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*Adam Sypniewski, 09/04/2013 10:46 AM *

# Slew Settling Test¶

During one of the laser alignment tests, there were concerns raised that the BCAMs seemed to have (or be measuring) a settling time which lasted approximately 30 seconds with large (several hundred micron) amplitude oscillations. This page details the results of an independent study which rapidly acquired BCAM data to test if this was a real effect. Naively, if such oscillations exist, we don't expect them to be due to settling in the BCAM system, since there isn't any piece of BCAM hardware that would have such a long settling time.

## Overview¶

All data was taken on 2013-08-30 between 18:30 and 20:00 (UTC). The telescope began at zenith, and then slewed 30 degrees in each of the cardinal directions. The order of the telescope positions was: zenith, N, W, E, S, Z, N. The four BCAM-measured mis-alignments are show here:

## Analysis¶

### Overall measurements¶

The vertical gray bars delineate times when the telescope was slewing and when it was stationary. By eye, there certainly doesn't seem to be any significant settling effects such as those described above. The BCAMs are accurate to <50um in (x, y) and <1'' in (tip, tilt). Here, we subtract out the means at each telescope position and plot the residual distribution of BCAM measurements:

The standard deviations in (x, y, tip, tilt) are (39.2, 29.5, 0.64, 0.77) (um or arcsec), all within the BCAM error limits.

### End-of-slew comparisons¶

To see if there are any statistically significant settling effects, we compare the first five BCAM data points at each telescope pointing to the remaining data points. These first five data points cover approximately 30 seconds, the time scale suggested during the laser alignment test. The standard deviations for the BCAM data points at the beginning of each telescope pointing (that is, end-of-slew) are (47.6, 31.2, 0.71, 0.91). The standard deviations for the remaining, non-slew BCAM data points are (38.8, 29.7, 0.64, 0.76). All errors are well within BCAM error limits.

To compare these errors, we need to know if the means of the "end-of-slew" data points are consistent with the means of the "steady-state" data points. We compute the error on the mean of the "end-of-slew" data points, and compute the number of standard errors which separate the means of the two data sets. These numbers are (0.51, 0.99, 1.2, 0.7). This suggests that there is no statistically significant relation between end-of-slew data points and "steady-state" data points--certainly not any large-scale settling.

We also use the KS test to check if the two sets of data points could be drawn from the same statistical distribution. p-values are: (0.33, 0.22, 0.59, 0.25), respectively, suggesting that the two datasets could be statistically drawn from the same distribution. Chi-squared tests give the same results.

## Conclusions¶

The BCAMs do not find evidence for settling effects, and certainly not for any large amplitude or large time-scale effects. All measurements are consistent with BCAM statistical errors, and measurement statistics do not change significantly between "end-of-slew" and "not end-of-slew" data.