Aberration compensation strategy for the radius of curvature error of the primary mirror in off-axis three-mirror anastigmatic telescopes

Xiaoquan Bai; Xiaoquan Bai; Xiaoquan Bai; Boqian Xu; Boqian Xu; Guohao Ju; Guohao Ju; Hongcai Ma; Hongcai Ma; Chunyue Zhang; Chunyue Zhang; Shuaihui Wang; Shuaihui Wang; Shuyan Xu; Shuyan Xu

doi:10.1364/AO.431908

Applied Optics
Vol. 60,
Issue 21,
pp. 6199-6212
(2021)
•https://doi.org/10.1364/AO.431908

Aberration compensation strategy for the radius of curvature error of the primary mirror in off-axis three-mirror anastigmatic telescopes

Xiaoquan Bai, Boqian Xu, Guohao Ju, Hongcai Ma, Chunyue Zhang, Shuaihui Wang, and Shuyan Xu

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Xiaoquan Bai, Boqian Xu, Guohao Ju, Hongcai Ma, Chunyue Zhang, Shuaihui Wang, and Shuyan Xu, "Aberration compensation strategy for the radius of curvature error of the primary mirror in off-axis three-mirror anastigmatic telescopes," Appl. Opt. 60, 6199-6212 (2021)

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Abstract

This paper discusses compensation strategies for the aberration fields caused by the error in the radius of curvature (ROC) of the primary mirror (PM) in pupil-offset off-axis three-mirror anastigmatic (TMA) astronomical telescopes. Based on the nodal aberration theory framework, the specific astigmatic and coma aberrations of the off-axis three-mirror system in the presence of the ROC error of the PM are derived. It is demonstrated that some field-dependent aberration components can be induced by ROC error in the off-axis TMA telescopes, apart from the dominating field-constant aberration terms. To reduce the influence of the ROC error on the aberration fields, we propose two aberration compensation strategies: adjusting the position of the PM and introducing axial misalignment of the secondary mirror (SM). Through theoretical analysis and simulations, we conclude that the compensation strategy of changing the axial position of the PM can make the aberration distribution close to the nominal state; the compensation strategy of axially adjusting the SM can make the aberration distribution meet the observation requirements, which is more suitable for space applications. We also discuss compensating the effect of the ROC error using lateral misalignments.

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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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		NST		WFIRST-Like Telescope
( $H_{x}$ , $H_{y}$ )		A/632.8 nm	B/632.8 nm	A/632.8 nm	B/632.8 nm
(0, 1)	$Δ C_{7}$	0	0	0.0000	0.0000
(0, 1)	$Δ C_{8}$	0.0876	0.1127	−0.0811	−0.0946
(1, 0)	$Δ C_{7}$	0.0013	0	0.0037	0.0073
(1, 0)	$Δ C_{8}$	0.0864	0.1127	−0.0855	−0.1019
(−1/2, −1/2)	$Δ C_{7}$	−0.0006	0	−0.0015	−0.0036
(−1/2, −1/2)	$Δ C_{8}$	0.0861	0.1127	−0.0875	−0.1055
(−1, −1)	$Δ C_{7}$	−0.0013	0	−0.0024	−0.0073
(−1, −1)	$Δ C_{8}$	0.0859	0.1127	−0.0899	−0.1091

		NST		WFIRST- Like Telescope
( $H_{x}$ , $H_{y}$ )		A/632.8 nm	B/632.8 nm	A/632.8 nm	B/632.8 nm
(0, 1)	$Δ C_{5}$	−0.3322	−0.3887	−0.2331	−0.2346
(0, 1)	$Δ C_{6}$	0.0000	0.0000	0.0000	0.0000
(1, 0)	$Δ C_{5}$	−0.3224	−0.3887	−0.2387	−0.2892
(1, 0)	$Δ C_{6}$	0.0099	0.0000	−0.0214	−0.0402
(−1/2, −1/2)	$Δ C_{5}$	−0.3182	−0.3887	−0.2610	−0.3022
(−1/2, −1/2)	$Δ C_{6}$	−0.0050	0.0000	0.0144	0.0165
(−1, −1)	$Δ C_{5}$	−0.3145	−0.3887	−0.2749	−0.3223
(−1, −1)	$Δ C_{6}$	−0.0099	0.0000	0.0364	0.0258

Field Point	Nominal	In the Presence of ROC Error	Compensated by −0.1 mm	Compensated by −0.11 mm
(0°, 0.07°)	0.0125	0.9156	0.0453	0.0143
(0°, 0.30°)	0.0340	0.8935	0.0776	0.0362
(0°, 0.53°)	0.0533	0.8873	0.0946	0.0553
(−0.54°, 0.07°)	0.0431	0.9288	0.0384	0.0451
(−0.54°, 0.30°)	0.0402	0.9179	0.0462	0.0426
(−0.54°, 0.53°)	0.0614	0.9259	0.0576	0.0616
(0.54°, 0.07°)	0.0431	0.9288	0.0384	0.0451
(0.54°, 0.30°)	0.0402	0.9179	0.0462	0.0426
(0.54°, 0.53°)	0.0614	0.9259	0.0576	0.0616

	Radius/mm	Conic	Thickness/mm
PM (stop)	−6066.314	−0.96363	−2383
SM	−1688.162	−2.21337	4767
TM	−2364.172	−0.50021	−2032.83
FP	FLAT	—	—

	Radius/mm	Conic	Thickness/mm
PM (stop)	−7700	−1	−4150.05
SM	573.5828	−0.83087	6490.259
FP	FLAT	—	—

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Applied Optics