Optimization for calibration of large-scale optical measurement positioning system by using spherical constraint

Ziyue Zhao; Jigui Zhu; Bin Xue; Linghui Yang

doi:10.1364/JOSAA.31.001427

Journal of the Optical Society of America A
Vol. 31,
Issue 7,
pp. 1427-1435
(2014)
•https://doi.org/10.1364/JOSAA.31.001427

Optimization for calibration of large-scale optical measurement positioning system by using spherical constraint

Ziyue Zhao, Jigui Zhu, Bin Xue, and Linghui Yang

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Ziyue Zhao, Jigui Zhu, Bin Xue, and Linghui Yang, "Optimization for calibration of large-scale optical measurement positioning system by using spherical constraint," J. Opt. Soc. Am. A 31, 1427-1435 (2014)

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Abstract

The measurement accuracy of a large-scale optical measurement positioning system largely depends on the calibration procedure. A more reliable calibration approach for the system by using spherical constraints is presented in this paper, and both the adjustment model based on spherical constraint and the calculation method for the optimization are given. This approach can provide constraint in every direction of the system in the workspace and thereby estimate the orientation parameters more accurately than by using current methods. The experimental data show that by using the proposed method, which improves the accuracy of the depth direction, the average 3D coordinate error of the system compared with the laser tracker is about 0.18 mm in the whole workspace.

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	TP1	TP2	TP3	TP4	TP5
Measured length	1132.618	1133.296	1133.364	1133.334	1132.347
Standard length	1132.902	132.902	1132.902	1132.902	1132.902
Error	$- 0.284$	0.394	0.462	0.432	0.345

	TP1	TP2	TP3	TP4	TP5
Measured length	1132.755	1133.171	1133.201	1133.202	1133.072
Standard length	1132.902	132.902	1132.902	1132.902	1132.902
Error	$- 0.127$	0.269	0.299	0.300	0.170

	Calibration Using Two Spheres		Calibration Using Four Spheres		Calibration Using Eight Spheres
	Transmitter 2	Transmitter 3	Transmitter 2	Transmitter 3	Transmitter 2	Transmitter 3
r1	0.998313	$- 0.908825$	0.998267	$- 0.908881$	0.998258	$- 0.908889$
r2	0.055688	$- 0.416444$	0.055725	$- 0.416413$	0.055731	$- 0.416408$
r3	0.019337	0.022908	0.019351	0.022926	0.019352	0.022928
r4	$- 0.054918$	0.416632	$- 0.054878$	0.416667	$- 0.054877$	0.416668
r5	$- 0.997648$	$- 0.909080$	$- 0.997609$	$- 0.909031$	$- 0.997601$	$- 0.909025$
r6	0.042227	0.007885	0.042195	0.007858	0.042193	0.007857
r7	0.021613	0.017522	0.021647	0.017563	0.021657	0.017570
r8	0.041054	0.016692	0.041057	0.016694	0.041058	0.016695
r9	0.998954	0.999742	0.998929	0.999712	0.998922	0.999706
t1	559.12	1418.85	558.85	1418.59	558.60	1418.37
t2	13879.82	6874.74	13879.55	6874.54	13879.22	6874.16
t3	$- 5.37$	3.63	$- 5.32$	3.71	$- 5.23$	3.82

	Max	Min	Average	Standard Deviation
$x$	10135.65	10135.54	10135.60	0.02
$y$	$- 8940.42$	$- 8940.54$	$- 8940.48$	0.02
$z$	$- 38.07$	$- 38.11$	$- 38.09$	0.01

Point Name		$X$	$Y$	$Z$	$d X$	$d Y$	$d Z$	dMag
1	LOMPS	10135.60	$- 8940.48$	$- 38.09$	$- 0.05$	0.07	$- 0.02$	0.09
1	Tracker	10135.66	$- 8940.54$	$- 38.07$	$- 0.05$	0.07	$- 0.02$	0.09
2	LOMPS	14396.85	$- 6205.49$	$- 60.64$	0.05	0.10	$- 0.01$	0.11
2	Tracker	14396.81	$- 6205.59$	$- 60.62$	0.05	0.10	$- 0.01$	0.11
3	LOMPS	15785.56	$- 6718.42$	$- 68.29$	0.06	0.10	0.06	0.13
3	Tracker	15785.50	$- 6718.52$	$- 68.35$	0.06	0.10	0.06	0.13
4	LOMPS	15076.60	$- 4925.21$	$- 66.23$	0.01	$- 0.13$	0.11	0.17
4	Tracker	15076.59	$- 4925.08$	$- 66.34$	0.01	$- 0.13$	0.11	0.17
5	LOMPS	15185.98	$- 4638.66$	360.34	0.16	$- 0.10$	$- 0.03$	0.19
5	Tracker	15185.82	$- 4638.56$	360.37	0.16	$- 0.10$	$- 0.03$	0.19
6	LOMPS	14118.05	$- 6446.05$	368.62	0.16	0.18	$- 0.04$	0.24
6	Tracker	14117.89	$- 6446.23$	368.66	0.16	0.18	$- 0.04$	0.24
7	LOMPS	16070.75	$- 7123.32$	356.68	0.14	0.14	$- 0.08$	0.21
7	Tracker	16070.61	$- 7123.47$	356.77	0.14	0.14	$- 0.08$	0.21
8	LOMPS	10715.81	$- 6874.15$	379.66	0.16	0.11	$- 0.13$	0.23
8	Tracker	10715.65	$- 6874.26$	379.79	0.16	0.11	$- 0.13$	0.23
9	LOMPS	9052.23	$- 7334.39$	$- 386.63$	0.06	$- 0.22$	0.05	0.23
9	Tracker	9052.18	$- 7334.17$	$- 386.68$	0.06	$- 0.22$	0.05	0.23
10	LOMPS	13245.91	$- 6794.09$	$- 407.23$	$- 0.18$	0.09	0.05	0.21
10	Tracker	13246.10	$- 6794.18$	$- 407.28$	$- 0.18$	0.09	0.05	0.21
11	LOMPS	8789.74	$- 9268.70$	$- 382.92$	$- 0.17$	$- 0.18$	0.02	0.25
11	Tracker	8789.91	$- 9268.52$	$- 382.94$	$- 0.17$	$- 0.18$	0.02	0.25
Standard deviation					0.12	0.13	0.07	0.19
Average					0.18

Point Name		$X$	$Y$	$Z$	$d X$	$d Y$	$d Z$	dMag
1	LOMPS	10135.53	$- 8940.58$	$- 38.09$	$- 0.13$	$- 0.03$	$- 0.02$	0.13
1	Tracker	10135.66	$- 8940.54$	$- 38.07$	$- 0.13$	$- 0.03$	$- 0.02$	0.13
2	LOMPS	14396.94	$- 6205.45$	$- 60.64$	0.13	0.14	$- 0.01$	0.19
2	Tracker	14396.81	$- 6205.59$	$- 60.62$	0.13	0.14	$- 0.01$	0.19
3	LOMPS	15785.70	$- 6718.42$	$- 68.29$	0.20	0.10	0.06	0.23
3	Tracker	15785.50	$- 6718.52$	$- 68.35$	0.20	0.10	0.06	0.23
4	LOMPS	15076.68	$- 4925.24$	$- 66.19$	0.08	$- 0.16$	0.14	0.23
4	Tracker	15076.59	$- 4925.08$	$- 66.34$	0.08	$- 0.16$	0.14	0.23
5	LOMPS	15186.05	$- 4638.66$	360.37	0.23	$- 0.11$	$- 0.01$	0.26
5	Tracker	15185.82	$- 4638.56$	360.37	0.23	$- 0.11$	$- 0.01$	0.26
6	LOMPS	14118.23	$- 6445.91$	368.53	0.34	0.32	$- 0.14$	0.49
6	Tracker	14117.89	$- 6446.23$	368.66	0.34	0.32	$- 0.14$	0.49
7	LOMPS	16071.11	$- 7123.36$	356.69	0.50	0.10	$- 0.07$	0.51
7	Tracker	16070.61	$- 7123.47$	356.77	0.50	0.10	$- 0.07$	0.51
8	LOMPS	10715.80	$- 6874.12$	379.69	0.16	0.14	$- 0.09$	0.23
8	Tracker	10715.65	$- 6874.26$	379.79	0.16	0.14	$- 0.09$	0.23
9	LOMPS	9051.96	$- 7334.34$	$- 386.66$	$- 0.22$	$- 0.17$	0.03	0.28
9	Tracker	9052.18	$- 7334.17$	$- 386.68$	$- 0.22$	$- 0.17$	0.03	0.28
10	LOMPS	13245.87	$- 6794.09$	$- 407.16$	$- 0.22$	0.09	0.12	0.27
10	Tracker	13246.10	$- 6794.18$	$- 407.28$	$- 0.22$	0.09	0.12	0.27
11	LOMPS	8789.58	$- 9268.97$	$- 382.94$	$- 0.33$	$- 0.45$	$- 0.01$	0.56
11	Tracker	8789.91	$- 9268.52$	$- 382.94$	$- 0.33$	$- 0.45$	$- 0.01$	0.56
Standard Deviation					0.26	0.20	0.08	0.34
Average					0.31

Abstract

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Tables (6)

Equations (14)

Journal of the Optical Society of America A