L. Dartez, J. Kissel, E. Goetz

We compared the correction to the deltaL_external/Pcal TF as produced by pyDARM (0.0.6) against the long standing correction used by the DTT templates in broadband Pcal injections (eg that from LHO 65879). A comparison of the deltaL/Pcal correction is attached. Here's a brief description of what is shown in the attached plots:

Page 1: shows the two deltaL_external/Pcal corrections plotted over each other in a Bode diagram in the left column. The Bode diagram in the right column shows the residual between the deltaL_external/Pcal correction given by pyDARM and the same used in the DTT template.
Page 2: compares the deltaL_external correction produced by pyDARM with the same from the DTT template.
Page 3: compares the DTT template's Pcal correction (a simple ZPK filter with two poles at 1Hz) with the Pcal correction from pyDARM, which has the same ZPK filter and AA filters.  

Aside from a few differences that we think we understand, the deltaL_external/Pcal correction produced by the latest point release of pyDARM agrees with the correction used by the DTT template.

On the differences showing up in the deltaL_external residual (page 2):

    - The high frequency (2+ kHz) rolloff is due to the fact that the DTT template has not been adjusted to account for the new analog sensing chain, which has five ~10kHz poles as opposed to the 11kHz, 17kHz, and 32kHz poles in the old sensing chain.
    - The 1Hz-~200Hz wiggle: pyDARM now uses the full mathematical expressions in T1900169 (see Eqs. 98 & 99) for modeling the deltaL_external/Pcal correction instead of relying on incomplete approximations as was done during O3.
    - The phase offset from 0 degrees shown in the phase residual plot: This is due to an erroneous minus sign present in "the old" pyDARM 1.0 (before pyDARM was tracked on gitlab) from O3. This was discovered by Evan earlier today. This error was (and is) also present in the DTT template's correction of deltaL_external. It hasn't been noticed in the control room because the Wall_FOM DTT template shows an ASD which drops the phase. See an example here on L42. 

On the high frequency rolloff in the Pcal correction residual plots (page 3): The DTT template is just ("lazily") using 2 poles at 1Hz and has not corrected for the digital and analog anti-aliasing filters, whereas the pyDARM correction does.

As a note, three DTT templates will need to be updated. These are the Pcal2DARM broadband, the Pcal2DARM swept sine, and the wall FOM DTT templates.

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Plots: /ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/O3/H1/Results/CALCS_FE/20221128_deltal_over_pcal_comparison.pdf
Script: /ligo/gitcommon/Calibration/ifo/scripts/calcs/deltal_over_pcal_compare.py
deltaL_external/Pcal correction exported from DTT template: /ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/O3/H1/Measurements/CALCS_FE/2022-11-18_H1PCALY2DARMTF_BB_deltaL_only_calibrationtf_2018version.txt