L. Dartez, E. Goetz, J. Kissel

Now that 
    - we're confident in our post-processing of (H1:CAL-DELTAL_EXTERNAL_DQ / H1:CAL-PCALY_RX_PD_DQ) "what's the current level of systematic error in the calibration" transfer functions (First half of LHO:66062) 
    - we've have written the first example scripts on how to use the latest pyDARM infrastructure to resurrect our ability to compare several of these measurements together (LHO:66069), and
    - we're reminded that this systematic error transfer function evolves as the IFO evolves its thermal and alignment state (Second half of LHO:66062)
we can finally show you how the systematic error in the calibration is "/Different/, Not Necessarily Better" as quoted after our 2022-11-23 update to the calibration in LHO:65973.

In the attached plot, I show the systematic error transfer function,
    (a) Before (2022-11-23 ~2240 UTC) vs. After (2022-11-23 ~0005 UTC) the calibration change,
    (b) Using both a band-limited colored random noise excitation (2236 UTC and 0002 UTC), aka the "broadband" excitation method, as well as the (actually much broader band) swept-sine excitation method (2243 UTC and 0008 UTC),
    (c) Hoping, but not sure, that the IFO is stable in its alignment / thermalization state is stable enough that this is a fair comparison.

IMPORTANT NOTE: I've plotted the systematic error transfer function as (H1:CAL-PCALY_RX_PD_DQ / H1:CAL-DELTAL_EXTERNAL_DQ), the inverse of the transfer function we typically show when we drive the excitation, so as to cast the transfer function in terms of a multiplicative transfer function, $\eta_R$, one should apply to the calibrated output of the detector, H1:CAL-DELTAL_EXTERNAL_DQ to make it more like absolute reference, H1:CAL-PCALY_RX_PD_DQ, i.e. what we believe to be a "more correct" measure of the differential arm length change.
This way, one can read off the systematic error at a given frequency without having to think about inverses. If the $\eta_R$ transfer function is high by 3%, then an amplitude spectral density of the (post-processed) H1:CAL-DELTAL_EXTERNAL_DQ is to low by 3% (over estimating our sensitivity and BNS inspiral range) and multiplying by this $\eta_R$ function will fix that.

As always, one can't effectively quantify the change with a "XX% / YY deg" single phrase, but we're never-the-less forced to try, so here goes: 
    - the maximum and minimum excursions from "perfect" calibration (represented by a unity magnitude, and zero phase transfer function across the frequency band) have shifted 
        :: from (pre-calibration change) broad features focused on 20 Hz (magnitude error is -3%) and 70 Hz (magnitude error +1%)      
        :: to (post-calibration change) broad features focused on 30 Hz (error is +3%) and 170 Hz (error is -3%).
    - the error below 15 Hz remains a jumbled mess, where our best guess at this point is that it's due to the nasty features in the sensing function discussed most recently in LHO:65502.
    - What little data we have from the swept sine excitations tell us that error is not terrible above 1 kHz, but we'll need to resurrect our "roaming calibration lines" and integrate for a very long time to really measure the the error from 1 - 5 kHz. 

This level of systematic error is consistent with what we were able to achieve at the end of O3, at the best of times, after many many moons of understanding a stable detector. We have this level of understanding well before the next run starts. That's awesome. 

At this level of systematic error, the point of changing the calibration is not to make the systematic error *better* per say, but its to have installed filters and gains that are self-consistent with measurements and fits for which we have quantifiable uncertainty, rather than by-hand fudges that were installed to make a poorly post-processed (H1:CAL-DELTAL_EXTERNAL_DQ / H1:CAL-PCALY_RX_PD_DQ) transfer function look flat.
This allows us to do a lot more things:
    - Finally have full and complete confidence in man of the new features of pyDARM as well as our understanding of the 50W O4-like IFO, including
    - (albiet, "by hand," via "bespoke" scripts) Fully process a suite of IFO measurements to obtain the last, critical, only-measure-able-wtih-the-full-IFO parameters of the DARM loop model, install the results, and have the IFO (well, PCAL) tell is that the process is legit (to acceptable levels of systematic error)
    - Resurrect the calibration-line tracking of time-dependent correction factors, aka TDCFs
    - Build up a systematic error budget from the underlying measurements that informed the filters and gains
    - Pass a model parameter set we're confident in for the low-latency GDS pipeline to correct
    - Begin development on the future leaning-tasks that we didn't have in O3 like 
        - commissioning the front-end calibration pipeline where we pre-compensate for time-dependence, aka the "CFTD" path 
        - commissioning the front-end, real-time version of the super-Nyquist corrections.
        - constant systematic error characterization over many frequency points.

Achievement unlocked!