## 2 Materials and Methods
### Methods  
#### 2.2.1 The Proposed Calibration Method for OHS  
In the laboratory tests of the OHS before launch, an integrating sphere system was used to evaluate the relationship between the measured counts of the OHS and the integration stages. The sphere's spectral radiance was varied to test the sensor at different radiance levels. The test results are shown in Figure 7a, which shows that the DN value increased linearly with the increase in the integration stage. We also calculated the ratio of measured counts at integration stages 2-8 to that at integration stage 1, which is shown in Figure 7b. The ratios were approximately constant when the radiance level of the integrating sphere changed. Therefore, assuming the relationship between the measured counts of the OHS  
Figure 6: The BOA reflectance provided by RadCalNet used to calibrate OHS-F CMOS2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Date**} & **Overpass Time** & \multirow{2}{*}{**AOD**} & \multirow{2}{*}{**WVC (g/cm\({}^{2}\))**} & **Ozone Content** \\  & **(UTC)** & & & **(atm-cm)** \\ \hline
5 April 2020 & 11:41:23 & 0.038 & 4.387 & 0.289 \\
16 October 2020 & 5:54:45 & 0.073 & 0.005 & 0.280 \\
24 November 2020 & 11:34:35 & 0.038 & 2.168 & 0.276 \\
5 December 2020 & 20:55:12 & 0.018 & 0.128 & 0.260 \\
22 December 2020 & 20:57:11 & 0.016 & 0.686 & 0.285 \\
31 January 2021 & 20:53:12 & 0.025 & 0.441 & 0.305 \\
6 March 2021 & 20:51:37 & 0.056 & 0.388 & 0.296 \\
3 April 2021 & 20:53:09 & 0.043 & 0.366 & 0.296 \\
12 May 2021 & 20:54:29 & 0.092 & 0.244 & 0.341 \\
5 June 2021 & 5:52:40 & 0.077 & 0.508 & 0.331 \\
9 June 2021 & 12:54:55 & 0.133 & 2.336 & 0.328 \\
26 June 2021 & 11:31:11 & 0.071 & 1.969 & 0.273 \\
7 July 2021 & 11:31:56 & 0.066 & 1.380 & 0.285 \\
9 August 2021 & 11:32:32 & 0.109 & 1.519 & 0.277 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The atmosphere parameters when the satellites pass over the RadCalNet sites. and the integral stages was linear, we established the radiometric calibration equation considering different integration stages. Regarding OHSs with multiple integral stages, based on the traditional radiometric calibration equation, as shown in Equation (1), a new comprehensive gain \(T_{i}\) is defined as Equation (2). For a specific band of an OHS, assuming \(T_{i}\) is fixed:  
\[L_{i} =G_{i}\times DN_{i}+B_{i} \tag{1}\] \[T_{i} =G_{i}\times N_{stages} \tag{2}\]  
where \(G_{i}\) is the physical gain, \(DN_{i}\) is the \(DN\) value, \(B_{i}\) is the offset in calibration equation, \(N_{stages}\) is the integral stage, and \(L_{i}\) is the apparent radiance. Combining Equations (1) and (2), the radiometric calibration equation for an OHS considering different integral stages is obtained, as shown in Equation (3). \[L_{i}=T_{i}\times\frac{DN_{i}}{N_{stages}}+B_{i} \tag{3}\]  
According to the calibration equation shown above, using OHS images with different integration stages and the corresponding ground measurement data provided by RadCalNet, the comprehensive gain \(T_{i}\) of different bands can be solved using the least squares method. Figure 8 shows the procedures in the calibration method proposed for use with OHSs. As shown in the figure above, the main steps of the proposed calibration method are as follows:  
* The regions of interest (ROIs) are extracted from OHS images over RadCalNet sites, and the surface reflectance and atmosphere parameters, such as AOD, WCV, and ozone content, are also extracted from the RadCalNet product. * Then, the Second Simulation of the Satellite Signal in the Solar Spectrum (6S) radiative transfer (RT) model [18] is used to simulate the TOA radiance, which will be used with the DN value to calculate the comprehensive gains. * An adaptive weighted least squares method is used to solve the comprehensive gains, and then, they will be evaluated. The absolute radiometric correction is carried out using the fitting comprehensive gains to obtain the TOA radiance.