J. Kissel

In order to assess its time-dependence, and to go a little bit further to confirm the effect, we repeated last week's measurement of the DARM sensing function's low-frequency response to SRCL offset (see LHO aLOG 51440), this time with a SRCL offset of 
    - 0 ct (what we've been running with since O3 started), 
    - 100 ct, and 
    - today, newly 200 ct (we lost lock 3/4s of the way through the measurement suite, but enough to salvage the data)
to make some definitive conclusions and decisions about it.

%%%% Executive Summary%%%%
We installed a 100 ct digital offset in the SRCL loop, and modified the ISC_LOCK guardian to turn it on during the LOWNOISE_LENGTH_CONTROL state; it succeeded, and we've accepted it into the OBSERVE SDF. This improves the low-frequency sensing function by reducing the detuned SRC optical spring effects, reducing the complexity of the DARM response to displacement. We have not yet updated the calibration to reflect this, and I think we may not have to.

Also, more details later (see point 5 below), but just so we're no longer sad about the physical interpretation of this digitally requested, I give you my crude calibration for the digitally requested SRCL offset: 
  Digital      SRC Phase             SRC Length
      0 ct = - 0.34 (+/- 0.02) deg = - 57.6 (+/-3.4) nm
    100 ct = + 0.00 (+/- 0.01) deg =    0.0 (+/-1.7) nm
    200 ct = + 0.28 (+/- 0.02) deg = + 47.4 (+/-3.4) nm
(with dl- = [ lambda / (2*pi) ] * phase, and lambda = 1064e-9 m)

%%%% DETAILS and FIGURES %%%%
Here're the conclusions:
 
(1) A requested digital SRCL offset of 100 ct can repeatedly reduce the amount of detuning seen in the DARM sensing function -- however, what's left over is still time-dependent.
See first attachment: 2019-08-28_H1_SRCLOffsetTest_Jul100ct_sensingFunction_referenceModel_vs_allMeasurements.pdf
This compares last week's and this week's measurements in the pre-August spot positions against a model.
As in previous aLOGs, I divided the measurement by an hand-tuned sensing function model with no optical spring, in order to show / expose what response is down there, since we know we can't attribute the response entirely to just SRC detuning; some parasitic L2A2L coupling remains. And indeed, we can't disentangle whether it's the parasitic L2A2L or the SRC detuning that's time dependent.

This hand-tuned model parameter set: 
/ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/O3/H1/params/
    modelparams_H1_20190416_byopticalresponseforjulspot100ctSRCLoffset.py

which only differs from the nominal O3 model in 
    - lack of optical spring (detuneSpringFreq = 0.0), 
    - the optical gain (ccOpticalGain) is 3.16e6 (corresponding to a \kappa_C of 0.972, as expected from the lack of updating for power up from 35W to 37W), and 
    - the cavity pole frequency (ccPoleFreq) is 417.0 Hz

but at least, (yes, only a sample size of 2),  we conclude the low-frequency response is still time dependent with a 100 ct offset, but not by much.

(2) While we lost lock halfway through the PCAL2DARM sweep, I had a full DARM Loop Suppression measurement in the can during the time which the IFO had a requested digital SRCL offset 200 ct. Thankfully this is enough data to resolve the low-freqnecy response. 
See second attachment: 2019-08-28_H1_SRCLOffsetTest_OffsetComp_sensingFunction_referenceModel_vs_allMeasurements.pdf
This compares the three measurements of the above mentioned offsets. One can clearly see that between a digital offset of 0 to 200 ct, we're flipping between an pro-spring (0 ct offset) an anti-spring (200 ct offset), and some how, miraculously 100 ct offset lands use pretty darn close to perfectly tuned.

However, as is seen in the first and now the second plots -- at 100 ct, there remains some for of stuff going on. We'll blame it on parasitic L2A2L, so we won't for now, try to find the "perfect" SRCL offset, and continue down the Sheila / Matt path of trying to crush the parasitic L2A2L. From these two plots, we conclude that a 100 ct SRCL offset is good, and we'll now stick permanently with it.

(3) Now -- what does this mean for the calibration? 
See third attachment: 2019-08-28_H1_SRCLOffsetTest_Jul100ct_NomModel_sensingFunction_referenceModel_vs_allMeasurements.pdf
Here, I show the currently installed reference model against the two data sets we have with the July spot positions, but with a 100 ct SRCL offset. 
    - We already know the optical gain is too high at 3.25e6 ct/m, but that's covered by \kappa_C at 0.97.
    - We already know that the cavity pole is a bit too low at 411, but that's covered by f_cc which nicely is reporting 418 Hz or so at the beginning of a nominal lownoise stretch after power-up, and settles in to about 414 Hz after thermalization.
    - So it's only the low-frequency response that should concern us: since there's essential no detuning at a 100 ct SRCL offset, the current model, which has a pro-spring of 4.47 Hz, gives as much as 4% systematic error at 20 Hz, and 14% error at 10 Hz. BUT -- as Evan inadvertently shows in the Action Item Follow-up Slides of G1901479, if we have a systematic error in the sensing function (as represented by the 68% CI shaded region), then it's not until that error starts getting about a factor of 2 worse -- ~8% at 20 Hz (25-30% at 10 Hz) -- that we really start to spoil the systematic error of the entire response function. 

So I think we're OK here. The resulting low-frequency systematic error created by improving the sensing function reality without updating the calibration model of it is smaller than other dominant overall response function systematic errors and uncertainties in this frequency region.

I wouldn't be opposed to creating a new reference model starting with this data set, but there's *a lot* of things to remember to do besides just updating the front-end model (see, e.g., an incomplete list here: T1800469.)

(4) What if we went forward with our existing techniques and pushed a new model that is derived from the MCMC fit infrastructure we have?
See fourth and fifth attachment: 
    2019-08-28_H1_SRCLOffsetTest_Jul100ct_NomModel_sensingFunction_mcmcModel_vs_measurement.pdf
    2019-08-28_H1_SRCLOffsetTest_Jul100ct_NomModel_sensingFunction_mcmcModel_paramCornerPlot.pdf
The MCMC puts forth a pretty solid fit, with 
       Optical gain, H_c (ct/m)                 | 3.159e+06 (+1041,-959.4) or (+0.03297%,-0.03037%)
       Cavity pole, f_cc (Hz)                   | 419.8 (+0.7607,-0.8149) or (+0.1812%,-0.1941%)
       Detuned SRC spring frequency, f_s (Hz)   | 2.152 (+0.02577,-0.02861) or (+1.198%,-1.33%)
       Detuned SRC spring quality factor, Q_s   | 97.36 (+2007,-4929) or (+4.85%,-1.975%)
       Residual time delay, tau_c (usec)        | 1.987 (+0.4861,-0.5282) or (+24.46%,-26.58%)
which is consistent with my by-hand fit, has .... let's say 1-2% / 2 deg scatter level systematic error down to at least 7 Hz, and only has a few walkers in parameter "islands." I would be comfortable attributing the rest of the systematic error to the parasitic L2A2L coupling, and moving on without having to worry about a detuned spring anymore. Plus -- if Sheila / Matt are getting closer to trying out their L2A decoupling, then maybe this secondary effect will also disappear...
I'm getting ahead of myself though.

I've gotta sleep on this (and we've gotta replace an HEPI pump tomorrow), but stay tuned for a decision on whether to update the reference model.

(5) The promised details on the calibration of the SRCL offset: 
This calibration / fit to the data uses the very handy Cahillane DARM Plant interactive plotter python script from LHO aLOG 48366, updated for an input power of 36.8 W, with a PRG of 45, and (perhaps incorrectly, oddly the data demands that) the SRM transmission is 36.05% (where "we know" that the SRM has been replaced with SRM-06 Post O2, which galaxy, says LIGO measured 32.34%, but the report is empty, and the vendor data sheet says 31.80%).
I agree that 
    (a) I've probably done something wrong, 
    (b) that the physical values for the detuning appear to be an order of magnitude larger than what they were in O1/O2 (see LHO aLOG 27675)
so forgive me for now while I still try to get an understanding of how the calibration of this offset works.
*I've* done nothing complicated -- Craig has done all the work for me of making the amazing tool which converts physical parameters into a sensing function -- and gives you interactive control over the important ones that influence the shape of the response function. 
So -- that's what I did. Eyeballed the fits (with the above state precision), and came up with that kind of SRC phase.
See sixth attachment: 2019-08-28_H1DARM_SensingFunction_CraigModel.pdf
    This shows three pages for the three measurements with three different offsets. Virtually all physical parameter values are kept at their nominal measured values, except for -- as mentioned above -- the SRM transmission.  (well, and yes, OK, there's a 0.07 log-scale correction to the optical gain, but optical gain loss could be anything). Importantly though -- between the three fits, I only varied the SRC detuning phase.
    Anyways -- more to sleep on.