## 2 Instrument, Model, and Method
### Experimental Method  
To obtain the coefficient of RTDC model G(T) over a large temperature range, the basic principle of this experiment is to obtain the normalized results of radiation response by changing the PST of the detector under the same radiation conditions. The model  
Figure 4: Example of the photosensitivity temperature dependence of detector used in the PSAC 2250 nm channel. Two PSTs used for comparison are independent of RTDC experiments. G\({}_{\text{det}}\)(T) and G\({}_{\text{ins}}\)(T) were obtained by detector-level experiments and instrument-level experiments, respectively. To meet the range of T, two different experimental conditions were set in experiments. The experimental structure of detector-level and instrument-level experiments is shown in Figure 5.  
The instrument-level experiment contains three sub-experiments. First, a bench stability experiment was conducted. Then, combined with PSAC active-passive detector temperature control, the experiment was conducted in a vacuum chamber that can simulate the on-orbit operation environment (T \(<-35\)\({}^{\circ}\)C) and ambient laboratory temperature (T \(>-35\)\({}^{\circ}\)C). A schematic diagram of the instrument-level RTDC experimental method is shown in Figure 6. By adjusting the CCC current, the PST could span the PSAC operation conditions on orbit and in the laboratory (\(-65\)\({}^{\circ}\)C \(<\) T \(<-25\)\({}^{\circ}\)C). With a constant radiation source provided by the integrating sphere, G\({}_{\text{ins}}\)(T) was obtained by fitting the relationship between the PST and the PSAC DN normalization results with a cubic spline function. However, the accuracy of G\({}_{\text{ins}}\)(T) over two instrument-level sub-experiments faced challenges of inconsistent experimental conditions, such as different optical path transmittance and different background radiation associated with a changing heat sink temperature. The difference in background radiation was mitigated with the DCR function using the PSAC fixed-point observation mode with a dark reference provided by a chopper. As for different optical path transmittance, normalization based on overlapping temperatures between two sub-experiments was applied. The correspo  
Figure 5: Diagram of the RTDC experimental structure. Figure 6: Schematic diagram of the instrument-level RTDC experimental method. Equation (3), where gvac(T) and glab(T) represent the DN values in the thermal vacuum sub-experiment and the ambient laboratory temperature sub-experiment, respectively. \[\mathrm{G_{ins}(T)=\frac{g_{vac}(-35)}{g_{vac}(-30)}.\frac{g_{lab}(T)}{g_{lab}(-35 )}\ (T>-35^{\circ}C)} \tag{3}\]  
The detector-level experiment contains three sub-experiments; a schematic diagram of the detector-level RTDC experimental method is shown in Figure 7. Gfil(t) represents the filter transmissivity temperature model, where t represents the temperature of the filter. Limited to the temperature difference between the photosensitive surface and heat sink of the detector being attained only by the active cooling of the TEC inside the detector, the detector-level experiment was divided into two sub-experiments with different heat sink cooling conditions, one under a water-cooling condition (T \(<-50\)\({}^{\circ}\)C) and one under ambient laboratory temperature (T \(>-50\)\({}^{\circ}\)C), to meet the range of T. Furthermore, a filter transmittance temperature experiment was conducted considering the temperature characteristics of the filter. Compared with the instrument-level experiment, to meet the substitution and accuracy of Gdet(T), the detector-level experiment not only needs to solve the internal interferences caused by its own characteristics, such as the changing background radiation and detector dark current, but also needs to overcome the external interferences from the inconsistent operation state compared with the instrument-level experiment. Based on the dark reference provided by the chopper, the internal interferences at different temperatures had little influence on Gfil(t) measurement.