Optical Design of Compact Space Autonomous Docking Instrument with CMOS Image Sensor and All Radiation Resistant Lens Elements

: Built-in autonomous stereo vision devices play a critical role in the autonomous docking instruments of space vehicles. Traditional stereo cameras for space autonomous docking use charge-coupled device (CCD) image sensors, and it is di ﬃ cult for the overall size to be reduced due to the size of the CCD. In addition, only the few outermost elements of the camera lens use radiation-resistant optical glass material. In this paper, a complementary metal–oxide semiconductor (CMOS) device is used as the image sensor, and radiation-resistant optical glass material is introduced to all lens elements in order to make a compact and highly reliable space grade instrument. Despite the limited available material, a ﬁxed focus module with 7 lens elements and overall length of 42 mm has been achieved, while meeting all the required performance demands for the ﬁnal vision-guided Author and methodology, S.-F.L.; software, S.-F.L.; validation, S.-F.L.; formal preparation, writing—review and editing,


Introduction
In order to realize the objectives of continuous return to the lunar surface, work in low-Earth on-orbit, and paving the way for the deployment of missions to the Moon and Mars, a new item called "Autonomous Systems" has been revealed in the NASA technical classification published in 2020 [1]. Built-in autonomous stereo vision devices play a vital role in position sensing and perception or pose estimation to facilitate the autonomous docking of multiple daughter-mother space vehicles, so as to expand their versatile applications in planetary science exploration. The final docking phase is the most challenging, particularly for re-docking the daughter space vehicles to the mother space vehicles [2].
In the final docking stage, fiducial targets are employed for the algorithms of autonomous docking navigation to improve the reliability of lateral control; within the operational range of 10 m and ±30 • field of view (FOV), the required accuracy is 1 cm [3]. The space docking cameras play the chief role of image capturing in autonomous stereo vision-guided docking devices. The captured image will be integrated into the algorithm for the autonomous docking system [3][4][5]. Currently, those space docking cameras are often equipped with charge-coupled device (CCD) image sensors [3,6]. Due to the technical issue in further reducing the size of the CCD device, it, in turn, becomes difficult to make A fixed focus lens, which does not contain moving parts, and is thus less sensitive to launching in an on-orbit environment, is preferable for the docking camera. With the fixed focus and small-aperture, a pan-focus lens is capable of giving deep depth of field (DOF) by setting the object distance at a hyperfocal distance [11]. The aperture can then be calculated with this object distance or hyperfocal distance. The procedure for evaluating hyperfocal distance/object distance and f-number are listed in Equations (1)-(6) [11].
Appl. Sci. 2020, 10, 5302 or where H: Hyperfocal distance (mm); f : Effective focal length (EFL); FN: f-number; C: Circle of confusion (CoC); N L : Near focus limit (mm); S: Object distance (mm); F L : Far focus limit (mm); in the hyperfocal condition: The operation range condition required FOV around ±30 • [3]. In addition, the image height should be larger than the active imager size in diagonal (7.13 mm). Assume the image height given is 3% larger than the active imager size, i.e., estimated image height h i ≈ 7.4 mm. The estimated EFL obtained is: In the CoC estimation, common practice was a realistic blur spot diameter of 0.2 mm (5 lp/mm) at a distance of 25 cm in print diagonal (218.44 mm) for print CoC of 5 (inch) × 7 (inch). Given the MT9P031 CIS active imager size in sensor diagonal was 7.13 mm. The estimated MT9P031 CIS's CoC obtained: The following assumption was made: S = H ≈ 900 mm for a reasonable hyperfocal distance in Equation (5) or Equation (6),

thus
FN ≈ 8 has been obtained from Equation (6) for targeting specification of system f-number, Based on the evaluation described above, the optical specification of the camera module is summarized in Table 2.
The camera will be operated in a harsh radiation environment, which will include solar radiation, galactic cosmic rays, heavy ions, electrons and protons, therefore, they must be tolerant toward these radiation effects. Figure 1 shows a collection of radiation resistant optical glass materials for the design of compact radiation resistant lenses, as shown in the glass codes and glass types that are shown side by side in the glass chart to serve as a reference in the design process [12,13].
In contrast to BK7G18 and K5G20, some glasses (such as SF6G05 and F2G12) are subjected to a transmittance loss of approximately 0.25% at the range of wavelength longer than 500 nm after they absorb more than 1.0 × 10 +6 Gy radiation dose of gamma radiation [12].
Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 8 The camera will be operated in a harsh radiation environment, which will include solar radiation, galactic cosmic rays, heavy ions, electrons and protons, therefore, they must be tolerant toward these radiation effects. Figure 1 shows a collection of radiation resistant optical glass materials for the design of compact radiation resistant lenses, as shown in the glass codes and glass types that are shown side by side in the glass chart to serve as a reference in the design process [12,13].
In contrast to BK7G18 and K5G20, some glasses (such as SF6G05 and F2G12) are subjected to a transmittance loss of approximately 0.25% at the range of wavelength longer than 500 nm after they absorb more than 1.0 × 10 +6 Gy radiation dose of gamma radiation [12].

Optical Design and Simulation
Optical design program Synopsys CODE V ® [14] is used for optimization and simulation. In making the optical layout, chief ray angle (CRA), as shown in Table 2, is a major concern. CRA is associated with the photometric efficiency of CIS detectors. The CRA of MT9P031 CIS is specified to be 7° @ Max. image height ℎ = 7.13 mm. Therefore, the position of the exit pupil must be controlled to be located around ℎ 2 ⋅ 7 ∘ ⁄ ≈ 29 mm in front of the image plane. As shown in Figure 2, the final lens module is comprised of 7 elements and 3 different radiation resistant optical glasses, LF5G15, LAK9G15, and SF6G05; the total length of the lens is 42 mm, and the outer diameter is less than 20 mm.

Optical Design and Simulation
Optical design program Synopsys CODE V ® [14] is used for optimization and simulation. In making the optical layout, chief ray angle (CRA), as shown in Table 2, is a major concern. CRA is associated with the photometric efficiency of CIS detectors. The CRA of MT9P031 CIS is specified to be 7 • @ Max. image height h i = 7.13 mm. Therefore, the position of the exit pupil must be controlled to be located around h i /(2 · tan(7 • )) ≈ 29 mm in front of the image plane.
As shown in Figure 2, the final lens module is comprised of 7 elements and 3 different radiation resistant optical glasses, LF5G15, LAK9G15, and SF6G05; the total length of the lens is 42 mm, and the outer diameter is less than 20 mm. Table 3 lists the optical parameters of the lens module. The air thickness space between lens L7 and CIS's cover glass was approximately 3.5 mm, which will be used for compensation and focus tuning to achieve a deeper depth of field under hyperfocal conditions [11]. Figure 3 shows the CRA curve of the designed lens versus the specified CRA of MT9P031 CIS. These two curves match almost perfectly with a maximum deviation below 0.15 • . associated with the photometric efficiency of CIS detectors. The CRA of MT9P031 CIS is specified to be 7° @ Max. image height ℎ = 7.13 mm. Therefore, the position of the exit pupil must be controlled to be located around ℎ 2 ⋅ 7 ∘ ⁄ ≈ 29 mm in front of the image plane. As shown in Figure 2, the final lens module is comprised of 7 elements and 3 different radiation resistant optical glasses, LF5G15, LAK9G15, and SF6G05; the total length of the lens is 42 mm, and the outer diameter is less than 20 mm.    Table 3 lists the optical parameters of the lens module. The air thickness space between lens L7 and CIS's cover glass was approximately 3.5 mm, which will be used for compensation and focus tuning to achieve a deeper depth of field under hyperfocal conditions [11].  Figure 3 shows the CRA curve of the designed lens versus the specified CRA of MT9P031 CIS. These two curves match almost perfectly with a maximum deviation below 0.15°.  The thermal effect of the extreme temperatures in space could cause serious deviation of the optical path length. The evaluation of Modulation Transfer Function (MTF) should take the thermal effect into consideration. The dimension of both mechanical mounting material and optical material will be affected by the temperature which can be evaluated through the coefficient of thermal expansion. The refractive index of optical material is also temperature-dependent. The material of lens barrel is assumed to be aluminum. Figure 4 shows the MTF and through-focus performance values across the entire field (i.e., F1: on axis, F2: image height = 1 mm, F3: image height = 2 mm, F4: image height = 2.8 mm, and F5: full image height) of the lens at object distances of 0.4 m (Figure 4a), 1 m (Figure 4b), and 20 km (Figure 4c), under Normal Temperature and Pressure (NTP; 20 • C, 760 mm-Hg) conditions. As can be seen in Figure 4c, a favorable allowance of focal shift (approximately −0.1 mm) is observed when the object distance moved towards infinity.      (Figure 5c). As can be seen in Figure 5c, a favorable allowance of focal shift (approximately −0.1 mm) is observed when the temperature rises to 115 • C. Figure 6 shows the optical distortion curve of the system with wavelengths ranging from 500 to 800 nm and the distortion grid of entire image fields. The absolute values of mustache type distortion of the lens system are less than 1% throughout entire image fields. Figure 5 shows the MTF and the through-focus MTF performance value across the entire field (i.e., F1: on axis, F2: image height = 1 mm, F3: image height = 2 mm, F4: image height = 2.8 mm, and F5: full image height) of the lens at an object distance of around 1 m at the temperatures of −100 °C (Figure 5a), NTP conditions ( Figure 5b) and 115 °C (Figure 5c). As can be seen in Figure 5c, a favorable allowance of focal shift (approximately −0.1 mm) is observed when the temperature rises to 115 °C.  Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 8 Figure 6 shows the optical distortion curve of the system with wavelengths ranging from 500 to 800 nm and the distortion grid of entire image fields. The absolute values of mustache type distortion of the lens system are less than 1% throughout entire image fields.

Conclusions
Optical analysis shows that the design results meet all the required optical specifications of the camera dedicated for autonomous docking, especially at the final stage, where the approaching distance is between 0.5 and 20 m, with all lens elements exploiting radiation resistant material. By introducing CIS as the image sensor, the overall length of the docking camera module was reduced to 42 mm, nearly half of the side length of the existing smallest space vehicles for the potential application in the CubeSat (e.g., 1U-CubeSat), the shortest of the same kind in exist.

Conclusions
Optical analysis shows that the design results meet all the required optical specifications of the camera dedicated for autonomous docking, especially at the final stage, where the approaching distance is between 0.5 and 20 m, with all lens elements exploiting radiation resistant material. By introducing CIS as the image sensor, the overall length of the docking camera module was reduced to 42 mm, nearly half of the side length of the existing smallest space vehicles for the potential application in the CubeSat (e.g., 1U-CubeSat), the shortest of the same kind in exist.