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Curr. Opt. Photon. 2022; 6(4): 420-429

Published online August 25, 2022 https://doi.org/10.3807/COPP.2022.6.4.420

## Design of an Optical System for a Space Target Detection Camera

Liu Zhang1,2, Jiakun Zhang1,2, Jingwen Lei1, Yutong Xu1, Xueying Lv1,2

1College of Instrumentation & Engineering Electrical, Jilin University, Changchun 130000, China
2National Geophysical Exploration Equipment Engineering Research Center, Jilin University, Changchun 130000, China

Corresponding author: *lvxueying@jlu.edu.cn, ORCID 0000-0003-0422-6034

Received: December 29, 2021; Revised: February 28, 2022; Accepted: May 11, 2022

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

In this paper, the details and design process of an optical system for space target detection cameras are introduced. The whole system is divided into three structures. The first structure is a short-focus visible light system for rough detection in a large field of view. The field of view is 2°, the effective focal length is 1,125 mm, and the F-number is 3.83. The second structure is a telephoto visible light system for precise detection in a small field of view. The field of view is 1°, the effective focal length is 2,300 mm, and the F-number is 7.67. The third structure is an infrared light detection system. The field of view is 2°, the effective focal length is 390 mm, and the F-number is 1.3. The visible long-focus narrow field of view and visible short-focus wide field of view are switched through a turning mirror. Design results show that the modulation transfer functions of the three structures of the system are close to the diffraction limit. It can further be seen that the short-focus wide-field-of-view distortion is controlled within 0.1%, the long-focus narrow-field-of-view distortion within 0.5%, and the infrared subsystem distortion within 0.2%. The imaging effect is good and the purpose of the design is achieved.

Keywords: Coaxial two-mirror system, Composite aperture, Space-based monitoring, Space exploration

OCIS codes: (220.3620) Lens system design; (220.3630) Lenses

In the 21st century, humankind has accelerated the pace of space exploration, and thousands of spacecrafts have been sent into space. These spacecraft can be roughly divided into two categories according to their different functions: earth observation and space target detection. The spacecraft used for space target detection are currently a popular research topic around the world [1]. At present, the tasks of space exploration mainly include reconnaissance, surveillance, and the early warning of space debris and meteorites that pose potential threats to spacecraft. The space camera, as the eye of the spacecraft, plays an irreplaceable role in the space monitoring of the spacecraft [27].

The United States was the first country to carry out observation and research on space targets and is in a leading position in the world. In 1996, the United States launched the MSX satellite [8, 9], which is equipped with three optical remote sensors: a spectral imager, a space-based visible optical camera, and an infrared imaging system [1012]. Among them, the visible light camera adopts an off-axis structure with an entrance pupil diameter of 150 mm and an F number of 3. The successful test of the camera provided a solid foundation for the U. S. space monitoring mission. In 2010, the United States launched the first satellite of the SBSS system [13]. The optical camera structure of the satellite is off-axis, the entrance pupil diameter is 300 mm, its detection target is space-based on the deep space background, and it can monitor targets in geosynchronous orbit. In 2013, the United States launched the STARE satellite for a feasibility study of high-precision collision warning. The camera structure is coaxial, and it can use optical band imaging at the position closest to the satellite. Ephemeris update functionality is implemented for all satellites and debris for verification. With the development of miniaturization and of light-weight spacecraft, a multifunctional optical detection camera that can cover the visible and infrared bands and realize wide-field detection and narrow-field fine detection functions is urgently needed.

At present, the optical system of aerospace cameras can be divided into coaxial reflection and off-axis [1418]. The off-axis type has the advantage of a large field of view, but with the increase in the field of view, various aberrations of the optical system will increase, which are not conducive to light splitting. The coaxial optical system has a smaller field of view in which it is easy to correct system aberrations, and it is easier to split light. Since a multifunctional optical camera needs to split visible light and infrared light, the optical structure of the camera described in this paper is a coaxial type.

The design parameters of this system is shown in Table 1.

TABLE 1 Optical system design parameters

CharacteristicWavelength RangeField of View (deg)Resolution (m)Track Height (km)Observation Distance (km)Number of Pixels
Wide Field of View400–900 nm20.43001005056 × 2968
Narrow Field of View400–900 nm10.2
Infrared Field of View7–9 µm13.61024 × 768

In order to ensure the detection of space objects, a spatial optical high-resolution camera should have a wide spectrum, high resolution, and long focal length, and should be designed with a reflective optical system. At present, the optical mechanism of aerospace optical cameras can be either of two types: coaxial reflection or off-axis reflection. Since this system must split visible and near-infrared light, and considering the difficulty of camera installation and adjustment, the system’s optical mechanism adopts the coaxial two-reflection system. The light is split through a cubic prism to form three working modes: visible wide field of view, high-resolution field of view, and infrared field of view. The selection of the detector is very important for the imaging quality of the optical system. The pixel size of the detector for the visible wide-field-of-view detector and the high-resolution field of view (narrow field of view) is 4.6 µm × 4.6 µm, and the pixel size of the detector for infrared-field-of-view detection is 14 µm × 14 µm. The relationship between the focal length of the optical system and the charge-coupled-device pixel size P, resolution ground sample distance (GSD), and track height is expressed in the following equation [19]:

f=HPGSD

where f is the focal length of the optical system and H is the observation distance. Through calculation using Eq. (1), it can be seen that the focal length of the wide field-of-view system is 1,125 mm, that of the high-resolution field-of-view system is 2,300 mm, and that of the infrared field-of-view system is 390 mm. The Nyquist cutoff frequency is [20, 21]:

N=12a=12Dλf

where a is the size of the pixel, λ is the central wavelength, and D is the entrance pupil diameter. From the formular in Eq. (2), D ≥ 275 mm. Considering the influence of assembly and processing, take D = 300 mm, where the F-number of the long-focus wide-field system, the short-focus narrow-field system, and the infrared field of view system is 3.83, 7.67, and 1.3, respectively.

### III. INITIAL OPTICAL DESIGN OF COAXIAL TWO-MIRROR REFLECTION SYSTEM

Coaxial two-mirror reflection system is a common optical structure in aerospace cameras [22, 23]. The principle of the coaxial dual-reverse system is shown in Fig. 1 and expressed by the Eqs. (3) and (4):

Figure 1.Schematic of coaxial two-mirror reflection system.

α=l2f1'h2h1

β=l2'l2

The blocking ratio α is the ratio of the height of the secondary mirror to the height of the primary mirror, which also indicates the distance between the secondary mirror and the first focal point, which directly determines the imaging quality of the system. The obstruction ratio of the remote-sensing satellite optical system generally does not exceed 0.3. β is the magnification of the secondary mirror. e1 and e2 are the conic coefficients of the primary and secondary mirrors, respectively.

The aberration of the optical system of the coaxial two-mirror system is shown by Eq. (5). S1, S2, S3, S4, and S5 are five optical system aberrations, i.e. spherical aberration, coma, astigmatism, field curvature, and distortion. The initial structure of the system is calculated using Eq. (5), as shown in Table 2.

TABLE 2 Coaxial two-mirror system initial structural parameters

(mm)
Distance (mm)Cone Coefficient
Primary Mirror−642.8571−241.0714−1.0544
Secondary Mirror−225281.25−3.8373

S1=[α(β1)2(β+1)4α(β+1)34e22]β34(1e12),S2=1αα[α(β+1)34βe22α(β1)2(β+1)4β]12,S3=1αα2[α(β1)2(β+1)4β2α(β+1)34β2e22](1α)(β+1)(β1)αβαββ1α,S4=β1+βα,S5=1αα3[α(β+1)34β3e22α(1β)2(1+β)4β3]32(1α)2(β+1)(β1)α2β22(1α)(1+β)α2β,

The design process is as follows: the calculated initial structure is optimized; the radius of curvature of the primary and secondary mirrors, the F number of the primary lens, the curvature and conic coefficients between the lenses, and the distance between the lenses are controlled. For the lens group, first, focal power distribution is performed on the lens group, and then the radius of curvature of the lens group, the distance between the lenses, and the material of the lens group are controlled, and multiple iterations are performed. An appropriate number of lenses are added to the lens group during the optimization process. The results are shown in Fig. 2.

Figure 2.Complete structure of optical system.

### 4.1. Data Optimization

The optimized primary and secondary mirror data are shown in Table 3, and the detailed data of the corrective mirror groups of each structure are shown in Tables 46.

TABLE 3 Optimized structural parameters of the coaxial two-mirror system

(mm)
Distance (mm)Cone Coefficient
Primary Mirror−898.3203−325.6991−1.0058
Secondary Mirror−303.4184346.2467−2.0751

TABLE 4 Structure 1 parameters

1161.03611.971LAK21
2−1961.3064.092-
3607.6055SF66
4203.0474-
5164.08711.221ZK12
6−632.0203.701-
769.06610.223BK6
8100.7025.187-
944.6639.856N-LAK10
1034.50613.195-
11−153.3003F2
1284.04418.446-

TABLE 5 Structure 2 parameters

1−725.7429LITHOTEC-CAF2
279.7578-
3−155.78412H-LAK50A
4−113.47610-
5−82.8308.307N-SF6HTULTRA
6−118.60512-
769.29110H-ZF4AGT
81965.12610-
960.9758H-LAK53A
10−63.66312-
11−457.20012BALF50
1237.47026.345-

TABLE 6 Structure 3 parameters

1−129.74212.077AL2O3
2−124.8615-
3−87.05410.400GE_LONG
4−547.2905.643-
590.0036.4AGCL
6−50.58511.732-
752.01212ZNSE
852.7414.402-
9−57.62210GE_LONG
10−159.87010.511-

Structure 1 in Fig. 2 is a wide-field-of-view optical system. After passing through the splitting prism, visible light enters the wide-field-of-view correction lens group to reach the detector. This optical path is used to achieve short-focal-length, wide-field-of-view, and wide-area detection. Structure 2 in Fig. 2 shows the narrow-field-of-view, long-focal-length precision sighting optical system. Behind the beam-splitting prism, a flat mirror is added as a mode selection mirror for switching between the visible wide-field-of-view detection system and the visible high-resolution detection system. The splitting prism separates the visible and infrared bands, and the infrared light is reflected by the splitting surface of the prism and then transmitted to the infrared mirror group to reach the infrared detector. After the visible light is transmitted through the prism’s dichroic surface, it reaches the visible light rear lens group. When the mode selection mirror is outside the optical path, the visible light reaches the detector through the visible light wide-field lens group. When the mode-selection lens cuts into the light path, the visible light reaches the detector through the high-resolution lens group to achieve tracking and aiming at a long focal length.

To evaluate the optical system of aerospace cameras, modulation transfer function (MTF) curves, distortion curves, and dot diagrams were used.

### 4.2. MTF Analysis

The MTF curves are closely related to the imaging quality of the optical system. The closer the MTF curve to the diffraction limit, the higher the imaging quality. As shown in Fig. 3, the MTF curves of the optical system are close to the diffraction limit.

Figure 3.Modulation transfer function (MTF) image of the system: MTF curve of (a) short-focal-length, wide-field-of-view system, (b) long-focal, narrow-field-of-view system, and (c) infrared system.

### 4.3. Distortion Analysis

Distortion affects the shape of the image. The distortion of the optical system is around 0.2% [20], and the image quality is better. It can be seen from Fig. 4 that the distortion of the optical system meets the requirements.

Figure 4.Distorted image of the system: distortion curve of (a) wide-field-of-view system, (b) narrow-field-of-view system, and (c) infrared system.

### 4.4. Distortion Analysis

The spot diagram of the optical system represents the energy concentration. It can be seen from Fig. 5 that the energy concentration of the spot diagrams of the three structures of the optical system is good and meets the design requirements.

Figure 5.System point diagram of (a) wide-field-of-view system, (b) narrow-field-of-view system, and (c) infrared system.

### 4.4. Vertical chromatic aberration

Vertical chromatic aberration, which affects the color reproduction and clarity of the image, is one of the important indicators for evaluating the optical system. It can be seen from Fig. 6 that the vertical chromatic aberration of structure 1, structure 2, and structure 3 is within 1, 2, and 4 μm, respectively, and that of the three structures is all within the airy disk, satisfying design requirements.

Figure 6.Vertical chromatic aberration of (a) structure 1, (b) structure 2, and (c) structure 3.

The design of a common-aperture multifunctional space target detection camera is reported in this paper; in addition, the design ideas of the camera are introduced in detail. In terms of function, it can be seen that infrared light and visible light are reflected by the coaxial two-mirror system, and then the visible light and the infrared light are separated by the beam splitter. The plane mirror is used as a mode selection mirror to divide the visible light into two working modes and switch between them, which can realize a large field of view: (1) a short-focal-length, wide-field-of-view mode, and (2) a long-focal-length, narrow-field-of-view mode, respectively, realize the functions of wide-area coarse-pointing detection and small-field precision detection. The transfer function of the system is close to the diffraction limit, and most of the energy of the diffuse spot and vertical axis color difference curve are concentrated in the airy disk, which achieves the purpose of the design. In addition, further miniaturization and multi-functionalization of space optical cameras have been realized, which is a new way of thinking for the development of space optical cameras.

The authors declare no conflicts of interest.

Data underlying the results presented in this paper are not publicly available at this time of publication, which may be obtained from the authors upon reasonable request.

The authors thank National Natural Science Foundation of China for help identifying collaborators for this work.

Pre-research project (6B2B5347).

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### Article

#### Article

Curr. Opt. Photon. 2022; 6(4): 420-429

Published online August 25, 2022 https://doi.org/10.3807/COPP.2022.6.4.420

## Design of an Optical System for a Space Target Detection Camera

Liu Zhang1,2, Jiakun Zhang1,2, Jingwen Lei1, Yutong Xu1, Xueying Lv1,2

1College of Instrumentation & Engineering Electrical, Jilin University, Changchun 130000, China
2National Geophysical Exploration Equipment Engineering Research Center, Jilin University, Changchun 130000, China

Correspondence to:*lvxueying@jlu.edu.cn, ORCID 0000-0003-0422-6034

Received: December 29, 2021; Revised: February 28, 2022; Accepted: May 11, 2022

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

### Abstract

In this paper, the details and design process of an optical system for space target detection cameras are introduced. The whole system is divided into three structures. The first structure is a short-focus visible light system for rough detection in a large field of view. The field of view is 2°, the effective focal length is 1,125 mm, and the F-number is 3.83. The second structure is a telephoto visible light system for precise detection in a small field of view. The field of view is 1°, the effective focal length is 2,300 mm, and the F-number is 7.67. The third structure is an infrared light detection system. The field of view is 2°, the effective focal length is 390 mm, and the F-number is 1.3. The visible long-focus narrow field of view and visible short-focus wide field of view are switched through a turning mirror. Design results show that the modulation transfer functions of the three structures of the system are close to the diffraction limit. It can further be seen that the short-focus wide-field-of-view distortion is controlled within 0.1%, the long-focus narrow-field-of-view distortion within 0.5%, and the infrared subsystem distortion within 0.2%. The imaging effect is good and the purpose of the design is achieved.

Keywords: Coaxial two-mirror system, Composite aperture, Space-based monitoring, Space exploration

### I. INTRODUCTION

In the 21st century, humankind has accelerated the pace of space exploration, and thousands of spacecrafts have been sent into space. These spacecraft can be roughly divided into two categories according to their different functions: earth observation and space target detection. The spacecraft used for space target detection are currently a popular research topic around the world [1]. At present, the tasks of space exploration mainly include reconnaissance, surveillance, and the early warning of space debris and meteorites that pose potential threats to spacecraft. The space camera, as the eye of the spacecraft, plays an irreplaceable role in the space monitoring of the spacecraft [27].

The United States was the first country to carry out observation and research on space targets and is in a leading position in the world. In 1996, the United States launched the MSX satellite [8, 9], which is equipped with three optical remote sensors: a spectral imager, a space-based visible optical camera, and an infrared imaging system [1012]. Among them, the visible light camera adopts an off-axis structure with an entrance pupil diameter of 150 mm and an F number of 3. The successful test of the camera provided a solid foundation for the U. S. space monitoring mission. In 2010, the United States launched the first satellite of the SBSS system [13]. The optical camera structure of the satellite is off-axis, the entrance pupil diameter is 300 mm, its detection target is space-based on the deep space background, and it can monitor targets in geosynchronous orbit. In 2013, the United States launched the STARE satellite for a feasibility study of high-precision collision warning. The camera structure is coaxial, and it can use optical band imaging at the position closest to the satellite. Ephemeris update functionality is implemented for all satellites and debris for verification. With the development of miniaturization and of light-weight spacecraft, a multifunctional optical detection camera that can cover the visible and infrared bands and realize wide-field detection and narrow-field fine detection functions is urgently needed.

At present, the optical system of aerospace cameras can be divided into coaxial reflection and off-axis [1418]. The off-axis type has the advantage of a large field of view, but with the increase in the field of view, various aberrations of the optical system will increase, which are not conducive to light splitting. The coaxial optical system has a smaller field of view in which it is easy to correct system aberrations, and it is easier to split light. Since a multifunctional optical camera needs to split visible light and infrared light, the optical structure of the camera described in this paper is a coaxial type.

### II. DESIGN STEPS

The design parameters of this system is shown in Table 1.

TABLE 1. Optical system design parameters.

CharacteristicWavelength RangeField of View (deg)Resolution (m)Track Height (km)Observation Distance (km)Number of Pixels
Wide Field of View400–900 nm20.43001005056 × 2968
Narrow Field of View400–900 nm10.2
Infrared Field of View7–9 µm13.61024 × 768

In order to ensure the detection of space objects, a spatial optical high-resolution camera should have a wide spectrum, high resolution, and long focal length, and should be designed with a reflective optical system. At present, the optical mechanism of aerospace optical cameras can be either of two types: coaxial reflection or off-axis reflection. Since this system must split visible and near-infrared light, and considering the difficulty of camera installation and adjustment, the system’s optical mechanism adopts the coaxial two-reflection system. The light is split through a cubic prism to form three working modes: visible wide field of view, high-resolution field of view, and infrared field of view. The selection of the detector is very important for the imaging quality of the optical system. The pixel size of the detector for the visible wide-field-of-view detector and the high-resolution field of view (narrow field of view) is 4.6 µm × 4.6 µm, and the pixel size of the detector for infrared-field-of-view detection is 14 µm × 14 µm. The relationship between the focal length of the optical system and the charge-coupled-device pixel size P, resolution ground sample distance (GSD), and track height is expressed in the following equation [19]:

$f=H⋅PGSD$

where f is the focal length of the optical system and H is the observation distance. Through calculation using Eq. (1), it can be seen that the focal length of the wide field-of-view system is 1,125 mm, that of the high-resolution field-of-view system is 2,300 mm, and that of the infrared field-of-view system is 390 mm. The Nyquist cutoff frequency is [20, 21]:

$N=12a=12⋅Dλf$

where a is the size of the pixel, λ is the central wavelength, and D is the entrance pupil diameter. From the formular in Eq. (2), D ≥ 275 mm. Considering the influence of assembly and processing, take D = 300 mm, where the F-number of the long-focus wide-field system, the short-focus narrow-field system, and the infrared field of view system is 3.83, 7.67, and 1.3, respectively.

### III. INITIAL OPTICAL DESIGN OF COAXIAL TWO-MIRROR REFLECTION SYSTEM

Coaxial two-mirror reflection system is a common optical structure in aerospace cameras [22, 23]. The principle of the coaxial dual-reverse system is shown in Fig. 1 and expressed by the Eqs. (3) and (4):

Figure 1. Schematic of coaxial two-mirror reflection system.

$α=l2f1'≈h2h1$

$β=l2'l2$

The blocking ratio α is the ratio of the height of the secondary mirror to the height of the primary mirror, which also indicates the distance between the secondary mirror and the first focal point, which directly determines the imaging quality of the system. The obstruction ratio of the remote-sensing satellite optical system generally does not exceed 0.3. β is the magnification of the secondary mirror. e1 and e2 are the conic coefficients of the primary and secondary mirrors, respectively.

The aberration of the optical system of the coaxial two-mirror system is shown by Eq. (5). S1, S2, S3, S4, and S5 are five optical system aberrations, i.e. spherical aberration, coma, astigmatism, field curvature, and distortion. The initial structure of the system is calculated using Eq. (5), as shown in Table 2.

TABLE 2. Coaxial two-mirror system initial structural parameters.

(mm)
Distance (mm)Cone Coefficient
Primary Mirror−642.8571−241.0714−1.0544
Secondary Mirror−225281.25−3.8373

$S1=[α(β−1)2(β+1)4−α(β+1)34e22]−β34(1−e12),S2=1−αα[α(β+1)34βe22−α(β−1)2(β+1)4β]−12,S3=（1−αα）2[α(β−1)2(β+1)4β2−α(β+1)34β2e22] −(1−α)(β+1)(β−1)αβ−αβ−β−1α,S4=β−1+βα,S5=（1−αα）3[α(β+1)34β3e22−α(1−β)2(1+β)4β3] −32(1−α)2(β+1)(β−1)α2β2−2(1−α)(1+β)α2β,$

### IV. DESIGN RESULTS

The design process is as follows: the calculated initial structure is optimized; the radius of curvature of the primary and secondary mirrors, the F number of the primary lens, the curvature and conic coefficients between the lenses, and the distance between the lenses are controlled. For the lens group, first, focal power distribution is performed on the lens group, and then the radius of curvature of the lens group, the distance between the lenses, and the material of the lens group are controlled, and multiple iterations are performed. An appropriate number of lenses are added to the lens group during the optimization process. The results are shown in Fig. 2.

Figure 2. Complete structure of optical system.

### 4.1. Data Optimization

The optimized primary and secondary mirror data are shown in Table 3, and the detailed data of the corrective mirror groups of each structure are shown in Tables 46.

TABLE 3. Optimized structural parameters of the coaxial two-mirror system.

(mm)
Distance (mm)Cone Coefficient
Primary Mirror−898.3203−325.6991−1.0058
Secondary Mirror−303.4184346.2467−2.0751

TABLE 4. Structure 1 parameters.

1161.03611.971LAK21
2−1961.3064.092-
3607.6055SF66
4203.0474-
5164.08711.221ZK12
6−632.0203.701-
769.06610.223BK6
8100.7025.187-
944.6639.856N-LAK10
1034.50613.195-
11−153.3003F2
1284.04418.446-

TABLE 5. Structure 2 parameters.

1−725.7429LITHOTEC-CAF2
279.7578-
3−155.78412H-LAK50A
4−113.47610-
5−82.8308.307N-SF6HTULTRA
6−118.60512-
769.29110H-ZF4AGT
81965.12610-
960.9758H-LAK53A
10−63.66312-
11−457.20012BALF50
1237.47026.345-

TABLE 6. Structure 3 parameters.

1−129.74212.077AL2O3
2−124.8615-
3−87.05410.400GE_LONG
4−547.2905.643-
590.0036.4AGCL
6−50.58511.732-
752.01212ZNSE
852.7414.402-
9−57.62210GE_LONG
10−159.87010.511-

Structure 1 in Fig. 2 is a wide-field-of-view optical system. After passing through the splitting prism, visible light enters the wide-field-of-view correction lens group to reach the detector. This optical path is used to achieve short-focal-length, wide-field-of-view, and wide-area detection. Structure 2 in Fig. 2 shows the narrow-field-of-view, long-focal-length precision sighting optical system. Behind the beam-splitting prism, a flat mirror is added as a mode selection mirror for switching between the visible wide-field-of-view detection system and the visible high-resolution detection system. The splitting prism separates the visible and infrared bands, and the infrared light is reflected by the splitting surface of the prism and then transmitted to the infrared mirror group to reach the infrared detector. After the visible light is transmitted through the prism’s dichroic surface, it reaches the visible light rear lens group. When the mode selection mirror is outside the optical path, the visible light reaches the detector through the visible light wide-field lens group. When the mode-selection lens cuts into the light path, the visible light reaches the detector through the high-resolution lens group to achieve tracking and aiming at a long focal length.

To evaluate the optical system of aerospace cameras, modulation transfer function (MTF) curves, distortion curves, and dot diagrams were used.

### 4.2. MTF Analysis

The MTF curves are closely related to the imaging quality of the optical system. The closer the MTF curve to the diffraction limit, the higher the imaging quality. As shown in Fig. 3, the MTF curves of the optical system are close to the diffraction limit.

Figure 3. Modulation transfer function (MTF) image of the system: MTF curve of (a) short-focal-length, wide-field-of-view system, (b) long-focal, narrow-field-of-view system, and (c) infrared system.

### 4.3. Distortion Analysis

Distortion affects the shape of the image. The distortion of the optical system is around 0.2% [20], and the image quality is better. It can be seen from Fig. 4 that the distortion of the optical system meets the requirements.

Figure 4. Distorted image of the system: distortion curve of (a) wide-field-of-view system, (b) narrow-field-of-view system, and (c) infrared system.

### 4.4. Distortion Analysis

The spot diagram of the optical system represents the energy concentration. It can be seen from Fig. 5 that the energy concentration of the spot diagrams of the three structures of the optical system is good and meets the design requirements.

Figure 5. System point diagram of (a) wide-field-of-view system, (b) narrow-field-of-view system, and (c) infrared system.

### 4.4. Vertical chromatic aberration

Vertical chromatic aberration, which affects the color reproduction and clarity of the image, is one of the important indicators for evaluating the optical system. It can be seen from Fig. 6 that the vertical chromatic aberration of structure 1, structure 2, and structure 3 is within 1, 2, and 4 μm, respectively, and that of the three structures is all within the airy disk, satisfying design requirements.

Figure 6. Vertical chromatic aberration of (a) structure 1, (b) structure 2, and (c) structure 3.

### V. CONCLUSIONS

The design of a common-aperture multifunctional space target detection camera is reported in this paper; in addition, the design ideas of the camera are introduced in detail. In terms of function, it can be seen that infrared light and visible light are reflected by the coaxial two-mirror system, and then the visible light and the infrared light are separated by the beam splitter. The plane mirror is used as a mode selection mirror to divide the visible light into two working modes and switch between them, which can realize a large field of view: (1) a short-focal-length, wide-field-of-view mode, and (2) a long-focal-length, narrow-field-of-view mode, respectively, realize the functions of wide-area coarse-pointing detection and small-field precision detection. The transfer function of the system is close to the diffraction limit, and most of the energy of the diffuse spot and vertical axis color difference curve are concentrated in the airy disk, which achieves the purpose of the design. In addition, further miniaturization and multi-functionalization of space optical cameras have been realized, which is a new way of thinking for the development of space optical cameras.

### 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 of publication, which may be obtained from the authors upon reasonable request.

### ACKNOWLEDGMENT

The authors thank National Natural Science Foundation of China for help identifying collaborators for this work.

### FUNDING

Pre-research project (6B2B5347).

### Fig 1.

Figure 1.Schematic of coaxial two-mirror reflection system.
Current Optics and Photonics 2022; 6: 420-429https://doi.org/10.3807/COPP.2022.6.4.420

### Fig 2.

Figure 2.Complete structure of optical system.
Current Optics and Photonics 2022; 6: 420-429https://doi.org/10.3807/COPP.2022.6.4.420

### Fig 3.

Figure 3.Modulation transfer function (MTF) image of the system: MTF curve of (a) short-focal-length, wide-field-of-view system, (b) long-focal, narrow-field-of-view system, and (c) infrared system.
Current Optics and Photonics 2022; 6: 420-429https://doi.org/10.3807/COPP.2022.6.4.420

### Fig 4.

Figure 4.Distorted image of the system: distortion curve of (a) wide-field-of-view system, (b) narrow-field-of-view system, and (c) infrared system.
Current Optics and Photonics 2022; 6: 420-429https://doi.org/10.3807/COPP.2022.6.4.420

### Fig 5.

Figure 5.System point diagram of (a) wide-field-of-view system, (b) narrow-field-of-view system, and (c) infrared system.
Current Optics and Photonics 2022; 6: 420-429https://doi.org/10.3807/COPP.2022.6.4.420

### Fig 6.

Figure 6.Vertical chromatic aberration of (a) structure 1, (b) structure 2, and (c) structure 3.
Current Optics and Photonics 2022; 6: 420-429https://doi.org/10.3807/COPP.2022.6.4.420

TABLE 1 Optical system design parameters

CharacteristicWavelength RangeField of View (deg)Resolution (m)Track Height (km)Observation Distance (km)Number of Pixels
Wide Field of View400–900 nm20.43001005056 × 2968
Narrow Field of View400–900 nm10.2
Infrared Field of View7–9 µm13.61024 × 768

TABLE 2 Coaxial two-mirror system initial structural parameters

(mm)
Distance (mm)Cone Coefficient
Primary Mirror−642.8571−241.0714−1.0544
Secondary Mirror−225281.25−3.8373

TABLE 3 Optimized structural parameters of the coaxial two-mirror system

(mm)
Distance (mm)Cone Coefficient
Primary Mirror−898.3203−325.6991−1.0058
Secondary Mirror−303.4184346.2467−2.0751

TABLE 4 Structure 1 parameters

1161.03611.971LAK21
2−1961.3064.092-
3607.6055SF66
4203.0474-
5164.08711.221ZK12
6−632.0203.701-
769.06610.223BK6
8100.7025.187-
944.6639.856N-LAK10
1034.50613.195-
11−153.3003F2
1284.04418.446-

TABLE 5 Structure 2 parameters

1−725.7429LITHOTEC-CAF2
279.7578-
3−155.78412H-LAK50A
4−113.47610-
5−82.8308.307N-SF6HTULTRA
6−118.60512-
769.29110H-ZF4AGT
81965.12610-
960.9758H-LAK53A
10−63.66312-
11−457.20012BALF50
1237.47026.345-

TABLE 6 Structure 3 parameters

1−129.74212.077AL2O3
2−124.8615-
3−87.05410.400GE_LONG
4−547.2905.643-
590.0036.4AGCL
6−50.58511.732-
752.01212ZNSE
852.7414.402-
9−57.62210GE_LONG
10−159.87010.511-

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Wonshik Choi,
Editor-in-chief