Fig. 12

(a) The \(k_{ref}\)-value as the standard deviation of the difference of two gain references according to Eq. 81 as a function of signal strength. The signal strength was increased by summing up w frames with a target intensity of \(g\cdot \hat{S}_{ref,c}\approx 7050\) Counts. By fitting Eq. 57 to the data, the smoothed gain \(\beta \cdot g\) of the detector can be found as a parameter knowing the variance of the detector noise \(\sigma _{d}^{2}\). The resulting curve is shown in red. To demonstrate the validity of the model (b) shows the residual plot of the difference between fit and measured data, which indicates no significant deviation. The errorbars are mainly given as the uncertainty of the standard deviation of the difference images from the signal and background frames. In (c) the autocovariance function resulting from Eq. 83 of the gain reference as acquired from 30 signal and background frames is shown, where the central element gives \(k_{ref}^{2}\). Comparing the \(k_{ref}\)-values from method (a) \(k = 0.0027111 \pm 0.000002\) with method (c) \(k = 0.0027101 \pm 0.0000002\), according to Eq. 83 shows marginal differences most likely occurring due to the restriction of Eq. 41. To get a correct comparison between both methods, we altered (c) by a smoothing with Eq. 22 due to the correlation.