Application of torque sensitivity in the alignment of a Cassegrain system

Junhong Qian; Xiugang Ma; Xiaoyan Wu; Jiawen Li; Hewei Liu; Ting Liu; Ye Tao; Rongzhu Zhang

doi:10.1364/AO.459163

Applied Optics
Vol. 61,
Issue 19,
pp. 5686-5694
(2022)
•https://doi.org/10.1364/AO.459163

Application of torque sensitivity in the alignment of a Cassegrain system

Junhong Qian, Xiugang Ma, Xiaoyan Wu, Jiawen Li, Hewei Liu, Ting Liu, Ye Tao, and Rongzhu Zhang

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Junhong Qian, Xiugang Ma, Xiaoyan Wu, Jiawen Li, Hewei Liu, Ting Liu, Ye Tao, and Rongzhu Zhang, "Application of torque sensitivity in the alignment of a Cassegrain system," Appl. Opt. 61, 5686-5694 (2022)

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Abstract

In order to improve the alignment accuracy of a Cassegrain system, to the best of our knowledge, a novel computer-aided alignment method based on torque sensitivity is proposed. Different from the traditional position sensitivity curve guiding scheme, the accurate position of the secondary mirror is not necessary while the torque sensitivity curve is generated. By establishing the relationship between the torque of the secondary mirror setting screw and the Zernike coefficients of the system, a practical quantitative alignment scheme for the Cassegrain system can be realized. For a two-mirror Cassegrain optical-mechanical system, an alignment scheme based on torque sensitivity is designed. The results show that the wavefront aberrations of three Cassegrain systems reach ${0.0479}\lambda$, ${0.0537}\lambda$, and ${0.0698}\lambda$ respectively. It proves that the torque sensitivity curves can well guide the real alignment process.

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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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Parameters	Value
Primary mirror	220 mm
Secondary mirror	36 mm
Exit pupil diameter	24 mm
Full field of view	0.2°
Radius of curvature of primary mirror	987.297 mm
Radius of curvature of secondary mirror	118.414 mm
Distance between the primary and secondary mirrors	434.439 mm
Distance tolerance between the secondary mirror and the primary mirror	$\pm 0 . 02 m m$
Tilt error of secondary mirror ( $X$ direction and $Y$ direction)	${\pm 0 . 02}^{\circ}$
Nonaxiality error ( $X$ direction and $Y$ direction)	$\pm 0 . 02 m m$
Alignment requirements	$R M S \leq λ / 8$

Coefficient	Polar Coordinates	Aberration
Z5	$ρ^{2} \cos 2 φ$	Astigmatism 0° or 90°
Z6	$ρ^{2} \sin 2 φ$	Astigmatism 45°
Z7	$(3 ρ^{2} - 2) ρ \cos φ$	Coma $X$
Z8	$(3 ρ^{2} - 2) ρ \sin φ$	Coma $Y$
Z9	$6 ρ^{4} - 6 ρ^{2} + 1$	Spherical aberration

NO.	Method	RMS	Z5	Z6	Z7	Z8	Z9
1	Before adjustment	1.78	0.34	−0.42	0.39	−0.52	0.18
	Coarse alignment	0.32	0.056	−0.043	0.037	−0.054	0.021
	Position sensitivity curve	0.0817	0.0128	−0.0153	0.0131	0.0241	−0.0164
	Torque sensitivity curve	0.0479	0.0082	−0.0076	−0.0011	0.0018	−0.0015
2	Before adjustment	1.98	−0.42	−0.79	0.37	−0.46	0.52
	Coarse alignment	0.31	−0.051	−0.048	0.072	−0.051	0.022
	Position sensitivity curve	0.1185	−0.0142	0.0231	−0.0072	−0.0092	0.0181
	Torque sensitivity curve	0.0537	−0.0052	0.0057	−0.0013	−0.0034	0.0022
3	Before adjustment	2.43	0.64	−0.73	−0.69	0.32	0.68
	Coarse alignment	0.38	0.049	−0.057	−0.064	0.071	0.014
	Position sensitivity curve	0.1350	0.0316	0.0271	−0.0242	−0.0064	0.0072
	Torque sensitivity curve	0.0698	0.0125	−0.0096	0.0053	−0.0025	−0.0026

Parameters	Value
Primary mirror	220 mm
Secondary mirror	36 mm
Exit pupil diameter	24 mm
Full field of view	0.2°
Radius of curvature of primary mirror	987.297 mm
Radius of curvature of secondary mirror	118.414 mm
Distance between the primary and secondary mirrors	434.439 mm
Distance tolerance between the secondary mirror and the primary mirror	$\pm 0 . 02 m m$
Tilt error of secondary mirror ( $X$ direction and $Y$ direction)	${\pm 0 . 02}^{\circ}$
Nonaxiality error ( $X$ direction and $Y$ direction)	$\pm 0 . 02 m m$
Alignment requirements	$R M S \leq λ / 8$

Coefficient	Polar Coordinates	Aberration
Z5	$ρ^{2} \cos 2 φ$	Astigmatism 0° or 90°
Z6	$ρ^{2} \sin 2 φ$	Astigmatism 45°
Z7	$(3 ρ^{2} - 2) ρ \cos φ$	Coma $X$
Z8	$(3 ρ^{2} - 2) ρ \sin φ$	Coma $Y$
Z9	$6 ρ^{4} - 6 ρ^{2} + 1$	Spherical aberration

Abstract

Data availability

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Figures (12)

Tables (3)

Equations (9)

Applied Optics