Jeff K., Evan G.

Summary:
We've reprocessed the measurement transfer function sweeps taken yesterday, and have found the coupled cavity pole was measured to be 429 Hz +/- 6 Hz, quite consistent with computing the pole from the arm reflectivities reported in galaxy (and use Eq 12 from T1500325) -- 433 Hz. We've since identified that Craig's single pole MCMC model (see LHO aLOG 44351) did not include detuned spring, and had a flaw in its log likelihood function resulting in an incorrect fit. The other physical parameters are fit with this process as well and described in the details below.

Details:
We used the new pyDARM infrastructure that has been developed over the last several months to analyze the transfer function sweeps taken yesterday evening. These measurements were quick 'n dirty; leading into and during an observing run, we would have more careful measurements to reduce any uncertainty. So we expect some reduction in uncertainty in future measurements.

pyDARM can perform MCMC fitting to the physical parameters of the coupled cavity optical response. The results of that fit are listed below:

Optical Gain                K_C         [ct/m]        3.552e6 +/- 3e4
Couple Cav. Pole Freq.      f_c         [Hz]          429 +/- 6
Residual Sensing Delay      tau_C       [us]          2.75 +/-1.7
SRC Detuning Spring Freq.   f_s         [Hz]          5.815 +6/-4
Spring Qual. Factor         Q_s         [ ]           4.2 +/- 6.5


A Gaussian process regression was used to establish potential unknown systematic errors, but this is merely for practice. We know
   - This was a quick 'n dirty measurement with poor uncertainty and limited frequency range, and
   - This is only one measurement, and we really want several to many measurements to nail down real unknown systematics

Here's the resulting design string we have put into Foton and loaded into the CAL-CS model (in the H1:CAL-CS_DARM_ERR filter bank) to improve on what was installed yesterday
    SRCD2N (as "O3_D2N" in FM9): zpk([428.9869;5.1756;-6.5327],[0.1;0.1;7000],1,"n")gain(3380.64)
    Gain (as "O3Gain" in FM10): gain(2.815e-07)

We fit these results with the following code:
/ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/O3/H1/Scripts/process_sensingmeas_20181004.py