J. Kissel

One of the many minor things we have to do before the run -- re-tune the DCPD SUM and NULL balance matrix after installing an entirely new electronics readout chain (new in-vac transimpedance amplifiers, new whitening chassis, new lack of anti-aliasing chassis, new analog copying 4 times, new ADC, and new digital averaging of those copies after digitization).

I've followed the lead of Stefan Ballmer's work doing this in the past, see LHO aLOGs 45734 and 47228 with the methods nicely described in 47217.

As such, I grabbed a time while the detector was nicely thermalized, and the SQZ system was OFF in order to gather both the coherent transfer function as well as the incoherent amplitude spectral density ratio (and cross-spectral density) between the DCPDs (see first attachment).

Using this data (exported from DTT), I grabbed the median of high coherence points (coh = C > 0.99999, N_avg = 100, unc = sqrt( (1-C) / (2*N_avg*C) )) of the transfer function, and the median of low coherence points (coh < 0.0001) of the amplitude spectral density ratio, to determine the quantities
    g = PD_A/PD_B coherent signal amplitude ratio (best done by looking at the PD_A/PD_B transfer function at low frequencies)
    h = PD_A/PD_B shot noise signal amplitude ratio (by matching the amplitude spectra ratio - a transfer function does not work here)

For both the transfer function and the ASD ratio, I use DCPD A in the numerator, and DCPD B in the denominator.

See the attached .pdf for the collection of result pages, but in short, I get
    g = 1.03572; 
    h = 1.02327; 

which in turn, using Stefan's OMCmatrix.m from LHO:47221, that yields a proposed balance matrix of
    MM_proposed =
          0.99455       1.0055
          0.98259      -1.0177


I'll check with Stefan to make sure I've interpreted his methods correctly, and to be sure if I should be using DCPD A / DCPD B.

Note, the current balance matrix is
    MM_current = 
          1.01039    0.98961
          0.98961   -1.01039