# Open loop optical matrix

## Introduction

A finesse simulation has been set up to measure the optical matrix of the interferometer, which is the set of transfer functions from all degrees of freedom to all photo-diode signals. The plane wave approximation was used, therefore no defects nor thermal effects were included.

The interferometer was tuned at the operating point, which corresponds in this case to the point of maximum/minimum powers. Monochromatic perturbations were added to the different dofs with the fsig command and the frequency swept over a wide range.

Demodulation phases have been tuned using a procedure similar to the experimental one:

B1_AC maximize P/Q of a DARM line

B5_AC maximize P/Q of a CARM / FREQ line

B7_AC and B8_AC maximize P/Q of a DARM line

B2_8MHz_AC maximize P/Q of a MICH line (same result using a PRCL line)

Frequency noise was simulated introducing a dummy beam splitter at the input and moving it. This generates phase noise. The resulting transfer function can be converted to real frequency noise by multiplication with 1/(iw) where w is the signal frequency.

MICH driving is the same as in Virgo, as explained also here.

The finesse input file can be found here.

## Results

The output files of finesse have been read and processed using a Python/matplotlib script, to produce the plots. Here are the amplitude of transfer functions from all DOFs to all photo-detectors. Solid lines refers to ACp, dotted lines to ACq.

Some general comments:

- as expected DARM and CARM/FREQ are the dominant DOFs in all signals;
- even without any thermal effects, MICH and PRCL degrees of freedom are well visible in both B5_ACq and B2_8MHz_ACp, with similar amplitudes