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Abstract
Target searching and tracking photoelectric systems are widely used in civil and military fields. Achieving both efficient search and fine-observation imaging while minimizing the volume and weight of the system is the most concerning problem. In this paper, a dual-mode integrated optical system is proposed, which shares large size components between large field of view (FOV) search module and high-resolution tracking module by using the Biconic Zernike freeform mirrors. Compared with the traditional searching and tracking system utilizing multi-camera matching, this scheme significantly reduces the volume and weight of the remote sensing payload. At the orbit altitude of 500 km, this proposed system has a swath of 87.5 km with a ground resolution of 10 m in search mode. In tracking mode, it can observe an area of 19 km2 with a ground resolution of 1 m. It can meet the requirements of wide-area search and focus tracking simultaneously, providing a feasible scheme for the lightweight design of space optical cameras.
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1. Introduction
Optical systems with large field of view (FOV) and high-resolution have been widely used in space remote sensing, astronomical observation and ecological monitoring. For an optical system, a larger FOV means a wider swath at the same orbit altitude, thereby shortening the scan period and effectively improving the camera's wide-area search ability. Meanwhile, the high-resolution imaging results are beneficial to more accurately identifying the details of the target information.
The high-resolution images are usually obtained through the large diameter coaxial optical structures. For example, the primary optical system of the ‘GF-4’ satellite tracking camera adopts an R-C structure with a diameter of 700 mm, making the ground sample distance (GSD) in the visible and near-infrared spectrum better than 50 m [1]. The American ‘KH-12’ camera optical system adopts a 3 m aperture reflective Cassegrain structure to achieve the GSD of 0.1 m [2], which is the highest resolution optical reconnaissance satellite so far. However, as the aperture increases, the optical path difference (OPD) between the on-axis rays and the off-axis rays will increase, resulting in large aberrations, limiting the FOV of the large-aperture optical system. Therefore, it is difficult to obtain wide FOV images for a single monolithic large aperture camera with a fixed focal length.
However, an optical system with a wide FOV is necessary to achieve efficient search, so an off-axis structure with freeform optics is usually adopted. Freeform optics breaks the conventional rotational symmetry structure, has excellent aberration correction ability, which can provide more degrees of freedom for optical design and expand the observation field of the system. For example, an off-axis four-mirror freeform optical system with a large linear 76° FOV [3] and another off-axis reflective infrared imaging system with a wide rectangular 40°×30° FOV [4] both applied the freeform optics.
If the off-axis TMA structure is designed with a large aperture to improve the resolution, in addition to the primary mirror, the tertiary mirror also needs to be designed with a large aperture to accommodate the light from the wide FOV. Compared with the volume of the coaxial structure of the same resolution level, the volume of the off-axis structure has at least doubled because of the enlarged FOV. From the perspective of application and cost control, it is not necessary to achieve high-resolution imaging in a wide FOV. Therefore, the traditional searching and tracking camera generally relies on two kinds of cameras to complete the tasks. A search camera with wide FOV and small aperture quickly captures the objects in scanning mode, and then another tracking camera with large aperture, high-resolution but narrow FOV makes continuous observation in gaze mode. For example, ‘GF-6’ is equipped with a 2 m panchromatic / 8 m multi-spectral high-resolution camera with a swath of 90 km, and a 16 m multi-spectral medium-resolution wide-field camera with a swath of 800 km [5], which combines high resolution and wide coverage to realize precision agriculture observation.
However, the scheme of two cameras’ collaboration makes the entire system bulky. Therefore, how to realize a compact multi-mode operating system has attracted more and more attention. Zhao et al. developed a prototype of two optical channels with separate focal lengths so that wide-area search and focus tracking can be realized in one optical system. All components except the first mirror are shared, and a deform mirror is used to switch between the two channels [6]. Lei et al. proposed an off-axis dual-channel system based on XY polynomial freeform optics, and each channel is a relayed TMA optical system. Two channels share one common entrance pupil and use a beam splitter to realize wide-area search and focus tracking [7]. The adjacent off-axis mirrors are often integrated to form a large optical component on a single substrate for easy installation and calibration [8].
In this paper, an integrated optical system with searching and tracking functions is proposed, which significantly reduces the volume and weight of the searching and tracking system by sharing large-size optical components and using freeform mirrors. Additionally, it simultaneously meets the needs of wide-area search and high-resolution detection in a compact structure. The aperture of the search mode is 200 mm, the relative aperture is 1/3.75, the FOV is 10°, and the angular resolution is 20 µrad. The aperture of the tracking mode is 750 mm, the focal length is 3750 mm, the FOV is 0.5°× 0.5° and the angular resolution is 2.1 µrad.
The remaining parts of this paper are organized as follows: The design strategy is introduced in Section 2. The specific design process is described in Section 3. The design results and performance evaluation are discussed in Section 4. Finally, the paper is concluded in Section 5.
2. Design strategy
In this paper, we propose an integrated optical system sharing the large size components of the coaxial and off-axis structures. The proposed system has two working modes to realize the wide-area search and target tracking. It will make full use of the system space and avoid the problem of matching multiple cameras.
The schematic diagram of the system prototype is shown in Fig. 1. An off-axis structure and a coaxial structure are combined into a dual-mode search and tracking optical system by sharing an integrated primary mirror (IM). The off-axis structure serves as the search camera. The target light is successively reflected by primary mirror (M1), secondary mirror (M2), and tertiary mirror (M3), and then converges on the image plane (Sensor 1). Here, M1 and M3 are designed as IM, which is reused as the primary mirror of coaxial structure and serves as the tracking camera. The light reflected from IM to a secondary mirror (OM2) finally reaches another image plane (Sensor 2). In this way, the idea of sharing large size components can be realized. Compared with multi-camera matching work, the configuration of integrated searching and tracking optical system will greatly reduce the volume and weight. At the same time, it can carry out both large FOV search and high-resolution tracking imaging.
3. Optical design and optimization
Based on the above design strategy, an integrated searching and tracking optical system sharing large size optical components is designed in this section. The system design parameters are shown in Table 1.
Table 1. Optical system specifications
Since the system has two structures that need to be designed separately, the design can be divided into two cases in order. One is to design the complex off-axis structure first and then adjust the coaxial structure. The other is to start with the simple coaxial structure and then focus on improving the image quality of the off-axis structure.
For the former case, since the shape of the M1 is not consistent with that of the M3 in the off-axis structure, M1 and M3 will be designed as coaxial primary mirrors respectively in the coaxial design. The separation of the two optical paths involves sub-aperture stitching imaging. It is necessary to solve the problem of making two path beams co-phase to make the OPD zero [9]. In addition, considerations such as the precision control of beam synthesis error will complicate the coaxial design.
For the latter case, once the coaxial structure is designed first, part of the IM is functionally used as M1 and M3 of the off-axis structure, which can bypass the steps of phase matching, optical path adjustment, beam synthesis, etc. Therefore, this design adopts the second case. The R-C system structure is adopted, and the primary mirror is set as a hyperboloid. The coaxial primary mirror is also used as the off-axis primary-tertiary mirror, and only the secondary mirror needs to be adjusted and optimized. According to this scheme, the design process is as follows.
3.1 Initial structure design of the tracking module
The tracking module adopts the R-C configuration in the main optical system structure. The initial structure parameters are found by solving the primary aberration of the paraxial ray [10]. Due to the large diameter of the IM, it is difficult to correct off-axis aberrations in the reflective system. A calibration lens set is added to optimize the image quality within the ±0.25° field range. The initial structure of the tracking module is shown in Fig. 2.
3.2 Initial structure design of the search module
The starting point of the search module is to find the position of mirrors by inheriting the coaxial primary mirror and imposing proper constraints. According to the idea of sharing large components, the coaxial primary mirror mentioned above is also used as M1 and M3 of the off-axis structure. Considering that the integration of the primary-tertiary mirror reduces the design freedom of the system, and the large IM needs to serve the operating modes of two structures at the same time, the TMA configuration is not enough to realize the search system functions, so select the system configuration of off-axis four-mirror by adding a fourth mirror (M4) after M3, as shown in Fig. 3.
The stop of the off-axis structure is placed on M2, and the entrance pupil is off-axis to obtain an off-axis optical path. Since the primary mirror of the system has been determined, the light has been reflected twice by the IM. According to the path of the reflected light, the positions of M2 and M4 can be preliminarily determined while keeping the central field of the two modules overlapped. Then optimize offset, tilt and surface parameters of M2 and M4 to balance reducing light obscure and improving image quality.
3.3 System optimization strategy
Compared with traditional rotationally symmetrical surfaces, multi-degree-of-freedom free-form surfaces are more adaptable to special optical structures and have higher system performance improvement capabilities [11]. This article uses this feature to optimize the integrated system. The key points of the optimization strategy are as follows:
First of all, the selection of the free-form surface shape is a key point. There are various forms of representation for freeform surfaces, which can be selected according to different application scenarios [12]. In this design, due to the non-rotational symmetry of the off-axis structure, the focused spot of the beam emitted by the off-axis object point has a large difference in the tangential and sagittal direction. Meanwhile, the Biconic Zernike freeform surface has different curvature and conical coefficients in the X and Y directions [13]. It is appropriate to correct the large astigmatism of the system [14]. Therefore, Biconic Zernike surface is selected.
The Biconic Zernike surface is composed of three parts: quadric term, higher-order term and zernike term. The sag of a Biconic Zernike is given by Eq. (1):
Secondly, it is another key point to optimize the position and surface parameters of M2 and M4 to suppress light obscuration in the system. Two structures are combined into one system by the multiconfiguration editor in ZEMAX design. On the premise of satisfying the system configuration, adding the structural constraints to avoid interference between mirrors and rays as much as possible, as illustrated in Fig. 4.
There are three control points to suppress light obscuration in the system: the first control point P1 is located between the upper edge L1of the off-axis incident beam and the lower edge of M2; the second control point P2 is located between the upper edge of M2 and the light L2 reflected by OM2 to the lower edge of the image plane; the third control point P3 is located between the incident upper edge light L3 of the coaxial system and the lower edge of M4.
Control the distance from the endpoint of the mirror to the light at P1, P2, and P3 to avoid obscurations and reserve some space for mechanical structure and system installation by writing a macro program in ZEMAX [15].
4. Design results and performance evaluation
According to the design parameter requirements of the system shown in Table 1, based on Biconic Zernike freeform surfaces after optimization, the overall optical layout of the integrated searching and tracking optical system is shown in Fig. 5(a). Considering the obscuration of incident light by secondary mirrors of two structures, the final light-through ratio of the coaxial structure is 92.74%. The light trace of incident rays on IM is shown in Fig. 5(b), the blue filled area represents the effective incident rays of coaxial structure, The green filled area represents the effective incident rays of off-axial structure. The surface parameters for the final system of the coaxial tracking module are listed in Table 2, Table 3 and Table 4. Table 4 shows the parameters of M2 and M4 of integrated optical system with Biconic Zernike coefficients for search module.
Table 2. The parameters of the coaxial tracking module
Table 3. The parameters of the off-axis search module
Table 4. The surface parameters of freeform M2 and M4 in the off-axis search module
The surface sag of M2 and M4 are symmetrical about y-axis, as shown in Fig. 6, M2 is a circular aperture, and its surface sag is symmetrical about the y-axis, as shown in Fig. 6(a), the aperture of M4 is close to a rectangle, and its surface sags It is also symmetrical about the y-axis, as shown in Fig. 6(b).
The spot diagram, modulation transfer function (MTF) and grid distortion of the system are the key criteria for evaluating the imaging quality of the system. The spot diagram of each FOV in the system is shown in Fig. 7. The RMS radius of the tracking module is less than the airy radius as Fig. 7(a) shown, which is 3.6 µm according to the wavelength and F number, and the RMS radius of the search module is less than 15 µm in the specified FOV as Fig. 7(b) shown.
The angular resolution $\alpha $ is determined by the pixel size and the focal length, which can be calculated by Eq. (2):
where, $pixel$ is the pixel size and f is the focal length of the system. When the pixel size of sensors is 8 µm and 15 µm for search and tracking module, respectively, the angular resolutions are 2.1 µrad and 20 µrad, which meets the design requirements.The ground sample distance (GSD) and the swath width ${S_w}$ are two important indicators to measure the imaging resolution and FOV of the remote sensing optical system, they are defined by Eq. (3) and Eq. (4):
where, H is the orbit altitude, $\omega $ is the full field of view in degree. Therefore, at the orbit altitude of 500 km, the tracking mode with a FOV of 0.5°× 0.5° can realize a GSD of 1 m among an observation area of 19 km2. While in the search mode with a linear FOV of 10°, it will fulfil a survey swath of 87.5 km with a ground resolution of 10 m.The MTF of the final system is shown in Fig. 8. In the visible band, the MTF of the tracking module is greater than 0.52 at 62.5 lp /mm as Fig. 8(a) shown, while that of the search module is greater than 0.48 at 33 lp /mm as Fig. 8(b) shown, which proves that the system has great imaging quality.
The grid distortion of the system is shown in Fig. 8. The maximum distortion of the tracking module is 2.03% as Fig. 9(a) shown, and that of the search module is constrained within 11% as Fig. 9(b) shown. The distortion of the search mode is relatively large. The actual distortion in the image plane is shown in Table 5.
Table 5. Distortion of search module in the image plane
In general, this system performs good imaging quality and meets the needs of large FOV and high resolution. Additionally, the system is compact comparatively by sharing a large integrated primary mirror and combining two structures in one system.
5. Conclusion
The traditional searching and tracking camera cannot simultaneously guarantee wide-area search and high-resolution detection in a compact construction. Based on the idea of integration, we proposed a compact dual-mode integrated searching and tracking optical system, which significantly reduces the volume and weight by sharing large size components between two structures. The off-axis structure with low resolution but wide FOV imaging sensor searches for the area of interest, and the coaxial structure with narrow FOV but high-resolution imaging sensor makes focus tracking within the selected area. This particular integrated optoelectrical system is realized by using freeform mirrors that improve the image quality. Finally, at an orbit altitude of 500 km, it will realize wide-area search with a swath of 87.5 km and a GSD of 10 m, and obtain high-resolution details with a GSD of 1 m within a target area of 19 km2. The results indicate that the system has potential application value in the remote sensing field.
Funding
National Natural Science Foundation of China (62105350); Youth Innovation Promotion Association (Y201951).
Acknowledgments
We express our sincere thanks to Jialiang Chen, Ben Ge and other fellow students at Shanghai Institute of Technical Physics of Chinese Academy of Sciences, who reviewed the original paper and provided valuable comments.
Disclosures
The authors declare no conflicts of interest. The second author of this article, Xisheng Xiao, provided good design ideas for this article during his Ph.D. Then he received his PhD in 2020 and is currently working in other companies.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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