# 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
For an optical engine, its \(\text{PST}(\theta_{i},\varphi_{i})\) can be represented by the transmittance \(T_{p}\) of P light, the transmittance \(T_{s}\) of S light, the reflectance \(R_{p}\) of P light, and the reflectance \(R_{s}\) of S light, as shown in Equation (9):  
\[PST=\frac{T_{p}R_{p}+R_{s}T_{s}}{R_{s}T_{p}+R_{p}T_{s}+T_{p}R_{p}+R_{s}T_{s}} \tag{9}\]  
Based on the analysis of the working principle of the illumination system and the optical engine, combined with the propagation path of the light in the optical engine, it can be seen that the beam forming two LCOS image planes can be regarded as the spectroscopic film passing through PBS twice, so the process is simplified by using the characteristic matrix of the double-layer film system [18], as shown in Equation (10):  
\[\left[ \begin{array}{c}B\\ C\end{array} \right]=\left\{\prod_{j=1}^{2}\left[ \begin{matrix}\cos\delta_{j}&i \sin\delta_{j}/\eta_{j}\\ i\eta_{j}\sin\delta_{j}&\cos\delta_{j}\end{matrix} \right]\right\}\left[ \begin{array}{c}1\\ \eta_{3}\end{array} \right] \tag{10}\]  
where \(\left[ \begin{array}{c}B\\ C\end{array} \right]^{T}\) is the characteristic matrix of a single-layer spectroscopic film determined by film system and substrate parameters, P component film admittance is \(\eta_{p}=n/\cos\theta\), S component film admittance is \(\eta_{s}=n\cos\theta\), \(n\) is the refractive index of the substrate film, \(\theta\) is the beam incident azimuth, film phase thickness is \(\delta_{j}=2\pi rad\cos\theta/\lambda\), and \(d\) is the film layer spacing. Then, the reflectance R and transmittance T of the film system can be shown as Equation (11):  
\[\left\{ \begin{array}{c}R=\left(\frac{\eta_{0}B-C}{\eta_{0}B+C}\right)\left( \frac{\eta_{0}B-C}{\eta_{0}B+C}\right)^{*}\\ T=\frac{4\eta_{0}\eta_{3}}{(\eta_{0}B+C)(\eta_{0}B+C)^{*}}\end{array} \right. \tag{11}\]  
where \(\eta_{0}\) is the admittance of the incident medium. Considering that the polarized stray light in the optical engine propagates in three-dimensional space, and for the spectroscopic film system, the angle affecting its reflectivity and transmittance is the angle between the incident light and the normal of the film layer; the light azimuth angle \(\theta^{\prime}\) of the second incident spectroscopic film can be represented by the azimuth angle \(\theta_{c}\) of the incident optical engine and the space angle \(\varphi\), as shown in Equation (12):  
\[\cos\theta^{\prime}=-\sin 45^{\circ}\sin\theta_{c}\cos\varphi+\cos\theta_{c} \cos 45^{\circ} \tag{12}\]  
Assuming that the light source emits a uniform beam that meets the critical incidence angle of the depolarization spectroscopic prism, the corresponding PST size can be obtained when the incident azimuth varies from 0\({}^{\circ}\) to 20\({}^{\circ}\) at different incident space angles, as shown in Figure 7.  
When PST = 6.88 \(\times\) 10\({}^{-9}\), the critical incidence angle of the depolarizing spectroscopic prism is about 9.2\({}^{\circ}\). When the incident angle is greater than the critical incident angle, the PST of the optical engine will continue to increase, which will cause the stray light suppression ability of the optical engine to decrease, and PST can not meet the requirement of signal recognition. Therefore, the divergence angle of the illumination optical system should match the critical incidence angle of the depolarization spectroscopic prism, so that the depolarization optical engine can effectively suppress stray light.