Got home, check the locking status ... the arm had dropped lock .... I commanded 'caput H2:ALS-Y_REFL_SERVO_IN1EN 0' followed by 'caput H2:ALS-Y_REFL_SERVO_IN1EN 1'  and the cavity locked ... even more surprising it had a REFL power of 7000 ... and it started to move up automatically to 9200!! It seemed that the WFS are working

I tried to write an auto locker script but I hidiously failed. Although it may have something to do with a remote shell. I disengaged the REFL servo as it dropped lock and would not come back in the time I was trying to write the script.

We centered the WFS and repeated the measurement of the sensing matrix. We did it in two ways: a) measuring the frequency response of the PIT and YAW outputs of both BFS A and B when exciting the POS and ANG mode of the cavity at about 4 Hz; b) introducing offsets in the cavity's POS and ANG degrees of freedom and measuring the displacement of the PIT and YAW output of the WFS.

The first method gave us almost degenerate sensing matrix. The second one seemed a bit better. The measured matrix M was:

M =
    0.0157   -0.7306         0         0
    0.0708   -0.6684         0         0
         0         0    0.0598    0.1663
         0         0   -0.0210    0.3363

The PIT and YAW inverted matrices were:

iP =
  -16.2163   17.7263
   -1.7176    0.3814
iY =
   14.2483   -7.0453
    0.8899    2.5339

These are the matrices used for the overnight arm cavity locking.

Th eigenvectors of these matrices are:

VP =
   -0.9931   -0.7741
   -0.1177   -0.6331

VY =
    0.9968    0.5341
    0.0795    0.8454

(see below)

This doesn't look crazy, though the two WFS heads are not optimally placed and the table astigmatism is not minimal either.

PIT sensing matrix that Bram posted in the above elog entry actually means this:

|WFSA| = |0.0157  -0.7306| x |POS| = |-0.7306  0.0000| x |-0.021  1| x |POS|
|WFSB|    |0.0708  -0.6684|    |ANG|    | 0.0000 -0.6684|   |-0.110  1|   |ANG|

The columns correspond to POS and ANG excitation, and the rows represent the WFS heads. (Sorry for the crappy formatting, I hope you get that I'm trying to write a matrix equation.)

POS refers to the translation of the cavity axis caused by the rotation of ETM and ITM in the opposite direction by the same amount. ANG refers to the rotation of the cavity axis by the rotation of the ETM and ITM in the same direction by the same amount.

For WFSA, ANG PIT generates a factor of 50-ish bigger signal than POS PIT. For WFSB, ANG IT is about a factor of 10 bigger.

Similarly, if you take the YAW matrix it's this:

|WFSA| = | 0.0598 0.1663| x |POS| = |0.1663 0.0000| x | 0.36 1| x |POS|
|WFSB|    |-0.0210 0.3363|    |ANG|    |0.0000 0.3363|   |-0.06 1|   |ANG|

If you look at the YAW numbers (not shown here but see the above entry by Bram), WFSA is a factor of 3-ish more sensitive to POS YAW than ANG YAW, and for WFSB this is a factor of 16.

Because of the cavity geometry (see below) ANG naturally produces a factor of 3 larger signal than POS. That means that, in terms of Gouy shift from the center of the cavity, WFSA for example is located at atan(-0.021*3) = -3.6 degrees away for PIT. Note that there's an uncertainty of n times pi that is common to all DOFs, and also the sign is sort of arbitrary though it should be consistent for both WFSs.

Anyway, below is the table of Gouy shift: from the waist of the arm in degrees (the above caveat about uncertaintly applies).

           PIT         YAW 
WFSA |  -3.6 deg | +47   deg|
WFSB | -18   deg | -10.6 deg|

PIT and YAW difference in WFSA looks kind of suspiciously large, but I would say that the crappy beam quality on the table could be blamed. It's not the TMS telescope (if it is, we'll see the same thing in WFSB too).

All in all the WFS locations could be adjusted better, and certainly the beam on the table is not passing through the center of lenses, but if the servo works (which we'll find eventually) I'll leave it.

----

Why a factor of 3 naturally?

Because we're using ETM substrate for both ETM and ITM, ROC of both is about 2300 m (2312 for EY, 2307 for IY).

Waist (w0=11.5mm for green) is at the center of the cavity, and the divergence angle is theta0=14.6 urad.

If we rotate both of the mirrors by the same amount (theta) as if one is the mirror image of the other, the cavity axis is purely translated by 2000m*theta. In terms of the higher order mode excitation, this is equivalent of

Normalized POS = 2000m * theta / w0 = 1.7e5 * theta.

ANG: If we rotate both of the mirrors by the same amount (theta) in the same direction, the cavity axis is purely rotated around the waist by (2300m * theta * 2)/600m. This is equvalent of

Normalized ANG = (2300m * theta * 2)/600m/theta0 = 5.3E5 * theta.

Therefore a factor of 3.