Here is the result of the measurement of the sensing matrix in the PRMI configuration.
If we believe the resultant matrix, it is somewhat different from what we expected from a finesse simulation (summary of simulated sensing matrix).
(Motivation)
As a part of the DRMI test plan, we wanted to check the sensing matrices and consequently diagonalize the LSC input matrix.
The matrix of the DRMI configuration has been measured (#4857), but it was a bit too complicated as a start point.
So first in order to make sure we are doing a right measurement, we moved onto a simpler configuration, that is PRMI.
(measurement)
The technique I used was the same as before (#4857) except for the fact that SRM wasn't included this time.
 PRC was locked to the carrier resonant point. The UGF of MICH and PRC were ~ 110 Hz and 200 Hz respectively.
 Longitudinally shook BS, ITMs and PRM at 283.103 Hz with an amplitude of 1000 counts using the LOCKIN oscillator in C1LSC.
 Took the I and Q phase signals from the LOCKIN outputs.
The table below is the raw data obtained from this measurement :
(Conversion of matrix)
With the matrix shown above, we should be able to obtain the sensing matrix which gives the relation between displacements in each DOF to each signal port.
The measured matrix connects two vectors, that is,
(signal port vector) = [Measured raw matrix] (SUS actuation vector),  eq.(1)
where
(signal port vector) = (AS55_I, AS55_Q, REFL11_I, REFL11_Q)^{T} in unit of [counts],
(SUS actuation vector) = (BS, ITMX, ITMY, PRM)^{T} in units of [counts].
Now we break the SUS actuation vector into two components,
(SUS actuation vector [counts]) = (actuator response matrix [m/counts])^{1} * (MICH, PRM [m] )^T  eq.(2)
where
(actuator response matrix) = 2.05x10^{13} * ( [1 , 0.217, 0.216, 0 ],
[ 0.5, 0.109 0.108, 0.862] ) in unit of [m/counts]
These values are coming from the actuator calibration measurement.
In the bracket all the values are normalized such that BS has a response of 1 for MICH actuation.
Combining eq.(1) and (2) gives,
(signal port vector) = (measured raw matrix) * (actuator response matrix)^{1} * (MICH, PRM)^{T}
And now we define the sensing matrix by
(sensing matrix) = (measured raw matrix) * (actuator response matrix)^{1}
The sensing matrix must be 4x2 matrix.
For convenience I then converted the I and Q signals of each port into the absolute value and phase.
ABS = sqrt((AAA_I)^{2} +(AAA_Q)^{2} ),
PHASE = atan (AAA_Q / AAA_I),
where AAA is either AS55 or REFL11.
(Resultant matrix)
The table below is the resultant sensing matrix.
ABS represents the strength of the signals in unit of [cnts/m], and PHASE represents the demodulation phases in [deg].
There are several things which I noticed :
 The demodulation phase of MICH=>AS55 and PRC=>REFL11 are close to 0 or 180 deg as we expected.
This is a good sign that the measurement is not something crazy.
 AS55 contains a big contribution from PRC with a separation angle of 152 deg in the demodulation phase.
In AS55 the signal levels of MICH and PRC were the same order of magnitude but PRC is bigger by a factor of ~4.
However the finesse simulation (see wiki page) shows a different separation angle of 57 deg and MICH is bigger by factor of ~6.
 REFL11 is dominated by PRC. The PRC signal is bigger than MICH by a factor of ~100, which agrees with the finesse simulation.
However the separation angle between PRC and MICH are different. The measurement said only 19 deg, but the simulation said ~ 90 deg.
 Woops, I forgot to calibrate the outputs from the LOCKIN module.
The whole values must be off by a certain factor due to the lack of the calibration , but fortunately it doesn't change the demodulation phases.
Quote from #4884 
I was able to measure the sensing matrix in the PRMI configuration.
The results will be posted later.

