Reports until 20:57, Wednesday 05 December 2018
H1 ISC
stefan.ballmer@LIGO.ORG - posted 20:57, Wednesday 05 December 2018 - last comment - 13:44, Friday 01 March 2019(45734)
Setting the OMC DCPD matrix

We lost recent changes in the OMC DCPD input matrix. And the previous settings were not totally consistent between SUM and NULL.
So here is how we set it:

There are 4 conditions that define the OMC DCPD input matrix (referred to as [A,B;C,D] ):
1) Total gain for sum. This is arbitrary, since it will be absorbed by the calibration. We chose the condition A+B=2, which seems to be what was done in the past.
2) The signal-to-shotnoise ratio in SUM must be maximal.
3) There is no signal in NULL.
4) The shot noise in NULL must be equal to the shot noise in SUM

We can measure two numbers (ratios):
     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 - a transfer function does not work here)

with these definitions and conditions, the solution is
   A=(2*g)/(h^2 + g);
   B=2-A
   C=sqrt((A^2*h^2+B^2)/(h^2+g^2));
   D=-g*C;

We measured g=1.0323 and h=1.0134. This results in the matrix
  M =   [1.0026    0.9974;
            0.9842   -1.0160;
 

The matrix is loaded and SDF accepted.

Attached is also a MATLAB script that derives the solution and calculates the matrix.

 

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stefan.ballmer@LIGO.ORG - 13:44, Friday 01 March 2019 (47223)

See alog 47217 for additional explanations and illustrations.