Improved Adjustment Method Applied in Transformation of Laser Tracker

Tao Luo; Zhijun Qi; Wei Wang; Xiaoye He

doi:10.3788/CJL230555

Journals >Chinese Journal of Lasers >Volume 51 >Issue 2 >Page 0204001 > Article

Chinese Journal of Lasers
Vol. 51, Issue 2, 0204001 (2024)

Improved Adjustment Method Applied in Transformation of Laser Tracker

Tao Luo^1、3, Zhijun Qi², Wei Wang¹, and Xiaoye He^1、*

Author Affiliations

¹National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, Anhui , China

²School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, Hubei , China

³Institute of Advanced Science Facilities, Shenzhen (IASF), Shenzhen 518107, Guangdong , China

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DOI: 10.3788/CJL230555 Cite this Article Set citation alerts

Tao Luo, Zhijun Qi, Wei Wang, Xiaoye He. Improved Adjustment Method Applied in Transformation of Laser Tracker[J]. Chinese Journal of Lasers, 2024, 51(2): 0204001 Copy Citation Text

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Fig. 1. Coordinate system of laser tracker

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Fig. 2. Flow chart of solution to SCTLS

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Fig. 3. Schematic diagram of measurement by different stations

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Fig. 4. Absolute bias in 100 simulations. (a)

ε (\hat{R})

; (b)

ε (\hat{t})

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Fig. 5. Errors of points after transformation

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Items	WTLS	SCTLS
Functional model	$y + e_{y} = (A + E_{A}) ξ$	Eqs. (2) and (5)
Statistics model	$b l k d i a g (Q_{A}, Q_{y})$	$Q_{e e}$
Dimension of $Q$	$13 n \times 13 n$	$6 n \times 6 n$
Character of $Q$	Off-diagonal	Diagonal
Expression of $e$	$e = {[v e c^{T} (E_{A}) e_{y}^{T}]}^{T}$	Eq. (7)
Dimension of $e$	$13 n \times 1$	$6 n \times 1$
Repeated elements	Different	Same
Character of ${\hat{R}}_{1}$	Non-orthogonal	Orthogonal
Number of independent elements of $ξ$	12	7
Precision evaluation	None	Eq. (19)

Table 1. Comparison between WTLS and SCTLS

Method	$ε (\hat{R})$ /10^-4	$ε (\hat{t}) / m m$
SCTLS	1.144	0.196
WTLS	1.776	0.315
LS	2.698	0.510

Table 2. Average of absolute bias in simulation

Number	Name	Laser tracker A observation			Laser tracker B observation
Number	Name	$d$ /mm	$α$ /（ $^{\circ}$ ）	$β$ /（ $^{\circ}$ ）	$d$ /mm	$α$ /（ $^{\circ}$ ）	$β$ /（ $^{\circ}$ ）
1	P2	5130.34	-149.7184	84.7385	3679.01	-89.9996	55.3951
2	P3	1804.06	-97.0605	74.8887	3679.01	-0.0035	55.3948
3	P4	2728.38	113.2676	80.0798	3678.79	89.9947	55.3928
4	HCG07	1410.30	121.7104	174.2693	2677.13	37.3065	85.3736
5	HCG08	4836.53	173.0513	106.8160	1969.89	-164.6853	83.5931
6	HCG09	4286.10	-171.1741	109.0869	1404.26	-122.2511	81.0910
7	HCG10	1819.21	123.8746	140.3887	2334.53	59.5167	84.6475
8	HCG11	3126.54	176.5045	116.5998	317.92	137.0496	46.4115

Table 3. Observations from laser tracker in Hefei Light Source

Tao Luo, Zhijun Qi, Wei Wang, Xiaoye He. Improved Adjustment Method Applied in Transformation of Laser Tracker[J]. Chinese Journal of Lasers, 2024, 51(2): 0204001

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