# Analysis of SNR for High-Orbit Target Detected by Ground-Based Photoelectric System
## 4 Simulation Results  
As HOTs are low SNR objects, integration time was set at less than 40 ms due to the brightness of the sky background. The telescope aperture was 1.2 m, and the area of the target was 1 m\({}^{2}\) and consisted of material in 200 K. First, we assumed that the target was at an orbit of 10,000 km above the observer. Combined with the data calculated from MODTRAN, the SNR of the target at different Zenith angles is shown in Figure 3.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Spectrum** & **Wavelength (Micrometers)** & **Astronomical Band** \\ \hline Near Infrared & 1.1–1.4 & J \\ Short Infrared & 1.5–1.8 & H \\ Short Infrared & 2.0–2.4 & K \\ Mid Infrared & 3.0–4.0 & L \\ Mid Infrared & 4.6–5.0 & M \\ Long Infrared & 7.5–14.5 & N \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main window from short infrared to long infrared.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Default Value** \\ \hline Optics transmission & 0.75 \\ Quantum efficiency & 0.85 \\ Pixel size & 30 \(\mu\)m \\ F-number & 4 \\ Focal length & 4.8 m \\ Dark current & 450 e-rms \\ Readout noise & 6400 e-/pix/s \\ \hline \hline \end{tabular}
\end{table}
Table 2: List of parameters used to calculate signal-to-noise ratio (SNR) for simulation.  
Figure 2: Average transmittance and sky radiance of infrared band with the Mid-Latitude Summer model at a different Zenith angle: (**a**) Atmospheric transmittance trend of each infrared band at different Zenith angles; (**b**) The radiance sky radiance trend of each infrared band at different Zenith angles.  
The short infrared band had a better response. Generally, SNR defined as greater than five at the basis of the target can be effectively detected. Using our calculation parameters, only the J, H, and K bands could identify the target due to the elliptical trajectory of the satellite. With the increase of the zenith angle, the gap between the J band and H band became smaller. Until 68 degrees of the zenith angle, the detectability of the H band was better than the J band. The K band was always smaller than the other two bands.  
The moving orbit of the spatial target was dynamic, and the range was assumed to be 7500-15,000 km. The relationship between distance and SNR is shown in Figure 4. Detection SNR was greater than 10 at the perigee, and with the increase of orbit distance, the SNR was gradually reduced. The SNR had the best response at the J band, which was 3.6 at the apogee. The three kinds of short-wave limit detection distances were 1.283 \(\times\) 10\({}^{4}\) km, 1.161 \(\times\) 10\({}^{4}\) km, and 1.044 \(\times\) 10\({}^{4}\) km. Therefore, the target could not be effectively detected when approaching the apogee.  
The use of reflected sunlight as a target energy is inaccurate, as the constant motion of the target causes the reflected sunlight to become irregular, and the satellite's own working components also radiate energy. Therefore, our model used temperature as a standard for calculation [13,14]. The space target temperature ranged from 150-300 K at a zenith angle of 45 degrees, as shown in Figure 5.  
Figure 4: SNR at different detection distances.  
Figure 3: SNR of the target in different infrared bands.  
At different center wavelengths, the bandwidth was proportional to the sensitivity of the SNR [15] and the N band had the most notable promotion. Thus, at the same range of temperature, the selection of bandwidth had an influence on the noise immunity of the system.