Hidden point measurement method of laser tracker and precision analysis based on sphere center fitting

Keliang DING; Xi ZHANG; Zhenqiang HE; Tong WANG; Zhiyong KE; Jing LIANG; Na MA; Bo LI; Zhiduo LI

doi:10.3788/IRLA20240292

Infrared and Laser Engineering, Volume. 53, Issue 11, 20240292(2024)

Hidden point measurement method of laser tracker and precision analysis based on sphere center fitting

Keliang DING¹, Xi ZHANG¹, Zhenqiang HE^2,3, Tong WANG^2,3,4,5、*, Zhiyong KE^2,3, Jing LIANG^2,3, Na MA^2,3, Bo LI^2,3, and Zhiduo LI^2,3,6

Author Affiliations

¹School of Geomatics and Urban Spatial Informatics, Beijing University of Civil Engineering and Architecture, Beijing 102616, China

²Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

³Spallation Neutron Source Science Center, Dongguan 523803, China

⁴Institute of Microelectronics of the Chinese Academy of Sciences, Beijing 100029, China

⁵University of Chinese Academy of Sciences, Beijing 100049, China

⁶National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230000, China

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Figures & Tables(11)

Fig. 1. (a) Simulated standard measurement scene; (b) Relationship between different angles

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Fig. 2. (a) Hidden fiducial bar; (b) Radiation zone hidden fiducial bar; (c) Measurement method in radiation area

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Fig. 3. Simulated error sequence

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Fig. 4. Different radius spherical point simulation

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Fig. 5. Measurement site

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Table 1. Time take by different ball fitting
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Table 1. Time take by different ball fitting
Method Time/ms
Gauss-Newton 4.8857（+1.1352）
Improved 1.1352

Table 2. The impact of changing the radius of the sphere on the fitting accuracy
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Table 2. The impact of changing the radius of the sphere on the fitting accuracy
Method Parameter R/m
0.5 1 1.5 2 3
Improved MEAN/μm 26.89 26.74 26.64 26.59 26.87
RMSE/μm 29.77 29.64 29.59 29.63 30.19
Gauss-Newton MEAN/μm 26.89 26.74 26.64 26.59 26.87
RMSE/μm 29.77 29.64 29.59 29.63 30.19

Table 3. Four groups of experimental site distribution schemes

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Table 3. Four groups of experimental site distribution schemes

Plan	Horizontal angle range	Zenith angle
Scheme 1	0°-360°	60°
Scheme 2		30°
Scheme 3		20°
Scheme 4		10°
Scheme 5		5°

Scheme 6	180°-360°	60°
Scheme 7		30°
Scheme 8		20°
Scheme 9		10°
Scheme 10		5°

Scheme 11	180°-270°	60°
Scheme 12		30°
Scheme 13		20°
Scheme 14		10°
Scheme 15		5°

Table 4. The impact of point distribution on fitting accuracy

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Table 4. The impact of point distribution on fitting accuracy

Plan	Improved		Gauss-Newton
Plan	MEAN/μm	RMSE/μm	MEAN/μm	RMSE/μm
Scheme 1	26.63	29.53	26.63	29.53
Scheme 2	26.74	29.64	26.74	29.64
Scheme 3	26.76	29.67	26.76	29.67
Scheme 4	26.78	29.68	26.78	29.68
Scheme 5	26.78	29.69	26.78	29.69
Schemes6	26.79	29.67	26.79	29.67
Scheme 7	26.82	29.71	26.82	29.71
Scheme 8	26.81	29.71	26.81	29.71
Scheme 9	26.80	29.70	26.80	29.70
Scheme 10	26.79	29.70	26.79	29.70
Scheme 11	28.07	30.62	28.07	30.62
Scheme 12	27.33	29.93	27.33	29.93
Scheme 13	27.02	29.66	27.02	29.66
Scheme 14	26.71	29.38	26.71	29.38
Scheme 15	26.56	29.25	26.56	29.25

Table 5. Fitting result comparison table

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Table 5. Fitting result comparison table

Point	Methods of acquisition	X/μm	Y/μm	Z/μm	R/μm
1#	Direct measurement value	2614725.75	−354785.00	−590587.34	300000.00
	SA fitting	2614722.84	−354787.13	−590575.72	299997.78
	Deviation	2.91	2.14	11.62	2.22
	Improved fitting	2614722.85	−354787.13	−590575.73	299997.79
	Deviation	2.90	2.13	11.61	2.21
2#	Direct measurement value	2610612.45	−434959.85	−590587.44	300000.00
	SA fitting	2610593.63	−434946.94	−590553.26	299973.59
	Deviation	18.82	12.91	34.18	26.41
	Improved fitting	2610593.63	−434946.93	−590553.25	299973.59
	Deviation	18.82	12.92	34.18	26.41
3#	Direct measurement value	2552549.28	472.69	−432385.57	300000.00
	SA fitting	2552558.63	463.68	−432364.15	299987.77
	Deviation	9.35	9.01	21.42	12.23
	Improved fitting	2552558.62	463.68	−432364.15	299987.77
	Deviation	9.34	9.01	21.42	12.23
4#	Direct measurement value	2552545.96	462.49	−432394.14	300000.00
	SA fitting	2552548.54	461.41	−432382.46	300004.33
	Deviation	2.58	1.08	11.68	4.33
	Improved fitting	2552548.54	461.41	−432382.47	300004.33
	Deviation	2.58	1.08	11.67	4.33

Table 6. Comparison of component errors
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Table 6. Comparison of component errors
Method MEAN/μm RMSE/μm
SA 22.58 25.54
Improved 22.57 25.53

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Keliang DING, Xi ZHANG, Zhenqiang HE, Tong WANG, Zhiyong KE, Jing LIANG, Na MA, Bo LI, Zhiduo LI. Hidden point measurement method of laser tracker and precision analysis based on sphere center fitting[J]. Infrared and Laser Engineering, 2024, 53(11): 20240292

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