After we had a rough idea of what the output matrix looks like (see this elog),
I tried to measure the transfer function coefs (TFCs) between mirror degrees of freedom and the WFS sensors (WFS1, WFS2 and MC_Trans QPD)
I found that the TFCs that I obtained at 10.15 Hz did not have any resemblance to the previously identified output matrix.
The problem, I realised, arises because the various lockins used
in the C1IOO model do not have the same relative phase; So if we try to excite a mirror with one of them
and demodulate a sensor signal on any of the other lockins the resulting output would not have the correct phase
(relative to the 1st lockin output). As a result unless we can reset the phase of all the lockins
simultaneously, we cannot demodulate multiple signals at the same time. (Joe/Jamie, Is it possible to
reset/reinitialise the phase of the CLK signals of the lockings? )

To get around this problem Koji suggested that I use just one lockin and determine all the 36 elements of the transfer matrix with it one at a
time rather than six at a time.  When I did that, I got results consistent with the previoulsly determined outmatrix. It, of course, takes six times longer.

The matrix I first got is this one

Note that when MC2 is excited all the sensors showed a response about 75 deg out of phase with the reference (MC1 --> WFS1_PIT ) This was traced to the fact that while there is a 28Hz Elliptic LP filter on

both MC1 and MC3, while it is absent on MC2.  The Transfer functions  below show the difference in the phase of their response

Since the MC2 POS is used in servos involving MCL we cannot afford to install a 28 Hz LP filter into the MC2 coil drivers.  However a module with the 28 Hz ELP was switched on, in each of the

 MC2 PIT and YAW filter banks.   I then checked to see if this has affected the relative phase of variour sensors.  The Phase angle between I and Q on each sensor channel was checked and corrected. 

Below are the spectra with the "before" and "after" correction of phases.

Before:

Obviously this needed adjustment to reduce Q phase.   

  After twealkng the angle "R":

And again determined the transfer matrix (below). 

This time the signals are all nearly in the same phase and in agreement with the  outmatrix estimate made earlier.

I plugged these TFCs into the matrix inversion code: wfsmatrix2.m.   And get the following inverse:

I have ignored the MC2_Trans_P and Y sensors for now.