[Lydia, Teng]
Motivated by the strange pitch/yaw coupling behavior we ran into while doing diagonalization, we looked at the oplev pitch and yaw free swing spectra for all 4 test masses (see attachment 1). We saw the same behavior there: At the peak frequencies for the angular degress of freedom, the oplevs saw significant contributions from both pitch and yaw. We also examined the phase between pitch and yaw at these peaks and found that consistently, pitch and yaw were in phase at one of the resonance frequencies and out of phase at the other (ignoring the pos and side peaks).
This corresponds physically to angular motion about some axis that is diagonal, ie not perfectly vertical or horizontal. If we trust the oplev calibration, and Eric says that we do, then the angle of this axis of rotation with the horizontal (pitch axis) is
Where Y and P are yaw and pitch ASD values. This will always give an angle between 0 and 90 degrees; which quadrant the axis of rotation occupies can be dermined by looking at the phase between pitch and yaw at the same frequencies. 0 phase means that the axis of rotation lies somewhere less than 90 degrees counterclockwise from the horizontal as viewed from the AR face of the optic, and a phase of 180 degrees means the axis is clockwise from horizontal (see attachment 2). Qualitatively, these features show up the same way for segments of data taken at different times. In order to get some quantitative sense of the error in these angles, we found them using spectrogram values with a bandwidth of 0.02 Hz averaged over 4000 seconds.
Results (all numbers in degrees unless otherwise specified):
ITMY
peak 1 ( 0.692 Hz):
mean: 24.991
std: 1.23576
ptich/yaw phase: 179.181
peak 2 ( 0.736 Hz):
mean: 21.7593
std: 0.575193
pitch/yaw phase: 0.0123677
ITMX
peak 1 ( 0.502 Hz):
mean: 17.4542
std: 0.745867
ptich/yaw phase: 179.471
peak 2 ( 0.688 Hz):
mean: 74.822
std: 0.455678
pitch/yaw phase: 0.43991
ETMX
peak 1 ( 0.73 Hz):
mean: 43.1952
std: 1.54336
ptich/yaw phase: 0.227034
peak 2 ( 0.85 Hz):
mean: 60.7117
std: 0.29474
pitch/yaw phase: 179.856
ETMY
peak 1 ( 0.724 Hz):
mean: 78.2868
std: 2.18966
ptich/yaw phase: 6.03312
peak 2 ( 0.844 Hz):
mean: 26.0415
std: 2.10249
pitch/yaw phase: 176.838
ETMY and ITMX both show a more significant (~4x) contribution from pitch on one peak, and from yaw on the other. This is reflected in the fact that they each have one angle somewhat close to 0 (below 30 degrees) and one close to 90 (above 60 degrees). The other two test masses don't follow this rule, meaning that the 2 angular frequency peaks do not correspond to pitch and yaw straightforwardly.
Also, besides ITMX, the axes of rotation are at least several degrees away from being perpendicular to each other.
