Oscillations, Waves, and Interactions - GWDG

290 Schreiber
n1
D
A B
n
Figure 8. Determination of the orientation of a non triangular ring laser. While n represents
the orientation of the square ABCD, a non-planar ring has to be subdivided into
triangles, which then have to be summed up.
good agreement between the model and the FSR measurements is found, while the
scale factor variations coming from the strain effects are not visible in the time series
of the Sagnac frequency.
6.4 Geometric scale factor correction
The two monolithic smaller ring lasers and their monuments are geometrically very
stable and beamwalk effects have not been observed so far. In contrast the very large
ring lasers UG1 and UG2 are subject to deformations of the Cashmere Cavern as
a result of thermoelastic strain and atmospheric pressure variations. Small mirror
tilts in the laser beam steering cause changes in area and perimeter. This results
in a drift of the geometrical scaling factor and the normal vector of the respective
ring laser. Other systematics come from the fact that the gyroscopes are He-Ne gas
lasers and therefore they suffer from a continuous degradation of the laser gas purity
caused by outgassing from the cavity enclosure. As the laser gain reduces with time
a substantial drift of the measured Sagnac frequency develops. The obtained beat
frequency from a ring laser gyro is proportional to the scaling factor, the rotational
velocity and the orientation of the area normal vector and the vector of rotation as
shown in Eq. (2). The normal vector on the plane of the laser beams is well defined
for a triangular ring only.
Since most of the very large ring lasers existing to date have a square or rectangular
shape, one needs to modify the definition of orientation for these instruments.
Figure 8 outlines the procedure. On the assumption of a square ring laser completely
planar along the corners ABCD, one finds the normal vector n representing the entire
area. If however one corner (C ∗ ) is slightly tilted out of plane, the effective area may
be obtained by subdividing the full area into triangles and projecting the normal
vector ni of each triangle onto the vector of rotation and summing them up.
Nearly all the large ring lasers mentioned in Table 1 are orientated horizontally
on the Earth. Because Earth rotation is the most dominant measurement signal,
they show a strong latitude dependence of Ωeff = sin(φ + δN), with φ corresponding
to the latitude of the instrumental site and δN representing a tilt towards North.
East-west tilts are nearly negligible, since the cosine of an angle representing a small
tilt towards East δE ≈ 0 is so close to 1 that it can be neglected, except for strong
seismic motions.
n2
C*
C