S. Dwyer, J. Kissel

As we continue to explore the IFO parameter space looking for optimal goodness, Sheila and I compared several "goodness" metrics under the conditions of either 
    - the "August" test mass beam spot positions with everything otherwise in is nominal "August" configuration or 
    - the "August" spot position and nominal other things but with a ~0.5 nm length offset in the signal recycling cavity (by adding 100 ct digital offset to the SRCL1 control filter bank).
(The "August" spot position is what's reported as "37W Post-Tuesday" in LHO aLOG 50965.)
(Sheila reports a corresponding "what happened today" log in LHO aLOG 51394.)

The metric about which I report here is the IFO's response to DARM, aka the "sensing function" as measured by the ratio of a DARM IN1 / PCALY RXPD = C / (1+G) transfer function and a DARMIN2 / DARMEXC = 1/ (1+G) transfer function.

We gathered a "no offset" reference measurement set, 
/ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/O3/H1/Measurements/FullIFOSensingTFs/
    2019-08-19_H1_NominalConfig_DARM_OLGTF_LF_SS_5to1100Hz_15min.xml
    2019-08-19_H1_NominalConfig_PCALY2DARMTF_LF_SS_5t1100Hz_10min.xml
and a "with offset" measurement set, 
/ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/O3/H1/Measurements/FullIFOSensingTFs/
    2019-08-19_H1_100ctSRCLOffset_DARM_OLGTF_LF_SS_5to1100Hz_15min.xml
    2019-08-19_H1_100ctSRCLOffset_PCALY2DARMTF_LF_SS_5t1100Hz_10min.xml
Note that these measurements were taken of different lock stretches, and an initial alignment was performed in between them BUT the IFO was thermalized in both measurements, and in the beam was steered to the same spot positions on the test masses.

Attached are the results:
    (1) 2019-08-19_H1_augspotcomparison_sensingFunction_referenceModel_vs_allMeasurements.pdf: a comparison of all measurements in the "August" spot positions, since the optical plant has (a) been relatively stable, and (b) roughly (and much more accurately) obeyed a model for a detuned SRC optical spring. The data is divided by a model of hand-fit optical plant parameters*** so that I can, with confidence, say that -- in August, with the "August" spot positions and no intentional SRCL offset -- the optical parameters are/have been:

          Parameter          Value         Unit              2019-04-16 Reference Value 
          ccOpticalGain       3.13e+06    #cnts/meter              3.25e+06
          ccPoleFreq        395.0         #Hz                    410.6
          detuneSpringFreq    7.35j       #Hz                      4.368j
          detuneSpringQ      30.0         #dimensionless          52.14
though it's clear, 
        (i) The spring is time-dependent, and
        (ii) There are still some non-spring-like effects going on

    (2) 2019-08-19_H1_100ctSRCLOffset_sensingFunction_referenceModel_vs_allMeasurements.pdf: a comparison of today's "no offset" vs. "100 ct SRCL offset". Here, instead of the hand-tuned model from above, I show the data against a model with NO detuned spring, the same above hand-tuned optical gain, and the reference model cavity pole. This shows many things:
        (I) The optical gain is remarkably consistent between lock stretches, with a \kappa_C optical gain correction factor of ~0.96 +/- 0.001 (and that difference from the reference model is primarily due to the IFO input power increase from 35 to 37 W).
        (II) The cavity pole has increased from 395 Hz to 411 Hz (+/- 2 Hz), and I attribute that to the intentional SRCL offset. 
        (III) The apparent optical spring has been drastically reduced and/or pushed lower in frequency. I attribute this to the intentional SRCL offset
        (IV) There remains a "wiggle" that I suspect is residual parasitic Length (DARM) to Angle (ASC) to Length (DARM) coupling at these "August" spot positions interacting with whatever left--over optical spring is present, because the phase of the transfer function increases as frequency decreases "unphysically" as we've seen with the "July" early-O3 spot positions. I attribute the exposure of this effect to the intentional SRCL offset.

***Since we've recently identified that our MCMC algorithm stinks at trying to make sense of the sensing function optical parameters, instead of trying to play tricks on the algorithm to make it work (like modifying the frequency range of data input in to the algorithm, or modifying / restricting the priors, etc.), I just spent 5 minutes noodling around the values to make the meas / model residual flat and close to unity magnitude and zero phase.

Sheila's got a lot more conclusions about this result coupled with the data she gathered from the squeezer in a pending aLOG, but for now, all I have to conclude is "meessa likey da intentional SRCL offset!" #NobodyLikesJarJar