J. Kissel, K. Venkateswara

We were able to take overnight measurement with everything working smoothly. I have analysed 35000 seconds of data starting from ~7 PM to ~5 AM this morning. The first file shows a similar plot as I had posted yesterday. The subtraction is done a bit differently:
Yesterdays subtraction -
Residual = BRSout  +  T240X * (w/g)

This simply accounts for the inertial angular acceleration measured by the bar and assumes d = 0.

Todays subtraction - 
Residual = BRSout  +  T240X * (w/g) + T240X * ( 1/w * M * d * g/I)

where BRSout is the BRS output (in rad), T240X is the velocity output, w is angular frequency (2 pi f), M is the total mass of the balance (4.2 kg), d is the distance between CoM and the suspension point ( (39 +/- 5) microns), g is 9.8 m/s^2, and I is the moment of inertia of the beam (0.59 kg m^2).
This subtraction accounts for inertial angular acceleration and horizontal acceleration coupling based on an estimate of d, which is explained below.

The second file shows the raw T240X displacement output and the tilt-subtracted output.

The third file shows the angular acceleration measured by the bar. This is similar to the first plot, but rotated by f^2. This makes the effect of various terms a bit clearer. The first plot shows the influence of inertial angular acceleration and the horizontal acceleration coupling. This allowed me to estimate d by varying it until the green curve lined up with the blue at low frequencies. In the next plot I added the residual and the autocollimator noise. Note that the residual is worse below ~8 mHz due to the influence of the low-frequency high-pass filters which mess up the phase.

To make a long story short, the Beam Rotation Sensor works as expected. The subtraction scheme we showed above is easily implementable and presently gives a factor of ~5 improvement in displacement noise below 0.1 Hz down to ~10 mHz. The d offset is larger than I expected which was due to the inaccuracies in the transfer function measurement scheme. Still, it does not present any difficulties in doing the subtraction. If we have to open up the vacuum can for whatever reason in the future, we can correct it easily.

We have learnt many lessons and if we get the opportunity to do this again, we will do better. We have some ideas for implementing a simple damping scheme to remotely damp the balance, which we will try out at UW. 

I have had a great time installing/commissioning the tiltmeter and would like to thank everybody at LHO for all the asistance. The atmosphere and energy here is terrific and I hope to be back here soon :)



edit: The matlab file I used for the above analysis is : /ligo/home/controls/tmp/BRSanalyze.m
It is very badly written and I will add comments, polish it and upload it soon.