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Abstract
In order to meet the ground calibration requirements of optical detection equipment to identify optical characteristics of dim targets, an optical simulation method of dim targets based on passive detection link analysis and bidirectional scattering distribution function model is proposed. The off-axis collimation system for long focal length, the simulated energy transmission model of dim targets and the simplified model of bidirectional scattering distribution function are established. An internal stray light suppression baffle was designed to effectively suppress secondary scattering, and an optical simulation system for dim targets was built. The experimental results show that the system can simulate +7 Mv∼+20 Mv, and the simulation accuracy is better than 0.07 Mv. At the same time, the detection ability of the camera is tested by using the +15 Mv point simulated by the system. The signal-to-noise of the star point target reaches 6.7, which meets the requirements of detection rate and false alarm rate, and realizes the ground test of the camera's detection ability of the dim target.
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1. Introduction
High-precision detection of dim targets is one of the urgent problems to be solved in the exploration activities of extraterrestrial space. How to effectively reduce the detection false alarm rate [1,2]and improve the pointing accuracy is the main technical research direction in the field of space science at present. With the development of space detection into deeper space, the detection of dim targets becomes more and more difficult and challenging due to the long target distance, low signal-to-noise ratio (SNR) and complex spectrum. Due to the limited resources of the platform for on-orbit verification, physical simulation of dim targets on the ground is one of the most important guarantees for planetary exploration missions.
So far, the development of space target simulation technology can be mainly divided into the research progress of the equivalent magnitude, spectral width and color temperature types of the target [3]. As the most direct optical feature of space targets, magnitude has attracted much attention since the early stage of space exploration. ZEISS initially only used transmitted parallel light tubes and transparent micro holes to simulate star points [4]. So far, relevant simulation technologies have formed a number of representative product sequences. For example, Eastman Kodak Company and Ball Aerospace and Technologies Corp use optical fiber to simulate star points [5,6]. Airbus Defence and Space and Jena-Optronik use liquid crystal on silicon (LCOS) to generate star points [7]. However, the highest simulated magnitude of these star point simulators is generally in the range of +6.5Mv∼+8.7 Mv.
In order to meet the increasingly developed requirements of detection system ground test, the relevant research has gradually developed to the extremely weak magnitude, but there are still many constraints and challenges in the research on the optical simulation technology of dim targets. Xu et al. developed a dim light ultraviolet star simulator that can simulate +16 Mv by using the method of double integrating sphere and xenon lamp, and the simulation accuracy reached 0.1 Mv. However, since the high-magnitude irradiance could not be measured, the simulation magnitude results were obtained only by theoretical calculation [8,9]. R.w. Ansevin et al. proposed the method of using optical fiber and xenon lamp to achieve the weakest +17 Mv target energy, but it was only used for the image stabilization accuracy test of space telescopes, and the aperture size could not meet the ground calibration requirements of dim target detection equipment [10]. At the same time, the problem of internal stray light is more prominent and serious in the dim target simulation system because of the long optical path, large aperture, complex structure and low energy of the target. Moreover, among the existing ground calibration devices that can simulate high-magnitude targets, there is still a lack of analysis and suppression of stray light in the system. For example, Feng Guangjun et al proposed to use a variable diaphragm and integrating sphere to achieve a magnitude simulation range of +6Mv∼+14 Mv with a simulation accuracy of 0.2 Mv, but did not analyze and design the stray light suppression structure in the system [11]. Due to the problems such as stray light, magnitude irradiance test and aperture mismatch, it is difficult to realize and verify the accurate simulation of high magnitude targets in the existing optical simulation systems that can be applied to the ground calibration test of dim target detection equipment.
In summary, aiming at the influence and suppression of dim target simulation method and stray light in dim target simulation system, this paper analyzes the relationship between aperture, signal and stray light, proposes a design method of dim target simulation system based on passive detection link analysis, and establishes a simplified model of dim target simulation system Bidirectional Scattering Distribution Function (BSDF). The law of endogenous stray light generation in the system was revealed, and the stray light suppression blocking baffle of the dim target simulation system was designed, and the propagation law of the secondary scattering stray light was analyzed and verified based on the Monte Carlo method. Finally, the simulation system was built to realize the optical simulation of dim targets under laboratory conditions.
2. Analysis of the influence of optical characteristics of dim targets in passive detection link
The optical passive detection technology of dim targets is a passive detection technology. Taking remote space objects and stars as detection objects, different working bands are adopted to collect and process the radiation energy of the target according to the different characteristics of the target and environmental background, and the formed target images are used to analyze the optical characteristics of the target or obtain spacecraft attitude information [12].
Taking the M-magnitude star detection target as an example, when the detection distance is relatively far, the target irradiance ${E_{wt}}$ at the point where the target reaches the detection system's entry pupil can be calculated according to the zero-magnitude star irradiance ${E_0}$ [13], as shown in Eq. (1).
At this time, after the detection optical system, under the action of exposure time ${t_s}$, the radiation energy is converted into the number of target signal photons that the detection system can receive, and the number of target signal photons is affected by the detector quantum efficiency ${\eta _s}$ and the filling factor ${K_{fill}}$, and finally received by the corresponding pixel of the detection system in the form of the signal equivalent charge number S, as shown in Eq. (2).
When the detection target is a dim target, in order to ensure that the equivalent charge output number of the signal is available, the exposure time needs to be increased. At this time, the background noise with ${E_n}$ illumination is also amplified and received by the corresponding pixel of the detection system in the form of noise equivalent charge number B [14], as shown in Eq. (3).
At this time, the relationship between the SNR of the detection system and the incident energy of the target ${E_{\textrm{ob}}}$, the aperture ${A_{in}}$ of the optical system, the total number of detector noise electrons $\sum {N_{ele}^2}$, the noise charge number B and the SNR threshold is shown in Eq. (4).
As can be seen from the above formula, the SNR of the detection system can meet the requirements of detection rate and false alarm rate performance, and increasing the system aperture is conducive to improving the $SNR$ of the dim target, but the system is more susceptible to the impact of background noise. Therefore, in the ground calibration and testing of the optical passive detection system for dim targets, in addition to designing a matching dim target simulation system, the simulation system should also be analyzed and suppressed for stray light to avoid interference with the test results.
3. Method and analysis of optical simulation of dim targets
Aiming at covering the full aperture of the dim detection equipment, reducing the influence of internal stray light and accurately simulating the dim magnitude, a ground simulation system for dim targets consisting of three parts: control room, light source room and primary mirror room is designed, as shown in Fig. 1. The light source room comprises a wide spectrum light source, a color temperature and magnitude feedback detector, a mixed-light integrating sphere, a filter component and a star-point divider component. The primary mirror room consists of a dim target collimation optical system and a stray light suppression system. The control room contains various parts of the control system.
Under the control of the control system, the light beam that meets the color temperature requirement is emitted by the wide spectrum light source, and enters the mixed light integrating sphere uniformly. Then, the light beam output of a specific spectral range is realized by the filter component, and the light beam is illuminated by the star splitter component. The star splitter component puts the marking hole at the focal plane position of the collimating optical system, and then emits the light beam in the form of parallel light to simulate the target at infinity. The color temperature and magnitude feedback detector monitor the spectral type and energy in real time. The star size can be changed by changing the star-point divider component with different size of star.
3.1 Design of dim target collimation optical system
A collimating optical system is designed to simulate the dim target at infinite distances. Considering that the object of the system is an on-axis point and the simulated target has a low illuminance, based on the paraxial theory and the primary aberration theory [15], an off-axis reflection collimating optical system consisting of a parabolic primary mirror and a planar folding mirror is designed, with a light aperture of 500 mm and a focal length of 5000 mm. The spectral range is 450 nm∼1000 nm, and the system aberration is calibrated. The design results are shown in Fig. 2.
Fig. 2. Design results of the collimating optical system: (a) Curvature of field and distortion; (b) spot diagrams; (c) wave aberration.
The design results show that the system distortion is better than 0.002%, the curvature of field is better than 0.2 mm, the diffraction spots of each field are within the Airy spot range, and the root mean square (RMS) of wave aberration is less than λ/15. The designed off-axis reflection collimating optical system can adapt to the requirements of the simulation system with wide emission spectrum and large emission aperture, overcome the center blocking, and reduce the system size by using a folding mirror [16]. However, it is precisely such optical characteristics as long focal length, large aperture and optical path folding that cause the existence of non-imaging optical paths in the system, and the stray light path is more complex than that of the coaxial optical system. Therefore, in order to achieve very low energy collimated beam emission, it is necessary to carry out targeted stray light elimination design in the future.
3.2 Analysis of system energy transfer
In order to clarify the radiation transfer process of the imaging optical path, satisfy the magnitude simulation range of the dim target simulation system, and ensure the magnitude simulation accuracy, it is necessary to establish the radiation energy transfer model of the optical path. Combined with the working principle of the simulation system, the wide-spectrum light-emitting diode (LED) light source emits luminous flux ${\phi _0}$, and after mixed light integrating sphere uniformity, the neutral filter attenuates and band pass filter modulated, the star plate is uniformly illuminated. Then the dim target simulation at infinity is formed from the star hole to the target surface. The overall structure and radiation energy transfer model are shown in Fig. 3.
According to the transfer model, the energy utilization rate ${\delta _{sou}}$ of the light source room is composed of the product of the energy utilization rate ${\delta _{sph}}$ of the integrating sphere, the transmittance ${\delta _{tem}}$ of the neutral filter and the transmittance ${\delta _{mag}}$ of the band pass filter. Among them, ${\delta _{sph}}$ is affected by the reflectivity of the integrating sphere $\rho $, the radius of the light inlet hole ${r_i}$, the radius of the light outlet hole ${r_\textrm{o}}$ and the radius of the integrating sphere R, and ${\delta _{tem}}$ is affected by the spectral curve ${f_{LED}}(\lambda )$ of the wide-spectrum LED and the transmittance curve ${T_{\textrm{filter}}}(\lambda )$ of the band pass filter. The specific relation is shown in Eq. (5).
The energy utilization rate of the star splitter board ${\delta _{\textrm{star}}}$ is determined by the half angle of the light beam behind the star splitter board being $\alpha $, the baffle of the collimating optical system being d and the focal length of the system being f, as shown in Eq. (6).
The energy utilization rate of the collimating optical system ${\delta _{col}}$ is the product of the reflectance ${\delta _{\textrm{mirror}}}$ of the two mirrors, ${\delta _{col}} = {\delta _{\textrm{mirror}}}^2$.
To sum up, the energy utilization rate of the dim target simulation system ${\delta _{tot}}$ is shown in Eq. (7).
The relationship between the luminous flux ${\phi _0}$ required by the light source, the target illuminance E and the target surface aperture D is shown in Eq. (8).
According to the brightest magnitude simulation target and redundancy design principle, the superposition of multiple LED lights with different power is used to meet the magnitude energy range, so the combination of a 200W LED light and three 5W LED lights is selected as the simulation system light source.
In the above transfer process, the main light energy loss is absorbed by the filter and the integrating sphere, and a large light energy loss also occurs between the star plate and the folding mirror. The partial loss ${E_{loss}}$ will not be absorbed by the star splitter, but may participate in the light energy transfer of the subsequent collimating optical system and become stray light ${E_{stray}}$, as shown in Eq. (9).
where, ${\delta _{\sup }}$ is the system's stray light rejection ratio.In summary, it is necessary to reduce ${\delta _{\sup }}$ and ${E_{stray}}$ levels by suppressing stray light, so as to avoid affecting target illuminance E, that is, affecting magnitude simulation accuracy.
4. Stray light analysis and suppression structure design of dim target simulation system
The stray light of the dim target simulation system mainly comes from the multiple scattering inside the system, that is, the disturbance of internal stray light [17]. It can be seen from the analysis in the above section that because the outgoing light of the integrating sphere is Lambertian radiation, the half angle of the beam exiting from the star hole is larger than the luminous half angle, and this part of the unexpected light incident on the rough inner wall of the system will be scattered. At the same time, due to the surface of precision optical components such as mirrors still have certain processing errors (usually pay attention to scratches, pits and roughness during processing, so that the RMS is less than 1 nm to minimize scattering [18,19]), it is expected that the light path will also scatter on the surface after incident on the mirror, and will be diffused around the center of the mirror reflected light. The non-collimated light is emitted as noise, which is received by the optical system to be measured and affects the magnitude simulation accuracy of the simulator. Therefore, the internal system must be optimized based on the transmission link of endogenous stray light.
4.1 Stray light scattering analysis model
The BSDF was used to quantify the degree of beam dispersion on the surface of the material [20]. As shown in Fig. 4, taking the amplified scattered light on a micro surface $\delta \textrm{A}$ on a rough surface as an example, BSDF is defined as the function of the incident angle ${\theta _i}$ and the azimuth angle ${\varphi _i}$ of the incident light, and the scattering angle ${\theta _s}$ and the azimuth angle ${\varphi _s}$ of the scattered light, as shown in Eq. (10).
In combination with the figure above, the calculation methods of other parameters are shown in Eq. (11) ∼ (14).
This model analyzes and calculates BSDF based on the Gauss statistical characteristics of the material surface [27], avoids the high cost caused by measured BSDF and the high error caused by the Lambert scattering model for large angle stray light [28], and conforms to the structural characteristics of the dim simulated collimation optical system.
4.2 Two-dimensional space simplification of scattering model
The actual propagation path of light in the three-dimensional space is scattered into the three-dimensional space, which is closer to the real scattering of light, but also brings twice the number of parameters and more complex integrals in the analysis of multiple scattering.
Based on the above model, when the light illuminates the surface of the material at an incidence angle of 10° (${\theta _i} = 10^\circ$) and 25° (${\theta _i} = 25^\circ$) respectively, BSDF in the 0° incident plane (${\varphi _s} = 0^\circ$) and in the plane with an angle of 5° from the incident plane (${\varphi _s} = 5^\circ$) are analyzed. The distribution trend of BSDF is shown in Fig. 5.
It can be seen that most of the energy of the scattered light is concentrated in the same plane as the incident light, and with the increase of the incident angle, the energy concentration will also increase [29]. Considering the internal space structure of the off-axis reflection collimation system, model $BSDF({\theta _i},{\varphi _i};{\theta _s},{\varphi _s})$ is simplified into a two-dimensional space model, that is, ${\varphi _i} = {\varphi _s} = 0$, which will greatly reduce the number of parameters in multiple scattering analysis on the basis of ensuring the rationality of the model.
4.3 Endogenous stray light suppression baffle design
According to the simplified scattering model in two-dimensional space and the existing mask design method for suppressing exogenous stray light in the detection optical system [30], the blocking baffle on the inner wall of the dim target simulation system is designed based on the geometric principle, and its light aperture is subject to the non-blocking imaging beam.
4.3.1 Determination of the starting position of the blocking baffle (Vane0)
According to the relative positions and sizes of the star hole and the folding mirror in the optical path, the stray light action model is established for the beam with half angle $\beta $ emitted by the star hole, as shown in Fig. 6.
Fig. 6. Schematic diagram of setting the start position of the stray light suppression baffle (Vane0).
In the figure, d is the aperture of the folding mirror, $\alpha $ is the half angle of the corresponding beam, $D^{\prime}$ is the aperture of the light at the edge of the light source, and ${\xi _0}$ is the distance between the star plate and the stray light suppression baffle. The relationship between them is shown in Eq. (15).
If Vane0 is located at position b or further away from the star hole, a single scattered light approaching the reflection angle will enter the system through Vane0 (blue). If Vane1 is located between a and b in the figure, the above first scattered light will not enter the system, but the first scattered light in other directions can still enter the system (rose red), If Vane0 is located at position a or closer to the star hole, the first scattered light will not pass through Vane0, and the second scattered light (yellow) will occur between the vanes. Therefore, Vane0 can be set at position a.
4.3.2 Determination and analysis of block baffle interval
The segmented design method is used to divide the optical path into three sections at the interval of two mirrors. The maximum projected width of the optical element in each segment in the plane perpendicular to the optical axis of the segment is taken as the outer profile of the baffle, and the edge light is taken as the inner profile of the baffle, and the number of the baffle is increased without interference between the baffle structure and the optical path.
Take the second paragraph, as shown in Fig. 7. After $D^{\prime\prime}$ and $Vane{0_2}$ are determined by the above method, O is connected with the edge of the opposite parabolic mirror $B^{\prime}$, and the intersection point of the edge ray is the vertex ${P_1}$ of $Vane{1_2}$, Connect $A^{\prime}P$, extend and intersect the outer contour of the vane at C, connect $CB`$, and the intersection point with the edge ray is the vertex ${P_2}$ of $Vane{2_2}$, And so on to build multiple baffles. It should be noted that due to the folding of the optical path of the off-axis reflective optical system, the $Vane{0_2}$ established in the initial design interferes with the preceding optical path, so this part should be discarded in the end, as shown in the gray vane in the figure.
In addition, in actual processing, in order to reduce the edge scattering of the blocking baffle, the vertex of the blocking baffle is usually slightly removed from the inner contour of the blocking baffle by about 1 mm, and the top of the blocking baffle is processed into an arc shape with inclination [31].
4.3.3 Approximation and calculation of secondary scattering
Because the simulated dim target energy is low, the secondary scattering light path is analyzed for the designed blocking baffle structure. Taking $Vane{1_3}$, $Vane{2_3}$ and $Vane{3_3}$ as an example, the image plane behind the optical path is regarded as a detector, and the red part between ${P_3}{C_1}$ and ${P_4}{C_2}$ is the visible region relative to the secondary scattering optical element. Taking $Vane{2_2}$ and $Vane{3_2}$ as an example for further analysis, for these visible regions, the secondary scattered light that can enter the optical path of the collimation system has only two propagation modes, as shown in Fig. 8(a) and 8(b), where ${\theta _1}$ represents the primary scattering angle and ${\theta _2}$ represents the secondary scattering angle.
By analyzing the scattering types in the two modes, it can be seen that the secondary scattering mode must contain one forward scattering and one backward scattering, that is, Model 1 ${\theta _1}> 0$, ${\theta _2}< 0$ or Model 2 ${\theta _1}< 0$, ${\theta _2}> 0$. Based on the simplified two-dimensional space BSDF model, $BSDF = \textrm{ }BSD{F_1} \times BSD{F_2}$ after secondary scattering is calculated, and the results are shown in Table 1.
Table 1. Results of secondary scattering BSDF
The results show that the BSDF of the designed off-axis reflection collimation system is much less than 10% after secondary scattering, that is, the design effect of suppressing the endogenous stray light blocking baffle can meet the simulation accuracy requirements of the dim target simulation system for high magnitude.
4.4 Simulation analysis of stray light suppression method
Lighttools was used to analyze the effect of light suppression on endogenous stray light. All surface properties were set to ideal properties, Monte Carlo ray tracing was performed on the optical system model [32], and the theoretical illuminance of the outlet without stray light interference was obtained. Set the surface of the primary mirror and the folded mirror as the actual reflection characteristics, and set the blackening characteristics of the reflectivity of 0.001% on the surface of other mechanical structures and the surface of the stray light suppression baffle to obtain the stray light path with or without the stray baffle, as shown in Fig. 9. Different colors in the figure represent different propagation paths of light. It can be seen that most of the light paths in Fig. 9(b) are similar, and the amount of stray light is effectively reduced.
Fig. 9. Simulation results of non-ideal optical system: (a) no baffle simulation results (baffles are not involved in ray tracing); (b) baffle simulation results.
By calculating the difference between the outlet illuminance of an ideal optical system and that of a non-ideal optical system using baffles under different magnitude, the equivalent illuminance of the residual stray light suppressed by the baffles can be obtained, and the ratio between it and the theoretical illuminance value is the illuminance simulation error, as shown in Fig. 10.
By comparing the theoretical illuminance values corresponding to different magnitudes and those corresponding to stray light in Fig. 10. The ratio of residual and theoretical illuminance is less than 3.35%, and the simulation accuracy of magnitude is less than ±0.1 Mv. The results show that the designed stray light suppression baffle can inhibit both non-imaging beams with definite directionality and irregular stray light.
5. Calibration and performance testing of dim target simulation system
The dim target optical simulation system based on passive detection link analysis was built, and the magnitude simulation range and magnitude simulation accuracy of the simulation system were calibrated by using a dim illuminometer. The calibration results are shown in Fig. 11. According to the calibration results, the optical simulation system based on passive detection link analysis can simulate +7Mv∼+20 Mv, and the magnitude simulation accuracy is better than ±0.07 Mv.
Fig. 11. Magnitude test results of optical simulation system for dim targets based on passive detection link analysis.
Using the dim target simulation system to output +15 Mv star target, the magnitude detection ability of the dim target camera is tested. The pixel response of the working scene and the camera detector acceptance surface is shown in Fig. 12.
Fig. 12. Dim target optical simulation system working scene and camera detector received star map images: (a) work scenarios; (b) star images; (c) grayscale analysis of star points.
It should be noted that Fig. 12(b) and 12(c) only show the 100 × 100 area near the star point target. Considering the detector noise in the entire camera frame, the SNR of the star point target is calculated by using Eq. (4) to be 6.7, which meets the requirements of detection rate and false alarm rate [33] and realizes the ground test of the camera's detection ability to dim targets.
6. Conclusion
Based on the requirements of ground calibration and testing of dim target photoelectric detection equipment, this paper proposes a dim target simulation technology based on passive detection link analysis, aiming at the dim target ground simulation technology and the influence and suppression of stray light in the simulation system. The influence of optical characteristics of dim targets in passive detection links is studied, and the relationship between detection system aperture, signal and target SNR is revealed. An off-axis collimation system with long focal length, a simulated energy transmission model of dim target and a simplified model of dim target simulation system BSDF are constructed, and endogenous stray light suppression baffle is designed. The residual secondary scattering in the system is calculated and analyzed, and the dim target simulation system is built and its calibration and application performance are tested. The test results show that the optical simulation system based on passive detection link analysis can simulate +7Mv∼+20 Mv, the magnitude simulation accuracy is better than ±0.07 Mv, and the output of +15 Mv star targets can realize the ground test of the camera's detection ability of dim targets.
However, due to the limitations of cost and structural complexity, this study only uses the wide-spectrum LED and filter as the spectral simulation means, and does not further fine-modulation the spectrum, which has certain limitations on the multi-color temperature target observation. Therefore, how to design multi-color temperature simulation light source and achieve fine spectrum modulation on the basis of high magnitude [34] is the next research focus.
This study provides an effective reference for improving the ground simulation calibration technology of photoelectric detection equipment, and is expected to promote the engineering application of dim target simulation technology, and make contributions to improving the performance of spacecraft photoelectric detection system and ensuring the effective implementation of deep space exploration missions.
Funding
State Administration for Science, Technology and Industry for National Defense (HTKJ2022KL502004); Department of Science and Technology of Jilin Province (20210201034GX); Ministry of Education of the People's Republic of China; 111 Project of China (D21009).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but can be obtained from the authors upon reasonable request.
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