## 6 Conclusions  
In this work, the issue of the calibration of the gain \(G_{APD}\) and energy resolution \(\delta E/E\) of the APDs used in the readout of Compton scattering polarimeters for space applications has been addressed. In particular, since the use of these components for the CUSP mission exposes them to significant temperature, \(T\), variations that affect their performance, the \(G_{APD}\) dependence on \(T\) has to be experimentally determined. To address this, a system was developed to measure the \(G_{APD}\) of the APDs over a wide range of temperatures (from \(-20\)\({}^{\circ}\)C to \(60\)\({}^{\circ}\)C) and applied bias voltage \(V_{bias}\) (from \(260\) V to \(410\) V) to investigate the possibility of stabilizing the gain by adjusting \(V_{bias}\), thereby counteracting the fluctuations introduced by the \(T\) variations. The designed and implemented system was tested in a climate chamber. The system consists of a charge amplifier to convert the charge signal into a voltage, a spectroscopy amplifier necessary to adjust the gain and appropriately shape the signal while minimizing pulse pileup effects, and an MCA to categorize the received pulses based on their amplitude. The developed measurement system was used to characterize a test APD. The results show the \(G_{APD}\) dependence, as a function of \(T\) and \(V_{bias}\), that is qualitatively consistent with expectations for these devices. The obtained surface \(G_{APD}(T,V_{bias})\) was then fitted with a simple 2D exponential model to analyze its potential use for determining control functions useful for the stabilization of \(G_{APD}\). The experimentally obtained curves were found to be simple linear functions; see Equation (8). An uncertainty analysis, conducted using a combination of uncertainty propagation methods and distribution-based approaches, allowed the determination of the accuracy with which \(G_{APD}\) can be stabilized with \(T\). The results indicate that the uncertainties increase rapidly with the desired gain. However, it should be noted that this type of uncertainty primarily indicates a range of values within which \(G_{APD}\) is expected to fall when polarized according to a chosen control curve. Given the high coefficient of determination obtained from the curve fitting, once a curve is followed, significant fluctuations in \(G_{APD}\) with \(T\) are not expected due to the good correspondence between measured data and the fitting curves. Therefore, despite the seemingly large uncertainties, the stability of \(G_{APD}\) will largely depend on the temperature measurement system of the APDs on the satellite and the stability and accuracy of the onboard high-voltage generator. For the CUSP mission, since measuring the number of incident photons is not necessary, achieving high accuracy in the APD gain is less critical than maintaining its stability. Uncontrolled variations in \(G_{APD}\) would in fact be associated with erroneous photon detection at different energies. A thorough assessment of the control curves' effectiveness will therefore be possible only after setting up the same system that will be used on the satellite to determine how the metrological characteristics of this would affect \(G_{APD}\) stability. Figure 14: Relative standard uncertainty of the APD gain \(u(G_{APD})/G_{APD}\) obtainable with the stabilization curves reported in Figure 13. In the insert is a zoom of the curve near the minimum. For \(G_{APD}\leq 16.2\), the curve is not defined; see Equation (8). **Author Contributions:** Conceptualization, A.A., S.F., E.D.M. and P.S. ; methodology, S.F., A.R. and P.S. ; software, M.C., G.D.C., G.D.P. and E.S. ([PERSON]); formal analysis, A.A. and F.C. ; investigation, A.A., S.F., N.D.A., A.K., P.L. ([PERSON]), G.L. and A.R. ; resources, A.A., E.S. ([PERSON]), S.D.C. and P.L. ([PERSON]); data curation, F.C. ; writing--original draft preparation, A.A. and E.S. ([PERSON]); writing--review and editing, A.A., F.C., S.F., K.T., E.S.