craig.cahillane@LIGO.ORG - posted 17:17, Friday 04 September 2015 - last comment - 21:34, Friday 04 September 2015(21225)
Calibration Line Statistical Uncertainty
C. Cahillane I have been busy trying to calculate kappa_tst, kappa_pu, kappa_C,and f_c from ER8 data so I might begin finding the uncertainty associated with these numbers. The uncertainty in all of these calibration coefficients depend heavily on our calibration line measurements (See T1500377 for the calculation of these coefficients from model params and calibration lines). I was curious to see if uncertainty in our calibration line measurements will be a significant source of uncertainty in the total budget, or if I can ignore it for now. I took 100 GPS times starting at 1125316818, each ten seconds apart, and computed the 10 second FFT of DARM_ERR, X_TST, X_CTRL, and X_PCAL. Then, I found their values at the calibration line frequencies at H1: f_tst = 35.9 Hz f_pcal = 36.7 Hz f_ctrl = 37.3 Hz f_pcal2= 331.9 Hz and took the following ratios: X_TST(f_tst) / DARM_ERR(f_tst) X_PCAL(f_pcal) / DARM_ERR(f_pcal) X_CTRL(f_ctrl) / DARM_ERR(f_ctrl) X_PCAL(f_pcal2) / DARM_ERR(f_pcal2) and plotted their amplitudes below. Percent uncertainties: X_TST(f_tst) / DARM_ERR(f_tst) = 0.98% X_PCAL(f_pcal) / DARM_ERR(f_pcal) = 0.95% X_CTRL(f_ctrl) / DARM_ERR(f_ctrl) = 0.84% X_PCAL(f_pcal2) / DARM_ERR(f_pcal2) = 1.05% Since I am just starting to compute the uncertainty expressions for the calibration coefficients in Mathematica, this study informed me that there is ~1% uncertainty in all of our calibration line amplitudes, which is significant enough to be included in all uncertainty calculations. Two notes: (1) I am assuming for now there is no quantization noise in our digital signals DARM_ERR, DARM_CTRL, X_TST, X_CTRL, and X_PCAL. This is almost certainty a secondary consideration in the total budget for now. (2) The method I used for dewhitening X_PCAL is known to be incorrect, so their absolute values should not be taken too seriously. But since all I cared about here is the statistical uncertainty, any systematic errors are a simple gain that is common to all data points, so this result is still valid.
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C. Cahillane, E. Hall
I have made some updates because of Evan.
He suggested that I switch the measurements to be Response / Excitation as is the norm with transfer functions, so now my plots are of DARM_ERR / X_{TST, CTRL, PCAL}.
In addition he suggested that I take more data and make histograms of the DARM_ERR / X_{TST, CTRL, PCAL} plots to better see the distribution, to see if it looks like a Gaussian or Rayleigh distribution. (Plot 2 is the Histogram, Plot 1 is the standard scatterplot)
Plot 3 is the line amplitude. In the case of PCAL, we can make readouts, leading to the statistical uncertainty we see only in X_PCAL on this plot. The others, X_CTRL and X_TST, we cannot make readouts and must trust that our excitation is constant over all time.
Plot 2 looks like a nice Gaussian distribution for all the observed calibration lines. We will still need to consider these statistical uncertainties in the total uncertainty budget.
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