J. Kissel

After resolving some problems with CAL-DELTAL_EXTERNAL yesterday (LHO aLOG 48012), we left off with
    - 2% / 4 deg systematic error in PCAL2DELTAL transfer function below 40 Hz. 
    - achieved by scaling down the overall actuator function reproduction by 4% (i.e. gain of 0.96), and 
    - some poorly understood confusion with the 2019-03-28 reproduction of the sensing function.
    - leaving the relative path delay at 7 clock cycles (though the model predicts 7.7 clock cycles)

This morning, after some sleep and a bit more exploring, we are now better:
    - Systematic error within 1%  / 1 deg in PCAL2DELTAL transfer function from 20 Hz to 500 Hz (and above, only 2% / 1 deg from 500-1000 Hz).
    - No time-dependent change in the PCAL2DELTAL transfer function over the course of 16 hours -- the interferometer's TDCFs must be *very* stable
    - A direct one-to-one map of the 2019-03-28 sensing function model, with no gain adjustment (i.e. gain of 1.0) 
    - A 5% scale down (gain of 0.95) of the overall actuator function.
    - leaving the relative path delay at 7 clock cycles.

Now I'm confident we no longer need to change the CAL-CS DELTAL EXTERNAL, and it's systematic error (+/- 1%) is within a factor of 2 of the stated current PCAL's uncertainty (0.5% at 68% confidence interval).

Attached are some more broadband PCAL2DELTAL transfer functions, demonstrating 
    - the exploration of whether the 2%-below-40Hz systematic error was because of a *relative* gain mismatch between actuator stages, or if it was an overall actuator scale error. The answer is as discussed above -- we only needed a minor adjustment of overall scale from 4% to 5% (i.e. gain of 0.96 to 0.95).
    - the "BEST YESTERDAY" and "BEST TODAY" -- measurements 16 hours apart, in the same lock stretch in the same CAL-CS configuration. This demonstrates that, within a single lock stretch at least, all time-dependent corrections must be very stable, much better than O2.

What remains: 
    - Understand the necessary 5% scale of the actuator (OFFLINE WORK)
    - Update the pyDARM loop model parameters to reflect this scale difference, and call it the reference model (OFFLINE WORK)
    - Fix the recreation of reference model values at calibration line frequencies used to create the front-end computed time-dependent correction factors. (OFFLINE WORK)
    - Create GDS correction filters from the reference model, and update the filters to create GDS-CALIB_STRAIN
    - Compare outputs of GDS and DELTAL EXTERNAL against PCAL and confirm systematic errors are understood at the +/- 1% level
    - Compare outputs of time-dependent correction factors computed by GDS and CAL-CS, and confirm they make sense at the +/- 1% level
    - Start the run!