The sensing matrix was measured in the DRMI configuration for the first time.
The measurement was done by an automatic script and the realtime LOCKIN module built in the c1lsc model.
The resultant matrix is still too primitive, so I will do some further analysis.
(Measurement of sensing matrix)
The quantities we want to measure are the transfer functions (TFs) from displacement (or change in optical phase) of each DOF to sensors in unit of [counts/m].
So essentially the measurement I did is the same as the usual TF measurement. The difference is that this measurement only takes TFs at a certain frequency, in this case 283 Hz.
The measurement goes in the following order :
(1) Lock DRMI
(2) Shake an optic of interest longitudinally with an amplitude of 1000 counts at 283.103 Hz, where no prominent noise structures are present in any spectra of the sensor signals.
(3) Put a notch filter at the same frequency of 283.103 Hz in each DOF (MICH, PRC and SRC) to avoid unwanted suppression due to the control loops.
(This technique is essentially the same as this one, but this time the control loops are shut off only at a specific frequency )
The notch filter I put has a depth of 60 dB and Q of 20. The filter eats the phase of ~10 deg at 200 Hz, which still allow servos to run with a high UGF up to 200Hz.
(4) Take the output signal from a signal port of interest (i.e. REFL11_I, etc.,) and then put it into the realtime LOCKIN module.
(5) Measure the resultant I and Q signals coming out from the LOCKIN module.
(6) Repeat the procedure from (2) through (5) for each optic and sensor.
Again, the resultant sensing matrix is still primitive, for example the optic-basis should be converted into the DOF basis.
The values listed in the matrix below is the absolute values obtained by operation of sqrt( I^2 + Q^2) plus the polarity according to the output from I and Q of LOCKIN.
Therefore they still contain the actuator response, which is not desired. i will calibrate them into [counts/m] later by using the calibration factor of the actuator responses.
All the raw data showed the relative phase between I and Q either ~ 127 deg or ~ -53 deg.
In my definition, the one has 127 deg is plus polarity and the one has -53 deg is minus polarity.
Technically speaking the polarity depends on the polarity of the actuator and also the direction of the actuator against the DOFs.
Without any excitation the absolute values fluctuated at about 10-4 - 10-5, so the excitation amplitude was big enough to observe the sensing matrix.
Though, I still need to estimate the statistical errors to make sure the SNR is reasonably big.
Fig.1 Measured sensing matrix from optic to sensors.
(Things to be done)
- convert the optic-basis (i.e. BS, ITMs, PRM and SRM) to the DOF-basis (i.e. MICH, PRC and SRC) so that the matrix is understandable from point of view of the interferometer control.
- estimate the optimum demodulation phase for each DOF at each sensor port.
- add some statistical flavors (e.g. error estimations and so on.)
- edit the script such that it will keep watching the ADC overflows and the coherence to make sure the measurement goes well.
- add some more signal ports (e.g. REFL55, POY55 and etc.)
- compare with an Optickle model
The result will be updated later.