Fig. 16

(a–c) The k-value is displayed as a function of binned pixels, as shown in Eq. 73. Here, the distribution factor \(\alpha =1\), as the signal is homogeneously distributed across the detector. The blue dots represent the results based on a regression analyzes, similar to Fig. 14b, but with binned pixels. The red line displays the reconstruction based on the Pearson correlation coefficients from Fig. 12c, following Eqs. 26, 27 and 22. The uncertainty of the non-linearity correction \(k_{lin}^{2}\) is independent of the binning (see Eq. 73). It is obtained by fitting an offset to the reconstructed uncertainty of the gain reference under binning \(k_{H,V}^{2} = k_{ref^{*},H,V}^{2} + k_{lin}^{2}\). Combining both uncertainties under a square root yields the green line. The results are shown for (a) horizontal binning with the binning value H (b) vertical binning with the binning value H and (c) diagonal binning along horizontal and vertical direction equally HV. In the lower row (d–f), we provide the difference between both methods. The shades depict the uncertainty within a \(95\%\) confidence interval. It can be seen that the reconstructions via Pearson coefficients plus the \(k_{lin}\) uncertainty are in good agreement with the regression analyzes.