# Research on Optical System of Dim Target Simulator Based on Polarization Stray Light Suppression
## 2 Analysis and Design of Optical System of Dim Target Simulator
### Analysis and Design of Depolarization Optical Engine
#### 2.2.2 Stray Light Analysis and Suppression of Dim Target Simulation System
 \tag{4}\]  
where \(\phi\) is the distortion angle of the liquid crystal molecule, \(\psi\) is the angle between the optical axis of the wave plate and the direction of the liquid crystal molecule, \(\lambda\) is the central wavelength of the incident light, \(\Delta n\) is the difference of the refractive index of the material to the light \(\circ\) and \(\mathbf{e}\), \(d\) is the thickness of the liquid crystal molecule, and \(X\) is the intermediate variable, as shown in Equation (5). \[X=\sqrt{\phi^{2}+\left(\frac{\pi\Delta nd}{\lambda}\right)^{2}} \tag{5}\]  
Figure 5: Star grayscale distribution and centroid extraction under different environments. (**a**) Star grayscale map and star centroid extraction map without stray light; (**b**) star grayscale map and star centroid extraction map with stray light. After one-quarter slide compensation, the outgoing light wavelength and dark state light leakage of the system are shown in Figure 6, and the maximum value of LCOS dark state light leakage is 0.0035%. (b) Calculation of critical incident angle matching of spectroscopic film  
The incident beam angle of the illumination optical system affects the effective thickness of the spectroscopic film in PBS [15]. If the incident angle of the illumination beam does not match the critical incident angle of the spectroscopic film, S light and P light in the transmitted and reflected light will be doped with each other, which greatly reduces the stray light suppression ability of the optical engine. Therefore, it is necessary to determine the critical incidence angle of the spectroscopic film to match the beam angle of the illumination system. Starting from the application scenario of the target simulator [16], the stray light is equivalent to the detector noise. When the detector receives the signal, the number of electrons \(N_{\mathrm{s}}\) produced is represented by Equation (6):  
\[N_{\mathrm{s}}=\frac{2.512^{-m}\times 2.65\times 10^{-6}\pi D^{2}\tau_{0}t_{0} \lambda\eta}{4 hc} \tag{6}\]  
where \(m\) is the signal equivalent magnitude number, the optical system entry pupil diameter is \(D\), the optical system transmittance is \(\tau_{0}\), the detector exposure time is \(t_{0}\), the signal wavelength is \(\lambda\), the spectral efficiency of the detector is \(\eta\), \(h\) is [PERSON]'s constant, and \(c\) is the propagation speed of light in vacuum. The system noise equivalent number of electrons \(N_{n}\) is represented by Equation (7):  
\[N_{n}=\sqrt{{n_{b}}^{2}+\left(\frac{\pi D^{2}\tau_{0}I(\theta_{i},\varphi_{i} )\mathrm{PST}(\theta_{i},\varphi_{i})t_{0}\lambda\eta_{0}}{4 hc}\right)^{2}} \tag{7}\]  
where \(I(\theta_{i},\varphi_{i})\) is the incident illuminance, \(\mathrm{PST}(\theta_{i},\varphi_{i})\) is the point source transmittance of the optical engine, both of which are functions of the incident azimuth angle \(\theta_{i}\) and incident space angle \(\varphi_{i}\), and \(n_{b}\) is the dark current noise detector. Figure 6: Relationship between wavelength of LCOS outgoing light and light leakage in dark state after compensation. Therefore, the signal-to-noise ratio (SNR) is expressed by Equation (8):  
\[SNR=N_{s}/N_{n}=\frac{2.512^{-m}\times 2.65\times 10^{-6}\pi D_{t}0_{t}\lambda\eta}{4 hc \sqrt{{n_{b}}^{2}+\left(\frac{\pi D^{2}\tau_{0}I(\theta_{i},\varphi_{i})\text{ PST}(\theta_{i},\varphi_{i})I_{0}\lambda\eta_{0}}{4 hc}\right)^{2}}} \tag{8}\]  
Taking +11 magnitude star as an example (+11 magnitude star illuminance is about 1.05 \(\times\) 10\({}^{-10}\) lx), when \(SNR\) = 5, the star sensor can identify the target [17], and the corresponding optical engine PST of the target simulator should be \(6.88\times 10^{-9}\).