Research on Optical System of Dim Target Simulator Based on Polarization Stray Light Suppression

Abstract

In view of the lack of high-precision optical simulation equipment for dim space targets at present, in this study, a simulation method for dim space targets based on polarization stray light suppression is proposed, the overall optical system architecture of the optical engine for depolarization stray light suppression is constructed, the mechanism of stray light generation is explored, and the dark state light leakage suppression method is presented by compensating the phase of LCOS reflected light with wave plate; a high-image quality collimating optical system with large field of view and flat aberration is designed based on the illumination system optimization method of the critical angle matching of the spectroscopic film; and the polarization stray light suppression effect and star position simulation error of the dim target simulator are tested. The test results show that the illumination of the simulated dim target is ≮10⁻¹⁰ lx, the contrast is 6.96, the non-uniformity of the bright state is only 5.88%, and the simulation error of the star position is 9.9″. This research can make some contributions to enhancing the observability of detecting dim targets, breaking through the detection technology of extremely dark targets in space, developing advanced deep space detection capabilities, and improving the engineering technology system of deep space exploration.

1. Introduction

Since Sputnik 1, with the development of deep space exploration technology, nearly 90,000 man-made space targets can be detected, and human exploration of space is also developing towards smaller and darker targets [1]. Therefore, effectively reducing the false alarm rate of optical detectors and realizing high-precision detection of smaller dim targets have become urgent problems in the field of space detection. However, due to the limited resources and high cost of the on-orbit platform [2], laboratory physical simulation of the optical characteristics of dim space targets has gradually developed into one of the important guarantees for the successful completion of the deep space exploration mission of optical detectors.

The field of dim target simulation mainly serves the ground calibration and correction of dim target observation equipment, so the important factor in this field is how to more accurately simulate the optical characteristics of the target observed by the observation equipment. Airbus DS’s Star Tracker Optical Simulator (STOS) [3], for the first time as the star chart display devices using LCOS, realize the dynamic display of the star chart, and star position simulation error is superior to 20″. Subsequently, Germany Jenaoptronik also launched an Optical Star Simulator (OSI) [4] and improved the star position correction algorithm; the star position simulation error is better than 18″, and the magnitude simulation range is +2~+8 Mv. With the development of dynamic display technology, the US Air Force Research Laboratory developed TASAT [5], which is used for the high-precision simulation of the photoelectric tracking process of the photoelectric detection system on the satellite and other targets. The STK EOIR module [6] developed by AGI is used for the simulation of various photoelectric payload imaging processes. Harbin Institute of Technology [7] proposed a digital image generation method for starry background statistics in an all-sky area, which used the imaging signal intensity model, the statistical function of the number and magnitude of stars, and the imaging characteristics of stars on the focal plane to generate starry background images above +10 magnitude stars. Although some progress has been made in the field of image simulation for space-based applications, this method is only validated for observation algorithms, and optical imaging methods for simulation images are still lacking for performance evaluation of space-based observation equipment. Changchun University of Science and Technology [8] applied the LCOS splicing display technology to the development of a dynamic star simulator; the star position simulation error was better than 25″, and the magnitude simulation error was better than ±0.5 Mv. In the subsequent research, the team developed a high-contrast LCOS splicing dynamic star simulator using multiple superimposed prisms to solve the influence of polarization degree on the stray light [9]. The star position simulation error is less than 18″. In view of the problem of stray light in optical engines, Qi Yan [10], E G Che [11], and other teams have also carried out relevant research, but the redesigned optical engine has problems such as increased volume and reduced energy utilization, and it is difficult to apply to the high-precision simulation of dim targets.

In summary, the dynamic dim target simulation technology has some problems, such as the difficulty of avoiding stray light in the dynamic display scheme, the increase in system volume caused by the method of eliminating stray light, and the difficulty of improving the simulation accuracy of dim targets. Therefore, an optical simulation method for dim targets based on polarization stray light suppression is proposed in this paper. From the perspective of suppressing LCOS dark state light leakage and polarized stray light of optical engines, the method uses the wave plate compensation phase and lighting critical angle matching method to effectively suppress polarized stray light in the target simulation equipment and improve the analog grayscale contrast of dim targets. This improves the simulation accuracy of dim targets while maintaining the simple overall layout of the traditional LCOS dynamic display optical system. In the Section 2, we analyze the causes of stray light from two aspects of LCOS dark state light leakage and polarization stray light doping, set the wave plate compensation phase, optimize the high-uniform illumination optical system, and improve the incident critical angle matching with the spectroscopic film. In the Section 3, we design a high-image quality collimating optical system with small distortion, flat image field, and apochromatic aberration. In the Section 4, the polarization stray light suppression verification and star position simulation error calibration tests are set up to verify the feasibility of the simulation method, effectively suppress the stray light of the optical simulation system for dim targets, and achieve high-precision simulation of dim targets. In the Section 5, we present our conclusions.

2. Analysis and Design of Optical System of Dim Target Simulator

2.1. Principle and Design Index of Optical System of Dim Target Simulator Based on Polarization Stray Light Suppression

For the simulation of dim targets, the overall structure of the dim target simulation optical system is proposed, which consists of two parts: depolarization optical engine and high-image quality collimation optical system. After the light emitted by the light source passes through the homogenization, collimation, and beam splitting, two spatial light modulators (LCOS) are lit at the same time, and the high-image quality collimation optical system projects the display content of the two LCOS located in its conjugate focal plane position to infinity. Among them, the depolarization spectroscopic prism eliminates the polarized stray light and ensures the energy balance and position accuracy of the simulated target through strict aberration correction. The principle is shown in Figure 1. The main technical indicators of the system are shown in

Table 1. Main technical index.

Item	Index
Effective field of view	10.2 × 10.2°
Single star angle	20″
Working caliber	≮$\varphi 18 \mathrm{mm}$
Operating band	380–760 nm
Illumination	≮10−10 lx

.

2.2. Analysis and Design of Depolarization Optical Engine

The depolarization optical engine is mainly composed of LCOS, depolarization spectroscopic prism, and high-uniform illumination optical system, which can increase the resolution of the image plane and reduce the stray light in the optical engine.

2.2.1. Selection and Splicing of Spatial Light Modulator

(1)

Selection of spatial light modulator

The field of view of the displayed star chart is 10.2 × 10.2°, the single star angle is 20″, and at least the display image elements should be shown in the orthogonal direction, as shown in Equation (1).

$$(10.2°\times 3600″)/{20}^{″}=1836$$

(1)

The number of single LCOS pixels is only 1920 × 1080, which cannot meet the minimum pixel requirement of the target simulation. Therefore, the full image plane of LCOS1 (1920 × 1080) and partial image plane of LCOS2 (1920 × 840) are used for stitching, and the size of the image plane after overlapping stitching is 16.128 × 16.128 mm. The selected LCOS is shown in Figure 2, and the main technical parameters are shown in

Table 2. Main technical index of LCOS.

Item	Index
Resolution	1920 × 1080
Pixel size	8.4 μm
Aperture opening ratio	90%
Size	16.128 × 9.072 mm

.

(2)

Two-piece LCOS splicing scheme

A pair of conjugate planes with equal optical path are formed by using a depolarization spectroscopic prism, and the two LCOS are respectively installed at the two equivalent focal planes of the target simulator. The splicing principle is shown in Figure 3. The light beam emitted from the light source passes through the depolarization spectroscopic prism and is divided into two optical paths, ➀ and ➁. The prism reflects the incident light S light, that is, the light path ➀, and transmits the incident light P light, that is, the light path ➁. After LCOS1 is lit by the optical path ➀, S light becomes P light and is reflected, and then image plane 1 is formed through the spectroscopic plane. After LCOS2 is lit by the optical path ➁, P light becomes S light and is reflected, and image plane 2 is formed by reflection on the spectral inclined plane, thus realizing the optical splicing of two LCOS. The size of the image plane after splicing is shown in Figure 4.

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).

(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 R₁ of the LCOS outgoing light is shown in Equation (2):

$$R_1=\left|(\cos \alpha ,\sin \alpha )W^T{M}^{T}MW\left(\begin{array}{c}\cos \alpha \\ \sin \alpha \end{array}\right)\right|$$

(2)

where α is the angle between the transmission axis of the polarizer and the orientation of the liquid crystal molecule at the incident point, ${(\cos \alpha ,\sin \alpha )}^T$ 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):

$$\left(\begin{array}{cc}\cos \varphi & -\sin \varphi \\ \sin \varphi & \cos \varphi \end{array}\right)\left(\begin{array}{cc}\cos X-i\frac{\pi \Delta nd\sin X}{X}& \varphi \frac{\sin X}{X}\\ -\varphi \frac{\sin X}{X}& \cos X+i\frac{\pi \Delta nd\sin X}{X}\end{array}\right)$$

(3)

$$W=\left(\begin{array}{cc}\cos \psi & -\sin \psi \\ \sin \psi & cos\psi \end{array}\right)\left(\begin{array}{cc}{e}^{-i\frac{\pi }{4}}& 0\\ 0& e^{i\frac{\pi }{4}}\end{array}\right)\left(\begin{array}{cc}\cos \psi & \sin \psi \\ -\sin \psi & \cos \psi \end{array}\right)$$

(4)

where $\varphi$ 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 o and e, d is the thickness of the liquid crystal molecule, and X is the intermediate variable, as shown in Equation (5).

$$X=\sqrt{{\varphi }^2+{\left(\frac{\pi \Delta nd}{\lambda }\right)}^2}$$

(5)

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 $N_s$ produced is represented by Equation (6):

$$N_s=\frac{{2.512}^{-m}\times 2.65\times {10}^{-6}\pi D^2{\tau }_0{t}_0\lambda \eta }{4hc}$$

(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 Planck’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):

$$N_n=\sqrt{{n_b}^2+{\left(\frac{\pi D^2{\tau }_{0}I\left({\theta }_i,{\phi }_i\right)\mathrm{PST}\left({\theta }_i,{\phi }_i\right)t_0\lambda {\eta }_0}{4hc}\right)}^2}$$

(7)

where $I\left({\theta }_i,{\phi }_i\right)$ is the incident illuminance, $\mathrm{PST}\left({\theta }_i,{\phi }_i\right)$ 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 ${\phi }_i$, and $n_b$ is the dark current noise detector.

Therefore, the signal-to-noise ratio (SNR) is expressed by Equation (8):

$$SNR=N_s/N_n=\frac{{2.512}^{-m}\times 2.65\times {10}^{-6}\pi D^2{\tau }_0{t}_0\lambda \eta }{4hc\sqrt{{n_b}^2+{\left(\frac{\pi D^2{\tau }_{0}I\left({\theta }_i,{\phi }_i\right)\mathrm{PST}\left({\theta }_i,{\phi }_i\right)t_0\lambda {\eta }_0}{4hc}\right)}^2}}$$

(8)

Taking +11 magnitude star as an example (+11 magnitude star illuminance is about 1.05 × 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 $6.88\times {10}^{-9}$. For an optical engine, its $\mathrm{PST}\left({\theta }_i,{\phi }_i\right)$ 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):

$$PST=\frac{T_p{R}_p+R_s{T}_s}{R_s{T}_p+R_p{T}_s+T_p{R}_p+R_s{T}_s}$$

(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):

$$\left[\begin{array}{l}B\\ C\end{array}\right]=\left\{{\displaystyle \prod _{j=1}^2\left[\begin{array}{cc}\cos {\delta }_j& i\sin {\delta }_j/{\eta }_j\\ i{\eta }_j\sin {\delta }_j& \cos {\delta }_j\end{array}\right]}\right\}\left[\begin{array}{l}1\\ {\eta }_3\end{array}\right]$$

(10)

where ${\left[\begin{array}{cc}B& C\end{array}\right]}^T$ 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 ${\delta }_j=2\pi nd\cos \theta /\lambda$, and $d$ is the film layer spacing.

Then, the reflectance R and transmittance T of the film system can be shown as Equation (11):

$$\left\{\begin{array}{l}R=\left(\frac{{\eta }_{0}B-C}{{\eta }_{0}B+C}\right){\left(\frac{{\eta }_{0}B-C}{{\eta }_{0}B+C}\right)}^{*}\\ T=\frac{4{\eta }_0{\eta }_3}{\left({\eta }_{0}B+C\right){\left({\eta }_{0}B+C\right)}^{*}}\end{array}\right.$$

(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 $\phi$, as shown in Equation (12):

$$\cos {\theta }^{\prime }=-\sin 45°\sin {\theta }_c\cos \phi +\cos {\theta }_c\cos 45°$$

(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° to 20° at different incident space angles, as shown in Figure 7.

When PST = 6.88 × 10⁻⁹, the critical incidence angle of the depolarizing spectroscopic prism is about 9.2°. 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.

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 ±9.2°. 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 bevel side length after splicing 22.96 mm. Considering the allowance for installation, the illumination area is $\varphi 25 \mathrm{mm}$. The design objectives of the illumination optical system are shown in

Table 3. Illumination optical system design objectives.

	Critical Incidence Angle	Uniformity	Illumination Area	Operating Band
Design objectives	Better than ±9.2°	>92%	$\varphi 25 \mathrm{mm}$	380–760 nm

.

(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.

(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 φ^′ can be expressed by Equation (13):

$${\phi }^{\prime }=E_{cpc}{E}_1{E}_2{E}_3{E}_4{E}_5\phi$$

(13)

where $\phi$ is the incident luminous flux, E_cpc is the CPC energy transfer function, E₁ is the homogenizing rod energy transfer function, E₂ is the energy transfer function of the collimation system, E₃ is the energy transfer function of the depolarization spectroscopic prism, E₄ is the LCOS energy transfer function, and E₅ is the energy transfer function of the collimation optical system. According to the experimental and empirical data, K_CPC = 0.115, E₁ = 0.69, E₂ = 0.89, E₃ = 0.25, E₄ = 0.95, and E₅ = 0.851. In order to meet the target illuminance of 10⁻¹⁰ lx and diameter of 25 mm, the minimum luminous flux $\phi$ of the incident light is shown in Equation (14).

$$\phi =\frac{{10}^{-10}{\left(0.009\right)}^2\pi }{E_{cpc}{E}_1{E}_2{E}_3{E}_4{E}_5}$$

(14)

The result is $\phi =3.44\times {10}^{-12} \mathrm{lm}$.

(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 $A{A}^{\prime }$ and $B{B}^{\prime }$ 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. Parabola $B{B}^{\prime }$ is shown in Equation (15):

$${\left[2\sqrt{f{k}_1}x+\left(f-k_1\right)y\right]}^2+8a{f}^{2}x-8a{k}_2\sqrt{f{k}_1}y=4a^{2}f\left(a+k_2\right)$$

(15)

where $k_1=2a-f$, $k_2=a+f$, $f$ is the focal length, $f=a(1+\sin {\theta }_{\max })$, $a$ is the radius of the LED, $a=b\sin {\theta }_{\max }$, $b$ is the radius of the light outlet hole $AB$, and ${\theta }_{\max }$ is the maximum beam absorption angle of the composite parabolic mirror.

The luminous intensity $I{\left({\theta }_i\right)}_z$ at the exit of the composite paraboloid mirror includes two parts: the luminous intensity ${\theta }_i$ directly emitted by the LED and the luminous intensity ${\theta }_i$ reflected by the composite paraboloid mirror. If the luminous intensity in the normal direction of the LED is $I_0$, the luminous intensity at the angle $I_0$ is $I_0\cos {\theta }_i$ and the luminous intensity at the exit of the composite paraboloid mirror can be shown by Equation (16):

$$I{\left(\theta \right)}_z=I_0\cos {\theta }_i+k{I}_0\frac{{\displaystyle {\int }_0^L\cos \left(F\left({\theta }_i,y\right)\right)dy}}{{\displaystyle {\int }_0^{{\theta }_{\max }}{\displaystyle {\int }_0^L\cos \left(F\left({\theta }_i,y\right)\right)dyd{\theta }_i}}}$$

(16)

where $F\left({\theta }_i,y\right)$ is the function of $\upsilon$ related to ${\theta }_i$ and $y$, $\upsilon$ is the outgoing light angle of the LED corresponding to ${\theta }_i$, $\upsilon =\pi -{\theta }_i-2\eta$, $y$ is the ordinate of the intersection point of the light with the incident angle of $\upsilon$ emitted by the LED and the CPC, $k$ is the reflectance of the reflector surface of the composite parabolic mirror, $L$ is the length of the composite parabolic mirror, and $L=\frac{f\cos {\theta }_{\max }}{{\sin }^2{\theta }_{\max }}$.

When ${\theta }_{\max }$ is larger, the range of ${\theta }_i$ is larger, and the reflected light is reflected and compensated on both sides of the irradiation surface. The radius of the LED is a = 1.88 mm and the incident light angle is 60°. In order to ensure that the CPC length is appropriate, ${\theta }_{\max }=\pm {17}^{\circ }$ and ${\theta }_i={\theta }_{\max }$ are used to calculate the CPC focal length f = 2.042 mm. CPC length L = 22.844 mm; CPC light output diameter 2b = 10.81 mm.

(c)

The design of the homogenizing rod

We designed a homogenizing rod for high uniform lighting. The homogenizing rod uses the principle of total reflection to reflect the light incident inside the rod many times and then emit it. The aperture ratio of the homogenizing rod determines the total reflection times, and the incident irradiation is divided according to the incident angle, so as to improve the irradiation uniformity of the system [20]. The principle of the homogenizing rod is shown in Figure 10, in which ① to ④ respectively represent the equivalent position of the edge light of ${\theta }_1$ to ${\theta }_4$ light from different incident angles.

The homogenizing rod shall satisfy Equation (17):

$$m=\frac{2}{n}\left(\frac{L_z}{L_y}\right)\tan {\theta }_m,{\theta }_m\langle {\theta }_{\max }$$

(17)

where m is the maximum number of total reflections in the homogenizing rod, n is the refractive index of the homogenizing rod, $L_z$ is the length of the homogenizing rod, $L_y$ is the cross-section width of the homogenizing rod, ${\theta }_m$ is the division angle of the homogenizing rod, and ${\theta }_{\max }$ is the incidence angle of the homogenizing rod.

Since the CPC incident angle in front of the homogenizing rod is 17° and the outlet diameter is 10.81 mm, $L_Y=10.81 \mathrm{mm}$. Considering that the effective irradiation surface size is 25 mm, the maximum number of total reflections should be greater than or equal to 25/10.81 = 2.3. The maximum number of total reflections is 3, and since JGS3 heat-resistant quartz glass n = 1.487 is selected as the homogenizing rod, $l_z=78 \mathrm{mm}$ can be calculated.

(d)

Illumination lens design

The system spot diagrams and axial aberration curve are shown in Figure 11. According to the spot diagrams, the color difference correction of each field of view is good, the dispersion spot of the optimized image surface is not large, and the energy concentration is high. According to the axial aberration map, the color difference is corrected at the maximum aperture, although there is a certain secondary spectrum; but because this system is an illumination system, there is no need to correct the secondary spectrum, and the system aberration meets the requirements of use.

(3)

Analysis of simulation results of illumination optical system

Tracepro 7.3 software was used to simulate the illumination system. The light tracing diagram and the outgoing light irradiance diagram of the illumination system are shown in Figure 12 and Figure 13.

The uniformity of luminous intensity $\Delta E$ over a range of $\varphi 25 \mathrm{mm}$ can be expressed by Equation (18):

$$\Delta E=1-\frac{E_{\max }-E_{\min }}{E_{\max }+E_{\min }}$$

(18)

where $E_{\max }$ is the maximum luminous intensity and $E_{\min }$ is the minimum luminous intensity. The uniformity was calculated to be 95%.

Therefore, the design parameters of the illumination optical system are better than ±9.2°, the uniformity is better than 92%, and the irradiation surface is $\varphi 25 \mathrm{mm}$, which meets the requirements of use.

3. Design of High-Image Quality Collimating Optical System

Considering that the optical sensor is based on the energy centroid of the star point to realize the attitude positioning of the spacecraft, the collimating optical system of the simulation system requires small distortion, flat image field, and apochromatic image quality in the 380–760 nm band, and the field of view is large, which increases the difficulty of its design. At the same time, the exit pupil of the collimating optical system should coincide with the entrance pupil of the attitude sensor (D ≮ $18 \mathrm{mm}$) to ensure that the light emitted by the stars everywhere in the full field of view is the same as the total luminous flux of the entrance pupil of the attitude sensor. The focal length $f^{\prime }$ of the optical system is determined according to the selected total effective size of LCOS. It is known that the size of a single LCOS image element is 8.4 × 8.4 µm, the total effective size after splicing is 16.128 × 16.128 mm, and the designed field of view of the optical system of the star simulator is 10.2 × 10.2°.

Take the edge equal to 16.128 mm, and find the focal length from Equation (19):

$$16.128/f^{\prime }=\tan 10.2$$

(19)

The solution is $f^{\prime }=89.64 \mathrm{mm}$.

In order to meet the needs of the collimating optical system with the external exit pupil, large field of view, and low distortion, the non-distortion eyepiece is considered as the initial structure, and the focal length scaling and field of view setting make it meet the requirement of the index. According to the color difference of the system, the double-glued achromatic lens in the eyepiece structure is optimized, and the curvature radius and thickness are optimized to be achromatic. Set aberration optimization target, increase spherical aberration, coma, field curvature and other optimization weights. The curvature of the first and fourth sides is set as a variable, and local optimization is started. In the optimization process, if there is interference between the thickness and size of the lens, the air interval is adjusted for automatic optimization. Determine whether the current optimization results meet the conditions by judging MTF and field curvature and distortion chart. If the conditions are met, the optimization is stopped; if not, the operands are reset to optimize again, and the optimal value is found. The two-dimensional structure diagram, spot diagrams, field curvature and distortion curve, and transfer function curve of the optimized collimating optical system are shown in Figure 14. The design results show that the optical system is composed of six lenses, and the RMS radius of the full field of view is less than 3.103 μm. The system distortion is better than 0.04%, and the field curvature is better than 0.08 mm. At Nyquist frequency v = 68 lp/mm, full-field MTF is better than 0.7.

4. Experimental Results Verification

4.1. Verification Experiment of Polarization Stray Light Suppression Effect

In order to verify the suppression effect of the depolarization optical engine on polarized stray light, a dim target simulator based on polarized stray light suppression is constructed. A space detection camera was used to test the grayscale contrast of the simulated image of the simulator, as shown in Figure 15.

Under the condition that the relative position between the camera and the target simulator and the exposure time of the camera remain unchanged, the black and white grid images of the target simulator without depolarization stray light and the target simulator with depolarization optical engine are observed, respectively, and the grid data of the 2 × 2 black and white grid region are obtained and analyzed. The overall grayscale distribution and horizontal, vertical, and sloping grayscale distribution curves of bright areas before and after stray light elimination are obtained, respectively, as shown in Figure 16 and Figure 17.

The average grayscale value $g_{light}$ in the bright area and the average grayscale value $g_{dark}$ in the dark area, as well as the maximum grayscale value $g_{MAX}$ and the minimum grayscale value $g_{MIN}$ in the bright area, can be obtained from the grid data. The image contrast $C$ and grayscale non-uniformity $\eta$ in the bright area before and after the stray light elimination can be calculated by using Equations (20) and (21):

$$C=\frac{g_{light}}{g_{dark}}$$

(20)

$$\eta =\frac{g_{MAX}-g_{MIN}}{g_{MAX}+g_{MIN}}$$

(21)

The results show that without depolarizing stray light, the grayscale contrast of the image is only 2.51, and there is an obvious transition between the bright and dark areas; there is a serious grayscale non-uniformity in the bright area; the non-uniformity is as high as 33.99%, which cannot meet the needs of dim target simulation. After the polarization stray light is eliminated, the image contrast is 6.96, which is increased by nearly 2.8 times, and the space occupied by the transition area between the bright area and the dark area is greatly reduced; the grayscale non-uniformity of the bright area is 5.88%, which is only 17.3% before the polarization stray light, meeting the simulation requirements of the dim target.

4.2. Star Position Simulation Error Calibration

A star position simulation error calibration test was set up using the theodolite and most of the adjustment tables. Before the test, the relative positions of the target simulator and the theodolite were adjusted to ensure that their optical axes coincided, as shown in Figure 18.

The star position simulation error is obtained from the difference between the measured angular distance between stars ${\gamma }_{reality}$ and the theoretical angular distance between stars ${\gamma }_{ideal}$ relative to the central star position [21], as shown in Equation (22):

$$\begin{array}{l}\rho =\arccos \left[\cos \beta \cos {\beta }_{O^{\prime }}\cos (\alpha -{\alpha }_{O^{\prime }})+\sin \beta \sin {\beta }_{O^{\prime }}\right]\\ -\arccos \left[\frac{d\left({\left(x-x_0\right)}^2+{\left(y-y_0\right)}^2\right)+2{f_0}^2}{\sqrt{d\left({\left(x-x_0\right)}^2+{\left(y-y_0\right)}^2\right)+{f_0}^2}}\right]\end{array}$$

(22)

where $\alpha$ and $\beta$ are the azimuth and pitch angle of the measured star point, ${\alpha }_{O^{\prime }}$ and ${\beta }_{O^{\prime }}$ are the azimuth and pitch angle of the measured central star point, $x$ and $y$ are the theoretical star point coordinates, respectively, and $f_0$ is the focal length of the collimating optical system.

The display area is divided into a 10 × 10 grid, with a total of 100 measured star points. The theodolite is used to measure the azimuth angle $\alpha$ and pitch angle $\beta$ of each star point, respectively, and the simulation error $\rho$ of each star point position is calculated according to Equation (22). The same method was used to obtain the simulation error ${\rho }^{\prime }$ of each star position before depolarizing stray light. The test results are shown in Figure 19.

The maximum error of each star position is taken as the simulation error of star position of the target simulator. The test results show that the star position simulation error of the target simulator without depolarizing stray light is ${18.99}^{″}$, while the star position simulation error of the depolarizing stray light dim target simulator in this study is ${9.90}^{″}$, and the star position simulation accuracy is improved to 1.92 times of that before depolarizing stray light, meeting the accuracy requirements of dim target simulation. The comparison of main parameters of the target simulation system before and after depolarization stray light is shown in

Table 4. Comparison of main parameters of the target simulation system before and after depolarization stray light.

Parameters	Traditional Dynamic Target Simulation Method with Unpolarized Stray Light	Dim Target Simulation Method Based on Polarized Stray Light Suppression
Grayscale contrast	2.51	6.96
Grayscale non-uniformity	33.99%	5.88%
Simulation error of star position	${18.99}^{″}$	${9.90}^{″}$

.

5. Conclusions

In order to meet the optical simulation requirements of dim space targets, a simulation method of dim space targets based on LCOS splicing display technology and polarization stray light suppression technology is proposed. The mechanism of generating stray light in the optical engine is analyzed. Quarter slide phase compensation is used to reduce dark state light leakage, optimizing the matching of the illumination system and critical incident angle of the spectroscopic film to improve the optical engine stray light suppression ability. At the same time, the collimation optical system with large field of view and high image quality and flat aberration is designed, and the polarization stray light suppression effect verification test and star position simulation error calibration test are set up. The results show that the grayscale contrast of the dim target simulator is 6.96, the non-uniformity of the bright state is only 5.88%, and the simulation error of star position is ${9.9}^{″}$.

However, it can be seen from the experimental results of the simulated black and white grid that the high contrast between bright and dark regions of the target simulation system after depolarization stray light is reduced in the transition area, but there is a sudden increase in the grayscale of pixels in some regions. Therefore, the research should be further aimed at reducing the transition area and clarifying the abnormal grayscale mechanism.

Compared with the traditional dynamic target simulation method, the proposed dim target simulation method based on polarized stray light suppression technology can effectively suppress the polarized stray light in the optical engine, meet the ground calibration requirements of dim target detection system, provide strong technical support for improving the simulation magnitude and simulation accuracy of dim targets, and have far-reaching influence on the development of advanced deep-space detection capabilities.