J. Betzwieser, L. Dartez, J. Kissel

Ryan Short recently updated the control room FOM for the BNS range (LHO:72415) which now shows -- with a clear legend -- the range computed using CAL-DELTAL_EXTERNAL_DQ vs. GDS-CALIB_STRAIN_CLEAN for both H1 and L1 observatories -- see example attached. 

This makes it dreadfully obvious that "L1's DELTAL_EXTERNAL range is right on top of the CALIB_STRAIN range -- but H1's is not, and DELTAL_EXTERNAL is *higher*." -- see First Attachment from the control room FOM screenshots.

The natural questions to ask then are "why?" "is something wrong with H1's calibration?"

No, there's nothing wrong.***
The discrepancy between DELTAL_EXTERNAL and CALIB-STRAIN at H1 is because the static test-mass stage actuation strength hasn't been updated since 2023-05-04 -- before the observing run started -- and it has slowly drifted due to test mass ESD charge accumulation -- and it's now at 8% larger than the May 04 2023 value. See the current value for the past 24 hours and a trend of the whole run thus far. L1's ESD strength has *not* drifted as much (see similar L1 trend), and they also regularly "fudge" their DELTAL_EXTERNAL actuator strength gains in order to get DELTAL_EXTERNAL more accurate (and they do so in a way that doesn't impact GDS-CALIB_STRAIN). H1 has chosen not to, to date.

This drift is tracked and accounted for in our "time dependent correction factor" or TDCF system for that test-mass stage actuation strength, \kappa_T -- and GDS-CALIB_STRAIN (and STRAIN_NOLINES, and STRAIN_CLEANED) all have this correction in place. Check out the Second attachment from the same day's "CAL" > "h(t) generation" summary page, and walk with me:
This plot is showing the ASD ratio (and thus roughly analogous to the magnitude of the transfer function) between all of the various stages of the calibration pipeline.
    - GDS-CALIB_STRAIN, GDS-CALIB_STRAIN_NOLINES, and GDS-CALIB_STRAIN_CLEANED are all this same from this perspective. Thus the ratio between these three channels with DELTAL_EXTERNAL in the denominator is highlighting the DELTAL_EXTERNAL is a preliminary product, and NOT corrected for TDCFs and thus there's a huge ~16% systematic difference between the two "stages" of product.
    - Recall that *all* of the four paths of the calibraion -- UIM, PUM, TST, and Sensing -- are being summed, and the cross-over frequency for these sums are all culminating around 50-200 Hz -- and in that region there's a factors of 2x to 3x gain peaking (see e.g. Figure 4 of P1900245) -- and thus the 8% drift in the TST stage strength means 16% systematic error in the DELTAL_EXTERNAL calibration.
    - However, the front-end version of the preliminary product that is corrected for TDCFs is also shown in the plot -- CFTD-DELTAL_EXTERNAL. The ASD ratio between this channel has MUCH less systematic discrepancy -- indicating that correcting for time-dependence (get it? CFTD!) does a LOT of the heavy lifting of accounting for this 8% TST drift. 

Of course, these ratios of different portions of the calibration pipeline don't *really* tell you if you've *really* done the right thing in an absolute sense. They only tell you what changes from step to step. (And indeed, the CFTD-DELTAL_EXTERNAL to GDS-CALIB_CLEANED ratio still shows *some* discrepancy.)

The fact that fifth attachment, from the archive showing the constant *direct measurement* of the systematic error in the calibration -- from the absolute reference, the PCALs -- is nice and low (i.e. the transfer function is close to unity magnitude and zero phase) indicates that all of the correction for time-dependence is doing the right thing.

*** Yet. In O3, L1 suffered a lot from TST strength drift. Joe has shown repeatedly that if you let an actuator TDCF drift too far beyond 10%, then the approximation we use to calculate these TDCFs breaks down (and see Aaron's work discussing it as a motivation for P2100107). In addition, since the real ESD strength is changing -- :: -- which is corroborated by the in-lock charge measurements -- I think -- see highlighted red region of sixth attachment from LHO:72310 -- :: -- that means the DARM open loop gain TF gain is also changing. 

This may impact the DARM loop stability (see e.g. LLO aLOGs 50900 and 50639). So, *eventually* we should resurrect the two things we've done in O3:
    (1) Reset the model of the static actuation strength for the TST stage to a more current value. (And thus start a new calibration epoch)
    (2) Potentially change the actual DARM loop by adjusting the DRIVEALIGN_L2L gain
    (3) Work up a solution to mitigate the drift -- perhaps doing something similar to what was done in O3, and play gains with turning on the ESD Bias voltage with the opposite sign when we're not in observing.