## 5 Ground-Based Calibrations
### Flux Accuracy Calibration  
#### 5.2.1 Calibration Methods  
The purpose of particle flux calibration is to calibrate the actual counting ability of the payload, obtain the corresponding accuracy to the particle flux (that is, with the relationship between the reconnection output and the incident particle counting), determine the detection sensitivity, and finally evaluate the impact of the background noise counting on the detector. Theoretically, the flux error can be directly calibrated by a particle source with a known flux to the detector. However, in fact, the particle flux is not stable regardless of the accelerator or radioactive source. Therefore, there is no accurate and reliable method for direct calibration of flux [25]. In order to calibrate the particle flux error, an indirect method of decomposing the flux error into various contributing errors, measuring them separately, and then superimposing them into the total flux error is adopted. The direct detection quantity of the detector is the counting N (counts/s). In order to facilitate the comparison of the data, the data need to be normalized. The counting is divided by the geometric factor G of the instrument, and then the flux of the detector is obtained as  
\[\mathrm{M(cm^{-2}s^{-1}sr^{-1})=\frac{N(\frac{counts}{s})}{G(cm^{2}sr)}} \tag{3}\]  
Therefore, there are two factors that affect the flux calibration accuracy, namely, the instrument counting accuracy and the geometric factor accuracy. The counting is the initial output data of the payload, and it is directly related to its sensor and electronics. Hence, the error of the counting includes the particle response error of the sensor and the response error of the electronics, as shown in Figure 17.  
Figure 16: Calibration results of the electron energy channel in three directions (650 keV). Assume that the relative accuracy of the detector flux M is \(\sigma_{M}\), the relative accuracy of the counting is \(\sigma_{N}\), and the relative accuracy of the geometric factor is \(\sigma_{G}\). According to the formula of error propagation,  
\[\sigma_{y}^{2}=\sum_{i}{(\frac{\partial y}{\partial xi})}^{2}\sigma_{xi}^{2} \tag{4}\]  
The relative accuracy of the flux is obtained as,  
\[\sigma_{M}^{2}={\left(\frac{\partial M}{\partial N}\right)}^{2}{\sigma_{N}}^{2 }+{\left(\frac{\partial M}{\partial G}\right)}^{2}{\sigma_{G}}^{2}=\frac{1}{G ^{2}}{\sigma_{N}}^{2}+\frac{N^{2}}{G^{4}}{\sigma_{G}}^{2} \tag{5}\]  
The sensor counting error calibration was tested separately using the silicon semiconductor detectors of the same batch. The sensor was placed in a test box, and the sensor was irradiated with a \({}^{207}\)Bi radioactive source. The total count recorded by the sensor per unit time was counted by the dedicated multi-channel system for sensor measurement. The above steps were repeated continuously to obtain a series of counting rates \(n_{i}\). Finally, the counting response error of the sensors of the batch was obtained by calculating the standard deviation method. The electronic counting error calibration was mainly obtained by writing software and using the random function generator in the program to simulate the time distribution of the space particle injecting into the sensor. If the signal collection time of the instrument is t, when the time difference between two particles incident is less than t, only one of the large signals is recorded. The counts that were \"eaten\" due to signal superposition and the actual counts of the detectors were recorded to obtain the electronic counting errors of the detector. The use of the particle incidence of different fluxes in the calibration yielded the corresponding relation between the number of incident particles and the detector output counts. The geometric factor is an important characteristic parameter of the detector. It is a necessary parameter for data normalization and data comparison.