# 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  
(1) Causes and effects of stray light  
The stray light in the simulation system of dim targets mainly comes from two aspects. First, the dark state light leakage phenomenon is caused by the difference between the response ability of LCOS to incident light of different wavelengths. Second, the illumination optical system does not match the spectroscopic prism. The spectroscopic prism is sensitive to the incident light angle [12], and its outgoing light cannot maintain a single-line polarization state, so more imaging polarized light is converted into polarized stray light. After the polarized stray light is emitted by PBS, the image surface of the detector will be covered with a layer of uneven stray light, which will reduce the contrast of the image surface, cause the centroid of the star point to deviate from the geometric center, and reduce the position accuracy of the star point. Figure 5 shows the grayscale extraction of the star point under different stray light distributions. Figure 5 shows the star point grayscale extraction diagram under different stray light distribution. If there is no stray light affecting the simulated star point, the theoretical position (x, y) of the simulated star point should be (5.5, 5.5) and the theoretical star point grayscale on the camera image plane should be 189.0. When there is a large amount of stray light in the simulation system, the overall background grayscale of the camera image plane will be increased. If the stray light is more uniform, the signal-to-noise ratio of the simulated star point will be reduced, resulting in difficulty in extracting the centroid position of the star point. If the stray light is not uniform, some maximum values of the stray light will easily affect the centroid position of the nearby star point, the grayscale of the star point will increase to 199.0, and the star point position will be mistakenly received by the camera as (6, 4). Figure 4: Splicing scheme and image surface size. Figure 5: _Cont._(2)  
Stray light suppression method  
(a) Dark state light leakage suppression  
When the LCOS is in the off state, the incoming polarized light is not regulated by the liquid crystal molecules, so it cannot exit the simulation system to achieve the off state. However, when the liquid crystal molecules appear under the dark state light leakage phenomenon, the light on the surface of the LCOS with the emission closed will have different polarization states, resulting in a partially polarized stray light emission simulation system. The quarter wave plate can be placed on the surface of LCOS to phase compensate the LCOS outgoing light, reduce the stray light of the outgoing simulation system, and achieve the effect of suppressing the dark state light leakage. For the quarter wave plate compensation method [13], the dark state light leakage \(R_{1}\) of the LCOS outgoing light is shown in Equation (2):  
\[R_{1}=\left|(\cos\alpha,\sin\alpha)W^{T}M^{T}MW\binom{\cos\alpha}{\sin\alpha}\right| \tag{2}\]  
where \(\alpha\) is the angle between the transmission axis of the polarizer and the orientation of the liquid crystal molecule at the incident point, \(\left(\cos\alpha,\sin\alpha\right)^{T}\) is the Jones vector of the incoming polarized light, \(M\) is the Jones matrix of the LCOS liquid crystal molecule, and \(W\) is the Jones matrix of the wave plate [14], as shown in Equations (3) and (4):  
\[\binom{\cos\psi}{\sin\psi}\binom{\cos X-i\frac{\pi\Delta nd\sin X}{X}}\frac{ \phi\frac{\sin X}{X}}{\cos X+i\frac{\pi\Delta nd\sin X}{X}} \tag{3}\]  
\[W= \begin{pmatrix}\cos\psi&-\sin\psi\\ \sin\psi&\cos\psi\end{pmatrix}\begin{pmatrix}e^{-i\frac{\pi}{4}}&0\\ 0&e^{i\frac{\pi}{4}}\end{pmatrix}\begin{pmatrix}\cos\psi&\sin\psi\\ -\sin\psi&\cos\psi\end{pmatrix}