J. Kissel

I've injected a broad-band PCAL EY excitation into the IFO and measured its response in CAL-DELTAL EXTERNAL to confirm that systematic errors are small. I've followed it immediately with a set of reference-measurement sensing function swept sines of PCAL2DARM and DARMOLG TFs that have been tuned to improve the low frequency (> 30 Hz) information. 

Attached are the results. I also attach the results for a never published measurement that was taken on Nov 21 2016 20:13:36 UTC.

One can see that
- The systematic error between 10-200 Hz (where the coherence is reasonable enough to make a statement) is frequency dependent, but less that 5% and 2 [deg]. 
- The swept sine version of the same measurement agrees with the frequency dependence, but confirms that the discrepancy flattens out in magnitude, sticking to around -5%
- Here're the fit results for physical parameters of the sensing function:
                                 [Units]  value(95% c.i.)      
Meas Date                 2016            Nov 21              Nov 30
IFO Input Power                  [W]      29.5                29.9
SRC1 Loop Status                          ON                  ON

Optical Gain              x 1e6  [ct/m]   1.150 (0.003)       1.124 (0.003)
DARM/RSE Cav. Pole Freq.         [Hz]     348.7 (6.0)         347.5 (5.8)
Detuned SRC Optical Spring Freq. [Hz]     7.09 (0.2)          7.40  (0.2)
Optical Spring Q-Factor (1/Q)    []       0.0413 (0.02)       0.0581 (0.02)
Residual Time Delay              [us]     1.87  (4.9)         0.84 (4.7)
 
aLOG                                      LHO 31994


- There is statistically significant evidence for what I'll call "DC flattening" in the sensing function, that we see for the first time with these two measurements because we've tuned the transfer function to have high precision there. This is interesting because our current simplified model of the sensing function (described in detail in LHO aLOG 31665, for example) does *not* include the influence of the test mass's finite stiffness at low frequency. The parametrization we currently use is based on the 2001 Buonanno and Chen Paper (via Evan Hall's thesis work and Kiwamu & Craig's similar derivation), but none of these incorporate a test mass with real dynamics and finite stiffness. The only study I've seen that does do this -- and shows evidence for the response flattening below a certain frequency -- was some work done by Adam Mullavey very early on, in which he used an Optickle simulation with (I believe) the full QUAD dynamical model included -- see pg 5 of G1400064. There are two impacts of this effect on the physical parameter estimation:
    (1) It distracts the lower-frequency fit of the optical spring frequency and Q slightly -- which means that there is systematic error, (albeit small for this level of detuning) in the sensing function as high as 30 Hz.
    (2) There is a few tens of percent discrepancy in the 5-10 Hz region. However, Adam's study hints that -- although the detuned spring frequency increase with power (as we have seen) the restoration-to-flatness frequency does not. I think this makes sense physically -- the finite stiffness of the suspension (at least in the longitudinal direction) should not change with power (of course the angular plant does -- see e.g. LHO aLOG 25368)

Other Notes:
- (I only re-discovered this today -- thanks Shivaraj!) that these templates come pre-calibrated. 
The swept-sine calibration is an imported text file that calibrates the DELTAL EXT / PCALY RX transfer function (i.e. not the individual channels) from preER10,
     /ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/PreER10/H1/Scripts/ControlRoomCalib/pcal2darm_calib.txt
written by Kiwamu, with the script 
     /ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/PreER10/H1/Scripts/ControlRoomCalib/H1_pcal2darm_correction.m
and originally mentioned in . 
The broad-band calibration is an imported text file that calibrates DELTAL EXT from the PreER9 model,
    /ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/PreER9/H1/Scripts/ControlRoomCalib/DARM_FOM_calibration_new_20160512.dat
written again by Kiwamu, with the script 
    /ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/PreER9/H1/Scripts/ControlRoomCalibH1DARM_FOM_correction.m

These scripts, regrettably, have a few FIXMEs and are not using the latest DARM model. We should update these script, regenerate the ASCII dump of calibration, and recalibrate this data to confirm that the systematic errors are still small (and in fact they may get smaller, who knows). 

- All data is exported from these templates always use the raw channel's value so any matlab analysis done in the past is unaffected by the above imported DTT calibrations.

- The time of the broadband injection was about 40 [sec] between Nov 30 2016 02:53:00 to 02:53:40 UTC (enough to get 25 avgs at 0.1 Hz BW, or 10 sec FFT with 75% overlap). This will be used to make the same comparison of PCAL to GDS-CALIB_STRAIN, especially now that it is correcting from time-dependent systematic errors (see LHO aLOG 31926).

Measurement templates: 
/ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/ER10/H1/Measurements/
    PCAL/2016-11-30_H1_PCAL2DARMTF_BB_5to1000Hz.xml
    PCAL/2016-11-30_H1_PCAL2DARMTF_4to1200Hz_fasttemplate.xml
    DARMOLGTFs/2016-11-30_H1_DARM_OLGTF_4to1200Hz_fasttemplate.xml


DARM model / Sensing Function Fit constructed from:
/ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/ER10/
H1/Scripts/PCAL/fitDataToC_20161116.m (rev3908)

Common/params/IFOindepParams.conf (rev3829)
H1/params/H1params.conf (rev3855)
H1/params/2016-11-12/H1params_2016-11-12.conf (rev3855)