LLO Calibration Uncertainty Budget

C. Cahillane

I have completed the preliminary uncertainty analysis of the LLO detector for O1.

Joe Betzwieser was kind enough to provide the measurements and modify the directory infrastructure to match LHO, making my job easier.  Thanks Joe!

Currently, the budget only includes the Sept 14 LLO Sensing measurements and the Sept 3 LLO Actuation measurements.  I know that additional measurements have been taken in the meantime, and it should be simple to include those as soon as I know where they are/what they contain.
Some changes were necessary: The LLO L1 Actuation stage had a relatively short frequency vector, which is fine since its influence falls as 1/f^6.  The shortness of the frequency vector made the systematic fit unusual (Plot 10).  I also had to change the interpolation method from 'spline' to 'linear' for the LLO Actuation stages because interp1's extrapolation wasn't working properly on both ends of my frequency vector. (My freq vector is more dense than the measurement frequency vectors.)

Plots 1-4 show the Nominal O1 model, which includes systematic errors added quadractically with statistical uncertainty.
Plots 5-8 show the Systematic-corrected model, which includes only statistical uncertainty.
Plot 9 is the comparison between the Nominal and Systematic models and their uncertainty bars.
Plots 10-12 show the LLO L1, L2, and L3 Actuation stages and their systematic fits.
Plot 13 shows the LLO Sensing Measurement compared to the Sensing Model at the time.
Plot 14 shows the Sensing systematic fit

Next step is to improve the kappa uncertainties!  They are still hard-coded to be three percent and three degrees.  I think a full calibration group discussion is necessary to make sure everyone agrees on how to propagate this particular uncertainty/error.