Micro-motion detection of the 3-DOF precision positioning stage based on iterative optimized template matching

Hai Li; Xianmin Zhang; Benliang Zhu; Yihua Lu; Heng Wu

doi:10.1364/AO.56.009435

Applied Optics
Vol. 56,
Issue 34,
pp. 9435-9443
(2017)
•https://doi.org/10.1364/AO.56.009435

Micro-motion detection of the 3-DOF precision positioning stage based on iterative optimized template matching

Hai Li, Xianmin Zhang, Benliang Zhu, Yihua Lu, and Heng Wu

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Hai Li, Xianmin Zhang, Benliang Zhu, Yihua Lu, and Heng Wu, "Micro-motion detection of the 3-DOF precision positioning stage based on iterative optimized template matching," Appl. Opt. 56, 9435-9443 (2017)

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Table of Contents Category
- Instrumentation, Measurement, and Metrology
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About this Article
History
- Original Manuscript: June 27, 2017
- Revised Manuscript: September 28, 2017
- Manuscript Accepted: October 30, 2017
- Published: November 27, 2017

Abstract

This study presents a method for micro-motion detection of the three-degrees-of-freedom (3-DOF; $x$ , $y$ , $θ_{z}$ ) precision positioning stage (PPS) based on iterative optimized template matching (IOTM). In this method, a micro-vision system (MVS) is constructed and employed to capture magnified images of the measured PPS’s surface with high quality. In addition, an efficient and accurate IOTM algorithm, which includes a pyramid hierarchical matching step for generating the initial guess and an iterative searching step for 3-DOF fine matching, is proposed to detect the micro-motion of the 3-DOF PPS. The simulation results show that the locating accuracy of the translation component (TC) and rotation component of this algorithm can respectively reach 0.01 pixels and 0.01 deg when the image quality is high and the initial guess is close to the real location. Measurement tests of a nano-PPS verify that the proposed method is practical and effective for 3-DOF micro-motion detection and the absolute accuracy of the TC of the MVS can easily reach the nanometer level.

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Initial Guess	Matching Results [Ideal Location (513, 513, 0)]
$(p_{x 0}, p_{y 0}, θ_{0})$	$σ^{2} = 0$	$σ^{2} = 0.002$	$σ^{2} = 0.004$	$σ^{2} = 0.008$
(500, 500, 0)	(513.00, 513.00, −0.0009)	(513.00, 513.00, −0.0012)	(513.00, 513.00, −0.0009)	(513.00, 513.00, −0.0004)
(500, 500, 2)	(513.00, 513.00, −0.0070)	(513.00, 513.00, −0.0068)	(513.00, 513.00, −0.0050)	(513.00, 513.00, −0.0060)
(500, 500, 4)	(513.00, 513.01, −0.0236)	(513.00, 513.01, −0.0234)	(513.00, 513.00, −0.0231)	(513.00, 513.00, −0.0207)
(500, 500, 6)	(513.00, 513.01, −0.0508)	(513.00, 513.01, −0.0501)	(513.00, 513.01, −0.0486)	(512.00, 513.01, −0.0472)
(500, 500, 8)	(513.00, 513.01, −0.1000)	(513.00, 513.01, −0.0989)	(513.00, 513.01, −0.0979)	(512.00, 513.01, −0.0973)
(500, 500, 10)	(512.99, 513.00, −0.1813)	(512.99, 513.00, −0.1782)	(513.00, 513.00, −0.1787)	(512.99, 513.00, −0.1759)

Time Cost for Each Iteration		Template Resolution
Time Cost for Each Iteration		$100 \times 100$	$150 \times 150$	$200 \times 200$	$250 \times 250$
Image resolution	$400 \times 400$	7.5	11.4	17.1	25.3
	$800 \times 800$	14.9	19.1	25.6	32.3
	$1200 \times 1200$	29.7	34.2	39.3	46.8

No.	Input Angle	Measure Results	Deviation	Standard Error
1	0	0.0015	0.0015	0.0044
2	2	1.9813	−0.0187	0.0070
3	4	3.9786	−0.0214	0.0003
4	6	5.9705	−0.0295	0.0070
5	8	7.9753	−0.0247	0.0024
6	10	9.9673	−0.0327	0.0043
7	12	11.9866	−0.0134	0.0011
8	14	13.9986	−0.0014	0.0008
9	16	16.0009	0.0009	0.0012
10	18	18.0007	0.0007	0.0008
11	20	20.0107	0.0107	0.0026

No.	Input Disp.	Disp. MVS	Disp. LIM	Deviation	Parasitic Angle	Angle std
Unit	μm	μm	μm	nm	deg	deg
1	0	0	0	0	0.0002	0.0005
2	10	10.162	10.108	54	0.0030	0.0013
3	20	20.296	20.357	−60	0.0029	0.0006
4	30	30.425	30.445	−20	−0.0025	0.0004
5	40	40.550	40.655	−106	−0.0154	0.0007
6	50	50.683	50.675	9	−0.0229	0.0018
7	60	60.822	60.817	5	−0.0359	0.0015
8	70	70.931	70.874	56	−0.0564	0.0008
9	80	81.019	80.968	50	−0.0726	0.0018

Initial Guess	Matching Results [Ideal Location (513, 513, 0)]
$(p_{x 0}, p_{y 0}, θ_{0})$	$σ^{2} = 0$	$σ^{2} = 0.002$	$σ^{2} = 0.004$	$σ^{2} = 0.008$
(500, 500, 0)	(513.00, 513.00, −0.0009)	(513.00, 513.00, −0.0012)	(513.00, 513.00, −0.0009)	(513.00, 513.00, −0.0004)
(500, 500, 2)	(513.00, 513.00, −0.0070)	(513.00, 513.00, −0.0068)	(513.00, 513.00, −0.0050)	(513.00, 513.00, −0.0060)
(500, 500, 4)	(513.00, 513.01, −0.0236)	(513.00, 513.01, −0.0234)	(513.00, 513.00, −0.0231)	(513.00, 513.00, −0.0207)
(500, 500, 6)	(513.00, 513.01, −0.0508)	(513.00, 513.01, −0.0501)	(513.00, 513.01, −0.0486)	(512.00, 513.01, −0.0472)
(500, 500, 8)	(513.00, 513.01, −0.1000)	(513.00, 513.01, −0.0989)	(513.00, 513.01, −0.0979)	(512.00, 513.01, −0.0973)
(500, 500, 10)	(512.99, 513.00, −0.1813)	(512.99, 513.00, −0.1782)	(513.00, 513.00, −0.1787)	(512.99, 513.00, −0.1759)

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Applied Optics