is with the low noise ESD driver's low pass engaged, and the last 2015-05-31 measurement had a poorly scaled control system (see discussion below), we should use the parameter set and model from the second 2015-05-30 measurement.

TIME DOMAIN CALIBRATORS -- THIS PART'S FOR YOU
The model(s) have been seen saved to the following .mat file:
/ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/PreER7/H1/Results/DARMOLGTFs/2015-06-01_LVLNDriver_DARMOLGTF.mat
(apologies, it still composed of frequency response vectors, I didn't have time to convert everything to LTI objects).
The total actuation function is model(2).par.A.total with a delay of model(2).par.t.actuation microseconds.
The total sensing function is model(2).par.C.total with a delay of par.t.sensing + par.t.armDelay microseconds.
The stuff that's included in this model already that we don't plan on putting in the CAL-CS model that should be included in the GDS pipeline:
Actuation: 
     The digital and analog anti imaging filters -- model(2).par.A.antiimaging.total 
     The super-Nyquist-frequency pole of the new driver -- model(2).par.A.esdDriver.fc (at 2.42e4 [Hz]) << this one's tricky to include given the new hierarchy, just leave it out if you don't get how to do so.
Sensing
     The digital and analog anti aliasing filter -- model(2).par.C.antialiasing.total
     The super-Nyquist-frequency poles of the OMC whitening -- model(2).par.C.uncompensatedomcdcpd.c (at 13.7e3 and 17.8e3 [Hz])
END TIME DOMAIN PART

What we've learn about / explored so far trying to clean up the model:
- We need to invert the sign of the L3 / ESD stage in order to get the phase to even closely match the measurement. We have a couple of theories on this, and our "best" is that the charge is so large on ETMY that it's effectively flipping the sign of the ESD actuator. We saw hints of this during our ALS DIFF and FS MICH actuation coefficient measurements, but didn't need to pay attention to them at the time. Now (not that we weren't before, but), we should perform the same sign checks that Shivaraj and co performed at LLO (see LHO aLOG 18406).
- We've been have problems for the past month or so with our optical gain fluctuating, and I think we've narrowed it down to poor compensation / scaling of the OMC during the hand off to DCPDs. We thing we've addressed this now here: LHO aLOG 18768, but the last open loop gain transfer function (I took it -- LHO aLOG 18733) in which I had incorrectly scaled the DARM loop gain to compensate for the poor scale factor should probably, eventually, be thrown out. I kept it in this data set, simply because we've had so few, and one needs at least three to make a pattern.
- Recall the first measurement was taken with the new ESD driver's low pass filter engaged, and I release while writing this aLOG that I didn't properly include that in the model. However, I've received a spice model of the driver with and without the low pass engaged, so I've fit the poles and zeros to be
par.A.esdDriver.poles_Hz = [159.1 2.42e4]; % [Hz] 
par.A.esdDriver.zeros_Hz = 3189.4; 
see /ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/PreER7/H1/Scripts/Spice/model_LVLN_driver_20150601.m
- We did NOT have time enough to include all of the recent measurements of the analog AA and AI filters, but we're currently using the mean of the some 200 measured filters as before, and we don't expect this to have too much of an influence in the gravitational wave band. Certainly not the source of the bonkers frequency repsonse residual we have at the moment.
- We need to include the above poles and zeros properly into the ESDOUTF bank, and change the ESD driver's state machine so that it can handle all of the different configurations of the driver. After ER7.
- Now that we're using a sort of hybrid offloaded AND distributed control scheme for the three actuation stages of ETMY, we needed to rethink the loop math, specifically how each stage should be added together. In short, it changes from a simple
A_TOTAL = LOCK_L1 * SUS_L1toL3 + LOCK_L3 * SUS_L3toL3;
to a nasty
A_TOTAL =   LOCK_L1 * LOCK_L2 * LOCK_L3 * DRIVEALIGN_L1_L2L * SUS_L1toL3 
          + LOCK_L2 * LOCK_L3 * DRIVEALIGN_L2_L2L * SUS_L2toL3 
          + LOCK_L3 * DRIVEALIGN_L3_L2L * SUS_L3toL3

(plus the sign flip in front of the last term mentioned above).
- We've double checked and triple digital filters and gains, which are being read in from the foton file archive, so we're 80% confident (as confident as one can be at 3am) that we're not stupidly loading in bad filters or anything. 

That's all I've got steam for at the moment. I'll see y'all in the morning.

Dan, Jeff B, Evan

Some guardian tweaks to be aware of:

• Some settings in the OMC guardian were changed so that the AS45Q → OMC DC scaling factor calculation is more robust. The averaging time for the data is slightly longer, and the scaling is taken to be the median rather than the mean. Over the course of five lock acquisitions today, we measured the DARM OLTF both before and after transitioning to dc readout, and we did not see any degredation of the loop gain.
• On several occasions, the roll mode damping gains in the guardian were too large and caused lockloss. Therefore, they are now reduced by a factor of 5. The full gains are set in the DC_READOUT state.

J. Kissel, K. Izumi, S. Karki

I've culminated the results of the three different measurement techniques for determining the actuation strength of all three stages of ETMY, 
- Laser Wavelength: Free-swinging Michelson LHO aLOGs 18718
- Voltage Controlled Oscillator: ALS DIFF VCO LHo aLOG 18711
- Photon Radiation Pressure: Photon Calibrator LHO aLOG 18758 (Only for ETMY L3)
The numbers quoted below are what will be used in DARM model we'll use during ER7, which we'll then use to update the GDS pipeline and CAL-CS models.

    'Optic'      'Weighted Mean'    '1-sigma Uncertainty'    '1-sigma Uncertainty'
    'Stage'      '[m/ct]'           '[m/ct]'                 '%'                  
    'ETMY L1'    '5.12e-11'         '8.6e-13'                '1.7'                
    'ETMY L2'    '6.97e-13'         '1.2e-14'                '1.8'                
    'ETMY L3'    '6.07e-15'         '1.4e-16'                '2.4'                
    'ETMX L3'    '3.56e-13'         '8.2e-15'                '2.3'

See attached for a graphical representation of how the individual results compare against the weighted mean and uncertainty (Wikipedia).

Recall that all of these numbers' uncertainty arises from either the statistical uncertainty of the individual measurements which compose the result (i.e. the coherence of the transfer function), or a compression of each frequency point in a TF into one number via weighted means and uncertainties. In no way have we accounted for systematic uncertainty other than comparing using the three different methods (for ETMY L3 at least). Very encouraging that they agree to within 2.5%!

We have enough data to propagate PCal's number for L1 and L2 of ETMY, but we've just run out of time. However, we've found that with the other two methods (Free-swinging MICH, and ALS DIFF) that the L1 and L2 stages agree with the dead-reckoned model to within 4%, and we don't at all expect these actuators to be varying with time like we do the ESD stages.

Note that the ratio between EX and EY's ESDs confirms the factor of ~50 that was needed when scaling EX to EY during the initial attempts to relock the IFO with the low noise driver.

Further, it's encouraging to see that three measurement techniques each of which take several hours (save PCAL) taken over the course of a few days. I'm still not convinced that the actuation strength didn't actual increase between the FS MICH and ALS DIFF measurements (since they're all systematically higher), but we just need more data to confirm. However, now that we trust that PCAL agrees with ALS DIFF and FS MICH, we can focus our energy on PCAL. Surdarshan's working on grabbing past lock stretches from the frames and assessing how this coefficient has varied over time.

Observation Bit: Commissioning 

16:20 Take IFO to LCS_FF 
16:27 Lockloss – 
16:45 RO system down – Reset system
18:23 IFO locked at DC_Readout_Transition – Dan taking measurements
18:25 IFO locked at DC_Readout – Evan taking measurements
18:28 Increase ISS Diffracted power from @ 3% to 8%
18:33 IFO locked at LSC_FF 
18:35 Set Observation bit to Undisturbed
18:46 Set Observation bit to Commissioning – Dan working on OMC
18:49 Lockloss – Guardian recovering
19:22 Lockloss at DC_Readout – Guarding recovering
19:48 Lockloss at DC_Readout_Transition – Guardian recovering 
	     Evan & Dan working on Bounce, Roll, and Violin damping	
20:40 IFO locked at LCS_FF
20:53 Lockloss – Guardian recovering
22:00 Run initial alignment
23:00 Running Guardian locking

It seems that the pitch control signal sent to SR2 (from the AS_C sensor) is correcting mostly for motion of SR3, especially in the first hour after powering up. We should think about changing this feedback from SR2 to SR3 after the engineering run.  

Sudarshan, Duncan, Branson, Andrew, Michael T, Greg, Dave:

I got a lot further in installing the GRB alert system at LHO. It now runs, but fails after a couple of minutes. Here is a summary of the install:

LHO and LLO sysadmins decided to run the GRB code on the  front end script machine (Ubuntu12). At LHO it is called h1fescript0

I requested a Robot GRID Cert for this machine, Branson very quickly issued the cert for GraceDB queries last Friday

Following Duncan's and the GraceDB install instructions, I was able to install the python-ligo-gracedb module. The initial install failed, Michael resolved this, I was using the Debian Squeezy repository (which uses python2.6) rather than Wheezy which uses python2.7.

Greg told us how to install the GRID cert on the machine and setup the environment variable so the program could find it.

I found a bug in the code for the lookback, it appears the start,stop times were reversed in the arguments to client.events().

For testing, I saw that a GRB event had happened within the past 10 hours, so I ran the program with a 10 hour lookback. It found the event and posted it to EPICS (see attachement)

But afer running for several minutes, it stopped running with an error. This is reproducible.

controls@h1fescript0:scripts 0$ python ext_alert.py run -l 36000
Traceback (most recent call last):
  File "ext_alert.py", line 396, in
    events = list(client.events('External %d.. %d' % (start, now)))
  File "/usr/lib/python2.7/dist-packages/ligo/gracedb/rest.py", line 450, in events
    response = self.get(uri).json()
  File "/usr/lib/python2.7/dist-packages/ligo/gracedb/rest.py", line 212, in get
    return self.request("GET", url, headers=headers)
  File "/usr/lib/python2.7/dist-packages/ligo/gracedb/rest.py", line 325, in request
    return GsiRest.request(self, method, *args, **kwargs)
  File "/usr/lib/python2.7/dist-packages/ligo/gracedb/rest.py", line 200, in request
    conn.request(method, url, body, headers or {})
  File "/usr/lib/python2.7/httplib.py", line 958, in request
    self._send_request(method, url, body, headers)
  File "/usr/lib/python2.7/httplib.py", line 992, in _send_request
    self.endheaders(body)
  File "/usr/lib/python2.7/httplib.py", line 954, in endheaders
    self._send_output(message_body)
  File "/usr/lib/python2.7/httplib.py", line 814, in _send_output
    self.send(msg)
  File "/usr/lib/python2.7/httplib.py", line 776, in send
    self.connect()
  File "/usr/lib/python2.7/httplib.py", line 1157, in connect
    self.timeout, self.source_address)
  File "/usr/lib/python2.7/socket.py", line 571, in create_connection
    raise err
socket.error: [Errno 110] Connection timed out
 

Sudartian, Darkhan, Jeff, Kiwamu,

On this past Saturday, Sudartian, Darkhan and Jeff did a Pcal sweep in full lock on ETMY in order to complete the series of the calibration measurements we did in the past weekl (alog 18711 for ALS diff, alog 18718 for MICH free swing).

The point of doing three different techniques this time was to get an accurate calibration of the ETMY suspension responses such that we can reliably estimate the optical gain of DARM by measuring a DARM open loop transfer function. Again, we did not evaluate systematic error yet and all uncertainties come from statistical errors. Here is the result:

- - - -

ETMY ESD was weaker than the suspension model by 0.3932 +/- 0.0018

This corresnonds to an ESD force coefficient of 7.864e-11 +/- 3.7e-13 [N/V^2]

If we scale this value to 1 mHz, the actuator response of ESD is 5.951e-15 +/- 2.8e-17 [meters/counts]

- - - -

[The measurements]

In full lock, they swept the Pcal line from 2 to 7 Hz with an amplitude of 3e4 counts at PCALY_SWEPT_SINE_EXC and with the same number of data points as the other two methods. This basically gives us counts/meters calibration at DARM_IN1 which is of course suppressed by the DARM loop. Then they measured a transfer function from ETMY ESD to DARM_IN1 within the same lock stretch. Since we already knew the suppression from the previous Pcal sweep measurement, dividing the ETMY drive transfer function by the calibrated Pcal transfer function give us the ETMY response. Here are the plots showing the main results:

As you can see the measured ESD response was weaker than what the suspension model predicted by a factor of roughly 0.4. This is consistent with the other two methods (alog 18711 and alog 18718). Since the Pcal actuation strength was not big enough to have a good signal-to-noise ratio, the data below 4 Hz had low coherence and this is exactly the reason why the error bars are so large below 4 Hz. In addition, it seems that there is an phase offset of about 25 degrees in the measurement. This may be an indication of inaccurte suspnsion model in the Pcal calibration where they use a 1 / (1 + if)^2 response for the suspension response.

For completeness I post some other relevant plots:

• Pcal excitation, monitored at DARM_IN1 (3rd attachement)
• ETMY L3 drive to DARM_IN1 (4th attachment)

The analysis codes, data, and figures can be found in the usual svn place:

• aligocalibration/trunk/Runs/PreER7/H1/Measurements/PCAL2DARMTFs
• aligocalibration/trunk/Runs/PreER7/H1/Scripts/PcalETMs
• aligocalibration/trunk/Runs/PreER7/H1/Results/PcalETMs

09:22 Gerardo moving auxiliary pump cart out of LVEA
09:25 Gerardo done
09:40 Fire department car through gate
11:46 RO alarm, Bubba investigating
12:48 Tour in control room
13:15 5.9 EQ off Oregon coast breaks lock
15:10 Richard to end Y to look at cold cathode gauge used for high voltage ESD interlock
15:39 Richard back

Locking went well until the EQ off the coast of Oregon. Investigations primarily centered on why DARM optical gain is changing between locks.

J. Kissel, K. Izumi

While we were showing Sudarshan some things, we recalled that FM3 of the 
H1:CAL-CS_DARM_ANALOG_ETMX_L3
bank included a filter to compensate the 2e3 pole for the high voltage ESD driver. Since we'll be using ETMY for the engineering run, which has a new low noise driver without this pole, we have turned this filter off.

First update to the CAL-CS calibration for ER7 woo!

This change was seen by the SDF system, and I've accepted the change.

J. Kissel

Since we seem to have asymptotically approached the conclusion that we will NOT be engaging the new ESD driver's low pass filter for ER7, and ODC people are complaining that their numbers aren't green, I've restored the gain of the hardware injection bank to 1.0.

This re-increased the continuous wave injection amplitude to its originally intended value (see LHO aLOG 18681).

This had been reduced to 0.1 a few days ago when we were trying to commission the low noise driver in hopes we could get it running for ER7 (see LHO aLOG 18699).

Since Evan saved us from the case when the Oplev damping gets enabled while the suspension is in the damped, but not aligned state (thus having too little light on the QPD for the loop to work), we decided to enable the LIMITS.  (Thx Evan and Sheila)

LIMITs of 50 have been enabled on the ITMX and ITMY L3 OPLEV PIT and YAW loops.

LIMITs of 150 have been enabled on the BS L3 OPLEV PIT and YAW loops.

I've accepted these changes in SDF.

With the help of commissioners, I have been cleaning house on the SDF alarms today and last Fri.  Still a few to go...

However, when we switched a few things on some SUSes today during one of the lock loss periods, we noticed that the SDF put a strange time stamp on the DIFF.  See the ITM DIFFs attached.  We added a LIMIT value and turned the LIMIT switch on all within the same few minutes just now.  However, on both the ITMs (and the unpictured BS) the switch time stamp shows last Wed at ~11:57am.  What the heck?

Laser is ON
Output power is 33.1 W (should be about 30 W)
Watchdog is active
PSL SYSSTAT: VB program online is red, LRA out of range is red (only VB program online should be red)

PMC
Last relock 6 days, 1 hour ago (should be days/weeks)
Reflected power is ~ 11% of transmitted power (should be 7% or less)

FSS
Locked 1 hour (should be days/weeks)
TPD is ~ 1.4 V

ISS
Diffracted power is around 5.5% (should be around 7%)
Last saturation event was ~ 1 hour ago (should be days or weeks)

In the first observation intent time from today, there are DAC glitches in MC2 M3. They don't obviously appear in DARM at the time we checked, but they do appear in a number of channels. The first plot is an Omega scan showing glitches in MC_L, and the second shows that they correspond to zero crossings in MC2 M3 control.

THIS ALOG DISAPPEARED FROM THE ALOG LAST NIGHT, THIS IS A REPOST.

J. Kissel, K. Izumi

I've finished the analysis of the calibration of the H1 SUS ETMY actuators that are involved with global DARM control, where we've used the "free swinging Michelson method" (i.e. using the IR laser's wavelength as a frequency / length reference). The results are as follows:

    'iStage'     '[m/ct] @ DC'    '1-sigma Unc.'
    'ITMX L2'    [ 3.9461e-13]    [    0.013313]
    'ETMX L3'    [ 8.0906e-14]    [    0.026998]
    'ETMY L1'    [  4.851e-11]    [    0.026588]
    'ETMY L2'    [ 3.8468e-13]    [    0.026885]
    'ETMY L3'    [ 1.4543e-15]    [    0.027057]

The messages:
- Kiwamu is still finalizing his analysis, but we can safely see that a similar calibration using the ALS DIFF VCO as a frequency / length reference agrees with the above results.
- Assuming the ETMX ESD driver's DC gain is 40 [V/V] and the new ETMY driver's DC gain is 2 [V/V], then this translates to an ESD force coefficient of
    'optic'      '[N/V^2]'
    'ETMX L3'    [2.21e-10]
    'ETMY L3'    [7.96e-11]
This means that the ETMY ESD drive strength is 2.78 times weaker than ETMX.
- Though we've used the  full complex transfer functions for transfer function ratios and multiplication to get the final answers for each stage, what discrepancies we find in the phase of the final transfer function that determines the magnitude answer are ignored. This is because we determine the phase response / frequency dependence of the DARM actuator and DARM Sensor collectively when comparing the DARM Open Loop Gain Transfer Function against a model of the full loop, e.g. LHO aLOG 18186.
Curiosities that don't affect the answer, but are none-the-less irksome:
- We need to flip the sign of the measurement of the ITMY L2 stage drive to MICH, the ETMX L3 stage drive DARM, and the ETMY L3 stage drive to DARM in order for the overall phase of the final results to make sense.
- The phase of the ETMY L2 stage is offset from the model by ~10 [deg]. 
- We'll now use the above numbers to change the DC calibration of the DARM model parameter file that has been used for creating the DARM loop model, compare against a DARM OLGTF measurement and therefore make a statement about the optical gain.
- This method of determining the actuation coefficient -- especially for the very weak ETMY L3 stage -- is *very* time consuming, cumbersome and only gets quality results in the 4 to 7 [Hz] band, therefore we should do it rarely if at all in the future. PCal should become our new standard technique of determining the actuation coefficients and these kind of measurements should be the checks!

-------
Details
-------
MEASUREMENT METHOD
A lot of the methodology for this calibration technique has been outlined before (see most recently LHO aLOG 14135, most clearly (IMHO) P0900120, and originally in T030097), but I'll repeat it briefly here, because one needs to understand how we've augmented the technique further in order to obtain the ETMY L3 actuation strength.

One begins with the measurement from which the technique gets its name:
(A) After locking and aligning the IFO into a dark Michelson configuration (with PRM, SRM, and the ETMs misaligned), break the lock and measure the AS port's demodulated Q-phase signal ("AS_Q") and DC power ("AS_DC") while the Michelson freely swings through fringes. For the aLIGO IFO, that's H1:LSC-MICH_IN1_Q (a scaled version of H1:LSC-ASAIR_A_RF45_Q_ERR_DQ) and H1:LSC-ASAIR_A_LF_OUT, and we grabbed ~300 [sec] worth of data. As the Michelson evolves through fringes the AS_Q error signal proportional to the displacement of the mirrors:

AS_Q = (1/2) * A_{pp} * sin( (4*pi/lambda) * dl )             (1)

where A_{pp} is the peak-to-peak amplitude of the signal, lambda is the laser wavelength, and dl is the Michelson displacement, (lx - ly). We assume that the displacement is small (thanks SEI team!) such that 

AS_Q ~ A_{pp} * (2*pi/lambda) * dl = k * dl                   (2)

leaving the AS_Q signal proportional to the Michelson displacement by a real constant, k, the optical gain of the Michelson. Over the years, we've found that simply taking the peak-to-peak of the fringing time-series is prone systematic errors in determining A_{pp} due to drifts in alignment during the long uncontrolled stretch. As such, we've taken advantage of the sin / cos relationship of AS_Q and AS_DC and plot the ellipse they form as the Michelson fringes. We chuck up the long time series into several smaller time series and plot the ellipses, fit each to determine the semi-major axis of the AS_Q vs. AS_DC ellipse, and take the mean of each fit's semi-major axis to determine A_{pp} (see first page of attached). Because the fit of each chunk is a measurement of the inherent value of A_{pp}, we assign the standard error of the mean (i.e. d(A_{pp}) = std( A_{pp}^{i} ) / sqrt(N) ) as the uncertainty. For this measurement, 

k = 1.112e+08 +/- 1.7181e+05 [(MICH Displacement [m])/ (MICH Sensor [ct])]


(B) We eventually want to drive a given stage of the ITMs to determine the actuation strength of that stage with our newly calibrated MICH sensor, MICH_IN1 (AS_Q). However, we need the Michelson locked on a dark fringe so that the MICH error signal remains linear. So we must measure the MICH loop suppression. Now with the MICH locked, measure the MICH_IN2 / MICH EXC loop suppression transfer function. A little bit of loop math will show that 

MICH_IN2 / MICH EXC = 1 / (1 + G_{M})                          

as desired. Note that one *could* measure the open loop gain transfer function, G_{M}, directly, as MICH_IN1 / MICH_IN2 = - G_{M}, but for ease of uncertainty propagation, we've just measured the suppression directly. The open loop gain and suppression are shown in pgs 2 and 3. The uncertainty for each frequency point is determined from the coherence of the measurement and the number of averages,

                         1 - C  
d|TF| =  |TF| *  sqrt ( ------- )  [ same units as |TF| ]
                         2 C N  
                                                              (3)
                  1 - C  
d <(TF) = sqrt ( ------- )   [ rad ]
                  2 C N   

ref LHO aLOG 10506, or originally Bendat and Piersol, "Random Data" 2nd Ed, p317.

(C) Pick any stage of either ITM and take a driven transfer function of iStage ITM drive to MICH_IN1. With the data from (1) and (2), create an absolute calibration of this [(MICH IN1 [ct])/ (iStage ITM drive [ct])] transfer function in terms of [m] by inverting the optical gain and loop suppression:

  ITM Optic disp. [m]      MICH IN1       1            
--------------------- = ( ---------- ) * --- * (1 + G)                                       (6)
iStage ITM Drive [ct]      ITM EXC        k           

                              MICH IN1 [ct]            MICH [m]        MICH IN2 [ct]  -1          
                      = ( --------------------- ) * ------------  *  ( ------------- )       (5)
                          iStage ITM Drive [ct]      MICH IN1 [ct]     MICH EXC [ct] 

Each frequency point of the loop suppression and itm drive transfer function's uncertainty is determined by Eqs. 2 & 3, and are propagated to the uncertainty in each frequency point of the overall calibration by adding the relative magnitude and phase in quadrature. To compress each frequency point into an assessment of the overall DC actuation strength of that stage, we divide the resultant transfer function by a model of the actuation from that stage to it's optic. This way, if we've modeled the actuation strength as a function of frequency correctly, each frequency point becomes an independent measure of the overall strength of the actuator. As such, the single number and uncertainty for this stage is formed by the weighted mean and chi-squared weighted variance in the weighted mean,

          sum (x_{i} * sigma_{i}^{-2}) 
bar{x} =  ----------------------------                                                       (7)
             sum ( sigma_{i}^{-2} )                                                          Wikipedia
                             1                  1             (x_{i} - 1)^2
sigma_{bar{x}}^2 = ---------------------- *  ------- * sum ( --------------- )               (8)
                   sum ( sigma_{i}^{-2} )    (N - 1)           sigma_{i}^2                   Wikipedia
     

(D) The rest of the game is just using various parts of the interferometer to propagate this known "reference" actuator's absolute calibration to other optics. This is done by locking up a configuration that involves the reference actuator and actuator / optic you want to calibrate, and measuring the response of that IFO to both drives and taking the ratio of transfer functions:

  Optic Disp [m]           MICH [m]           ITM EXC [ct]        Some IFO [ct]
------------------   = ( ----------- ) *  ( -------------- ) * ( ----------------- )          (9)
iStage Drive [ct]        ITM EXC [ct]        Some IFO [ct]       iStage Drive [ct]

and the uncertainty is propagated in the same way as described in step C -- the frequency points of each new transfer function's uncertainty is determined by the coherence and number of averages, the uncertainty in the frequency points of the resulting product are the quadrature sum of the component TFs, the absolute calibration of the stage to optic is divided by a model, and the hopefully unity magnitude residual's weighted mean and weighted uncertainty are taken as the absolution calibration.

We found out Wednesday that the former method used in prior IFOs /science runs of just using a single arm IFO and propagating directly to the ETM doesn't work for the lowest strength actuators (i.e. ETMY L3) because the frequency noise of the Single Arm pollutes the measurement enough that one cannot get any coherence. As such, we've used many measurements to propagate the the absolute calibration to the ETMY L3: using the X single-arm to propagate ITMX L2 to ETMX L3, and then the full IFO in DC readout to propogate ETMX L3 to each stage of ETMY, e.g.

   ETMY L3 [m]         MICH [m]          ITM EXC [ct]        XARM IN1 [ct]         ETMX L3 EXC [ct]     DARM IN1 [ct]
---------------- = ( ----------- ) *  ( -------------- ) * ( -------------- ) * ( -------------- ) * ( --------------- )         (10)
ETMY L3 EXC [ct]     ITM EXC [ct]        XARM IN1 [ct]        ETMX L3 [ct]         DARM IN1 [ct]       ETMY L3 EXC [ct]


So if you're keeping track, that's six transfer functions and and a time series we have to take, and the transfer functions all need to take up a lot of time to get enough coherence that the uncertainty doesn't blow up. It's an all day adventure just to get all of these transfer functions. Thankfully, because of Kiwamu's care in getting the coherence super high, we still manage to get good data with reasonable error bars between 4 and 7 [Hz]. Any higher a frequency than this, and the original ITM to MICH transfer function hits the MICH noise floor. Below 4 [hz] the ITM to ETM transfer functions with the single arm loose coherence from frequency noise. So in addition to the many transfer functions we have to take, we only get a small frequency band where we can really get any sort of precision, and MICH isn't good enough to let us measure into the gravitational wave band.

WHERE EVERY THING EXISTS
The raw .xml files live here:
/ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/PreER7/H1/Measurements/FreeSwingMich/2015-05-28/
2015-05-28_H1DARM_ETMX_L3_Drive.xml
2015-05-28_H1DARM_ETMY_L1_State1_Drive.xml
2015-05-28_H1DARM_ETMY_L2_State2_Drive.xml
2015-05-28_H1DARM_ETMY_L3_LVLP_Drive.xml
2015-05-28_H1MICH_freeswingingdata.xml
2015-05-28_H1MICH_ITMDrives.xml
2015-05-28_H1MICH_OLG.xml
2015-05-28_H1XARM_ETMandITMDrives.xml
which have been exported to .txt files with corresponding _ts, _tf, or _coh tags to indicate the contents.

The analysis is done with 
/ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/PreER7/H1/Scripts/analyze_mich_freeswinging_data_20150528.m


Stay tuned for more actuation coefficient measurement technique comparisons, and an update to the DARMmodel, and therefore the CAL-CS and GDS calibration pipelines, and therefore the DARM spectrum and Inspiral range.

Jeff, Kiwamu,

This is a summary of the calibration of the ETMY suspension responses (in meters/counts) using the ALS diff VCO.

I have not evaluated systematic errors. The errors in this summary includes only statistical errors. The "models" I mean in this alog are the ones generated by the generate_QUAD_Model_Production matlab function in the suspension SVN. The model uses the "nominal" ESD force coefficient of 2e-10 [N/V^2]. The below is a summary of the results.

- - -

ETMY ESD is weaker than the model by 0.4242 +/- 0.0030

ETMY L2 is stronger than the model by 1.0344 +/- 0.0074

ETMY L1 is stronger than the model by 1.0269 +/- 0.0083

ETMX ESD is stronger than the model by 1.187 +/- 0.012

- - -

As for the ESDs, in terms of the force coefficient, they can be translated as

ETMY ESD force coeff. = 8.484 e-11 +/- 6.0e-13 [N/V^2]

ETMX ESD force coeff. = 2.374e-10 +/- 2.3e-12 [N/V^2]

[ETMY suspension responses]

I start from the results. See the attached two plots shown right below:

The first plot is a comparison of the measured response of all three stages with the models in units of [m/cnts]. Here "cnts" refers to the digital counts at the output of the ETMY_L1(2, 3)_LOCK_L filter bank. The second plot shows the ratio between the measured and modeled transfer functions. They are ratio of (measured) / (model). As you can see, the L1 and L2 stages agree with the model qualitatively. On the other hand, it is very clear that the ESD of ETMY is much weaker than what model predicts by a factor of 0.42. We don't know why this is so weak, but this is consistent with what the MICH free swing test says (see Jeff's alog for more details). Also, the L2 stage showed a phase lag of roughly 10 degrees. We don't know why at this point.

The steps for getting these results are something like the follows.

1. Calibrate ALS diff PLL loop in units of meters/Hz using a controllable frequency source (alog 18634 and some more details at the bottom of this entry)
2. Lock ALS diff and measure the ETMY L2 response
3. Take out the loop suppression from the measured L2 stage response by measuring the open loop of the ALS diff loop. This gives the absolute calibration of the L2 stage in m/cnts.
4. Fully lock the interferomter (at 3 W, DC readout on ETMX) and measure the response of all three stages to DARM_IN1.
5. Since we know the absolute response of L2, we can propagate it by having the ratio between L1 and L2, L3 and L2 stages that are measured in full lock.
6. done

If the ETMY ESD was stronger and as strong as that of ETMX, the steps in full lock are unncessary because we could measure it in the ALS diff configuration. However as we learned (see alog 18656), the low-voltage ETMY ESD needs a low-noise configuration. Note that the measured responses in full lock are also used in Jeff's analysis which had started from free-swing MICH fringes. Also, from the point of view of data points, we probably can go up to about 20 Hz at which the ALS diff signal is completely covered by some sensor noise. This time the frequency bins are chosen such that we can share them with the MICH calibration technique which was severely limited to frequency below 7 Hz due to high semsor noise in the simple MIchelson configuration.

As for the statistical error analysis, we used:

• measurement error in each transfer function using the coherence
• vco calibration error
• if the errors are distributed as Gaussian, all the errors I quote here correspond to 1 sigma.

For comparing the measured responses with the models, we assume that the models and measurements have the same transfer function shapes and therefore the scaling factor is the only parameter we estimate. Though, this assumption may not be true because we see a large differenence in the phase of the L2 stage.

For completeness, I attach all the relavant measured responses:

• ETMY_L2 drive supressed by ALS diff, or ETMY_L2_LOCK_L_EXC -> DIFF_PLL_CTRL_OUT (3rd attachment)
• ETMY supression or ETMY_L3_LOCK_EXC -> ETMX_L3_LOCK_IN2 (4th attachment)
• ETMY supressed responses of all three stages or ETMY_LOCK_L(1,2,3)EXC -> DARM_IN1 (5th attachment)

The ETMY suspension states (for all the measurements):

• L1 was in state 1 (LP1, LP2, LP3 all off)
• L2 was in state 2 (Acq on, LP off)
• L3 or ESD was in state 2 (LP on) and in low-voltage for all four segments. The bias voltage was +9.5 V at the DAC output or 124518.4 counts before the DACs. 
• No ESD linearization

[ETMX ESD response]

At a different time, we measured the response of the ETMX ESD using a similar technique to the ETMY measurement. The steps went as follows.

1. Calibrate the ALS diff VCO (alog 18634 and more details in the next section)
2. Lock ALS diff and measure the ETMX ESD response
3. Take out the loop supression by measuring the open loop.
4. done

Since the ETMX ESD does not use a low-voltage driver, the measurement can be complete only with the ALS diff loop closed. This is a big difference from the ETMY measurement which required low-noise stage for accessing the ETMY ESD.

The two plots shown below are the main results.

As shown in the first plot, overall, the measuement qualitatively agree with the model. The second plot shows the ratio of (measured) / (modeled). The absolute magnitude was larger than what the model predicted by a factor of 1.19. As mentioned earlier, the model uses a force coefficient of 2e-10 [N/V^2]. Unlike the ETMY ESD, the phase deviation (or perhaps I should say phase lag) is a bit larger than that of the ETMY for some unknown reason. The error propragation was done in the same fashion as that of the ETMY measurement (i.e. we included only coherence-based errors and VCO calibration error).

ETMX ESD configuration:

• The bias was at +9.5 V at the DAC output or 124518.4 counts before the DAC.
• Linearization was on with a linearization coefficient of -124518.4 which we have used since some time in this Feburary (for example alog 16798).

For completeness I post all the relevant transfer functions:

• ALS diff loop supression (8th attachment)
• ETMX_L3_LOCK_L -> DIFF_PLL_CTRL with ALS diff locked (9th attachment)

[ALS diff VCO calibration]

 On this past Tuesday, Dick and I measured the VCO response. We hooked up an IFR 2023 A which was synchronized to a 10 MHz rf signal (which is synchronized to GPS) to the diff PLL input or the PFD rf input with an amplitude of 0 dBm in order to simulate the beat note signal. Even though we could read out the display of the IFO 2023A, we used an external frequency counter (H1:ALS-C_DIFF_VCO_FREQUENCY) which should be at least as accurate as 5 Hz (see for example alog 6972). We locked the PLL loop and manually swept the frequency of the IFR until the PLL unlocks. The speed of the sweep was roughtly 25 kHz/minutes. Then we recorded the output of the DIFF_PLL_CTRL filter bank. One thing we have to pay attention is that this filter already contaied calibration filters which were meant to calibrate the VCO into microns, but as we measured the calibration factor was wrong by roughly a factor of 3.

The setting for DIFF_PLL_CTRL

• FM3, 4, 5 and 6 were engaged
• digital gain = 1

In theory FM3 should cancel the pole and zero at 1.4 and 40 Hz respectively in the VCO circuit. The meaured data is shown in the plot right below:

The data was then trancated such that the center frequency is located at 78.92 MHz with a range of +/- 30 kHz for a linear fitting purpose. Also, since we made a linear fitting at around 78.92 MHz, in any of the calibration measurement we tried to be as close as possible to this frequency by engaging the slow frequency couter servo to the ALS diff VCO, According to the fit the coefficient was of VCO -> PLL_CTRL was esimtimated to be 4.78268e-6 +-/ 0.002531e-6 [cnts/ Hz] using a least square fitting of gnuplot. These numbers were used for calibrating the ETM responses and estimating the errors.

Finally I attach a zip file which contains all the data (in ASCII not in xml), analysis codes and figures.