Athermal design of a space camera using a single lens material over a wide temperature range
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摘要:
折反式空间相机广泛应用于空间探测领域，但温度变化将会导致成像质量下降。针对该问题，本文对折反式空间相机进行了宽温度范围的无热化设计。首先对相关的光学元件、机械结构等部件进行了温度影响分析，并总结消热差的便捷方法。接着以工作在400 nm~
1000 nm波段，焦距为525 mm，F数为3.5的空间相机为设计对象，通过选择合适的反射镜基底材料和支撑结构材料，只使用熔融石英一种透镜材料校正像差，从而确保折反式光学系统在空间环境运行的性能稳定性并实现宽温度范围无热化。最终仿真结果表明空间相机经过设计优化后可在−60 °C~150 °C温度范围内奈奎斯特频率77 lp/mm处的调制传递函数值优于0.4。该相机的材料物理性能稳定、成像质量好、高低温环境内成像质量稳定，在空间探测等领域具有广泛的应用前景。Abstract:Catadioptric space cameras are widely used in space exploration, However, temperature variations can degrade their imaging performance. To address this issue, this paper presents an athermal design for a catadioptric space camera operating over a wide temperature range. Initially, the temperature effects on optical elements, mechanical structures, and other components were analyzed, and convenient methods for thermal aberration compensation are summarized. Subsequently, taking a camera with a spectral range of 400–
1000 nm, a focal length of 525 mm, and an F-number of 3.5 as the design case, an athermal solution is developed. By selecting appropriate materials for the mirror substrates and support structures, and using fused silica as the single lens material to correct aberrations, the optical system maintains stable performance in space environments. Final simulation results confirm that the optimized camera maintains a Modulation Transfer Function (MTF) value above 0.4 at 77 lp/mm (Nyquist frequency) over a temperature range of –60°C to 150°C. The camera exhibits stable material properties, excellent imaging quality, and consistent performance under extreme temperatures. This design demonstrates significant potential for applications in space exploration and related fields. -
图 1 同轴两反系统受温度影响示意图
Figure 1. Schematic of temperature effects on a coaxial two-mirror system
图 2 同轴两反系统等效高斯光路图
Figure 2. Schematic of equivalent gaussian optical path for coaxial two-mirror systems
图 4 初始光学系统垂轴色差图
Figure 4. Transverse chromatic aberration diagram for initial optical system
图 5 不同温度下初始光学系统MTF图
Figure 5. MTF charts of initial optical system at different temperatures
图 8 优化后不同温度下光学系统MTF图
Figure 8. MTF charts of optimized optical system at different temperature
图 9 优化后光学系统垂轴色差图
Figure 9. Transverse chromatic aberration diagram for optimized optical system
图 11 无热化前后热离焦量对比
Figure 11. Thermal defocus comparison before and after athermalization
表 1 空间相机部分常用材料参数
Table 1. Some commonly used material parameters of space cameras
Reflector
materialCoefficient of
thermal expansion
α（10−6/ °C）Mechanical
structural
materialCoefficient of
thermal expansion
α（10−6/ °C）glass-ceramics 0.05 4J36 Invar 1.8 Fused quartz 0.5 Titanium alloy 8.8 Silicon carbide 2.5 Aluminium alloy 23.6 
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表 2 设计指标
Table 2. Design indexes
Index Value Wavelength range 400 nm~ 1000 nmField of view 4° F 3.5 Focal length 525 mm Pixel size 6.5 μm×6.5 μm Temperature range −60 °C~150 °C
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表 3 初始光学系统结构参数
Table 3. Parameters of initial optical system configuration
Element Materials Coefficient of
thermal expansion
α（10−6/ °C）Radius
（mm）Constant of the
quadric surfaceThickness
（mm）Focal
（mm）Focal power
（mm−1）Paraxial ray
height
（mm）Primary mirror Silicon Carbide 2.5 −342.72 −1.18 −113.62 −171.36 − 0.00584 75 Secondary mirror Silicon Carbide 2.5 −174.08 −5.94 114.62 −87.04 − 0.01149 25.2725 Lens 1 Silica 0.5 −64.04 \ 6.06 735.35 0.00136 8.3877 Air \ −55.35 \ 11.86 Lens 2 Silica 0.5 57.48 \ 6.06 393.72 0.00254 6.2007 Air \ 81.82 \ 16.24 Lens 3 Silica 0.5 −28.65 −1.11 4.35 -92.14 - 0.01085 2.5471 Air \ −94.60 \ 15.00
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表 4 优化后光学系统结构参数
Table 4. Parameters of optimized optical system configuration
Materials Radius/mm Constant of the
quadric surfaceThickness/mm Silicon Carbide −347.98 −1.20 −114.55 Silicon Carbide −181.49 −6.33 99.97 Silica −55.15 \ 6.42 Air −53.20 \ 27.02 Silica 58.42 \ 4.29 Air 83.45 \ 20.47 Silica −29.45 −1.11 3.00 Air −78.77 \ 15.00
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表 5 各个温度下各个视场点列图的RMS直径
Table 5. RMS diameter of spot diagrams at various field points and temperatures
Temperatures/
°CRMS diameter /μm Field
angle0° 0.7° 1.4° 1.6° 1.8° 2° −60 4.294 5.5 4.314 3.784 4.518 7.252 −20 4.592 5.782 4.558 3.868 4.242 6.82 20 4.9 6.08 4.846 4.032 4.044 6.428 50 5.136 6.31 5.084 4.202 3.95 6.164 100 5.538 6.706 5.522 4.56 3.912 5.788 150 5.948 7.116 5.996 4.994 4.018 5.504
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表 6 对照组2各个温度下在奈奎斯特频率处的最低MTF值
Table 6. The lowest MTF value at the nyquist frequency for each temperature in the control group 2
Temperatures/ °C −60 −20 20 50 100 150 The lowest MTF value 0.452 0.473 0.475 0.475 0.483 0.481
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