Design of a free-form off-axis three-mirror optical system with a low f-number based on the same substrate

Yuanhe Sun; Yuanqi Sun; Xiaoyu Chen; Fang Wang; Xin Yan; Xuenan Zhang; Tonglei Cheng; Tonglei Cheng

doi:10.1364/AO.457646

Applied Optics
Vol. 61,
Issue 24,
pp. 7033-7040
(2022)
•https://doi.org/10.1364/AO.457646

Design of a free-form off-axis three-mirror optical system with a low f-number based on the same substrate

Yuanhe Sun, Yuanqi Sun, Xiaoyu Chen, Fang Wang, Xin Yan, Xuenan Zhang, and Tonglei Cheng

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Yuanhe Sun, Yuanqi Sun, Xiaoyu Chen, Fang Wang, Xin Yan, Xuenan Zhang, and Tonglei Cheng, "Design of a free-form off-axis three-mirror optical system with a low f-number based on the same substrate," Appl. Opt. 61, 7033-7040 (2022)

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Abstract

In this paper, we design a free-form off-axis three-mirror optical system with a low $f$-number and compact structure, which can be used as an infrared reflection imager. The initial structure is calculated from the near-axis optical transfer matrix based on third-order aberration theory. Particular constraints are designed to install all mirrors on the same substrate for simultaneous milling, which reduces the processing difficulty and effectively avoids errors caused by component assembly. Zernike free-form surfaces are introduced to correct aberrations. This optical system has a field of view of ${5}^\circ \times {5}^\circ$ and an $f$-number of 1.82; the modulation transfer function of the system is higher than 0.6 at 30 lp/mm. The results of the tolerance assignment of the system were verified by the Monte Carlo method, and the machining tolerance is reasonable and easy to achieve. This design not only improves the optical performance of the system but also enhances the feasibility of manufacturing.

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Term	Polar Coordinate System	Cartesian Coordinate System	Aberration
1	1	1	Piston
2	$ρ \cos θ$	$x$	$x$ -tilt
3	$ρ \sin θ$	$y$	$y$ -tilt
4	$ρ^{2} \cos 2 θ$	$x^{2} - y^{2}$	0° or 90° astigmatism
5	$2 ρ^{2} - 1$	$2 (x^{2} + y^{2}) - 1$	Defocus
6	$ρ^{2} \sin 2 θ$	$2 x y$	45° astigmatism
7	$ρ^{3} \cos 3 θ$	$x (x^{2} - y^{2}) - 2 x y^{2}$	$x$ -trefoil
8	$(3 ρ^{2} - 2) ρ \cos θ$	$x [3 (x^{2} + y^{2}) - 2]$	$x$ -coma
9	$(3 ρ^{2} - 2) ρ \sin θ$	$y [3 (x^{2} + y^{2}) - 2]$	$y$ -coma

Parameter	Specifications
Entrance pupil diameter/mm	110
Work spectrum/nm	1000–3000
$F$ -number	1.82
FOV/(°)	$5^{\circ} \times 5^{\circ}$
Detector pixel size	20 µm
Distortion	$< 0.5 %$

					High-Order Term
Mirror	Radius (mm)	Distance (mm)	Relative Deflection Angle	Conic	4th	6th	8th	10th
PM	$- 152.626$	$- 112.014$	25.0°	−0.320	$1.392 \times 10^{- 5}$	$- 2.572 \times 10^{- 7}$	0.025	$- 7.889 \times 10^{- 9}$
SM	721.029	133.646	67.2°	3.256	$- 1.425 \times 10^{- 8}$	$- 3.319 \times 10^{- 4}$	$1.177 \times 10^{- 4}$	$3.759 \times 10^{- 4}$
TM	$- 756.780$	$- 198.100$	98°	4.866	$1.781 \times 10^{- 6}$	$- 3.256 \times 10^{- 3}$	0.260	$4.712 \times 10^{- 12}$

Item	PM	SM	TM
Z4	4.886	$3.185 \times 10^{- 5}$	$- 3.634 \times 10^{- 7}$
Z5	$7.670 \times 10^{- 5}$	−2.564	$2.837 \times 10^{- 4}$
Z8	$- 1.675 \times 10^{- 2}$	$7.544 \times 10^{- 4}$	$- 2.687 \times 10^{- 10}$
Z9	$3.352 \times 10^{- 8}$	−0.279	1.490

Tolerance Term	Primary Mirror	Secondary Mirror	Tertiary Mirror
$X$ decentered tolerances (mm)	$\pm 0.03$	$\pm 0.05$	$\pm 0.03$
$Y$ decentered tolerances (mm)	$\pm 0.03$	$\pm 0.05$	$\pm 0.03$
$X$ tilt tolerances ( $^{''}$ )	$\pm 10$	$\pm 20$	$\pm 10$
$Y$ tilt tolerances ( $^{''}$ )	$\pm 10$	$\pm 20$	$\pm 10$
Radius tolerances (mm)	$\pm 0.5$	$\pm 0.3$	$\pm 0.5$
Thickness tolerances (mm)	$\pm 0.5$	$\pm 0.5$	$\pm 0.5$

Monte Carlo Probability	MTF Value at 30 mm
98%	0.28579
90%	0.35233
70%	0.50624
50%	0.61874

Monte Carlo Probability	MTF Value at 30 mm
98%	0.28579
90%	0.35233
70%	0.50624
50%	0.61874

Abstract

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Applied Optics