## 3 Optical Design and Simulation  
Optical design program Synopsys CODE V(r)[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\({}^{\circ}\) @ Max. image height \(h_{i}=7.13\) mm. Therefore, the position of the exit pupil must be controlled to be located around \(h_{i}/(2\cdot tan(7^{\circ}))\approx 29\) 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\({}^{\circ}\). \begin{table}
\begin{tabular}{c c} \hline
**Properties** & **Specification** \\ \hline f–number, \(FN\) & \(\approx\)8 \\ EFL, \(f\)(mm) & \(\approx\)6.4 \\ Wavelengths Range (nm) & 500–800 \\ As–Built MTF * @ 57 lp/mm (640 \(\times\) 480, with binning) ** & 0.25 \\ Focal Range, \(N_{L}\)–\(F_{L}\)(m) & \(<\)0.5–infinity \\ Hyperfocal Distance, \(H\)(mm) & \(\approx\)900 \\ Image Height, \(h_{i}\)(mm) & \(>\)7.13 + 10\% \\ FOV & \(\approx\pm\)30\({}^{\circ}\) \\ Max. Chief Ray Angle (CRA) & \(7^{\circ}\pm 1^{\circ}\) \\ Optical Distortion (\(Abs.|\pm\%\) ) & \(<\)2 \\ Relative Illumination (\%) & \(>\)70 \\ Overall Length (mm) & \(<\)50 \\ Operating Temperature (\({}^{\circ}\)C) & \(-\)30\(-\)70 \\ \hline \end{tabular} \({}^{\star}\) Modulation Transfer Function (MTF) ** Pixel binning for sub-pixel resolution [3,5].  
\end{table} 
Table 2: Specifications of the space autonomous docking camera. Figure 1: Radiation resistant optical glass materials. Figure 3: Chief ray angle (CRA) curve of the designed value and specified value of MT9P031 CIS. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Surface Number** & **Surface Name** & **Surface Type** & **Y Radius** & **Thickness** & **Glass** \\ \hline Objective & & Sphere & Infinity (N) & 400\(\infty\) & \\
1 & L1 & Sphere & 38.234000 & 3.000000 & LF5G15\_SCHOTT \\
2 & & Sphere & 5.991000 & 3.150000 & \\
3 & L2 & Sphere & \(-\)31.115000 & 8.570000 & LAK9G15\_SCHOTT \\
4 & & Sphere & \(-\)9.817000 & 5.850000 & \\
5 & L3 & Sphere & \(-\)4.831000 & 2.310000 & LF5G15\_SCHOTT \\
6 & & Sphere & \(-\)7.084000 & 0.500000 & \\
7 & Aperture Stop & Sphere & Infinity (N) & 0.500000 & \\
8 & L4 & Sphere & 50.501000 & 2.080000 & LAK9G15\_SCHOTT \\
9 & & Sphere & \(-\)11.744000 & 3.290000 & \\
10 & L5 & Sphere & 10.693000 & 2.610000 & LAK9G15\_SCHOTT \\
11 & & Sphere & \(-\)5.962000 & 0.570000 & \\
12 & L6 & Sphere & \(-\)4.730000 & 1.000000 & SF6G05\_SCHOTT \\
13 & & Sphere & 6.257000 & 1.190000 & \\
14 & L7 & Sphere & 11.893000 & 3.350000 & LF5G15\_SCHOTT \\
15 & & Sphere & \(-\)7.385000 & 3.50444 & \\
16 & Cover Glass & Sphere & Infinity (N) & 0.400000 & D263T\_SCHOTT \\
17 & & Sphere & Infinity (N) & 0.125000 & \\ Image & & Sphere & Infinity (N) & 0 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Lens data of the docking camera lens. Figure 2: Optical layout of the docking camera lens. 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.