J. Kissel, J. Betzwieser

Now that we're reasonably happy with the static components of the calibration which provide relatively low systematic error (LHO:68319), it's back to validating and understanding the TDCFs. 

Setting know issues aside (namely, that we haven't updated the so-called "EPICs records," the values of various DARM loop transfer functions at calibration line frequencies since the switchover to the new, completely different, faster 524 kHz OMC DCPD signal chain and new D2200215-style whitening chassis in Jan 24 2023; LHO:66992), Joe recently suggested that the new 410.2 PCALXY comparison line driven by PCALX -- also installed around Tuesday Jan 24 2023 -- has severely biased the estimate of certain "time dependent correction factors," (TDCFs) -- namely relative optical gain, \kappa_C, and the DARM coupled cavity pole frequency, f_cc -- the estimate of which is informed by the long-standing 410.3 Hz PCALY line. HE discovered this by browsing through the summary pages, comparing the f_cc answer from the TDCF summary pages before vs. after the change.

I've confirmed that, with the PCALY DEMOD settings as they stood prior to this aLOG, this new 410.2 Hz biases the estimate of TDCFs, but it drastically impacts the estimate of the relative optical gain, \kappa_C, *not* the estimate of the cavity pole frequency, f_cc.

Take a look at the 50 minute trend of TDCFs vs. 
    (a) The PCALX 410.2 Hz line being ON vs. OFF (H1:CAL-PCALX_PCALOSC2_OSC_SINGAIN) -- 3rd vertical panel
    (b) A real physical change in the optical plant of the IFO -- Evan Hall parasitically changing the alignment of the signal recycling cavity (H1:ASC-SRC1_Y_OFFSET) -- 4th vertical panel.

Recall that all TDCFs have a ~2 minute time-lag from impulse responses because there's online, rolling, averaging (really, median'ing) that lasts around 2 minutes.

One can see that
    (i) In the first panel, \kappa_C changes from 1.15 to 0.93 as the 410.2 Hz PCALX line changes from ON to OFF at -38 mins and -17 mins.
    (ii) In the second panel, while there is an impulse response to the change, f_cc does *not* change value as the 410.2 Hz PCALX line changes from ON to OFF, also at -38 mins and -17 mins
    (iii) When there's a physical change to the detector (the SRC1 offset) at -11 min and -5 min (with the line off), both the \kappa_C and f_cc are expected to change by some amount, and the TDCFs do.
    (iv) Also as expected, the relative actuator strength monitors, informed by calibration lines at much lower frequencies are unimpacted by the ON vs. OFF state of the 410.2 Hz PCALX line.

This led me to explore and change the collection of PCALY LINE 2 DEMOD "SIG" filters, in the banks
    - H1:CAL-CS_TDEP_PCAL_LINE2_PCAL_DEMOD_SIG
    - H1:CAL-CS_TDEP_PCAL_LINE2_ERR_DEMOD_SIG
    - H1:CAL-CS_TDEP_PCAL_LINE2_EXT_DEMOD_SIG
switching from a 0.2 Hz wide band pass to a 0.06 Hz wide band pass, or from 
    FM1     "BP410.3"      butter("BandPass",6,410.2,410.4)
to
    FM2     "NBP410.3"     butter("BandPass",6,410.27,410.33)
The attached bode plot comparison shows that the narrower band-pass filter
    :: Suppresses 410.2 Hz by a a factor of 1000x more (BP410.3 suppresses 410.2 Hz by 0.72x, NBP410.3 Hz suppresses 410.2 Hz by 7.6e-4x) , while still
    :: preserving the phase exactly at 410.3 Hz

The 15 minute trend of before and after the install of this filter demonstrates its effect,
    At the start of the trend, -18 min, the 410.2 PCALX line is OFF, and the DEMOD SIG filters are still the wider "BP410.3".
    At -15.5 min, I turn the 410.2 Hz PCALX line back ON, and at -13 min, the value of \kappa_C returns the the biased value of 1.15.
    At -10 min, I switch over all the DEMOD SIG filters over to the NBP410.3 filter, and the answer goes nuts for a bit as the filter settles.
    At -6.5 min, the calculation recovers, and one can see the familiar trend that was demonstrated during the earlier ON vs. OFF test, and \kappa_C eventually lands back at the unbiased value of 0.93, as though the 410.2 Hz line was "off."

Declaring victory, as of this aLOG, the PCALX 410.2 Hz line shall remain ON, but I've accepted the newer, narrower bandpasses around the DEMOD of the PCALY 410.3 Hz line, and the TDCFs are no longer biased by the PCALXY comparison. I've accepted this change in the CALCS SDF system.