基于自由曲面的大视场天基探测光学系统 
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Large Field of View Space-Based Optical Detection System Based on Freeform Surfaces
1 中国科学院西安光学精密机械研究所空间光学应用研究室, 陕西 西安 710119
2 中国科学院大学, 北京 100049
3 陕西师范大学物理学与信息技术学院, 陕西 西安 710119
图 & 表
图 1. 天基探测光学系统的结构图
Fig. 1. Structural diagram of space-based detection optical system
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图 2. 主镜Zernike自由曲面的面型。(a)二维;(b)三维
Fig. 2. Profile of Zernike freeform surface of primary mirror. (a) Two-dimensional; (b) three-dimensional
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图 3. 三镜XY自由曲面的面型。(a)二维;(b)三维
Fig. 3. Profile of XY freeform surface of tertiary mirror. (a) Two-dimensional; (b) three-dimensional
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图 4. 系统点列图
Fig. 4. Spot diagram of system
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图 5. 不同视场下的能量包围分布。(a) 0.5视场;(b) 0.7视场;(c)视场边缘
Fig. 5. Encircled energy distributions under different field views. (a) Field view of 0.5; (b) field view of 0.7; (c) edge field of view
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图 6. 检测光路。(a)自由曲面的CGH检测光路;(b)检测光路中的CGH元件
Fig. 6. Detecting optical path. (a) CGH detecting optical path of freeform surface; (b) CGH unit in detecting optical path
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图 7. CGH元件的刻线密度及检测系统的波像差。(a)刻线密度;(b)波像差
Fig. 7. Lithography linear density of CGH and wave aberration of detecting system. (a) Lithographic linear density; (b) wave aberration
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表 1Zernike多项式与像差之间的对应关系
Table1. Corresponding relationship between Zernike polynomials and aberration
| No. | Polynomial | Aberration |
|---|
| Polar coordinate system | Cartesian coordinate system |
|---|
| 1 | 1 | 1 | Piston | | 2 | ρcos θ | x | x-tilt | | 3 | ρsin θ | y | y-tilt | | 4 | ρ2cos(2θ) | x2-y2 | 0° or 90° astigmatism | | 5 | 2ρ2-1 | 2(x2+y2)-1 | Defocus | | 6 | ρ2sin(2θ) | 2xy | 45° astigmatism | | 7 | ρ3cos(3θ) | x(x2-y2)-2xy2 | x-trefoil | | 8 | (3ρ2-2)ρcos θ | x[3(x2+y2)-2] | x-coma | | 9 | (3ρ2-2)ρsin θ | y[3(x2+y2)-2] | y-coma |
|
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表 2探测器性能参数
Table2. Performance parameters of detector
| Parameter | Value |
|---|
| B | 8 | | Nc | 46 | | τ | 0.8 | | Integration time /s | 0.02 | | Eph /(10-19 J) | 3.4 | | fQE /% | 55 |
|
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表 3天基探测光学系统的主要技术指标
Table3. Main technical indexes of space-based optical detection system
| System parameter | Value |
|---|
| Focal length /mm | 64 | | Field of view /[(°) ×(°)] | 30×30 | | Entrance aperture /mm | 51 | | Equivalent visual magnitude | 9 | | Spectral band /nm | 400-900 |
|
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表 4光学系统的初始结构参数
Table4. Initial structural parameters of optical system
| Surface | Radius /mm | Thickness /mm |
|---|
| Primary mirror | 175.4386 | -150 | | Secondary mirror | 333.3333 | 150 | | Tertiary mirror | -330.3704 | -125 |
|
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表 5优化后的光学系统反射镜参数
Table5. Mirror parameters of optical system after optimization
| Mirror | Radius /mm | Distance /mm | Constant ofquadric surface | Y decenter /mm | x tilt /(°) |
|---|
| Primary mirror | 398.39 | -297.29 | -2.73 | 117.55 | 22.60 | | Secondary mirror | 1165.19 | 287.29 | 0 | 19.03 | 0 | | Tertiary mirror | -770.05 | -267.70 | -6.82 | -22.21 | 3.15 |
|
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表 6主镜的Zernike自由曲面参数
Table6. Parameters of Zernike freeform surface of primary mirror
| No. | Term | Coefficient |
|---|
| 1 | Z1 | 3.703732952805 | | 2 | Z2 | -0.005921378239 | | 3 | Z3 | 1.074318956926 | | 4 | Z4 | -0.000844676164 | | 5 | Z5 | 0.000225724509 | | 6 | Z6 | -7.298797621080×10-6 | | 7 | Z7 | 5.336916645650×10-8 | | 8 | Z8 | -2.419364792778×10-8 | | 9 | Z9 | 2.566383909345×10-6 | | 10 | Z10 | -1.197484299545×10-6 | | 11 | Z11 | 4.052592425289×10-10 | | 12 | Z12 | -2.946732238365×10-9 |
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表 7三镜的XY自由曲面参数
Table7. Parameters of XY freeform surface of tertiary mirror
| Item | Coefficient | Item | Coefficient |
|---|
| Y | 0.0657280763771848 | X4Y | -1.508575293882×10-13 | | X2 | 0.000526216242287311 | X2Y3 | -1.246876764365×10-12 | | Y2 | 0.000529147800335145 | Y5 | 1.859610071502×10-12 | | X2Y | -2.14467235342657×10-8 | X6 | 8.860132888429×10-15 | | Y3 | -3.04871515062429×10-8 | X4Y2 | 2.549695693063×10-14 | | X4 | -1.89146570020516×10-9 | X2Y4 | 1.780628633470×10-14 | | X2Y2 | -3.7733664377066×10-9 | Y6 | 1.292338859180×10-14 | | Y4 | -1.69502835366705×10-9 | - | - |
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表 8系统公差分配
Table8. Distribution of system tolerance
| Mirror | Manufacture tolerance | Alignment tolerance |
|---|
| ΔR /mm | ΔK | RMS of shapeerror /λ | Decenter /mm | Tilt /rad | DisplacementΔY /mm |
|---|
| Primary mirror | 0.02 | 0.01 | 1/50 | 0.02 | 3×10-4 | 0.02 | | Second mirror | 0.005 | 0.002 | 1/50 | 0.01 | 1.5×10-4 | 0.02 | | Tertiary mirror | 0.02 | 0.008 | 1/50 | 0.02 | 3×10-4 | 0.08 |
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表 9系统公差表现
Table9. Performance of system tolerance
| Field No. | Sagittal direction /(°) | Tangential direction /(°) | Design value /μm | Design tolerance /μm |
|---|
| 1 | 0 | -5 | 0.015416 | 0.023123 | | 2 | 0 | -20 | 0.010510 | 0.018538 | | 3 | 0 | -35 | 0.010699 | 0.018867 | | 4 | 5 | -5 | 0.009367 | 0.016026 | | 5 | 5 | -20 | 0.013022 | 0.022765 | | 6 | 5 | -35 | 0.007800 | 0.014165 | | 7 | 10 | -5 | 0.009585 | 0.017063 | | 8 | 10 | -20 | 0.013478 | 0.021934 | | 9 | 10 | -35 | 0.006847 | 0.012299 | | 10 | 15 | -5 | 0.009996 | 0.018456 | | 11 | 15 | -20 | 0.007032 | 0.012354 | | 12 | 15 | -35 | 0.006425 | 0.016219 |
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倪栋伟, 李旭阳, 杨明洋, 任志广. 基于自由曲面的大视场天基探测光学系统[J]. 光学学报, 2018, 38(11): 1122003. Dongwei Ni, Xuyang Li, Mingyang Yang, Zhiguang Ren. Large Field of View Space-Based Optical Detection System Based on Freeform Surfaces[J]. Acta Optica Sinica, 2018, 38(11): 1122003.
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