Abstract

Linear laser encoders have been widely used for precision positioning control of a linear stage. We develop a five-degrees-of-freedom (5-DOF) laser linear encoder to simultaneously measure the position, straightness, pitch, roll, and yaw errors along one moving axis. This study integrates the circular polarized interferometric technique with the three-dimensional diffracted ray-tracing method to develop a novel laser encoder with 5-DOF. The phases encoded within the +1 and 1 order diffraction lights reflected from the diffraction grating are decoded by the circular polarized interferometric technique to measure the linear displacement when the diffraction grating moves. The three-dimensional diffracted ray tracing of the +1- and 1-order diffraction lights induced by the motion errors of the moved grating were analyzed to calculate the other motion errors based on the detection of light spots on two quadrant photodiode detectors. The period of the grating is 0.83μm and the experimental results show that the measurement accuracy was better than ±0.3μm/±41μm for straightness, ±1arcsec/±215arcsec for angular error components, and ±160nm/2mm for linear displacement.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  15. J. A. Terrence, Applied Numerical Methods for Engineers (Wiley, 1993).
  16. R. M. Murray, Z. Li, and S. S. Sastry, A Mathematical Introduction to Robotic Manipulation (CRC Press, 2000).

2008

L. M. Sanchez-Brea and T. Morlanes “Metrological errors in optical encoders,” Meas. Sci. Technol. 19, 115104(2008).
[CrossRef]

2007

H. L. Huang, C. H. Liu, W. Y. Jywe, M. S. Wang, and T. H. Fang, “Development of a three-degree-of-freedom laser linear encoder for error measurement of a high precision stage,” Rev. Sci. Instrum. 78, 066103 (2007).
[CrossRef] [PubMed]

2005

2004

2000

D. Crespo, J. Alonso, and E. Bernabeu, “Reflection optical encoders as three-grating moiré systems,” Appl. Opt. 39, 3805-3813 (2000).
[CrossRef]

D. Crespo, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. 39, 817-824 (2000).
[CrossRef]

1995

J.-D. Lin and H. B. Kuo, “Development of a new optical scale system by the diffractive phase interference method,” Meas. Sci. Technol. 6, 293-296 (1995).
[CrossRef]

V. Greco, G. Molesini, and F. Quercioli, “Accurate polarization interferometer,” Rev. Sci. Instrum. 66, 3729-3734 (1995).
[CrossRef]

1981

Alonso, J.

Bernabeu, E.

D. Crespo, J. Alonso, and E. Bernabeu, “Reflection optical encoders as three-grating moiré systems,” Appl. Opt. 39, 3805-3813 (2000).
[CrossRef]

D. Crespo, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. 39, 817-824 (2000).
[CrossRef]

Chang, Y. C.

Chen, J. Y.

Chen, S. J.

Crespo, D.

D. Crespo, J. Alonso, and E. Bernabeu, “Reflection optical encoders as three-grating moiré systems,” Appl. Opt. 39, 3805-3813 (2000).
[CrossRef]

D. Crespo, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. 39, 817-824 (2000).
[CrossRef]

Fang, T. H.

H. L. Huang, C. H. Liu, W. Y. Jywe, M. S. Wang, and T. H. Fang, “Development of a three-degree-of-freedom laser linear encoder for error measurement of a high precision stage,” Rev. Sci. Instrum. 78, 066103 (2007).
[CrossRef] [PubMed]

Gonda, S.

Greco, V.

V. Greco, G. Molesini, and F. Quercioli, “Accurate polarization interferometer,” Rev. Sci. Instrum. 66, 3729-3734 (1995).
[CrossRef]

Heydemann, P. L. M.

Huang, H. L.

H. L. Huang, C. H. Liu, W. Y. Jywe, M. S. Wang, and T. H. Fang, “Development of a three-degree-of-freedom laser linear encoder for error measurement of a high precision stage,” Rev. Sci. Instrum. 78, 066103 (2007).
[CrossRef] [PubMed]

Huang, Q.

Jywe, W. Y.

H. L. Huang, C. H. Liu, W. Y. Jywe, M. S. Wang, and T. H. Fang, “Development of a three-degree-of-freedom laser linear encoder for error measurement of a high precision stage,” Rev. Sci. Instrum. 78, 066103 (2007).
[CrossRef] [PubMed]

Keem, T.

Kuo, H. B.

J.-D. Lin and H. B. Kuo, “Development of a new optical scale system by the diffractive phase interference method,” Meas. Sci. Technol. 6, 293-296 (1995).
[CrossRef]

Kurosawa, T.

Lee, C. K.

Li, Z.

R. M. Murray, Z. Li, and S. S. Sastry, A Mathematical Introduction to Robotic Manipulation (CRC Press, 2000).

Lin, J.-D.

J.-D. Lin and H. B. Kuo, “Development of a new optical scale system by the diffractive phase interference method,” Meas. Sci. Technol. 6, 293-296 (1995).
[CrossRef]

Liu, C. H.

H. L. Huang, C. H. Liu, W. Y. Jywe, M. S. Wang, and T. H. Fang, “Development of a three-degree-of-freedom laser linear encoder for error measurement of a high precision stage,” Rev. Sci. Instrum. 78, 066103 (2007).
[CrossRef] [PubMed]

Misumi, I.

Molesini, G.

V. Greco, G. Molesini, and F. Quercioli, “Accurate polarization interferometer,” Rev. Sci. Instrum. 66, 3729-3734 (1995).
[CrossRef]

Morlanes, T.

L. M. Sanchez-Brea and T. Morlanes “Metrological errors in optical encoders,” Meas. Sci. Technol. 19, 115104(2008).
[CrossRef]

D. Crespo, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. 39, 817-824 (2000).
[CrossRef]

Murray, R. M.

R. M. Murray, Z. Li, and S. S. Sastry, A Mathematical Introduction to Robotic Manipulation (CRC Press, 2000).

Quercioli, F.

V. Greco, G. Molesini, and F. Quercioli, “Accurate polarization interferometer,” Rev. Sci. Instrum. 66, 3729-3734 (1995).
[CrossRef]

Sanchez-Brea, L. M.

L. M. Sanchez-Brea and T. Morlanes “Metrological errors in optical encoders,” Meas. Sci. Technol. 19, 115104(2008).
[CrossRef]

Sastry, S. S.

R. M. Murray, Z. Li, and S. S. Sastry, A Mathematical Introduction to Robotic Manipulation (CRC Press, 2000).

Terrence, J. A.

J. A. Terrence, Applied Numerical Methods for Engineers (Wiley, 1993).

Wang, M. S.

H. L. Huang, C. H. Liu, W. Y. Jywe, M. S. Wang, and T. H. Fang, “Development of a three-degree-of-freedom laser linear encoder for error measurement of a high precision stage,” Rev. Sci. Instrum. 78, 066103 (2007).
[CrossRef] [PubMed]

Wang, Y. F.

Wu, C. C.

Wu, J. W. J.

Yu, L. B.

Appl. Opt.

Meas. Sci. Technol.

J.-D. Lin and H. B. Kuo, “Development of a new optical scale system by the diffractive phase interference method,” Meas. Sci. Technol. 6, 293-296 (1995).
[CrossRef]

L. M. Sanchez-Brea and T. Morlanes “Metrological errors in optical encoders,” Meas. Sci. Technol. 19, 115104(2008).
[CrossRef]

Opt. Eng.

D. Crespo, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. 39, 817-824 (2000).
[CrossRef]

Rev. Sci. Instrum.

H. L. Huang, C. H. Liu, W. Y. Jywe, M. S. Wang, and T. H. Fang, “Development of a three-degree-of-freedom laser linear encoder for error measurement of a high precision stage,” Rev. Sci. Instrum. 78, 066103 (2007).
[CrossRef] [PubMed]

V. Greco, G. Molesini, and F. Quercioli, “Accurate polarization interferometer,” Rev. Sci. Instrum. 66, 3729-3734 (1995).
[CrossRef]

Other

J. A. Terrence, Applied Numerical Methods for Engineers (Wiley, 1993).

R. M. Murray, Z. Li, and S. S. Sastry, A Mathematical Introduction to Robotic Manipulation (CRC Press, 2000).

Hewlett Packard Co., “Optics and laser heads for laser interferometer positioning systems,” product overview (2000).

Catalog, SIOS Messtechnik Gmbh (2003).

http://www.renishaw.com.

Catalog, Heidenhain, http://www.heidenhain.com/main.html.

http://www.sonysms.com.

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Figures (12)

Fig. 1
Fig. 1

Optical design configuration of the 5-DOF laser encoder.

Fig. 2
Fig. 2

Sensitivities of QPDs according to 4-DOF motions of the diffraction grating.

Fig. 3
Fig. 3

Associated coordinate frames of the 4-DOF part of the 5-DOF laser encoder.

Fig. 4
Fig. 4

Accuracy test results of the straightness error measurement of the 5-DOF laser encoder.

Fig. 5
Fig. 5

Accuracy test results of the pitch error measurement of the 5-DOF laser encoder.

Fig. 6
Fig. 6

Accuracy test results of the yaw error measurement of the 5-DOF laser encoder.

Fig. 7
Fig. 7

Accuracy test results of the roll error measurement of the 5-DOF laser encoder.

Fig. 8
Fig. 8

Linear displacement error: comparison between the HP 5529A laser interferometer and the 5-DOF laser encoder.

Fig. 9
Fig. 9

Straightness error of a linear moving stage: comparison between the HP laser interferometer and the 5-DOF laser encoder.

Fig. 10
Fig. 10

Pitch error of a linear moving stage: comparison between the HP laser interferometer and the 5-DOF laser encoder.

Fig. 11
Fig. 11

Yaw error of a linear moving stage: comparison between the HP laser interferometer and the 5-DOF laser encoder.

Fig. 12
Fig. 12

Roll error measurement of a linear moving stage by the 5-DOF laser encoder.

Equations (20)

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Δ w + 1 = v x × 2 π λ sin θ ,
Δ w 1 = v x × 2 π λ sin θ ,
E 1 = A p exp [ ( i ( ω + Δ w + 1 ) t ] ,
E 2 = A p exp [ ( i ( ω + Δ w 1 ) t ] .
I PD 1 = A B sin ( 2 Δ w t ) ,
I PD 2 = A + B sin ( 2 Δ w t ) ,
I PD 3 = A B cos ( 2 Δ w t ) ,
I PD 4 = A + B cos ( 2 Δ w t ) .
I 1 = 2 B sin ( 2 Δ w t ) ,
I 2 = 2 B cos ( 2 Δ w t ) .
ϕ = 2 Δ w d t = 4 π λ ν x sin θ d t = 4 π λ Δ X sin θ .
sin θ = λ d ,
Δ X = ϕ d 4 π ,
T G R = [ cos β cos γ sin α sin β cos γ cos α sin γ cos α sin β cos γ + sin α sin γ p x cos β sin γ sin α sin β sin γ + cos α cos γ cos α sin β sin γ sin α cos γ p y sin β sin α cos β cos α cos β p z 0 0 0 1 ] ,
T G R = [ R G R p G R 0 1 ] .
u 1 G = R R G u 1 R = u 1 G | x u 1 G | y u 1 G | z T .
u b m G = [ u 1 G | x + m λ d u 1 G | y 1 ( u 1 G | x + m λ d ) 2 ( u 1 G | y ) 2 ] T ,
s Q m p m = R R p m ( s G R + R G R | s b m G | s b m G ) + s R P m ,
| s b m G | = ( s R p m + R R p m s G R ) | z ( R R p m R G R u b m G ) | z ,
[ q j ] k + 1 = [ q j ] k + J J acobian 1 [ Δ e i ] ,

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