[gautam, yehonathan, paco]

We went back to the loss data from last week and more carefully estimated the ARM loss uncertainties.

Before we simply stitched all N=16 repetitions into a single time-series and computed the loss: e.g. see Attachment 1 for such a YARM loss data. The mean and stdev for this long time series give the quoted loss from last time. We knew that the uncertainty was most certainly overestimated, as different realizations need not sample similar alignment conditions and are sensitive to different imperfections (e.g. beam angular motion, unnormalizable power fluctuations, etc...).

Today we analyzed the individual locked/misaligned cycles individually. From each cycle, it is possible to obtain a mean value of the loss as well as a std dev *across the duration of the trace*, but because we have a measurement ensemble, it is also possible to obtain an ensemble averaged mean and a statistical uncertainty estimate *across the independent cycle realizations*. While the mean values don't change much, in the latter estimate we find a much smaller statistical uncertainty. We obtain an XARM loss of 37.6 2.6 ppm and a YARM loss of 38.9 0.6 ppm. To make the distinction more clear, Attachment 2 and  Attachment 3 the YARM and XARM loss measurement ensembles respectively with single realization (time-series) standard deviations as vertical error bars, and the 1 sigma statistical uncertainty estimate filled color band. Note that the XARM loss drifts across different realizations (which happen to be ordered in time), which we think arise from inconsistent ASS dither alignment convergence. This is yet to be tested.

For budgeting the excessive uncertainties from a single locked/misaligned cycle, we could look at beam pointing, angular drift, power, and systematic differences in the paths from both reflection signals. We should be able to estimate the power fluctuations by looking at the recorded arm transmissions, the recorded MC transmission, PD technical noise, etc... and we might be able to correlate recorded oplev signals with the reflection data to identify angular drift. We have not done this yet.