Alignment Method of a Large Aperture Telescope Based on the Eigen Coefficient

Qiongxin Liang; Jinlong Huang; Nian Pan; Kewei Chen

doi:10.3788/LOP202158.1211001

Journals >Laser & Optoelectronics Progress >Volume 58 >Issue 12 >Page 1211001 > Article

Laser & Optoelectronics Progress
Vol. 58, Issue 12, 1211001 (2021)

Alignment Method of a Large Aperture Telescope Based on the Eigen Coefficient

Qiongxin Liang^1、2, Jinlong Huang^1、*, Nian Pan¹, and Kewei Chen¹

Author Affiliations

¹Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China

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

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DOI: 10.3788/LOP202158.1211001 Cite this Article Set citation alerts

Qiongxin Liang, Jinlong Huang, Nian Pan, Kewei Chen. Alignment Method of a Large Aperture Telescope Based on the Eigen Coefficient[J]. Laser & Optoelectronics Progress, 2021, 58(12): 1211001 Copy Citation Text

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Fig. 1. Optical principle of wavefront curvature sensor

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Fig. 2. optical system structures. (a) 1 m on-axis three-mirror optical system structure; (b) 8.4 m LSST optical system structure

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Fig. 3. Relationship between eigenmode coefficient on the annular pupil and the degrees of freedom. (a) D_x; (b) D_y; (c) T_x; (d) T_y; (e) D_z

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Fig. 4. Axial decentered spot pattern of secondary mirror. (a) Front defocusing plane; (b) focal plane; (c) back defocusing plane

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Fig. 5. Horizontal decentered spot pattern of wavefront curvature sensor. (a) Front defocusing plane; (b) focal plane; (c) back defocusing plane

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Fig. 6. Tilted spot pattern of wavefront curvature sensor. (a) Front defocusing plane; (b) focal plane; (c) back defocusing plane

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Fig. 7. Defocus spot pattern of wavefront curvature sensor. (a) Front defocusing plane; (b) focal plane; (c) back defocusing plane

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Fig. 8. Horizontal decentered or tilted spot pattern of secondary mirror. (a) Front defocusing plane; (b) focal plane; (c) back defocusing plane

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α_k	α₁	α₂	α₆	α₇	α₈	α₁₃	α₁₄	α₂₂	α₂₃	α₂₄
n	1	1	2	2	2	3	3	4	4	4
m	1	-1	1	-1	0	1	-1	1	-1	0

Table 1. Eigenmode coefficient on the annular pupil

α_i	D_x	D_y	D_z	T_x	T_y
α₁	0.48	0	0.06	0.35	-10.88
α₂	0.01	0.51	0.04	10.44	-0.04
α₆	-1.49	0	-0.01	-0.02	21.68
α₇	0	-1.51	-0.01	-21.31	-0.04
α₈	0	0	-3.13	0	0.04
α₁₃	0.03	0	0	0.08	-1.21
α₁₄	0	0.04	0	1.13	-0.02
α₂₂	-0.42	0	-0.02	-0.01	6.41
α₂₃	0	-0.42	0	-6.29	-0.01
α₂₄	0	0	-1.28	0	0.01

Table 2. Eigenmode coefficient sensitivity matrix of design state

Parameter	1	2	3	4
D_z /mm	0.1570	-0.1140	-0.1080	0.0830
T_x /(°)	0.0820	0.0980	-0.1450	-0.1250
T_y /(°)	0.1130	-0.1060	0.1090	0.0990
D_x /mm	-0.0180	0.1230	-0.1640	0.0260
D_y /mm	0.0340	0.1150	0.2380	0.0310

Table 3. Misalignment introduced by the secondary mirror

Parameter		Before alignment	After alignment
Parameter		Before alignment	Calculated value 1		Residual value 1		Calculated value 2		Residual value 2
1	D_z /mm	0.1570		0.1562		0.0008		0.0122		-0.0114
	T_x /(°)	0.0820		0.0617		0.0203		0.0207		-0.0004
	T_y /(°)	0.1130		0.0891		0.0239		0.0238		0.0001
2	D_z /mm	-0.1140		-0.0797		-0.0343		-0.0362		0.0019
	T_x /(°)	0.0980		0.1168		-0.0188		-0.0100		-0.0088
	T_y /(°)	-0.1060		-0.1066		0.0006		-0.0078		0.0084
3	D_z /mm	-0.1080		-0.0903		-0.0177		-0.0174		-0.0003
	T_x /(°)	-0.1450		-0.1525		0.0075		0.0234		-0.0159
	T_y /(°)	0.1090		0.1073		0.0017		0.0129		-0.0112
4	D_z /mm	0.0830		0.0134		0.0696		0.0711		-0.0015
	T_x /(°)	-0.1250		-0.1170		-0.0080		-0.0074		-0.0006
	T_y /(°)	0.0990		0.0846		0.0144		0.0139		0.0005

Table 4. Misalignment before and after A1 alignment

Parameter		Before alignment	After alignment
Parameter		Before alignment	Calculated value 1		Residual value 1		Calculated value 2		Residual value 2
1	D_x /mm	-0.0180		-0.0121		-0.0059		-0.0086		0.0027
1	D_y /mm	0.0340		0.0255		0.0085		0.0102		-0.0017
2	D_x /mm	0.1230		0.0560		0.0670		0.0234		0.0436
2	D_y /mm	0.1150		0.0527		0.0623		0.0110		0.0513
3	D_x /mm	-0.1640		-0.0792		-0.0848		-0.0250		-0.0598
3	D_y /mm	0.2380		0.1247		0.1133		0.0291		0.0842
4	D_x /mm	0.0260		0.0164		0.0096		0.0126		-0.0030
4	D_y /mm	0.0310		0.0198		0.0112		0.0084		0.0028

Table 5. Misalignment before and after A2 alignment

Qiongxin Liang, Jinlong Huang, Nian Pan, Kewei Chen. Alignment Method of a Large Aperture Telescope Based on the Eigen Coefficient[J]. Laser & Optoelectronics Progress, 2021, 58(12): 1211001

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