J. Kissel

After all the infrastructure work over the past two weeks (see list below), we've finalized the live computation of the systematic error in calibration in the front-end. 

We've still got a lot of work to do in terms of validation, but you can see results here:
    - MEDM Screen Snippet -- this shows the numbers that are conveniently shown on the CAL CS TDEP screen (sitemap > CAL CS > DARM calib > pink "CAL LINE MONITORS" block)
    - ndscope trend -- this shows the trend of these numbers of a ~30 minute time window around ~17:00 UTC.
    - png and pdf of one snap-shot in time (i.e. informed by one 2-minute answer of the "calibration systematic error" calculated on a ~2 minute cadence), but shown as the traditional bode plot.

Here, we define the "calibration" as H1:CAL-DELTAL_EXTERNAL * (GDS / CALCS) corrections, i.e. the "DARM loop transfer function values at calibration line" (GDS/CALCS) correction at each calibration frequency for H1:CAL-DELTAL_EXTERNAL are 
    (GDS/CALCS) = (1/C_CORR) * ( (1 + G) / (1 + G * - angle(C_CORR * A_CORR) / (A_CORR * C_CORR)) )

as defined in T1900169. Similarly, the PCAL channels, H1:CAL-CS_TDEP_REF_PCAL_DQ (which is currently PCALY RX PD), and  PCAL X RX PD (which unfortunately NOT stored as an independent test point, or stored in the frames) are corrected at each calibration line frequency as 
    (PCAL [m]) / (PCAL_CALCS) = (arm sign) * (1/f^2) * (analog 65 kHz AA) * (digital 65kHz - 16kHz AA) * (corner-to-end, one 16 kHz clock cycle advance)


Some other important notes: 
    - the front-end *does not* use or need a whitening filter, the front-end (GDS/CALCS) correction does *not* need to account for the whitening filter that's applied to H1:CAL-DELTAL_EXTERNAL before creating H1:CAL-DELTAL_EXTERNAL_DQ. 
    - this systematic error measurement does not need to be corrected for time-dependent correction factors -- its measuring their impact live. The (GDS/CALCS) correction is only weakly dependent on TDCFs (see LHO:66062), so all the correction factors to the front-end computed answers are time-independent.
    - The uncertainty for each of these data points is the quadrature sum of 
        :: 0.28% 1-sigma, or 0.0028 radians [relative uncertainty], from G2300471 -- the "fundamental" uncertainty in our model of how much displacement PCAL causes, as it currently stands, and
        :: the measurement-, coherence-based, sqrt( (1-C) / (2 N C)) uncertainty.
      As such, the loud lines (e.g. 17.1, 410.2, and 410.3 Hz) are limited by the PCAL model's uncertainty, and the quieter lines are limited by the measurement noise. These should be the only uncertainties in this measurement -- drive the known PCAL displacement, and see what you measure out of DELTAL_EXTERNAL * (GDS/CALCS). *Maybe* you could argue that the (GDS/CALCS) corrections have some uncertainty, we'll have to think about that.
    - Here, in the bode plot, note that I've displayed DELTA L [m] / PCAL [m] -- which is the inverse of what we typically show when we show the modeled systematic error, PCAL [m] / DELTA L [m].

The list of "lost of work to do":
    - (potentially) tune the amplitude of PCAL lines (especially the PCALX) in order to get "satisfactory" uncertainty on the estimate of the systematic error. (Note, that also means figuring out what "satisfactory" *is*.)
    - Put this on the same plot as a "traditionally measured, offline processed" broad-band and swept-sine measurement of the same thing at a time *near* this calculation, e.g. those from LHO:66079.
    - Put this on the same plot as the "traditional *modeled* estimate of the systematic error," which is derived from MCMC fits, GPR fits of the residual, and time-dependent correction factors.
    - Figure out a nice way use animated plots to display a "3 dimensional" bode plot of these answer as a function of time
    - Compare against GDS processed values of the same thing (still working on figure out ways to store that answer for comparison).

And in the grand scheme of things, once this is validated, and we're confident in the uncertainty of the measured systematic error, *then* we can figure out how to alarm on these values when something significant changes in the calibration.

[1] Front-end code changes last Tuesday, LHO:68961, and yesterday LHO:69226
[2] MEDM screen updates to the graphical user interface for improved clarity and usage LHO:68999 and LHO:69263
[3] Understanding and populating the EPICs records that are "DARM loop model parameter values at calibration line frequencies" LHO:69061 and LHO:69159
[4] Understanding, LHO:69175, then synchronizing the demod low-pass corner frequencies with the FFT LENGTH and Number of Averages used to compute the measurement-, coherence-based uncertainty LHO:69265.