Off-axis four-mirror telescope with a wide field of view and a long focal length using double integrated mirrors

Liwei Zhu; Hongbo Xie; Jie Chen; Tong Yang; Lei Yang

doi:10.1364/AO.500149

Applied Optics
Vol. 62,
Issue 29,
pp. 7773-7782
(2023)
•https://doi.org/10.1364/AO.500149

Off-axis four-mirror telescope with a wide field of view and a long focal length using double integrated mirrors

Liwei Zhu, Hongbo Xie, Jie Chen, Tong Yang, and Lei Yang

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Liwei Zhu, Hongbo Xie, Jie Chen, Tong Yang, and Lei Yang, "Off-axis four-mirror telescope with a wide field of view and a long focal length using double integrated mirrors," Appl. Opt. 62, 7773-7782 (2023)

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Abstract

An off-axis four-mirror optical system has the advantages of a wide field of view (FOV) and a small telephoto ratio. However, it will bring difficulties in assembly and detection. Here we report an off-axis four-mirror free-form telescope with a long focal length and a wide field of view based on two integration mirrors. The initial structure of a coaxial four-mirror optical system is established based on the Seidel aberration theory. A Zernike Fringe free-form surface is introduced to correct aberrations. By gradually increasing the entrance pupil diameter and the FOV, we finally obtain an off-axis four-mirror telescope with a FOV of ${0.4}^\circ \times {20}^\circ$, an F-number of 11.5, a long focal length of 2000 mm, and a volume of $360\times 400\times 600\;{\rm mm}^3$. In addition, four mirrors remain coaxially aligned, remarkably facilitating detection and adjustment. The proposed off-axis four-mirror telescope, with double integration mirrors, holds great potential for application in aerospace remote sensing observations.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Parameter	Specification
Work spectrum	400–800 nm
Field of view	${0.4}^{\circ} \times 20^{\circ}$
Effective focal length	2000 mm
Entrance pupil diameter	165 mm

Mirror	Radius (mm)	Distance (mm)	Conic
M1 (stop)	−2663.935	−350	−2.343
M2	−3051.840	350	10.49
M3	−2663.935	−350	−10.49
M4	−3051.840	759.660	−2.343

					Aspheric Coefficient
Mirror	Surface Type	Radius	Thickness	Conic	4th	6th
M1 (stop)	Even asphere	−1828.580	−400	−8.938	$- 1.202 \times 10^{- 10}$	$3.027 \times 10^{- 16}$
M2	Zernike Fringe sag	72519.727	400	58.884	–	–
M3	Even asphere	−1828.580	−400	−8.938	$- 3.943 \times 10^{- 13}$	$3.837 \times 10^{- 16}$
M4	Even asphere	72519.727	997.486	−0.043	$1.074 \times 10^{- 10}$	$6.175 \times 10^{- 17}$

Term	Coefficient	Term	Coefficient	Term	Coefficient	Term	Coefficient
Z4	−4.238	Z12	−0.183	Z21	−0.029	Z31	$3.674 \times 10^{- 3}$
Z5	−0.427	Z15	−0.108	Z24	−0.011	Z32	$- 1.371 \times 10^{- 3}$
Z8	−0.389	Z16	0.022	Z25	$1.379 \times 10^{- 3}$	Z35	$- 3.496 \times 10^{- 4}$
Z9	0.151	Z17	0.073	Z27	−0.011	Z36	$1.763 \times 10^{- 5}$
Z11	0.229	Z20	0.052	Z28	$7.056 \times 10^{- 3}$	Z37	$7.720 \times 10^{- 7}$

Compensator Type	Compensator Range ( $\pm$ )
Image plane shift (µm)	70
Tilt about $x$ axis (arcmin)	8.9
Tilt about $y$ axis (arcmin)	2.4

Tolerance Term	Primary Mirror	Secondary Mirror	Tertiary Mirror	Quaternary Mirror
$X$ -decenter (mm)	—	$\pm 0.03$	—	$\pm 0.03$
$Y$ -decenter (mm)	—	$\pm 0.03$	—	$\pm 0.03$
$Z$ -decenter (mm)	—	$\pm 0.02$	—	$\pm 0.02$
$X$ -tilt (°)	—	$\pm 0.03$	—	$\pm 0.03$
$Y$ -tilt (°)	—	$\pm 0.03$	—	$\pm 0.03$
Radius (mm)	$\pm 0.5$	$\pm 0.5$	$\pm 0.5$	$\pm 0.5$
Conical coefficient	$\pm 0.01$	$\pm 0.01$	$\pm 0.01$	$\pm 0.01$
Zernike Fringe coefficient surface deformation ( $λ$ )	—	0.02	—	—

Monte Carlo Probability	MTF Value at 50 lp/mm
99.9%	0.3042
97.7%	0.3137
84.1%	0.3964
50%	0.4982

Monte Carlo Probability	MTF Value at 50 lp/mm
99.9%	0.3042
97.7%	0.3137
84.1%	0.3964
50%	0.4982

Abstract

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Applied Optics