During Tuesday maintance this week, we moved the upper (inner) beam of the Xend Pcal system down from it's nominal location by 2.5 mm on the surface of the ETM (see aLog entry 72063).
The observed change in the Pcal X/Y comparison should give a measurement of the vertical component of the displacement of the interferometer beam from the center of the ETM. This displacement, denoted by the b_y, is given by
Delta_XY = c/2 * b_y * M / I
where Delta_XY is the observed change in the Pcal X/Y comparison (after minus before), c is the change in the vertical position of upper Pcal beam, the factor of 1/2 results from only moving one of the two Pcal beams, b_y is the vertical component of the displacement of the interferometer beam from the center of the optic, M is the mass of the optic, and I is the moment of intertia of the ETM for rotation about an axis parallel to the face of the optic and and through the center of the face of the optic.
Thus the interferometer beam displacement can be estimated by b_y = 2* Delta_XY / (c * M / I).
For the Xend ETM, M / I = 0.94e-4 / mm^2 and c = - 2.5 mm. Thus b_y = -0.85e4 * Delta_XY mm
Using DTT to analyze data (1024 sec FFTs, 50% overlap, 10 avgs) during a lock stretch the day before we moved the beam, 08/07 from about 08:00 to 23:00 UTC, and after the move on 08/09 between 00:30 and 06:30 and between 11:30 and 15:30. We observe a change in the X/Y comparison of about - 24e-4 (see attached plot). This would indicate an interferoemter beam offset of about 20.7 mm in the positive y direction, ABOVE the center of the optic.
Info provided by JenneB (seel below) indicated that the pitch measurements using the electrostatic acutators indicate that the interferometer beam is offset by about 14.3 mm BELOW the center of the ETM.
We will look at more data from before and after the beam position move and double-check our calcuation to make sure we aren't missing a minus sign somewhere.
Next Tuesday, we plan to move the beam back to it's nominal vertical potition and offset it to the left (when viewing the fact of the optic from the BS side) by 2.5 mm to assess the horizontal component of the interferometer beam offset from center.
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From JenneD on 7/21/23:
Folder for getting the spot position is /opt/rtcds/userapps/trunk/isc/common/scripts/decoup/BeamPosition/
Using matlab....
help a2l_lookup: look up spot position for a given a2l gain on a test mass
Input:
1) 'PIT' or 'YAW'
2) a2l gain Output:
1) spot position in mm from test mass center ("spot position" is really the actuation node position; if the spot is co-located with the actuation node (eg. servo-ed there) then this also represents the spot position)
Sign convention for spot position: up (+Vert on SUS screens) is positive for pitch and farther to the left (+Trans on SUS screens) is positive for yaw.
a2l_lookup('PIT',4.0) Spot is -14.3 mm from the PIT center of the optic
a2l_lookup('YAW',4.4) Spot is 16.2 mm from the YAW center of the optic
ETMY:
a2l_lookup('PIT',4.60) Spot is -17.1 mm from the PIT center of the optic
a2l_lookup('YAW',3.2) Spot is 11.8 mm from the YAW center of the optic
