D. Tuyenbayev, J. Kissel

Darkhan and I have processed the measurements of the IFO's sensing function that we've made over the course of ER10 thus far. The measurements are compared against a model for the interferometer's optical plant, (a. la. T1600278, and G1601599)
      dS (f)     K exp(-2*pi*i*f*tau)               f^2
      ------  =  -------------------  * ---------------------------
      dL            1 + i*(f/f_cc)      f^2 + (f_s)^2 - i*(f*f_s/Q)
where 
      dS / dL = DARM_ERR error signal counts per differntial displacement of the test masses dL in [ct/m]
      K       = optical gain in [ct/m], though fundamental units are [A/m]
      f_cc    = DARM /RSE /coupled cavity pole frequency in [Hz]
      f_s     = detuned signal recycling cavity (SRC) "optical spring" frequency
      Q       = quality factor of said spring
      tau     = residual delay, after accounting for computational, light travel time, and FSR response delays

The resulting plots of model compared against measurement are attached. I also summarize the numerical values for the results in tabular form below for ease of comparison.

                                 [Units]  value(95% c.i.)

Meas Date                 2016            Nov 8         Nov 11        Nov 12        Nov 15        Nov 16        Nov 18  
IFO Input Power                  [W]      23.5          24.8          29.5          30.7          31.1          31.9
SRC1 Loop Status                          ON            ON            ON            OFF           ON            ON

Optical Gain              x 1e6  [ct/m]   1.15 (0.002)  1.15 (0.002)  1.15 (0.003)  1.12 (0.004)  1.14 (0.003)  1.12 (0.002)
DARM/RSE Cav. Pole Freq.         [Hz]     343.1(3.8)    351.1(3.1)    346.7(4.1)    342.0(5.9)    344.7(3.8)    348.4(5.1)
Detuned SRC Optical Spring Freq. [Hz]     5.5  (0.3)    4.9  (0.2)    7.4  (0.3)    7.8  (0.4)    8.1  (0.3)    8.5  (0.3)
Optical Spring Q-Factor (1/Q)    []       0.03 (0.01)   0.04 (0.01)   0.05 (0.01)   0.07 (0.01)   0.05 (0.01)   0.07 (0.01)
Residual Time Delay              [us]     -2.6 (3.4)    -1.7 (3.7)    2.3  (3.4)    2.8  (5.3)    0.6  (3.3)    5.1  (4.7)
 
aLOG                                      31303         31403         31433         31508         31527         31601


Conclusions: 
(1) We see a clear *decrease* in IFO optical gain between 25 [W] and 30 [W], but it may be a function of alignment not input power. We expect and *increase* as a function of power. This may be evidence for power/alignment dependent losses. It would interesting to compare these data sets to the spot-position measurements that we've been taking.
(2) The DARM /RSE /coupled cavity pole frequency (f_cc) is consistently 345.9(3.5) [Hz], regardless of input power or alignment.
(3) We continue to see the effects of a detuned SRC cavity, characterized/approximated by a pair of poles at spring frequency (f_s) and quality factor (Q), unlike LLO.
(3) The f_s shows statistically significant changes over the course of these measurements, unlike LLO. Difficult at best to tell if its correlated with any of the parameters we've tracked here, but it will be very interesting to use the 7.92 Hz PCAL line to confirm this in the future. This characteristic frequency will be another interesting thing to compare against spot positions.
(4) Though we only have one data point, having SRC1 loops OFF does not significantly change f_cc, and the trend in f_s seems unrelated. (However I still highly recommend that we run with them ON if at all possible)
(5) The residual time delay is consistent with zero. This is great -- it means we really have a handle on the high-frequency response of the IFO.

We'll take one more of these measurements to set the front-end calibration all within the same lock stretch, to make sure the time-dependent tracking for the relative optical gain and cavity pole frequency are as close to 1.0 and 346 [Hz] as possible.

Details:

CalSVN repo root: [~] = /ligo/svncommon/CalSVN/aligocalibration/

Analysis produced by running:
[~]/trunk/Runs/ER10/H1/Scripts/PCAL/fitDataToC_20161116.m          Revision: 3815
on each of the measurement config files listed below.

Model Config Files:
[~]/trunk/Runs/ER10/Common/params/IFOindepParams.conf              Revision: 3776
[~]/trunk/Runs/ER10/H1/params/H1params.conf                        Revision: 3811
[~]/trunk/Runs/ER10/H1/params/2016-11-12/H1params_2016-11-12.conf  Revision: 3800

Measurement Config Files:
[~]/trunk/Runs/ER10/H1/params/2016-11-07/measurements_2016-11-07_sensing.conf   Revision: 3800
[~]/trunk/Runs/ER10/H1/params/2016-11-10/measurements_2016-11-10_sensing.conf   Revision: 3800
[~]/trunk/Runs/ER10/H1/params/2016-11-12/measurements_2016-11-12_sensing.conf   Revision: 3800
[~]/trunk/Runs/ER10/H1/params/2016-11-15/measurements_2016-11-15_sensing.conf   Revision: 3800
[~]/trunk/Runs/ER10/H1/params/2016-11-16/measurements_2016-11-16_sensing.conf   Revision: 3800
[~]/trunk/Runs/ER10/H1/params/2016-11-17/measurements_2016-11-17_sensing.conf   Revision: 3800