Alexa, Sheila

Tonight we decided to try to charachterize the coupling of alingment fluctuations to the error between the arm resonance and the ALS COMM lock point. We did this using the normalized PDH error signal.  The frequency dependence of this spectrum is unclear- if we were staying on resonance we would just have the cavity pole, but the transfer function of the transmitted light will change as we move over the resonance.  So to make a good calibration we need to lock well enough to stay on resonance.  (This is why we have been trying the AO the last few nights).  For tonight we concentrated on low frequency noise that is dominating our RMS, where the frqeuency dependence won't matter anyway.

We put a 1 Hz excitation onto ETMX pitch, making it large enough to see the second harmonic.  We measured the spectrum of our REFL_DC_BIAS error signal when COMM was locked, and the op lev spectrum with and without the excitations.  The attached screenshot shows the spectrum with and without the excitation.

Measuring the peaks due to the excitation we estimated the coupling coefficient with excitations of 2 different amplitudes, 1.7kHz/urad and 1.5kHz/urad.  We also can esitmate the quadratic coupling from this data, we got 159Hz/(urad)^2 and 170 Hz/(urad)^2

Attached is a plot of linear and quadratic projections based on the Oplev data (up to 4Hz) into the REFL_DC_BIAS path.  It can explain all the noise around the pitch resonance (which is most of the RMS), but not elsewhere.  We had wondered if the coupling was nonlinear and some of our unexplained noise from 1 Hz-50Hz  (or below 0.3Hz) was upconverted angular fluctuations.  Our measurement suggests that this is not the case. 

We were planning to repeat this measurement for ITMX, but so far we have been prevented by and earthquake.