Abstract

A heterodyne grating-based interferometer for three-degree-of-freedom (3-DOF) displacement measurement is proposed. This technique has the merits of both heterodyne interferometry and grating interferometry. A heterodyne light beam is obtained using an electro-optic modulating technique for amplitude modulation. While the heterodyne light beam is normally incident into a transmission-type 2D grating, two detection parts for in-plane and out-of-plane displacement measurements will be obtained. The heterodyne light beam is utilized to carry the optical phase variation that results from grating displacement in three directions. The experimental results demonstrate that the proposed interferometer is capable of sensing the displacement of a motion stage in 3-DOF. The resolution and range of the measurement can achieve up to nanometric and millimetric levels.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruyant, S. Topcu, P. Royer, and Y. Alayli, “Enlarge near-field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
    [CrossRef]
  2. 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, 329–337 (2004).
    [CrossRef]
  3. C. Egami, N. Nishimura, and T. Okawa, “Jitter-free multi-layered nanoparticles optical storage disk with buffer ring,” Opt. Express 18, 15901–15906 (2010).
    [CrossRef]
  4. H. C. Yeh, W. T. Ni, and S. S. Pan, “Digital closed-loop nanopositioning using rectilinear flexure stage and laser interferometry,” Control Eng. Pract. 13, 559–566 (2005).
    [CrossRef]
  5. N. K. Mohan and P. Rastogi, “Phase-shifting whole-field speckle photography technique for the measurement of in-plane deformation in real time,” Opt. Lett. 27, 565–567 (2002).
    [CrossRef]
  6. H. J. Wang, J. Y. Chen, C. M. Liu, and L. W. Chen, “Phase-shifting moire interferometry based on a liquid crystal phase modulator,” Opt. Eng. 44, 015602 (2005).
    [CrossRef]
  7. C. C. Wu, C. C. Hsu, J. Y. Lee, H. Y. Chen, and C. L. Dai, “Optical heterodyne laser encoder with sub-nanometer resolution,” Meas. Sci. Technol. 19, 045305 (2008).
    [CrossRef]
  8. F. Restagno, J. Crassous, E. Charlaix, and M. Monchanin, “A new capacitive sensor for displacement measurement in a surface-force apparatus,” Meas. Sci. Technol. 12, 16–22 (2001).
    [CrossRef]
  9. D. E. Duffy, “Moire gauging of in-plane displacement using double aperture imaging,” Appl. Opt. 11, 1778–1781 (1972).
    [CrossRef]
  10. F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9, 1024–1030 (1998).
    [CrossRef]
  11. H. L. Hsieh, “Novel interferometric stage based on quasi-common-optical-path configuration for large scale displacement,” Ph.D. dissertation (National Central University, 2011).
  12. R. Dandliker, R. Thalmann, and D. Prongue, “Two-wavelength laser interferometry using super-heterodyne detection,” Opt. Lett. 13, 339–341 (1988).
    [CrossRef]
  13. Z. Sodnik, E. Fischer, T. Ittner, and H. J. Tiziani, “Two-wavelength double heterodyne interferometry using a method grating technique,” Appl. Opt. 30, 3139–3144 (1991).
    [CrossRef]
  14. R. G. Johnston and W. K. Grace, “Refractive index detector using Zeeman interferometry,” Appl. Opt. 29, 4720–4724 (1990).
    [CrossRef]
  15. J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A 137, 185–191 (2007).
    [CrossRef]
  16. F. Cheng and K. C. Fan, “Linear diffraction grating interferometer with high alignment tolerance and high accuracy,” Appl. Opt. 50, 4550–4556 (2011).
    [CrossRef]
  17. C. C. Hsu, C. C. Wu, J. Y. Lee, H. Y. Chen, and H. F. Weng, “Reflection type heterodyne grating interferometry for in-plane displacement measurement,” Opt. Commun. 281, 2582–2589 (2008).
    [CrossRef]
  18. H. Schreiber and J. Schwider, “Lateral shearing interferometer based on two Ronchi phase gratings in series,” Appl. Opt. 36, 5321–5324 (1997).
    [CrossRef]
  19. W. Gao and A. Kimura, “A three-axis displacement sensor with nanometric resolution,” CIRP Ann. 56, 529–532 (2007).
    [CrossRef]
  20. A. Kimura, W. Gao, W. J. 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, 576–585 (2012).
    [CrossRef]
  21. 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, 771–781 (2013).
    [CrossRef]
  22. D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
    [CrossRef]

2013 (1)

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, 771–781 (2013).
[CrossRef]

2012 (1)

A. Kimura, W. Gao, W. J. 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, 576–585 (2012).
[CrossRef]

2011 (1)

2010 (1)

2009 (1)

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruyant, S. Topcu, P. Royer, and Y. Alayli, “Enlarge near-field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

2008 (2)

C. C. Wu, C. C. Hsu, J. Y. Lee, H. Y. Chen, and C. L. Dai, “Optical heterodyne laser encoder with sub-nanometer resolution,” Meas. Sci. Technol. 19, 045305 (2008).
[CrossRef]

C. C. Hsu, C. C. Wu, J. Y. Lee, H. Y. Chen, and H. F. Weng, “Reflection type heterodyne grating interferometry for in-plane displacement measurement,” Opt. Commun. 281, 2582–2589 (2008).
[CrossRef]

2007 (2)

W. Gao and A. Kimura, “A three-axis displacement sensor with nanometric resolution,” CIRP Ann. 56, 529–532 (2007).
[CrossRef]

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A 137, 185–191 (2007).
[CrossRef]

2005 (2)

H. C. Yeh, W. T. Ni, and S. S. Pan, “Digital closed-loop nanopositioning using rectilinear flexure stage and laser interferometry,” Control Eng. Pract. 13, 559–566 (2005).
[CrossRef]

H. J. Wang, J. Y. Chen, C. M. Liu, and L. W. Chen, “Phase-shifting moire interferometry based on a liquid crystal phase modulator,” Opt. Eng. 44, 015602 (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, 329–337 (2004).
[CrossRef]

2002 (1)

2001 (1)

F. Restagno, J. Crassous, E. Charlaix, and M. Monchanin, “A new capacitive sensor for displacement measurement in a surface-force apparatus,” Meas. Sci. Technol. 12, 16–22 (2001).
[CrossRef]

1998 (1)

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9, 1024–1030 (1998).
[CrossRef]

1997 (1)

1996 (1)

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

1991 (1)

1990 (1)

1988 (1)

1972 (1)

Alayli, Y.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruyant, S. Topcu, P. Royer, and Y. Alayli, “Enlarge near-field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

Blaize, S.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruyant, S. Topcu, P. Royer, and Y. Alayli, “Enlarge near-field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

Bruyant, A.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruyant, S. Topcu, P. Royer, and Y. Alayli, “Enlarge near-field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

Charlaix, E.

F. Restagno, J. Crassous, E. Charlaix, and M. Monchanin, “A new capacitive sensor for displacement measurement in a surface-force apparatus,” Meas. Sci. Technol. 12, 16–22 (2001).
[CrossRef]

Chassagne, L.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruyant, S. Topcu, P. Royer, and Y. Alayli, “Enlarge near-field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

Chen, C. D.

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

Chen, H. Y.

C. C. Wu, C. C. Hsu, J. Y. Lee, H. Y. Chen, and C. L. Dai, “Optical heterodyne laser encoder with sub-nanometer resolution,” Meas. Sci. Technol. 19, 045305 (2008).
[CrossRef]

C. C. Hsu, C. C. Wu, J. Y. Lee, H. Y. Chen, and H. F. Weng, “Reflection type heterodyne grating interferometry for in-plane displacement measurement,” Opt. Commun. 281, 2582–2589 (2008).
[CrossRef]

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A 137, 185–191 (2007).
[CrossRef]

Chen, J. Y.

H. J. Wang, J. Y. Chen, C. M. Liu, and L. W. Chen, “Phase-shifting moire interferometry based on a liquid crystal phase modulator,” Opt. Eng. 44, 015602 (2005).
[CrossRef]

Chen, L. W.

H. J. Wang, J. Y. Chen, C. M. Liu, and L. W. Chen, “Phase-shifting moire interferometry based on a liquid crystal phase modulator,” Opt. Eng. 44, 015602 (2005).
[CrossRef]

Cheng, F.

Chiu, M. H.

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

Crassous, J.

F. Restagno, J. Crassous, E. Charlaix, and M. Monchanin, “A new capacitive sensor for displacement measurement in a surface-force apparatus,” Meas. Sci. Technol. 12, 16–22 (2001).
[CrossRef]

Dai, C. L.

C. C. Wu, C. C. Hsu, J. Y. Lee, H. Y. Chen, and C. L. Dai, “Optical heterodyne laser encoder with sub-nanometer resolution,” Meas. Sci. Technol. 19, 045305 (2008).
[CrossRef]

Dandliker, R.

Dejima, S.

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, 329–337 (2004).
[CrossRef]

Demarest, F. C.

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9, 1024–1030 (1998).
[CrossRef]

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, 771–781 (2013).
[CrossRef]

Duffy, D. E.

Egami, C.

Fan, K. C.

Fischer, E.

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, 771–781 (2013).
[CrossRef]

A. Kimura, W. Gao, W. J. 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, 576–585 (2012).
[CrossRef]

W. Gao and A. Kimura, “A three-axis displacement sensor with nanometric resolution,” CIRP Ann. 56, 529–532 (2007).
[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, 329–337 (2004).
[CrossRef]

Grace, W. K.

Hosono, K.

A. Kimura, W. Gao, W. J. 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, 576–585 (2012).
[CrossRef]

Hsieh, H. L.

H. L. Hsieh, “Novel interferometric stage based on quasi-common-optical-path configuration for large scale displacement,” Ph.D. dissertation (National Central University, 2011).

Hsu, C. C.

C. C. Wu, C. C. Hsu, J. Y. Lee, H. Y. Chen, and C. L. Dai, “Optical heterodyne laser encoder with sub-nanometer resolution,” Meas. Sci. Technol. 19, 045305 (2008).
[CrossRef]

C. C. Hsu, C. C. Wu, J. Y. Lee, H. Y. Chen, and H. F. Weng, “Reflection type heterodyne grating interferometry for in-plane displacement measurement,” Opt. Commun. 281, 2582–2589 (2008).
[CrossRef]

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A 137, 185–191 (2007).
[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, 771–781 (2013).
[CrossRef]

Ittner, T.

Johnston, R. G.

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, 329–337 (2004).
[CrossRef]

Kim, W. J.

A. Kimura, W. Gao, W. J. 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, 576–585 (2012).
[CrossRef]

Kimura, A.

A. Kimura, W. Gao, W. J. 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, 576–585 (2012).
[CrossRef]

W. Gao and A. Kimura, “A three-axis displacement sensor with nanometric resolution,” CIRP Ann. 56, 529–532 (2007).
[CrossRef]

Kiyono, S.

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, 329–337 (2004).
[CrossRef]

Lee, J. Y.

C. C. Hsu, C. C. Wu, J. Y. Lee, H. Y. Chen, and H. F. Weng, “Reflection type heterodyne grating interferometry for in-plane displacement measurement,” Opt. Commun. 281, 2582–2589 (2008).
[CrossRef]

C. C. Wu, C. C. Hsu, J. Y. Lee, H. Y. Chen, and C. L. Dai, “Optical heterodyne laser encoder with sub-nanometer resolution,” Meas. Sci. Technol. 19, 045305 (2008).
[CrossRef]

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A 137, 185–191 (2007).
[CrossRef]

Lerondel, G.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruyant, S. Topcu, P. Royer, and Y. Alayli, “Enlarge near-field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

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, 771–781 (2013).
[CrossRef]

Liu, C. M.

H. J. Wang, J. Y. Chen, C. M. Liu, and L. W. Chen, “Phase-shifting moire interferometry based on a liquid crystal phase modulator,” Opt. Eng. 44, 015602 (2005).
[CrossRef]

Mohan, N. K.

Monchanin, M.

F. Restagno, J. Crassous, E. Charlaix, and M. Monchanin, “A new capacitive sensor for displacement measurement in a surface-force apparatus,” Meas. Sci. Technol. 12, 16–22 (2001).
[CrossRef]

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, 771–781 (2013).
[CrossRef]

Ni, W. T.

H. C. Yeh, W. T. Ni, and S. S. Pan, “Digital closed-loop nanopositioning using rectilinear flexure stage and laser interferometry,” Control Eng. Pract. 13, 559–566 (2005).
[CrossRef]

Nishimura, N.

Okawa, T.

Pan, S. S.

H. C. Yeh, W. T. Ni, and S. S. Pan, “Digital closed-loop nanopositioning using rectilinear flexure stage and laser interferometry,” Control Eng. Pract. 13, 559–566 (2005).
[CrossRef]

Prongue, D.

Rastogi, P.

Restagno, F.

F. Restagno, J. Crassous, E. Charlaix, and M. Monchanin, “A new capacitive sensor for displacement measurement in a surface-force apparatus,” Meas. Sci. Technol. 12, 16–22 (2001).
[CrossRef]

Royer, P.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruyant, S. Topcu, P. Royer, and Y. Alayli, “Enlarge near-field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

Ruaux, P.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruyant, S. Topcu, P. Royer, and Y. Alayli, “Enlarge near-field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

Schreiber, H.

Schwider, J.

Shi, L.

A. Kimura, W. Gao, W. J. 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, 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, 771–781 (2013).
[CrossRef]

A. Kimura, W. Gao, W. J. 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, 576–585 (2012).
[CrossRef]

Sinno, A.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruyant, S. Topcu, P. Royer, and Y. Alayli, “Enlarge near-field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

Sodnik, Z.

Su, D. C.

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

Thalmann, R.

Tiziani, H. J.

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, 329–337 (2004).
[CrossRef]

Topcu, S.

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruyant, S. Topcu, P. Royer, and Y. Alayli, “Enlarge near-field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

Wang, H. J.

H. J. Wang, J. Y. Chen, C. M. Liu, and L. W. Chen, “Phase-shifting moire interferometry based on a liquid crystal phase modulator,” Opt. Eng. 44, 015602 (2005).
[CrossRef]

Weng, H. F.

C. C. Hsu, C. C. Wu, J. Y. Lee, H. Y. Chen, and H. F. Weng, “Reflection type heterodyne grating interferometry for in-plane displacement measurement,” Opt. Commun. 281, 2582–2589 (2008).
[CrossRef]

Wu, C. C.

C. C. Hsu, C. C. Wu, J. Y. Lee, H. Y. Chen, and H. F. Weng, “Reflection type heterodyne grating interferometry for in-plane displacement measurement,” Opt. Commun. 281, 2582–2589 (2008).
[CrossRef]

C. C. Wu, C. C. Hsu, J. Y. Lee, H. Y. Chen, and C. L. Dai, “Optical heterodyne laser encoder with sub-nanometer resolution,” Meas. Sci. Technol. 19, 045305 (2008).
[CrossRef]

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A 137, 185–191 (2007).
[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, 329–337 (2004).
[CrossRef]

Yeh, H. C.

H. C. Yeh, W. T. Ni, and S. S. Pan, “Digital closed-loop nanopositioning using rectilinear flexure stage and laser interferometry,” Control Eng. Pract. 13, 559–566 (2005).
[CrossRef]

Zeng, L.

A. Kimura, W. Gao, W. J. 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, 576–585 (2012).
[CrossRef]

Appl. Opt. (5)

CIRP Ann. (1)

W. Gao and A. Kimura, “A three-axis displacement sensor with nanometric resolution,” CIRP Ann. 56, 529–532 (2007).
[CrossRef]

Control Eng. Pract. (1)

H. C. Yeh, W. T. Ni, and S. S. Pan, “Digital closed-loop nanopositioning using rectilinear flexure stage and laser interferometry,” Control Eng. Pract. 13, 559–566 (2005).
[CrossRef]

J. Appl. Phys. (1)

G. Lerondel, A. Sinno, L. Chassagne, S. Blaize, P. Ruaux, A. Bruyant, S. Topcu, P. Royer, and Y. Alayli, “Enlarge near-field optical imaging,” J. Appl. Phys. 106, 044913 (2009).
[CrossRef]

Meas. Sci. Technol. (3)

C. C. Wu, C. C. Hsu, J. Y. Lee, H. Y. Chen, and C. L. Dai, “Optical heterodyne laser encoder with sub-nanometer resolution,” Meas. Sci. Technol. 19, 045305 (2008).
[CrossRef]

F. Restagno, J. Crassous, E. Charlaix, and M. Monchanin, “A new capacitive sensor for displacement measurement in a surface-force apparatus,” Meas. Sci. Technol. 12, 16–22 (2001).
[CrossRef]

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9, 1024–1030 (1998).
[CrossRef]

Opt. Commun. (1)

C. C. Hsu, C. C. Wu, J. Y. Lee, H. Y. Chen, and H. F. Weng, “Reflection type heterodyne grating interferometry for in-plane displacement measurement,” Opt. Commun. 281, 2582–2589 (2008).
[CrossRef]

Opt. Eng. (1)

H. J. Wang, J. Y. Chen, C. M. Liu, and L. W. Chen, “Phase-shifting moire interferometry based on a liquid crystal phase modulator,” Opt. Eng. 44, 015602 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Precis. Eng. (4)

A. Kimura, W. Gao, W. J. 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, 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, 771–781 (2013).
[CrossRef]

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[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, 329–337 (2004).
[CrossRef]

Sens. Actuators A (1)

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A 137, 185–191 (2007).
[CrossRef]

Other (1)

H. L. Hsieh, “Novel interferometric stage based on quasi-common-optical-path configuration for large scale displacement,” Ph.D. dissertation (National Central University, 2011).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1.

Optical configuration of the grating-based heterodyne interferometer. EOM, electro-optic modulator; AN1–AN7, analyzers (45°); D1–D4, detectors; M, mirror; BS, beam splitter; and PBS, polarizing beam splitter.

Fig. 2.
Fig. 2.

Measurement results of the displacement in 3-DOF (1 μm).

Fig. 3.
Fig. 3.

Experimental results for 2-DOF large displacement on the Z and Y axes.

Fig. 4.
Fig. 4.

Horizontal (Y direction) straightness of path 1.

Fig. 5.
Fig. 5.

Vertical (X direction) straightness of path 1.

Fig. 6.
Fig. 6.

Experimental results of stability testing (10 min).

Fig. 7.
Fig. 7.

Sketch of the misalignment caused from the pitch, yaw, and roll angles.

Fig. 8.
Fig. 8.

Sketch of the misalignment caused by the yaw angle (θx).

Fig. 9.
Fig. 9.

Sketch of the difference in the optical path caused by the yaw angle.

Fig. 10.
Fig. 10.

Sketch of the misalignment caused by the roll angle (θz).

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

E0=A0(eiωt/2eiωt/2),
Er=Areiklr+iθr(eiωt/2eiωt/2),
Em=Ameiklm+iθm(eiωt/2eiωt/2),
I1=|AN(45°)·(Er+Em)|2cos(ωt+k(lrlm)+(θrθm)).
I1cos(ωt+k(lrlm)).
I2cos(ωt).
Δθ=k(lrlm)=k×2Δdop,
Δdop=Δθ2k=Δθλ4π.
αm=sin1(mλpsinαin),
E±1qeikl±1q±iθiE0=(eiωt/2eiωt/2)eikl±1q±iθi,
E+1qp=AN(45°)PBS(0°)E+1q=(11)eiωt/2+ikl+1q+iφg,
E+1qs=AN(45°)PBS(90°)E+1q=(11)eiωt/2+ikl+1q+iφg,
E1qp=AN(45°)PBS(0°)E1q=(11)eiωt/2+ikl1qiφg,
E1qs=AN(45°)PBS(90°)E1q=(11)eiωt/2+ikl1qiφg,
I3,6=|E+1qp+E1qs|2cos[ωt+k(l+1ql1q)+2φg],
I4,5=|E+1qs+E1qp|2cos[ωt+k(l1ql+1q)+2φg],
Δφg=8πΔdqp,
Δdq=(Δφg)p8π.
Δde=Δφg8π(ppyaw)=ΔdY(1cosθx),
Δde=Δφg8π(pppitch)=ΔdX(1cosθy),
Δde=Δφg8π(prollp)=Δφg8πp(1cosθz1)=Δdq(1cosθz1),

Metrics