J. Kissel

Using data taken by Sheila last week Friday (LHO:46537), I've fit that day's sensing function (for a 30W IFO, with all actuation on ETMX) and now have new values for its parameters. As always, there are a caveats. Details below. 

Var.  Units    Value      Abs. Unc.             Rel. Unc.              Description
------------------------------------------------------------------------------------
H_c   (ct/m)   3.046e+06  (+1421,-1420)         (+0.04665%,-0.04661%)  Optical gain,            
H_c   (mA/pm)  3.77       (+0.001759,-0.001757) (+0.04665%,-0.04661%)  Optical gain,            

f_cc  (Hz)     424.9      (+1.042,-1.05)        (+0.2453%,-0.247%)     Cavity pole,             

f_s   (Hz)     0.2573     (+0.261,-0.1148)      (+101.5%,-44.63%)      Detuned SRC spring frequency
Q_s   (  )     0.4263     (+0.3431,-0.2164)     (+80.48%,-50.77%)      Detuned SRC spring quality factor   

tau_c (usec)   3.299      (+0.5827,-0.5765)     (+17.66%,-17.47%)      Residual time delay

The four attached plots support this information:
pg 1: the MCMC fit compared against the data
pg 2: the same plot, but with me copying the MCMC fit results into the 20180118 parameter file, and thus showing the model against the data (essentially just proving that I can copy-and-paste with good fidelity)
pg 3: the guassian process regression of the residual between model and measurement which would quantify any unmodeled systematic error (there are none -- the residuals are consistent with unity magnitude and zero phase)
pg 4: a corner plot of the MCMC fit showing the covariance of the parameters

Several comments:
(1) The fit detuned optical spring is completely bogus. I don't believe it! The fit is essentially saying there's no SRC detuning, which H1 has never seen. What has happened: In order to minimize time with the IFO, I created a set of measurement templates with a frequency vector that was sparse at low frequencies. Thus, there are only 2 data points below ~15 Hz, and they're of high uncertainty -- resulting in a poorly informed fit for this 5-10 Hz, low frequency feature. I'll change this for the next round of templates.

(2) The optical gain is reported in both (DARM IN1) / (DARM DELTAL), [ct/m], as well as (OMC DCPD Current) / (DARM DELTA L), [mA/pm] ("milliAmperes per picometer"). The latter is merely the former divided by the transfer function value between OMC_DCPD_SUM_OUT_DQ and LSC-DARM_IN1_DQ at 5 Hz, at the time of the PCAL sweep. That value is 1.23781e6 [mA/ct] (and then the meters are converted to picometers). However, the calibration of the OMC DCPDs into [mA] is NOT an accurate, rigorously verified calibration, and thus neither is the [mA/pm] number, so be wary of making any precise statements when using this number. I suspect it's good to the 10-20% level.

Other than this -- I'm pretty happy with the accuracy of the model -- roughly 1% in magnitude, and 1-ish degrees in phase. Nice! 

I'm actually a little surprised by this because we haven't updated any of the uncompensated OMC DCPD whitening chassis poles after modifying the the whitening stage (Jun 2018, LHO:42361); we're still using the average frequencies of the two DCPD paths from LHO:28087 -- 14.47 kHz, 18.625 kHz and 99.695 kHz. Maybe these poles come from a part of the chassis that wasn't modified. We know that the transimpedance amplifiers' poles at 13.7 and 17.8 kHz have not changed since O2, so these need not change. And I guess if the model matches the data, who am I to argue!

Using these results -- If we *must* update the sensing path immediately, one can install the following foton string in the H1:CAL-CS_DARM_ERR bank (please do it in a different filter bank, don't over-write what's in the "O3_D2N" and "O3Gain" filters that are in use).
   D2N filter (SRCD2N): zpk([424.8532;0.2094;-0.3190],[0.1;0.1;7000],1,"n")gain(6.68)
           Gain filter: gain(3.283e-07)
(and needless to say, one should make the EPICs gain of the filter 1.0).

I would prefer to have a complete DARM loop model that matches the total DARM open loop gain transfer function before launching forth with the install. 
SPOILER ALERT -- I've already made the plot, and model doesn't match the data in a frequency-dependent ~5% wiggle in magnitude, and a phase discrepancy increasing with frequency up to 10 deg by 1 kHz. More details in a subsequent aLOG.