# 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
#### 2.2.3 Analysis of Illumination Optical System Design Objectives  
According to the optimization results of the depolarizing spectroscopic prism, the illumination optical system of the dim target simulator needs to meet the constraint condition that the prism incidence angle is less than \(\pm\)9.2\({}^{\circ}\). At the same time, the uniformity of irradiation surface should be taken into account. When it is better than 92%, the uniformity has little influence on the accuracy of magnitude simulation. The LCOS side length is 16.24 mm, so the diameter of the illumination area should be greater than the level side length after splicing 22.96 mm. Considering the allowance for installation, the illumination area is \(\phi\)25 mm. The design objectives of the illumination optical system are shown in Table 3.  
(1) Composition and structure of illumination optical system  
The illumination optical system mainly consists of a light source, CPC, homogenizing rod, and illumination lens, and its system structure is shown in Figure 8. The light beam emitted by the light source is distributed through the CPC twice, the angle of the output beam is reduced and then homogenized by the light rod, and finally, the illumination lens is used to achieve small-angle and uniform illumination. \begin{table}
\begin{tabular}{c c c c c} \hline  & **Critical Incidence Angle** & **Uniformity** & **Illumination Area** & **Operating Band** \\ \hline Design objectives & Better than \(\pm\)9.2\({}^{\circ}\) & \(>\)92\% & \(\phi\)25 mm & 380–760 nm \\ \hline \end{tabular}
\end{table} 
Table 3: Illumination optical system design objectives. Figure 7: Variation of PST of the theoretical model of depolarization optical engine with incident azimuth. (2) Selection of light source and design of each component unit (a) Light source selection  
We selected LED as the target simulator light source and determined the LED luminous flux. The energy transfer function E of an optical system is defined as the ratio of the outgoing light energy to the incident light energy, and the outgoing luminous flux \(\varphi^{\prime}\) can be expressed by Equation (13):  
\[\varphi^{\prime}=E_{cpc}E_{1}E_{2}E_{3}E_{4}E_{5}\varphi \tag{13}\]  
where \(\varphi\) is the incident luminous flux, \(E_{cpc}\) is the CPC energy transfer function, \(E_{1}\) is the homogenizing rod energy transfer function, \(E_{2}\) is the energy transfer function of the collimation system, \(E_{3}\) is the energy transfer function of the depolarization spectroscopic prism, \(E_{4}\) is the LCOS energy transfer function, and \(E_{5}\) is the energy transfer function of the collimation optical system. According to the experimental and empirical data, \(K_{\text{CPC}}=0.115\), \(E_{1}=0.69\), \(E_{2}=0.89\), \(E_{3}=0.25\), \(E_{4}=0.95\), and \(E_{5}=0.851\). In order to meet the target illuminance of \(10^{-10}\) lx and diameter of 25 mm, the minimum luminous flux \(\varphi\) of the incident light is shown in Equation (14). \[\varphi=\frac{10^{-10}(0.009)^{2}\pi}{E_{cpc}E_{1}E_{2}E_{3}E_{4}E_{5}} \tag{14}\]  
The result is \(\varphi=3.44\times 10^{-12}\) lm. (b) CPC design  
The CPC is designed to collect the large-angle outgoing light of the LED, and after angle modulation, the outgoing light is superimposed to realize the control of the luminous intensity distribution in the irradiation center and the edge area and improve the uniformity and increase the utilization rate of light energy [19]. The working principle is shown in Figure 9.  
The composite parabolic mirror is mainly formed by the interceptor segments \(AA^{\prime}\) and \(BB^{\prime}\) of parabola \(l_{c}\) and parabola \(l_{D}\), rotating around the symmetry axis, which can be obtained by analyzing the edge ray principle in the non-imaging optics theory.