Optical design of the off-axis reflective system with wide fov

Yaqiong YU; Lingjie WANG; Shangnan ZHAO; Jianping ZHANG; Xin ZHANG

doi:10.37188/OPE.20233114.2019

Journals >Optics and Precision Engineering >Volume 31 >Issue 14 >Page 2019 > Article

Optics and Precision Engineering
Vol. 31, Issue 14, 2019 (2023)

Optical design of the off-axis reflective system with wide fov

Yaqiong YU^1,2, Lingjie WANG^1,*, Shangnan ZHAO^1,2, Jianping ZHANG¹, and Xin ZHANG^1,2

Author Affiliations

¹Changchun Institute of Optics，Fine Mechanics and Physics，Chinese Academy of Sciences， Changchun 30033，China

²University of Chinese Academy of Sciences，Beijing 100049，China

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DOI: 10.37188/OPE.20233114.2019 Cite this Article

Yaqiong YU, Lingjie WANG, Shangnan ZHAO, Jianping ZHANG, Xin ZHANG. Optical design of the off-axis reflective system with wide fov[J]. Optics and Precision Engineering, 2023, 31(14): 2019 Copy Citation Text

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Fig. 1. Schematic diagram of full field display evaluation method

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Fig. 2. Vector display of the coefficient of Zernike term

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Fig. 3. wavefront diagram of fringe Zernike polynomial

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Fig. 4. Flow diagram of design method based on decomposition of freeform surface

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Fig. 5. Schematic diagram of a conceptual optical system

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Fig. 6. Structural constraints diagram

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Fig. 7. Surface constraints diagram

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Fig. 8. Optical path diagram of optical system

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Fig. 9. Aspheric depatures from best-fitting sphere of M1

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Fig. 10. Freeform depatures from the best- fitting sphere of M2-M4

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Fig. 11. Gradient of the freeform depature of M2-M4

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Fig. 12. RMS wavefront error of optical system

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Fig. 13. Full-field wavefront polynomial coefficient vector display of optical system

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Fig. 14. Modulation transfer function curve of optical system

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Fig. 15. Optical system grid distortion

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条纹Zernike项	拟合系数	多项式表达式	像差类型
$Z_{5}$	$C_{5}$	$R^{2} \cdot c o s 2 θ$	初阶像散（ $0$ °或 $90$ °方向）
$Z_{6}$	$C_{6}$	$R^{2} \cdot s i n 2 θ$	初阶像散（ $\pm 45$ °方向）
$Z_{7}$	$C_{7}$	$(3 R^{3} - 2 R) \cdot c o s θ$	初阶彗差（x方向）
$Z_{8}$	$C_{8}$	$(3 R^{3} - 2 R) \cdot s i n θ$	初阶彗差（y方向）
$Z_{9}$	$C_{9}$	$6 R^{4} - 6 R^{2} + 1$	初阶球差
$Z_{10}$	$C_{10}$	$R^{3} \cdot c o s 3 θ$	初阶三叶草像差（x方向）
$Z_{11}$	$C_{11}$	$R^{3} \cdot s i n 3 θ$	初阶三叶草像差（y方向）
$Z_{12}$	$C_{12}$	$(4 R^{4} - 3 R^{2}) \cdot c o s 2 θ$	二阶像散（ $0$ °或 $90$ °方向）
$Z_{13}$	$C_{13}$	$(4 R^{4} - 3 R^{2}) \cdot s i n 2 θ$	二阶像散（ $\pm 45$ °方向）
$Z_{14}$	$C_{14}$	$(10 R^{5} - 12 R^{3} + 3 R) \cdot c o s θ$	二阶彗差（x方向）
$Z_{15}$	$C_{15}$	$(10 R^{5} - 12 R^{3} + 3 R) \cdot s i n θ$	二阶彗差（y方向）
$Z_{17}$	$C_{17}$	$R^{4} \cdot c o s 4 θ$	初阶四叶草像差（x方向）
$Z_{18}$	$C_{18}$	$R^{4} \cdot s i n 4 θ$	初阶四叶草像差（y方向）

Table 1. Expression of fringe Zernike polynomial

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参数	数值
波段/nm	400~750
焦距/mm	1000
相对孔径	1/10
视场角/（°）	40×16
探测器像元尺寸/μm	10
畸变	$\leq$ 18%

Table 2. Specifications of optical system

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表面名称	M1		M2	M3	M4		像面
表面名称	子曲面1	子曲面2	M2	M3	M4		子像面1	子像面2
表面类型	非球面		标准Zernike 自由曲面	标准Zernike 自由曲面	标准Zernike 自由曲面
曲率半径/mm	2 062.92	2 072.23	2 637.85	4 034.44	3 563.98
间隔/mm	-1 231.79		808.20	-808.20	1 423.52	1 428.40
圆锥常数	-1.948	-1.609	-0.544	-14.920	-22.475
倾斜/（°）	-8.250	-7.680	-9.280	-3.254	-9.330		-14.690	-14.608
偏心/mm	-38.769	-78.408	322.608	-65.818	165.329

Table 3. Structural parameters of optical system

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	4阶非球面系数	6阶非球面系数	8阶非球面系数
M1子曲面1	$2.36 \times 10^{- 11}$	$- 2.37 \times 10^{- 18}$	$- 3.45 \times 10^{- 24}$
M1子曲面2	$2.13 \times 10^{- 11}$	$- 6.49 \times 10^{- 18}$	$- 1.11 \times 10^{- 24}$

Table 4. Aspheric term coefficients of M1

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	$A_{4}$	$A_{5}$	$A_{9}$	$A_{10}$	$A_{11}$	$A_{12}$
M2	3.361	-2.561	-4.104	-1.737	$- 2.134 \times 10^{- 1}$	$- 4.465 \times 10^{- 1}$
M3	$- 9.017 \times 10^{- 2}$	$- 1.279 \times 10^{- 1}$	$- 6.180 \times 10^{- 3}$	$- 1.697 \times 10^{- 3}$	$1.626 \times 10^{- 5}$	$- 8.837 \times 10^{- 5}$
M4	-5.833	$3.877 \times 10^{- 1}$	-1.393	$- 5.535 \times 10^{- 1}$	$- 3.903 \times 10^{- 2}$	$- 7.145 \times 10^{- 2}$
	$A_{13}$	$A_{19}$	$A_{20}$	$A_{21}$	$A_{22}$	$A_{23}$
M2	$- 1.782 \times 10^{- 1}$	$5.861 \times 10^{- 2}$	$- 2.152 \times 10^{- 1}$	$- 3.941 \times 10^{- 1}$	$1.215 \times 10^{- 1}$	$3.464 \times 10^{- 2}$
M3	$- 8.294 \times 10^{- 6}$	$1.886 \times 10^{- 6}$	$1.407 \times 10^{- 5}$	—	—	$1.064 \times 10^{- 5}$
M4	$2.457 \times 10^{- 1}$	$- 2.513 \times 10^{- 2}$	$- 2.609 \times 10^{- 2}$	$2.612 \times 10^{- 2}$	$6.035 \times 10^{- 3}$	$- 2.638 \times 10^{- 3}$
	$A_{24}$	$A_{25}$	$A_{33}$	$A_{34}$
M2	$- 4.616 \times 10^{- 2}$	$4.967 \times 10^{- 2}$	$3.045 \times 10^{- 2}$	$3.950 \times 10^{- 3}$
M3	$- 2.498 \times 10^{- 6}$	—	—	—
M4	$4.843 \times 10^{- 3}$	$- 3.888 \times 10^{- 2}$	$1.770 \times 10^{- 3}$	$- 1.005 \times 10^{- 3}$

Table 5. Standard Zernike term coefficients of M2-M4

Yaqiong YU, Lingjie WANG, Shangnan ZHAO, Jianping ZHANG, Xin ZHANG. Optical design of the off-axis reflective system with wide fov[J]. Optics and Precision Engineering, 2023, 31(14): 2019

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