Estimating the table top motion of LIGO HAM tables from the motion
of the optics placed upon it
Raghuveer Dodda
It is important for the LIGO project to estimate the tabletop motion (translational and
rotatory) because there is no satisfactory data acquisition channel that describes the
motion of a table. A simple way to estimate this would be to calculate the motion of a
mirror on the required table from the data acquisition channels and multiply the mirror
motion with the mirror-tabletop transfer function. The result is the tabletop motion. This
experiment verified the accuracy of this process by using the calculated tabletop motion
to predict the motion of a different mirror on the same table. The results show that
calculating the tabletop motion from the motion of mirror placed on it is feasible.
INTRODUCTION
The Laser Interferometer Gravitational
Wave Observatory (LIGO) is a project
undertaken to detect gravitational waves.
The Interferometer uses several mirrors
suspended from a frame. The frame sits
on a table that is isolated from ground
noise. A simulation package called E2E
is being developed to simulate the
working of the interferometer. It is
necessary to understand how the tabletop
moves in response to the ground noise to
create an effective simulation.
MMT3
MMT1
HAM1 tabletop
Isolation stack
Fig 1 – Schematic diagram of the HAM1 table
with MMT1 and MMT3 on it
This experiment is aimed at calculating
the HAM1 tabletop motion from the
MMT1 mirror placed on top of it. The
accuracy of the calculation was tested by
checking how closely this calculated
tabletop motion predicted the motion of
the MMT3 mirror that is also placed on
the same table.
METHODS
The following steps were taken:
1. The readings of the coil magnets
behind the MMT1 and MMT3
were obtained as a function of
time for a certain period of time.
2. The translational and the yaw
motion of MMT1 and MMT3
were calculated as a function of
time.
3. The Fast Fourier Transform
(FFT) of the translational and
Yaw motions of MMT1 were
taken. This yielded the various
frequency components of the
motions, or the translational and
yaw motions as functions of
frequency.
4. These frequency functions were
multiplied with the Small Optic
Suspension
(SOS)
transfer
functions for translational and
yaw motion to obtain the HAM1
translational and yaw motions as
a function of frequency.
5. This
HAM1
motion
was
multiplied with the Large Optic
Suspension (LOS) to obtain the
translational and yaw motions of
MMT3
as
functions
of
frequency.
6. The Inverse FFT of the
calculated MMT3 motions were
taken to yield the predicted
translational and yaw motions of
MMT3 as a function of time.
7. The correlation between the
calculated MMT3 motions and
acquired MMT3 motions (step 1
& 2) were calculated.
The result of this process is two
correlation coefficients, one for the
translational motion and the other for the
yaw motion.
RESULTS
The correlation coefficients for the
MMT3 motions are (the Matlab code for
these calculations is here):
error
Translational
Corr.
Coeff
(r)
0.7714
Yaw
-0.7242
0.0037
0.0077
DISCUSSION
The HAM1 tabletop motion is believable
if there are peaks at the resonance
frequencies of the table.
The correlation of the recorded and
calculated motions of MMT3 is a direct
indicator of the effectiveness of the
process to calculate HAM1 motion from
MMT1. The closer to 1 the absolute
values of these coefficients are, the more
accurate the calculated HAM1 motion.
These coefficients can certainly be
improved if the location and orientation
of MMT1 and MMT3 on HAM1 are
taken into account.
Regardless, the results testify that
estimating tabletop motions from the
optics placed upon them is a feasible
process statistically.
REFERENCES
Findley. T, and K. Rogillio. 2004.
Matlab code for calculating MMT3
motion.