The value of the Finesse has been extracted from the fit of the cavity ringing, as usual. In particular, the measurements have been repeated for the North arm,( GPS north = 1222012818, Dur =60s), and for the West (GPS = 1222020890, Dur = 60s).

In order to improve the fit quality, the boundaries and fit options have been further refined. Moreover, the cavity speed, which used to be extracted from the fit, has been computed from the FSR reconstruction (figure 1) and this value of the velocity was used in the analytic function to fit the ringing and extract the value of the time constant. From this, it is possible to compute the Finesse, according to:

F = tau * pi * FSR   [1]

With this trick it's possible to reduce the number of parameters to be extracted from the fit and avoid a possible correlation between the speed and the Finesse.

As further figure of merit for the fit goodness, the fit residuals normalized by the related data were used to filter the outcomes of the fitting procedure. The reason why we chose this kind of figure of merit is that this allows to weight more the ringing side of the Airy peak, which is strongly affected by the Finesse value.

The Finesse histograms for the two arms are reported in figures 2 and 3.The mean value and the std are reported in the following table:

Finally, figures 4 and 5 show that there is no significant correlation between the Finesse value and the cavity speed.

Notice that these values of the Finesse are higher than the ones found from the decay time measurements.

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[1] - M. Rakhmanov - Dynamics of Laser Interferometric Gravitational Wave Detectors - (PhD Thesis)