# Modeling and Calculation of Limit Magnitude Detection of Orbital Optoelectric Tracking System
## 4 Calculation and Experiment Analysis
### Experiment Analysis  
In order to verify the calculation model of the limit magnitude detection performance, a certain type tracking platform is used. The tracking platform parameters are as follows: the optical lens focal length is 85 mm-120 mm, the transmittance is \(\tau_{0}=0.85\), the aperture is \(D=240\) mm, the electron number in the dark current is \(N_{d}=150e^{-}\), the spectral quantum efficiency of the average detecting wavelength by the CCD detector is \(\eta=0.65\), the CCD camera exposure time is \(t_{0}=0.2\) s, and the vertical distance of the tracking platform optical center to the predefined orbital is 58 m.  
The angles required for the predetermined tracking and actual control of the tracking platform are given, the unit time of the rotation angle control is set to 0.02 s, and the tracking effect can be seen from the target velocity measurement error. According to the optical spatial geometric relationships in Figure 2 and Equations (20) and (25), the limit magnitude and the corresponding distance are calculated and compared with the actual detection distance of the tracking platform. Table 1 is the experimental data obtained in the test.  
From the results of the data in Table 1, when the distance of the tracking platform is close to \(OH\), the detection distance model calculating data error is small; at the A and B ends of the ballistic, the detection distance model calculating data error is large, and the maximum error is 3.6 m. It is mainly reflected in the two ports of the ballistic; the distance between the target and the tracking platform is larger than the detection distance \(OH\), which makes the detection ability insufficient, and a large deviation in the tracking platform. In order to improve this condition, the effective aperture of the optical lens can be enlarged to improve the detection ability. At the same time, the model calculation detection distance is slightly larger than the distance of the actual test. That is mainly because in the actual test environment, there are many influence factors that are non-quantifiable, such as the atmospheric attenuation, the energy reflection of the target surface, the stability of the tracking rotary platform, and so on.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{\begin{tabular}{c} **Angle of** \\ **Predetermined** \\ **Tracking/\({}^{c}\)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Control Angle of** \\ **Tracking** \\ **Platform/\({}^{c}\)** \\ \end{tabular} } & \multicolumn{2}{c}{**Error between**} & \multicolumn{1}{c}{\begin{tabular}{c} **Detection** \\ **Tracking** \\ **Measured of** \\ **Target Velocity/\%** \\ \end{tabular} } & \multicolumn{1}{c}{\
\begin{tabular}{c} **Detection Distance** \\ **Calculated with** \\ **Model/m** \\ \end{tabular} } & \multicolumn{1}{c}{
\begin{tabular}{c} **Detection Distance from** \\ **Atual Test of Tracking** \\ **Platform/m** \\ \end{tabular} } \\ \hline
1 & 5.409 & 5.401 & 0.62 & 77.9 & 75.2 \\
2 & 10.356 & 10.349 & 0.13 & 72.9 & 70.5 \\
3 & 20.748 & 20.755 & 0.41 & 65.8 & 64.6 \\
4 & 30.061 & 30.075 & 0.05 & 62.1 & 61.3