The WFS error signals were recorded in the order

WFS1_PIT

WFS1_YAW

WFS2_PIT

WFS2_YAW

these measurements are made in the linear region, that is the MC is nearly perfectly aligned.

This is  the average and std. dev.of 5 measurements taken of the same signals over 10 secs each. The std. dev are under 10%. And hence, I will be using 10 secs for measurements for the WFS signals after perturbations to the mirrors.

avg =

829.4408
-517.1884
297.4168
-944.7892


std_dev =

9.0506
22.9317
15.4580
8.9827

I perturbed the Pitch and Yaw of the Three mirrors (in order MC1,2,3), using ezcastep and calculated the coefficients that relate these perturbations to the WFS error signals.

The perturbation made is of -0.01 in each dof , and after measuring the WFS error for it, the system is reverted back to the previous point before making the other perturbation.

I was able to calculate the coefficients since I have assumed a linear relationship..

Following are the coefficients calculated using 10 secs measurements

coef_mat =

   1.0e+05 *

                            MC1_P   MC1_Y  MC2_P   MC2_Y    MC3_P   MC3_Y  constant
WFS1_PIT        -0.1262    0.3677   -0.4539   -0.6297   -0.1889   -0.1356   0.013664
WFS1_YAW     -0.0112   -0.7415   -0.1844    2.4509   -0.0023   -0.3531  -0.016199
WFS2_PIT         0.1251    0.4824   -0.2028   -0.6188    0.0099   -0.1490   0.006890
WFS2_YAW      0.0120   -0.7957   -0.1793    0.9962   -0.0493    0.2672 -0.013695

Also, I measured the same thing for 100s, and to my surprize, even the signs of coeficients are different.

coef_mat =

   1.0e+05 *

                           MC1_P   MC1_Y  MC2_P   MC2_Y    MC3_P   MC3_Y   constant
WFS1_PIT       -0.1981    0.3065   -0.6084   -0.9349   -0.4002   -0.3538   0.009796
WFS1_YAW     0.0607   -0.6977    0.0592    2.8753    0.3507    0.0373   -0.008194
WFS2_PIT        0.0690    0.4769   -0.2859   -0.7821   -0.1115   -0.2953  0.004150
WFS2_YAW     0.0580   -0.8153   -0.0937    1.1424    0.0650    0.4203  -0.010629

The reason I can understand is that the measurements were not made at the same time, and hence conditions might have changed.

A thing to note in all these coefficients is that they relate the error signals to the 'perturbation' around a certain point (given below). That point is assumed to lie in the linear region.

MC1_PIT      2.6129
MC1_YAW   -5.1781
MC2_PIT       3.6383
MC2_YAW    -1.2872
MC3_PIT      -1.9393
MC3_YAW    -7.518