[J. Betzwieser, T. Mistry, M. Wade, A. Viets]

Timesh and Joe recently found evidence that the imaginary parts of the actuation kappas are inconsistent with measurements from calibration sweeps: LLO aLOG 48183.  I made some broadband injection plots for L1 to help us decide whether we should be applying corrections for these (See LLO aLOG 48245).  At H1, the GDS calibration pipeline has been applying corrections for the imaginary parts of the kappas since May 21.  This was seen to improve calibration accuracy at H1 near the end of O2 (see P1800313, especially plots on pages 6 and 7).  However, systematic errors in the estimates of the actuation kappas can also cause the imaginary parts to drift from zero, especially when other TDCFs drift substantially from their nominal values.  This has raised suspicion that correcting for the "complex kappas" is making systematic errors worse rather than better.  To test this, I've used 4 broadband injections from the Y-end Pcal to make comparisons.  In short, the results show that for now, we should correct for only the real parts (or magnitudes) of the actuation kappas.  The imaginary parts are probably dominated by systematic errors based on these results.  Since our sensing function model at low frequencies is under question as well, I also included comparisons of accuracy between h(t) that is corrected for time dependence in SRC detuning and h(t) that is not.  In total 4 versions of calibration are plotted in the attached figures:

1. Real kappas: This version applies corrections for real parts of kappa_T, kappa_P, and kappa_U, as well as kappa_C and fcc
2. Real kappas + SRC: This version applies corrections for real parts of kappa_T, kappa_P, and kappa_U, as well as kappa_C, fcc, f_s, and Q
3. Complex kappas: This version applies corrections for complex values of kappa_T, kappa_P, and kappa_U, as well as kappa_C and fcc
4. Complex kappas + SRC: This version applies corrections for complex values of kappa_T, kappa_P, and kappa_U, as well as kappa_C, fcc, f_s, and Q (everything)

To my eye, the four plots below seem to indicate that 1 is the most accurate calibration.  Each of the below plots used 180 seconds of data, and the start times are given below, in the same order as the attachments:

1. Wed Jun 12 20:28:29 GMT 2019
2. Wed Jul 03 21:57:03 GMT 2019
3. Wed Jul 17 20:40:20 GMT 2019
4. Thu Aug 01 18:10:23 GMT 2019

For now, the obvious solution is to turn off application of the imaginary parts of the kappas.  In the long run, it may be beneficial to use a solution for the TDCFs that is not subject to this systematic error.  Such a solution is in the works, but is not yet ready to be deployed.

These plots, as well as text files with the data, are available in the calibration SVN here:
aligocalibration/trunk/Runs/O3/H1/Measurements/FullIFOSensingTFs/DCS_BB_plots