First, we unwrap the number of fringes using the standard error signal used in locking (B8_ACq / B8_DC), which indicates the sign of the resonance crossing. The exact time of the crossing is then determined by taking the center-of-mass of the transmitted peak. The peak time and peak index are then interpolated using a cubic spline, which yields the position as a function of time, see fig 1. Next, the sub-peaks are identified based on their interpolated position and their exact position is again determined using the center-of-mass, see fig 2.
Fig 3 shows the obtained position versus the speed. At low speeds, there are clearly some strange error. This is probably caused by the interpolation, which is not very accurate at the turning points of the movement. In addition, there is a direction dependent bias due to the cavity ringing effect, which should hopefully be equal for all peaks when moving roughly at constant speed. We only use points with a positive speed higher than 14 fsr/sec for the further analysis.
Fig 4 shows the positions of the 3 sub-peaks as a function of time after the unlock. For a single crossing of a sub-peak, a position is obtained with a standard deviation of about 2e-4 free-spectral-range, so the 100-point averages should have an error of 2e-5 fsr. The TEM2 peak does indeed seem to shift a little bit, while the USB seems to stay perfectly stable. The LSB, which should also be stable, seems somewhat noisy. Maybe this is caused by alignment fluctuations (LSB is degenerate with TM1 of the carrier due to Anderson).
Fig 5, finally, shows an exponential fit to the movement of the TM2 peak. The fit gives a time-constant of 310 sec, which roughly agrees with the usual fast part of the thermal transient. Extrapolating to t=0 gives a shift of 5.7e-4 fsr for the hot interferometer, which is a factor of 5 less than expected (see Richard's talk). To improve the accuracy of the fit in future experiments, we should try to make the mirror swing with the right speed earlier. In this case, the first 3 minutes were unusable.
The analysis was repeated for this unlock, the results look similar. In this case, the mirror was swinging a little bit further, so the cutoff speed was increased to 19 fsr/sec. The valid data starts already after 100 seconds, so the fit of the exponential seems to be more accurate. The obtained decay time is 236 seconds and the shift of the hot interferometer is 7.0e-04 fsr.