On-line six-degree-of-freedom errors measurement and compensation for XY stages

Rongwei LIN; Zhenying CHENG; Yaxiong HE; Jie LI; Ruijun LI

doi:10.37188/OPE.20233112.1761

Optics and Precision Engineering, Volume. 31, Issue 12, 1761(2023)

On-line six-degree-of-freedom errors measurement and compensation for XY stages

Rongwei LIN... Zhenying CHENG*, Yaxiong HE, Jie LI and Ruijun LI |Show fewer author(s)

Anhui Province Key Laboratory of Measuring Theory and Precision Instrument，School of Instrument Science and Opto-electronic Engineering，Hefei University of Technology，Hefei230009，China

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Figures & Tables(19)

Fig. 1. Volumetric positional errors of functional point caused by 6-DOF errors

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Fig. 2. Positioning errors caused by non-compliance with Abbe principle

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Fig. 3. Straightness measuring errors caused by non-compliance with Bryan principle

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Fig. 4. Diagram of 6-DOF errors measurement methods

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Fig. 5. Diagram of relationship among measuring point， functional point and working volume of a XY stage

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Fig. 6. Schematic of 6-DOF errors measurement system

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Fig. 7. Schematic of measuring principle of PMI-X、PMI-Y and PMI-Z

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Fig. 8. Schematic of the measuring principle of angular errors

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Fig. 9. Photo of 6-DOF errors measurement system

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Fig. 10. Test results of the resolution of PMI-X，PMI-Y and PMI-Z

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Fig. 11. Schematic of calibration of PMIs

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Fig. 12. Schematic of calibration of Acs

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Fig. 13. Test results of the resolution of AC1 and AC2

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Fig. 14. The results of the stability test of the system

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Fig. 15. Schematic of experimental setup of positional accuracy test for the stage

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Fig. 16. Volumetric positional errors in RFP

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Table 1. Calibration results of PMI-X，PMI-Y and PMI-Z

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Table 1. Calibration results of PMI-X，PMI-Y and PMI-Z

位移/μm						残差/nm
SIOS激光干涉仪			位移测量单元			D_SIOS-X- D_PMI-X	D_SIOS-Y- D_PMI-Y	D_SIOS-Z- D_PMI-Z
D_SIOS-X	D_SIOS-Y	D_SIOS-Z	D_PMI-X	D_PMI-Y	D_PMI-Z	D_SIOS-X- D_PMI-X	D_SIOS-Y- D_PMI-Y	D_SIOS-Z- D_PMI-Z
1 000.229	999.112	999.599	1 000.236	999.117	999.601	-7	-5	-2
1 999.643	2 000.879	2 000.015	1 999.649	2 000.873	2 000.010	-5	6	5
3 000.049	3 000.718	3 000.454	3 000.058	3 000.728	3 000.447	-9	-10	7
4 000.123	4 001.318	3 999.816	4 000.116	4 001.316	3 999.817	8	2	-1
4 999.114	5 000.487	4 999.479	4 999.100	5 000.478	4 999.494	14	9	-15
5 999.586	5 999.942	5 999.629	5 999.576	5 999.937	5 999.628	10	5	1
7 001.210	6 999.785	6 999.104	7 001.206	6 999.786	6 999.102	4	-1	2
7 999.961	7 998.359	7 999.430	7 999.967	7 998.366	7 999.433	-6	-7	-3
8 999.394	8 998.623	8 999.875	8 999.390	8 998.619	8 999.874	4	4	1
9 999.273	9 999.597	9 999.996	9 999.287	9 999.601	9 999.992	-14	-4	4
残余标准差 $σ$ /nm						8.9	5.9	5.7

Table 2. Calibration results of AC1 and AC2

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Table 2. Calibration results of AC1 and AC2

角度/arcsec				残差/arcsec
角度产生装置	角度测量单元			$θ_{A G D}$ - $θ_{X}$	$θ_{A G D}$ - $θ_{Y}$	$θ_{A G D}$ - $θ_{Z}$
$θ_{A G D}$	$θ_{X}$	$θ_{Y}$	$θ_{Z}$	$θ_{A G D}$ - $θ_{X}$	$θ_{A G D}$ - $θ_{Y}$	$θ_{A G D}$ - $θ_{Z}$
30.00	29.62	29.95	29.55	0.38	0.05	0.45
24.00	23.95	24.17	24.12	0.05	-0.17	-0.12
18.00	18.14	18.02	18.6	-0.14	-0.02	-0.60
12.00	12.22	12.06	12.6	-0.22	-0.06	-0.60
6.00	6.22	6.02	6.55	-0.22	-0.02	-0.55
0.00	0.15	-0.05	0.50	-0.15	0.05	-0.50
-6.00	-5.92	-6.13	-5.73	-0.08	0.13	-0.27
-12.00	-11.93	-12.2	-11.84	-0.07	0.20	-0.16
-18.00	-18.12	-18.17	-17.82	0.12	0.17	-0.18
-24.00	-24.15	-23.99	-23.92	0.15	-0.01	-0.08
-30.00	-30.07	-29.65	-29.73	0.07	-0.35	-0.27
残余标准差 $σ$ /aresec				0.18	0.15	0.29

Table 3. Standard uncertainty of the measuring units

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Table 3. Standard uncertainty of the measuring units

不确定度来源	分布	传递系数	标准不确定度
不确定度来源	分布	传递系数	$u (Δ X)$ /nm	$u (Δ Y)$ /nm	$u (Δ Z)$ /nm	$u (θ_{x})$ /arcsec	$u (θ_{y})$ /arcsec	$u (θ_{z})$ /arcsec
合成标准不确定度			12.7	16.0	11.8	0.27	0.25	0.45
分辨力	均匀	1	$2 / \sqrt[]{3}$	$2 / \sqrt[]{3}$	$2 / \sqrt[]{3}$	$0.01 / \sqrt[]{3}$	0.01/ $\sqrt[]{3}$	0.01/ $\sqrt[]{3}$
示值误差	均匀	1	14/ $\sqrt[]{3}$	10/ $\sqrt[]{3}$	15/ $\sqrt[]{3}$	0.38/ $\sqrt[]{3}$	0.35/ $\sqrt[]{3}$	0.60/ $\sqrt[]{3}$
重复性	—	1	8.9	5.9	5.7	0.18	0.15	0.29
稳定性	均匀	1	6/ $\sqrt[]{3}$	24/ $\sqrt[]{3}$	10/ $\sqrt[]{3}$	0.11/ $\sqrt[]{3}$	0.12/ $\sqrt[]{3}$	0.08/ $\sqrt[]{3}$
参考仪器	—	1	0.1	0.1	0.1	0.02	0.02	0.02

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Rongwei LIN, Zhenying CHENG, Yaxiong HE, Jie LI, Ruijun LI. On-line six-degree-of-freedom errors measurement and compensation for XY stages[J]. Optics and Precision Engineering, 2023, 31(12): 1761

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