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Fig. 9 | EJNMMI Physics

Fig. 9

From: Efficiency determination of J-PET: first plastic scintillators-based PET scanner

Fig. 9

Registration efficiency is shown by blue symbols as the ratio of energy depositions spectra (Exp/Sim). The error bars indicate the statistical uncertainties. The energy range starts at 70 keV, since the simulations were performed with a threshold energy deposition of 70 keV. The red line shows the Boltzmann Sigmoid Function: BSF =\(A_1+(A_0-A_1)/\left( 1+exp\left( \left( A_2-\textit{E}_\text{dep} \right) /A_3 \right) \right)\), where \(\hbox {A}_0\) = 0.177 ± 0.005 and \(\hbox {A}_1\)= 0.996 ± 0.003 represent the minimum and maximum values of BSF, respectively. \(\hbox {A}_2\) represents the mean between the minimum and maximum values of BSF, which is 148.7 ± 0.5 keV, while \(\hbox {A}_3\) = 22.77 ± 0.48 keV indicates the slope of the function. The BSF is plotted with 3\(\sigma\) standard deviations. \(\sigma\) is calculated using the covariance matrices as a function of the uncertainties in the values of the parameters (\(\hbox {A}_0, \hbox {A}_1, \hbox {A}_2, \hbox {A}_3\)). \(\hbox {\textit{E}}_\text{dep}\) is the value of the energy deposition. The goodness-of-fit parameter (\(\chi ^{2}\)/ndf) is equal to 334/189

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