Abstract

This paper presents a common-path laser planar encoder (CLPE) for displacement measurements in the X- and Y- axes. The CLPE can effectively reduce the environmental disturbance to its lowest level. The experimental results of the CLPE match well with those of HP5529A for both short and long ranges. The CLPE can measure 2D displacement with high resolutions of 0.07 ± 0.021 nm and 0.07 ± 0.023 nm in the X- and Y- axes and also presents high system stabilities of −0.59 ± 0.43 nm/h and −0.63 ± 0.47 nm/h respectively in the X- and Y- axes. The CLPE has promising potential for nanometer resolution and large-range applications.

© 2013 OSA

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  1. C. C. Wu, J. S. Yang, C. Y. Cheng, and Y. Z. Chen, “Common-path laser encoder,” Sens. Actuat. A189, 86–92 (2013).
    [CrossRef]
  2. P. L. M. Heydemann, “Determination and correction of quadrature fringe measurement errors in interferometers,” Appl. Opt.20(19), 3382–3384 (1981).
    [CrossRef] [PubMed]
  3. J. D. Ellis, M. Baas, K.-N. Joo, and J. W. Spronck, “Theoretical analysis of errors in correction algorithms for periodic nonlinearity in displacement measuring interferometers,” Precis. Eng.36(2), 261–269 (2012).
    [CrossRef]
  4. W.-W. Chiang and C.-K. Lee, “Wavefront reconstruction optics for use in a disk drive position measurement system,” USPTO, ed. (International Bussiness Machines, America, 1995).
  5. V. V. Yashchuk, “Optimal measurement strategies for effective suppression of drift errors,” Rev. Sci. Instrum.80(11), 115101 (2009).
    [CrossRef] [PubMed]
  6. C.-M. Wu and R. D. Deslattes, “Analytical modeling of the periodic nonlinearity in heterodyne interferometry,” Appl. Opt.37(28), 6696–6700 (1998).
    [CrossRef] [PubMed]
  7. W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng.27(3), 289–298 (2003).
    [CrossRef]
  8. W. Gao, S. Dejima, H. Yanai, K. Katakura, S. Kiyono, and Y. Tomita, “A surface motor-driven planar motion stage integrated with an XYθZ surface encoder for precision positioning,” Precis. Eng.28(3), 329–337 (2004).
    [CrossRef]
  9. W. Gao, S. Dejima, and S. Kiyono, “A dual-mode surface encoder for position measurement,” Sens. Actuat. A117(1), 95–102 (2005).
    [CrossRef]
  10. W. Gao and A. Kimura, “A three-axis displacement sensor with nanometric resolution,” CIRP Annals - Manufacturing Technology56(1), 529–532 (2007).
    [CrossRef]
  11. A. Kimura, W. Gao, A. Yoshikazu, and L. Zeng, “Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness,” Precis. Eng.34(1), 145–155 (2010).
    [CrossRef]
  12. A. Kimura, W. Gao, and L. Zeng, “Position and out-of-straightness measurement of a precision linear air-bearing stage by using a two-degree-of-freedom linear encoder,” Meas. Sci. Technol.21(5), 054005 (2010).
    [CrossRef]
  13. A. Kimura, W. Gao, W. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. Zeng, “A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng.36(4), 576–585 (2012).
    [CrossRef]
  14. X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng.37(3), 771–781 (2013).
    [CrossRef]
  15. C. F. Kao, S. H. Lu, and M. H. Lu, “High resolution planar encoder by retro-reflection,” Rev. Sci. Instrum.76(8), 085110 (2005).
    [CrossRef]
  16. Y.-C. Chung, K.-C. Fan, and B.-C. Lee, “Development of a novel planar encoder for 2D displacement measurement in nanometer resolution and accuracy,” in Intelligent Control and Automation (WCICA), 2011 9th World Congress on(2011), pp. 449–453.
  17. H.-L. Hsieh, J.-C. Chen, G. Lerondel, and J.-Y. Lee, “Two-dimensional displacement measurement by quasi-common-optical-path heterodyne grating interferometer,” Opt. Express19(10), 9770–9782 (2011).
    [CrossRef] [PubMed]
  18. J.-Y. Lee, H.-L. Hsieh, G. Lerondel, R. Deturche, M.-P. Lu, and J.-C. Chen, “Heterodyne grating interferometer based on a quasi-common-optical-path configuration for a two-degrees-of-freedom straightness measurement,” Appl. Opt.50(9), 1272–1279 (2011).
    [CrossRef] [PubMed]
  19. K. C. Fan, B. H. Liao, Y. C. Chung, and T. T. Chung, “Displacement measurement of planar stage by diffraction planar encoder in nanometer resolution,” in 2012 IEEE International Conference on Instrumentation and Measurement Technology(2012), pp. 894–897.
    [CrossRef]
  20. C.-C. Hsu, M.-C. Kao, K.-C. Huang, and C.-C. Wu, “Reflection type displacement sensor with volume hologram for in-plane displacement measurement,” in 2012 International Conference on Measurement, Information and Control (MIC) (2012), pp. 13–16.
    [CrossRef]
  21. C.-C. Wu, C.-H. Liao, Y.-Z. Chen, and J.-S. Yang, “Common-path Laser Encoder with Littrow Configuration,” Sens. Actuat. A193, 69–78 (2013).
    [CrossRef]
  22. R. Petit and L. C. Botten, Electromagnetic Theory of Gratings (Springer-Verlag, 1980).
  23. L. E. Drain, The Laser Doppler Technique (John Wiley, 1980).
  24. http://www.newport.com .
  25. C.-F. Kao, C. C. Chang, and M.-H. Lu, “Double-diffraction planar encoder by conjugate optics,” Opt. Eng.44(2), 023603 (2005).
    [CrossRef]
  26. F. L. Pedrotti, L. M. Pedrotti, and L. S. Pedrotti, Introduction to Optics (Prentice-Hall International, 2006).
  27. http://www.piezosystem.com/home/ .
  28. P. Gregorcic, T. Pozar, and J. Mozina, “Quadrature phase-shift error analysis using a homodyne laser interferometer,” Opt. Express17(18), 16322–16331 (2009).
    [CrossRef] [PubMed]
  29. Sony Precision Technology, http://www.sonypt.com/ .

2013 (3)

C. C. Wu, J. S. Yang, C. Y. Cheng, and Y. Z. Chen, “Common-path laser encoder,” Sens. Actuat. A189, 86–92 (2013).
[CrossRef]

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng.37(3), 771–781 (2013).
[CrossRef]

C.-C. Wu, C.-H. Liao, Y.-Z. Chen, and J.-S. Yang, “Common-path Laser Encoder with Littrow Configuration,” Sens. Actuat. A193, 69–78 (2013).
[CrossRef]

2012 (2)

J. D. Ellis, M. Baas, K.-N. Joo, and J. W. Spronck, “Theoretical analysis of errors in correction algorithms for periodic nonlinearity in displacement measuring interferometers,” Precis. Eng.36(2), 261–269 (2012).
[CrossRef]

A. Kimura, W. Gao, W. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. Zeng, “A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng.36(4), 576–585 (2012).
[CrossRef]

2011 (2)

2010 (2)

A. Kimura, W. Gao, A. Yoshikazu, and L. Zeng, “Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness,” Precis. Eng.34(1), 145–155 (2010).
[CrossRef]

A. Kimura, W. Gao, and L. Zeng, “Position and out-of-straightness measurement of a precision linear air-bearing stage by using a two-degree-of-freedom linear encoder,” Meas. Sci. Technol.21(5), 054005 (2010).
[CrossRef]

2009 (2)

V. V. Yashchuk, “Optimal measurement strategies for effective suppression of drift errors,” Rev. Sci. Instrum.80(11), 115101 (2009).
[CrossRef] [PubMed]

P. Gregorcic, T. Pozar, and J. Mozina, “Quadrature phase-shift error analysis using a homodyne laser interferometer,” Opt. Express17(18), 16322–16331 (2009).
[CrossRef] [PubMed]

2007 (1)

W. Gao and A. Kimura, “A three-axis displacement sensor with nanometric resolution,” CIRP Annals - Manufacturing Technology56(1), 529–532 (2007).
[CrossRef]

2005 (3)

W. Gao, S. Dejima, and S. Kiyono, “A dual-mode surface encoder for position measurement,” Sens. Actuat. A117(1), 95–102 (2005).
[CrossRef]

C. F. Kao, S. H. Lu, and M. H. Lu, “High resolution planar encoder by retro-reflection,” Rev. Sci. Instrum.76(8), 085110 (2005).
[CrossRef]

C.-F. Kao, C. C. Chang, and M.-H. Lu, “Double-diffraction planar encoder by conjugate optics,” Opt. Eng.44(2), 023603 (2005).
[CrossRef]

2004 (1)

W. Gao, S. Dejima, H. Yanai, K. Katakura, S. Kiyono, and Y. Tomita, “A surface motor-driven planar motion stage integrated with an XYθZ surface encoder for precision positioning,” Precis. Eng.28(3), 329–337 (2004).
[CrossRef]

2003 (1)

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng.27(3), 289–298 (2003).
[CrossRef]

1998 (1)

1981 (1)

Araki, T.

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng.27(3), 289–298 (2003).
[CrossRef]

Baas, M.

J. D. Ellis, M. Baas, K.-N. Joo, and J. W. Spronck, “Theoretical analysis of errors in correction algorithms for periodic nonlinearity in displacement measuring interferometers,” Precis. Eng.36(2), 261–269 (2012).
[CrossRef]

Chang, C. C.

C.-F. Kao, C. C. Chang, and M.-H. Lu, “Double-diffraction planar encoder by conjugate optics,” Opt. Eng.44(2), 023603 (2005).
[CrossRef]

Chen, J.-C.

Chen, Y. Z.

C. C. Wu, J. S. Yang, C. Y. Cheng, and Y. Z. Chen, “Common-path laser encoder,” Sens. Actuat. A189, 86–92 (2013).
[CrossRef]

Chen, Y.-Z.

C.-C. Wu, C.-H. Liao, Y.-Z. Chen, and J.-S. Yang, “Common-path Laser Encoder with Littrow Configuration,” Sens. Actuat. A193, 69–78 (2013).
[CrossRef]

Cheng, C. Y.

C. C. Wu, J. S. Yang, C. Y. Cheng, and Y. Z. Chen, “Common-path laser encoder,” Sens. Actuat. A189, 86–92 (2013).
[CrossRef]

Chung, T. T.

K. C. Fan, B. H. Liao, Y. C. Chung, and T. T. Chung, “Displacement measurement of planar stage by diffraction planar encoder in nanometer resolution,” in 2012 IEEE International Conference on Instrumentation and Measurement Technology(2012), pp. 894–897.
[CrossRef]

Chung, Y. C.

K. C. Fan, B. H. Liao, Y. C. Chung, and T. T. Chung, “Displacement measurement of planar stage by diffraction planar encoder in nanometer resolution,” in 2012 IEEE International Conference on Instrumentation and Measurement Technology(2012), pp. 894–897.
[CrossRef]

Dejima, S.

W. Gao, S. Dejima, and S. Kiyono, “A dual-mode surface encoder for position measurement,” Sens. Actuat. A117(1), 95–102 (2005).
[CrossRef]

W. Gao, S. Dejima, H. Yanai, K. Katakura, S. Kiyono, and Y. Tomita, “A surface motor-driven planar motion stage integrated with an XYθZ surface encoder for precision positioning,” Precis. Eng.28(3), 329–337 (2004).
[CrossRef]

Deslattes, R. D.

Deturche, R.

Dian, S.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng.37(3), 771–781 (2013).
[CrossRef]

Ellis, J. D.

J. D. Ellis, M. Baas, K.-N. Joo, and J. W. Spronck, “Theoretical analysis of errors in correction algorithms for periodic nonlinearity in displacement measuring interferometers,” Precis. Eng.36(2), 261–269 (2012).
[CrossRef]

Fan, K. C.

K. C. Fan, B. H. Liao, Y. C. Chung, and T. T. Chung, “Displacement measurement of planar stage by diffraction planar encoder in nanometer resolution,” in 2012 IEEE International Conference on Instrumentation and Measurement Technology(2012), pp. 894–897.
[CrossRef]

Gao, W.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng.37(3), 771–781 (2013).
[CrossRef]

A. Kimura, W. Gao, W. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. Zeng, “A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng.36(4), 576–585 (2012).
[CrossRef]

A. Kimura, W. Gao, A. Yoshikazu, and L. Zeng, “Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness,” Precis. Eng.34(1), 145–155 (2010).
[CrossRef]

A. Kimura, W. Gao, and L. Zeng, “Position and out-of-straightness measurement of a precision linear air-bearing stage by using a two-degree-of-freedom linear encoder,” Meas. Sci. Technol.21(5), 054005 (2010).
[CrossRef]

W. Gao and A. Kimura, “A three-axis displacement sensor with nanometric resolution,” CIRP Annals - Manufacturing Technology56(1), 529–532 (2007).
[CrossRef]

W. Gao, S. Dejima, and S. Kiyono, “A dual-mode surface encoder for position measurement,” Sens. Actuat. A117(1), 95–102 (2005).
[CrossRef]

W. Gao, S. Dejima, H. Yanai, K. Katakura, S. Kiyono, and Y. Tomita, “A surface motor-driven planar motion stage integrated with an XYθZ surface encoder for precision positioning,” Precis. Eng.28(3), 329–337 (2004).
[CrossRef]

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng.27(3), 289–298 (2003).
[CrossRef]

Gregorcic, P.

Heydemann, P. L. M.

Hosono, K.

A. Kimura, W. Gao, W. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. Zeng, “A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng.36(4), 576–585 (2012).
[CrossRef]

Hsieh, H.-L.

Hsu, C.-C.

C.-C. Hsu, M.-C. Kao, K.-C. Huang, and C.-C. Wu, “Reflection type displacement sensor with volume hologram for in-plane displacement measurement,” in 2012 International Conference on Measurement, Information and Control (MIC) (2012), pp. 13–16.
[CrossRef]

Huang, K.-C.

C.-C. Hsu, M.-C. Kao, K.-C. Huang, and C.-C. Wu, “Reflection type displacement sensor with volume hologram for in-plane displacement measurement,” in 2012 International Conference on Measurement, Information and Control (MIC) (2012), pp. 13–16.
[CrossRef]

Ito, S.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng.37(3), 771–781 (2013).
[CrossRef]

Joo, K.-N.

J. D. Ellis, M. Baas, K.-N. Joo, and J. W. Spronck, “Theoretical analysis of errors in correction algorithms for periodic nonlinearity in displacement measuring interferometers,” Precis. Eng.36(2), 261–269 (2012).
[CrossRef]

Kao, C. F.

C. F. Kao, S. H. Lu, and M. H. Lu, “High resolution planar encoder by retro-reflection,” Rev. Sci. Instrum.76(8), 085110 (2005).
[CrossRef]

Kao, C.-F.

C.-F. Kao, C. C. Chang, and M.-H. Lu, “Double-diffraction planar encoder by conjugate optics,” Opt. Eng.44(2), 023603 (2005).
[CrossRef]

Kao, M.-C.

C.-C. Hsu, M.-C. Kao, K.-C. Huang, and C.-C. Wu, “Reflection type displacement sensor with volume hologram for in-plane displacement measurement,” in 2012 International Conference on Measurement, Information and Control (MIC) (2012), pp. 13–16.
[CrossRef]

Katakura, K.

W. Gao, S. Dejima, H. Yanai, K. Katakura, S. Kiyono, and Y. Tomita, “A surface motor-driven planar motion stage integrated with an XYθZ surface encoder for precision positioning,” Precis. Eng.28(3), 329–337 (2004).
[CrossRef]

Kim, W.

A. Kimura, W. Gao, W. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. Zeng, “A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng.36(4), 576–585 (2012).
[CrossRef]

Kimura, A.

A. Kimura, W. Gao, W. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. Zeng, “A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng.36(4), 576–585 (2012).
[CrossRef]

A. Kimura, W. Gao, and L. Zeng, “Position and out-of-straightness measurement of a precision linear air-bearing stage by using a two-degree-of-freedom linear encoder,” Meas. Sci. Technol.21(5), 054005 (2010).
[CrossRef]

A. Kimura, W. Gao, A. Yoshikazu, and L. Zeng, “Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness,” Precis. Eng.34(1), 145–155 (2010).
[CrossRef]

W. Gao and A. Kimura, “A three-axis displacement sensor with nanometric resolution,” CIRP Annals - Manufacturing Technology56(1), 529–532 (2007).
[CrossRef]

Kiyono, S.

W. Gao, S. Dejima, and S. Kiyono, “A dual-mode surface encoder for position measurement,” Sens. Actuat. A117(1), 95–102 (2005).
[CrossRef]

W. Gao, S. Dejima, H. Yanai, K. Katakura, S. Kiyono, and Y. Tomita, “A surface motor-driven planar motion stage integrated with an XYθZ surface encoder for precision positioning,” Precis. Eng.28(3), 329–337 (2004).
[CrossRef]

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng.27(3), 289–298 (2003).
[CrossRef]

Lee, J.-Y.

Lerondel, G.

Li, X.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng.37(3), 771–781 (2013).
[CrossRef]

Liao, B. H.

K. C. Fan, B. H. Liao, Y. C. Chung, and T. T. Chung, “Displacement measurement of planar stage by diffraction planar encoder in nanometer resolution,” in 2012 IEEE International Conference on Instrumentation and Measurement Technology(2012), pp. 894–897.
[CrossRef]

Liao, C.-H.

C.-C. Wu, C.-H. Liao, Y.-Z. Chen, and J.-S. Yang, “Common-path Laser Encoder with Littrow Configuration,” Sens. Actuat. A193, 69–78 (2013).
[CrossRef]

Lu, M. H.

C. F. Kao, S. H. Lu, and M. H. Lu, “High resolution planar encoder by retro-reflection,” Rev. Sci. Instrum.76(8), 085110 (2005).
[CrossRef]

Lu, M.-H.

C.-F. Kao, C. C. Chang, and M.-H. Lu, “Double-diffraction planar encoder by conjugate optics,” Opt. Eng.44(2), 023603 (2005).
[CrossRef]

Lu, M.-P.

Lu, S. H.

C. F. Kao, S. H. Lu, and M. H. Lu, “High resolution planar encoder by retro-reflection,” Rev. Sci. Instrum.76(8), 085110 (2005).
[CrossRef]

Mozina, J.

Muto, H.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng.37(3), 771–781 (2013).
[CrossRef]

Okazaki, Y.

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng.27(3), 289–298 (2003).
[CrossRef]

Pozar, T.

Shi, L.

A. Kimura, W. Gao, W. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. Zeng, “A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng.36(4), 576–585 (2012).
[CrossRef]

Shimizu, Y.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng.37(3), 771–781 (2013).
[CrossRef]

A. Kimura, W. Gao, W. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. Zeng, “A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng.36(4), 576–585 (2012).
[CrossRef]

Spronck, J. W.

J. D. Ellis, M. Baas, K.-N. Joo, and J. W. Spronck, “Theoretical analysis of errors in correction algorithms for periodic nonlinearity in displacement measuring interferometers,” Precis. Eng.36(2), 261–269 (2012).
[CrossRef]

Tomita, Y.

W. Gao, S. Dejima, H. Yanai, K. Katakura, S. Kiyono, and Y. Tomita, “A surface motor-driven planar motion stage integrated with an XYθZ surface encoder for precision positioning,” Precis. Eng.28(3), 329–337 (2004).
[CrossRef]

Wu, C. C.

C. C. Wu, J. S. Yang, C. Y. Cheng, and Y. Z. Chen, “Common-path laser encoder,” Sens. Actuat. A189, 86–92 (2013).
[CrossRef]

Wu, C.-C.

C.-C. Wu, C.-H. Liao, Y.-Z. Chen, and J.-S. Yang, “Common-path Laser Encoder with Littrow Configuration,” Sens. Actuat. A193, 69–78 (2013).
[CrossRef]

C.-C. Hsu, M.-C. Kao, K.-C. Huang, and C.-C. Wu, “Reflection type displacement sensor with volume hologram for in-plane displacement measurement,” in 2012 International Conference on Measurement, Information and Control (MIC) (2012), pp. 13–16.
[CrossRef]

Wu, C.-M.

Yamanaka, M.

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng.27(3), 289–298 (2003).
[CrossRef]

Yanai, H.

W. Gao, S. Dejima, H. Yanai, K. Katakura, S. Kiyono, and Y. Tomita, “A surface motor-driven planar motion stage integrated with an XYθZ surface encoder for precision positioning,” Precis. Eng.28(3), 329–337 (2004).
[CrossRef]

Yang, J. S.

C. C. Wu, J. S. Yang, C. Y. Cheng, and Y. Z. Chen, “Common-path laser encoder,” Sens. Actuat. A189, 86–92 (2013).
[CrossRef]

Yang, J.-S.

C.-C. Wu, C.-H. Liao, Y.-Z. Chen, and J.-S. Yang, “Common-path Laser Encoder with Littrow Configuration,” Sens. Actuat. A193, 69–78 (2013).
[CrossRef]

Yashchuk, V. V.

V. V. Yashchuk, “Optimal measurement strategies for effective suppression of drift errors,” Rev. Sci. Instrum.80(11), 115101 (2009).
[CrossRef] [PubMed]

Yoshikazu, A.

A. Kimura, W. Gao, A. Yoshikazu, and L. Zeng, “Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness,” Precis. Eng.34(1), 145–155 (2010).
[CrossRef]

Zeng, L.

A. Kimura, W. Gao, W. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. Zeng, “A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng.36(4), 576–585 (2012).
[CrossRef]

A. Kimura, W. Gao, A. Yoshikazu, and L. Zeng, “Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness,” Precis. Eng.34(1), 145–155 (2010).
[CrossRef]

A. Kimura, W. Gao, and L. Zeng, “Position and out-of-straightness measurement of a precision linear air-bearing stage by using a two-degree-of-freedom linear encoder,” Meas. Sci. Technol.21(5), 054005 (2010).
[CrossRef]

Appl. Opt. (3)

CIRP Annals - Manufacturing Technology (1)

W. Gao and A. Kimura, “A three-axis displacement sensor with nanometric resolution,” CIRP Annals - Manufacturing Technology56(1), 529–532 (2007).
[CrossRef]

Meas. Sci. Technol. (1)

A. Kimura, W. Gao, and L. Zeng, “Position and out-of-straightness measurement of a precision linear air-bearing stage by using a two-degree-of-freedom linear encoder,” Meas. Sci. Technol.21(5), 054005 (2010).
[CrossRef]

Opt. Eng. (1)

C.-F. Kao, C. C. Chang, and M.-H. Lu, “Double-diffraction planar encoder by conjugate optics,” Opt. Eng.44(2), 023603 (2005).
[CrossRef]

Opt. Express (2)

Precis. Eng. (6)

A. Kimura, W. Gao, W. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. Zeng, “A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng.36(4), 576–585 (2012).
[CrossRef]

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng.37(3), 771–781 (2013).
[CrossRef]

A. Kimura, W. Gao, A. Yoshikazu, and L. Zeng, “Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness,” Precis. Eng.34(1), 145–155 (2010).
[CrossRef]

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng.27(3), 289–298 (2003).
[CrossRef]

W. Gao, S. Dejima, H. Yanai, K. Katakura, S. Kiyono, and Y. Tomita, “A surface motor-driven planar motion stage integrated with an XYθZ surface encoder for precision positioning,” Precis. Eng.28(3), 329–337 (2004).
[CrossRef]

J. D. Ellis, M. Baas, K.-N. Joo, and J. W. Spronck, “Theoretical analysis of errors in correction algorithms for periodic nonlinearity in displacement measuring interferometers,” Precis. Eng.36(2), 261–269 (2012).
[CrossRef]

Rev. Sci. Instrum. (2)

V. V. Yashchuk, “Optimal measurement strategies for effective suppression of drift errors,” Rev. Sci. Instrum.80(11), 115101 (2009).
[CrossRef] [PubMed]

C. F. Kao, S. H. Lu, and M. H. Lu, “High resolution planar encoder by retro-reflection,” Rev. Sci. Instrum.76(8), 085110 (2005).
[CrossRef]

Sens. Actuat. A (3)

C. C. Wu, J. S. Yang, C. Y. Cheng, and Y. Z. Chen, “Common-path laser encoder,” Sens. Actuat. A189, 86–92 (2013).
[CrossRef]

W. Gao, S. Dejima, and S. Kiyono, “A dual-mode surface encoder for position measurement,” Sens. Actuat. A117(1), 95–102 (2005).
[CrossRef]

C.-C. Wu, C.-H. Liao, Y.-Z. Chen, and J.-S. Yang, “Common-path Laser Encoder with Littrow Configuration,” Sens. Actuat. A193, 69–78 (2013).
[CrossRef]

Other (10)

R. Petit and L. C. Botten, Electromagnetic Theory of Gratings (Springer-Verlag, 1980).

L. E. Drain, The Laser Doppler Technique (John Wiley, 1980).

http://www.newport.com .

Sony Precision Technology, http://www.sonypt.com/ .

F. L. Pedrotti, L. M. Pedrotti, and L. S. Pedrotti, Introduction to Optics (Prentice-Hall International, 2006).

http://www.piezosystem.com/home/ .

W.-W. Chiang and C.-K. Lee, “Wavefront reconstruction optics for use in a disk drive position measurement system,” USPTO, ed. (International Bussiness Machines, America, 1995).

Y.-C. Chung, K.-C. Fan, and B.-C. Lee, “Development of a novel planar encoder for 2D displacement measurement in nanometer resolution and accuracy,” in Intelligent Control and Automation (WCICA), 2011 9th World Congress on(2011), pp. 449–453.

K. C. Fan, B. H. Liao, Y. C. Chung, and T. T. Chung, “Displacement measurement of planar stage by diffraction planar encoder in nanometer resolution,” in 2012 IEEE International Conference on Instrumentation and Measurement Technology(2012), pp. 894–897.
[CrossRef]

C.-C. Hsu, M.-C. Kao, K.-C. Huang, and C.-C. Wu, “Reflection type displacement sensor with volume hologram for in-plane displacement measurement,” in 2012 International Conference on Measurement, Information and Control (MIC) (2012), pp. 13–16.
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

The optical configuration of the CLPE.

Fig. 2
Fig. 2

Schematic of the coordinate system of the three-dimensional diffraction for a 2D grating scale. θ represents the angle of incidence for a wavevector k in with respect to the Z -axis, and ϕ is the azimuth angle of the incidence plane with respect to the X -axis. ρ X and ρ Y are the grating pitches of a grating scale along the X - and Y - axes. O is the origin of the XYZ coordinate system. h is the grating depth.

Fig. 3
Fig. 3

Schematic of two-aperture phase shifting technique. a is the diameter of the circular apertures . Δ is the spatial shift between the aperture A 1 and the aperture A 2 in the fringe space.

Fig. 4
Fig. 4

Schematic of experimental setup with the CLPE configuration built in the readhead.

Fig. 5
Fig. 5

Results of 8-mm square path movement by the HP5529A and the CLPE.

Fig. 6
Fig. 6

Results of 20- μm triangular path movement by the HP5529A, the CLPE, and the strain gauge.

Fig. 7
Fig. 7

Results of 10-nm diameter circular movement by the strain gauge and the CLPE.

Fig. 8
Fig. 8

System stability measurement results of the CLPE and the HP5529A for three hours.

Equations (14)

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k Xmn = k 0 sinθcosϕ+ 2mπ ρ X ,
k Ymn = k 0 sinϕ+ 2nπ ρ Y ,
k Zmn = k 0 2 k Xmn 2 k Ymn 2 ,
Δ ω 1 =( k 10 k in ) v = 2π v X ρ X .
Δ ω 2 =( k 01 k in ) v = 2π v Y ρ Y
I 1 D C 1 +A C 1 cos( Δ ω 1 t πa q ),
I 2 D C 2 +A C 2 cos( Δ ω 1 t π(a+2Δ) q ),
I 3 D C 3 +A C 3 cos( Δ ω 2 t πa q ),
I 4 D C 4 +A C 4 cos( Δ ω 2 t π(a+2 Δ ) q ),
ΔX= ρ X 2π Δ Φ X ,
ΔY= ρ Y 2π Δ Φ Y .
D 2 ψ q 10000 ,
1 2 cos 1 ( k 10 k 10 // k 10 k 10 k 10 // k 10 // ) ( D 2 ) 2 + f 2 q 10000 ,
I i (p)= I i (p) {max[ I i (p)]+min[ I i (p)]} /2 {max[ I i (p)]min[ I i (p)]} /2 , i=1, 2, 3, 4,

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