Design of Large Field-of-View, Easy-to-Assemble Off-Axis Four-Mirror Optical System

En Liu; Yuquan Zheng; Chao Lin; Jialun Zhang

doi:10.3788/AOS250567

Acta Optica Sinica, Volume. 45, Issue 10, 1022001(2025)

Design of Large Field-of-View, Easy-to-Assemble Off-Axis Four-Mirror Optical System

En Liu^1,2,3, Yuquan Zheng^1,3、*, Chao Lin^1,3, and Jialun Zhang^1,3

¹Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, Jilin , China

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

³State Key Laboratory of Advanced Manufacturing for Optical Systems, Changchun 130033, Jilin , China

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Figures & Tables(15)

Fig. 1. Edge ray tracing diagram and principal ray tracing diagram. (a) Edge ray tracing diagram; (b) principal ray tracing diagram

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Fig. 2. Design flow chart

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Fig. 3. Error function iteration curve

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Fig. 4. Diagrams of on-axial and off-axis structure layouts and MTF curves. (a) On-axial structure layout diagram and MTF curve; (b) off-axis structure layout diagram and MTF curve

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Fig. 5. Structural constraint diagram of off-axis four-mirror system

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Fig. 6. Two important nodes during expansion processes of aperture and field-of-view. (a) System A; (b) system B

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Fig. 7. Final layout of off-axis four-mirror optical system

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Fig. 8. Modulation transfer function curves of final system

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Table 1. Design index parameters of off-axis four-mirror optical system
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Table 1. Design index parameters of off-axis four-mirror optical system
Parameter Technical index
Focal length /mm 1000
Entrance pupil diameter /mm 95
Waveband /nm 486‒656
Field of view /［（°）×（°）］ 23×0.6
Pixel size /（μm×μm） 10×10

Table 2. Initial parameters of off-axis four-mirror optical system
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Table 2. Initial parameters of off-axis four-mirror optical system
$r_{1}, r_{3}$ $r_{2}, r_{4}$ $t_{1}$ $t_{2}$ $t_{3}$ $k_{1}, k_{3}$ $k_{2}, k_{4}$
-4852.42 4992.48 -417.00 417.00 -417.00 -16.51 20.00
-958.47 -705.97 -208.60 208.60 -208.60 -1.77 -4.63
-1151.86 -941.10 -242.86 242.86 -242.86 3.23 18.78

Table 3. Final structural parameters of off-axis four-mirror optical system

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Table 3. Final structural parameters of off-axis four-mirror optical system

Mirror	Surface type	Radius/mm	Distance/mm	Conic	4^th order coefficient	6^th order coefficient
M1	XY polynomial	-932.337	-281.070	2.256
M2	Even asphere	-1240.809	281.070	11.326	1.922× $10^{- 9}$	4.864× $10^{- 15}$
M3	Even asphere	-932.337	-281.070	1.776	5.493× $10^{- 10}$	2.718× $10^{- 15}$
M4	Even asphere	-1240.809	295.418	11.326	6.779× $10^{- 10}$	9.976× $10^{- 14}$

Table 4. XY freeform surface coefficients

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Table 4. XY freeform surface coefficients

Term	Coefficient	Term	Coefficient	Term	Coefficient	Term	Coefficient
$X^{0} Y^{1}$	0	$X^{0} Y^{3}$	2.3341× $10^{- 6}$	$X^{4} Y^{1}$	5.2697× $10^{- 4}$	$X^{4} Y^{2}$	3.0531× $10^{- 3}$
$X^{2} Y^{0}$	2.6731	$X^{4} Y^{0}$	0.0694	$X^{3} Y^{2}$	0	$X^{3} Y^{3}$	0
$X^{1} Y^{1}$	0	$X^{3} Y^{1}$	0	$X^{2} Y^{3}$	8.2280× $10^{- 4}$	$X^{2} Y^{4}$	2.7270× $10^{- 3}$
$X^{0} Y^{2}$	2.6731	$X^{2} Y^{2}$	0.1391	$X^{1} Y^{4}$	0	$X^{1} Y^{5}$	0
$X^{3} Y^{0}$	0	$X^{1} Y^{3}$	0	$X^{0} Y^{5}$	3.4514× $10^{- 4}$	$X^{0} Y^{6}$	8.5466× $10^{- 4}$
$X^{2} Y^{1}$	1.2269× $10^{- 3}$	$X^{0} Y^{4}$	0.0694	$X^{6} Y^{0}$	1.4934× $10^{- 3}$	$X^{7} Y^{0}$	0

Table 5. Tolerance range

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Table 5. Tolerance range

Tolerance term	Primary mirror	Secondary mirror	Tertiary mirror	Quaternary mirror
X-decenter /mm	—	±0.03	—	±0.02
Y-decenter /mm	—	±0.02	—	±0.03
Z-decenter /mm	—	±0.02	—	±0.03
X-tilt /（°）	—	±0.03	—	±0.02
Y-tilt /（°）	—	±0.02	—	±0.03
Radius /mm	±0.5	±0.50	—	±0.50
Shape error RMS/λ	1/50	1/50	1/50	1/50

Table 6. Types and ranges of compensators
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Table 6. Types and ranges of compensators
Compensator type Compensator range
Image plane shift /μm ±50
Tilt about X axis /（'） ±5
Tilt about Y axis /（'） ±3

Table 7. Monte Carlo analysis results
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Table 7. Monte Carlo analysis results
Monte Carlo probability /% MTF /（50 lp/mm）
90 0.215
80 0.250
50 0.325
20 0.380
10 0.398

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En Liu, Yuquan Zheng, Chao Lin, Jialun Zhang. Design of Large Field-of-View, Easy-to-Assemble Off-Axis Four-Mirror Optical System[J]. Acta Optica Sinica, 2025, 45(10): 1022001

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