Abstract

In this paper, a nanometer-scale displacement sensor based on a phase-sensitive diffraction grating with interferometeric detection is described and experimentally demonstrated. The proposed displacement sensor consists of a coherent light source, a microstepping motor controller, an integrated grating, a mirror, and a differential circuit. Experimental results show that the displacement sensor has a sensitivity of about 6mV/nm and a resolution of less than 1nm. This displacement measurement is an attractive technology with high sensitivity, broad dynamic range, good reliability, and immunity to electromagnetic interference.

© 2011 Optical Society of America

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  1. G. G. Yaralioglu, A. Atalar, S. R. Manalis, and C. F. Quate, “Analysis and design of an interdigital cantilever as a displacement sensor,” J. Appl. Phys. 83, 7405–7414 (1998).
    [CrossRef]
  2. R. G. Knobel and A. N. Cleland, “Nanometer-scale displacement sensing using a single electron transistor,” Nature 424, 291–293 (2003).
    [CrossRef] [PubMed]
  3. Y. Li, X. Mi, M. Sasaki, and K. Hane, “Precision optical displacement sensor based on ultra-thin film photodiode-type optical interferometers,” Meas. Sci. Technol. 14, 479–483(2003).
    [CrossRef]
  4. A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photonics Technol. Lett. 15, 1129–1131 (2003).
    [CrossRef]
  5. W. Suh, O. Solgaard, and S. Fan, “Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs,” J. Appl. Phys. 98, 033102 (2005).
    [CrossRef]
  6. Y.-Z. Lam, J. W. McBride, C. Maul, and J. K. Atkinson, “Displacement measurements at the connector contact interface employing a novel thick-film sensor,” in Proceedings of the Fifty-First IEEE Holm Conference on Electrical Contacts (IEEE, 2005), pp. 89–96.
    [CrossRef]
  7. C. Stampfer, A. Jungen, R. Linderman, D. Obergfell, S. Roth, and C. Hierold, “Nanoelectromechanical displacement sensing based on single-walled carbon nanotubes,” Nano Lett. 6, 1449–1453 (2006).
    [CrossRef] [PubMed]
  8. S. Yana, Z. Ji, Y. Yan, X. Ye, Z. Zhou, and W. Zhang, “Design and modeling of a novel microdisplacement sensor-based optical frequency comb,” Proc. SPIE 750875080G (2009).
    [CrossRef]
  9. D. S. Nyce, Linear Position Sensors: Theory and Application (Wiley, 2003).
    [CrossRef]
  10. P. Hariharan, Optical Interferometry, 2nd ed. (Elsevier, 2003).
  11. X. Zeng, Y. Wu, C. Hou, and G. Yang, “High-finesse displacement sensor and a theoretical accelerometer model based on a fiber Fabry–Perot interferometer,” J. Zhejiang Univ. Sci. A 10, 589–594 (2009).
    [CrossRef]
  12. V. Etxebarria, J. Lucas, J. Feuchtwanger, A. Sadeghzadeh, H. Hassanzadegan, N. Garmendia, and J. Portilla, “Very high-sensitivity displacement sensor based on resonant cavities,” IEEE Sens. J. 10, 1335–1336 (2010).
    [CrossRef]
  13. J.-Y. Lee, H.-Y. Chen, C.-C. Hsu, and C.-C. Wu, “Optical heterodyne grating interferometer for displacement measurement with subnanometric resolution,” Sens. Actuators A 137, 185–191 (2007).
    [CrossRef]
  14. K.-S. Kim, R. J. Clifton, and P. Kumar, “A combined normal- and transverse- displacement interferometer with an application to impact of y-cut quartz,” J. Appl. Phys. 48, 4132–4139(1977).
    [CrossRef]
  15. J. Xu, D. Peng, W. Wan, and W. Yang, “New way of producing electrical traveling wave signal based on photoelectricity technology in design of time-grating displacement sensor,” Chin. J. Sens. Act. 20, 532–535 (2007).
  16. G. Zhou, L. Vj, and F. S. Chau, “An open-loop nanopositioning micromechanical digital-to-analog converter for grating light modulation,” IEEE Photonics Technol. Lett. 17, 1010–1012(2005).
    [CrossRef]
  17. W. Lee, N. A. Hall, Z. Zhou, and F. L. Degertekin, “Fabrication and characterization of a micromachined acoustic sensor with integrated optical readout,” IEEE J. Sel. Top. Quantum Electron. 10, 643–65 (2004).
    [CrossRef]
  18. N. A. Hall, W. Lee, and F. L. Degertekin, “Capacitive micromachined ultrasonic transducers with diffraction-based integrated optical displacement detection,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1570–1580 (2003).
    [CrossRef] [PubMed]

2010 (1)

V. Etxebarria, J. Lucas, J. Feuchtwanger, A. Sadeghzadeh, H. Hassanzadegan, N. Garmendia, and J. Portilla, “Very high-sensitivity displacement sensor based on resonant cavities,” IEEE Sens. J. 10, 1335–1336 (2010).
[CrossRef]

2009 (2)

S. Yana, Z. Ji, Y. Yan, X. Ye, Z. Zhou, and W. Zhang, “Design and modeling of a novel microdisplacement sensor-based optical frequency comb,” Proc. SPIE 750875080G (2009).
[CrossRef]

X. Zeng, Y. Wu, C. Hou, and G. Yang, “High-finesse displacement sensor and a theoretical accelerometer model based on a fiber Fabry–Perot interferometer,” J. Zhejiang Univ. Sci. A 10, 589–594 (2009).
[CrossRef]

2007 (2)

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

J. Xu, D. Peng, W. Wan, and W. Yang, “New way of producing electrical traveling wave signal based on photoelectricity technology in design of time-grating displacement sensor,” Chin. J. Sens. Act. 20, 532–535 (2007).

2006 (1)

C. Stampfer, A. Jungen, R. Linderman, D. Obergfell, S. Roth, and C. Hierold, “Nanoelectromechanical displacement sensing based on single-walled carbon nanotubes,” Nano Lett. 6, 1449–1453 (2006).
[CrossRef] [PubMed]

2005 (2)

G. Zhou, L. Vj, and F. S. Chau, “An open-loop nanopositioning micromechanical digital-to-analog converter for grating light modulation,” IEEE Photonics Technol. Lett. 17, 1010–1012(2005).
[CrossRef]

W. Suh, O. Solgaard, and S. Fan, “Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs,” J. Appl. Phys. 98, 033102 (2005).
[CrossRef]

2004 (1)

W. Lee, N. A. Hall, Z. Zhou, and F. L. Degertekin, “Fabrication and characterization of a micromachined acoustic sensor with integrated optical readout,” IEEE J. Sel. Top. Quantum Electron. 10, 643–65 (2004).
[CrossRef]

2003 (4)

N. A. Hall, W. Lee, and F. L. Degertekin, “Capacitive micromachined ultrasonic transducers with diffraction-based integrated optical displacement detection,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1570–1580 (2003).
[CrossRef] [PubMed]

R. G. Knobel and A. N. Cleland, “Nanometer-scale displacement sensing using a single electron transistor,” Nature 424, 291–293 (2003).
[CrossRef] [PubMed]

Y. Li, X. Mi, M. Sasaki, and K. Hane, “Precision optical displacement sensor based on ultra-thin film photodiode-type optical interferometers,” Meas. Sci. Technol. 14, 479–483(2003).
[CrossRef]

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photonics Technol. Lett. 15, 1129–1131 (2003).
[CrossRef]

1998 (1)

G. G. Yaralioglu, A. Atalar, S. R. Manalis, and C. F. Quate, “Analysis and design of an interdigital cantilever as a displacement sensor,” J. Appl. Phys. 83, 7405–7414 (1998).
[CrossRef]

1977 (1)

K.-S. Kim, R. J. Clifton, and P. Kumar, “A combined normal- and transverse- displacement interferometer with an application to impact of y-cut quartz,” J. Appl. Phys. 48, 4132–4139(1977).
[CrossRef]

Atalar, A.

G. G. Yaralioglu, A. Atalar, S. R. Manalis, and C. F. Quate, “Analysis and design of an interdigital cantilever as a displacement sensor,” J. Appl. Phys. 83, 7405–7414 (1998).
[CrossRef]

Atkinson, J. K.

Y.-Z. Lam, J. W. McBride, C. Maul, and J. K. Atkinson, “Displacement measurements at the connector contact interface employing a novel thick-film sensor,” in Proceedings of the Fifty-First IEEE Holm Conference on Electrical Contacts (IEEE, 2005), pp. 89–96.
[CrossRef]

Chau, F. S.

G. Zhou, L. Vj, and F. S. Chau, “An open-loop nanopositioning micromechanical digital-to-analog converter for grating light modulation,” IEEE Photonics Technol. Lett. 17, 1010–1012(2005).
[CrossRef]

Chen, H.-Y.

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

Cleland, A. N.

R. G. Knobel and A. N. Cleland, “Nanometer-scale displacement sensing using a single electron transistor,” Nature 424, 291–293 (2003).
[CrossRef] [PubMed]

Clifton, R. J.

K.-S. Kim, R. J. Clifton, and P. Kumar, “A combined normal- and transverse- displacement interferometer with an application to impact of y-cut quartz,” J. Appl. Phys. 48, 4132–4139(1977).
[CrossRef]

Degertekin, F. L.

W. Lee, N. A. Hall, Z. Zhou, and F. L. Degertekin, “Fabrication and characterization of a micromachined acoustic sensor with integrated optical readout,” IEEE J. Sel. Top. Quantum Electron. 10, 643–65 (2004).
[CrossRef]

N. A. Hall, W. Lee, and F. L. Degertekin, “Capacitive micromachined ultrasonic transducers with diffraction-based integrated optical displacement detection,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1570–1580 (2003).
[CrossRef] [PubMed]

Etxebarria, V.

V. Etxebarria, J. Lucas, J. Feuchtwanger, A. Sadeghzadeh, H. Hassanzadegan, N. Garmendia, and J. Portilla, “Very high-sensitivity displacement sensor based on resonant cavities,” IEEE Sens. J. 10, 1335–1336 (2010).
[CrossRef]

Fan, S.

W. Suh, O. Solgaard, and S. Fan, “Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs,” J. Appl. Phys. 98, 033102 (2005).
[CrossRef]

Feuchtwanger, J.

V. Etxebarria, J. Lucas, J. Feuchtwanger, A. Sadeghzadeh, H. Hassanzadegan, N. Garmendia, and J. Portilla, “Very high-sensitivity displacement sensor based on resonant cavities,” IEEE Sens. J. 10, 1335–1336 (2010).
[CrossRef]

Garmendia, N.

V. Etxebarria, J. Lucas, J. Feuchtwanger, A. Sadeghzadeh, H. Hassanzadegan, N. Garmendia, and J. Portilla, “Very high-sensitivity displacement sensor based on resonant cavities,” IEEE Sens. J. 10, 1335–1336 (2010).
[CrossRef]

Hall, N. A.

W. Lee, N. A. Hall, Z. Zhou, and F. L. Degertekin, “Fabrication and characterization of a micromachined acoustic sensor with integrated optical readout,” IEEE J. Sel. Top. Quantum Electron. 10, 643–65 (2004).
[CrossRef]

N. A. Hall, W. Lee, and F. L. Degertekin, “Capacitive micromachined ultrasonic transducers with diffraction-based integrated optical displacement detection,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1570–1580 (2003).
[CrossRef] [PubMed]

Hane, K.

Y. Li, X. Mi, M. Sasaki, and K. Hane, “Precision optical displacement sensor based on ultra-thin film photodiode-type optical interferometers,” Meas. Sci. Technol. 14, 479–483(2003).
[CrossRef]

Hariharan, P.

P. Hariharan, Optical Interferometry, 2nd ed. (Elsevier, 2003).

Hassanzadegan, H.

V. Etxebarria, J. Lucas, J. Feuchtwanger, A. Sadeghzadeh, H. Hassanzadegan, N. Garmendia, and J. Portilla, “Very high-sensitivity displacement sensor based on resonant cavities,” IEEE Sens. J. 10, 1335–1336 (2010).
[CrossRef]

Hierold, C.

C. Stampfer, A. Jungen, R. Linderman, D. Obergfell, S. Roth, and C. Hierold, “Nanoelectromechanical displacement sensing based on single-walled carbon nanotubes,” Nano Lett. 6, 1449–1453 (2006).
[CrossRef] [PubMed]

Hou, C.

X. Zeng, Y. Wu, C. Hou, and G. Yang, “High-finesse displacement sensor and a theoretical accelerometer model based on a fiber Fabry–Perot interferometer,” J. Zhejiang Univ. Sci. A 10, 589–594 (2009).
[CrossRef]

Hsu, C.-C.

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

Ji, Z.

S. Yana, Z. Ji, Y. Yan, X. Ye, Z. Zhou, and W. Zhang, “Design and modeling of a novel microdisplacement sensor-based optical frequency comb,” Proc. SPIE 750875080G (2009).
[CrossRef]

Johnson, E. G.

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photonics Technol. Lett. 15, 1129–1131 (2003).
[CrossRef]

Jungen, A.

C. Stampfer, A. Jungen, R. Linderman, D. Obergfell, S. Roth, and C. Hierold, “Nanoelectromechanical displacement sensing based on single-walled carbon nanotubes,” Nano Lett. 6, 1449–1453 (2006).
[CrossRef] [PubMed]

Kim, K.-S.

K.-S. Kim, R. J. Clifton, and P. Kumar, “A combined normal- and transverse- displacement interferometer with an application to impact of y-cut quartz,” J. Appl. Phys. 48, 4132–4139(1977).
[CrossRef]

Knobel, R. G.

R. G. Knobel and A. N. Cleland, “Nanometer-scale displacement sensing using a single electron transistor,” Nature 424, 291–293 (2003).
[CrossRef] [PubMed]

Kumar, P.

K.-S. Kim, R. J. Clifton, and P. Kumar, “A combined normal- and transverse- displacement interferometer with an application to impact of y-cut quartz,” J. Appl. Phys. 48, 4132–4139(1977).
[CrossRef]

Lam, Y.-Z.

Y.-Z. Lam, J. W. McBride, C. Maul, and J. K. Atkinson, “Displacement measurements at the connector contact interface employing a novel thick-film sensor,” in Proceedings of the Fifty-First IEEE Holm Conference on Electrical Contacts (IEEE, 2005), pp. 89–96.
[CrossRef]

Lee, J.-Y.

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

Lee, W.

W. Lee, N. A. Hall, Z. Zhou, and F. L. Degertekin, “Fabrication and characterization of a micromachined acoustic sensor with integrated optical readout,” IEEE J. Sel. Top. Quantum Electron. 10, 643–65 (2004).
[CrossRef]

N. A. Hall, W. Lee, and F. L. Degertekin, “Capacitive micromachined ultrasonic transducers with diffraction-based integrated optical displacement detection,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1570–1580 (2003).
[CrossRef] [PubMed]

Li, Y.

Y. Li, X. Mi, M. Sasaki, and K. Hane, “Precision optical displacement sensor based on ultra-thin film photodiode-type optical interferometers,” Meas. Sci. Technol. 14, 479–483(2003).
[CrossRef]

Linderman, R.

C. Stampfer, A. Jungen, R. Linderman, D. Obergfell, S. Roth, and C. Hierold, “Nanoelectromechanical displacement sensing based on single-walled carbon nanotubes,” Nano Lett. 6, 1449–1453 (2006).
[CrossRef] [PubMed]

Lucas, J.

V. Etxebarria, J. Lucas, J. Feuchtwanger, A. Sadeghzadeh, H. Hassanzadegan, N. Garmendia, and J. Portilla, “Very high-sensitivity displacement sensor based on resonant cavities,” IEEE Sens. J. 10, 1335–1336 (2010).
[CrossRef]

Manalis, S. R.

G. G. Yaralioglu, A. Atalar, S. R. Manalis, and C. F. Quate, “Analysis and design of an interdigital cantilever as a displacement sensor,” J. Appl. Phys. 83, 7405–7414 (1998).
[CrossRef]

Maul, C.

Y.-Z. Lam, J. W. McBride, C. Maul, and J. K. Atkinson, “Displacement measurements at the connector contact interface employing a novel thick-film sensor,” in Proceedings of the Fifty-First IEEE Holm Conference on Electrical Contacts (IEEE, 2005), pp. 89–96.
[CrossRef]

McBride, J. W.

Y.-Z. Lam, J. W. McBride, C. Maul, and J. K. Atkinson, “Displacement measurements at the connector contact interface employing a novel thick-film sensor,” in Proceedings of the Fifty-First IEEE Holm Conference on Electrical Contacts (IEEE, 2005), pp. 89–96.
[CrossRef]

Mehta, A.

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photonics Technol. Lett. 15, 1129–1131 (2003).
[CrossRef]

Mi, X.

Y. Li, X. Mi, M. Sasaki, and K. Hane, “Precision optical displacement sensor based on ultra-thin film photodiode-type optical interferometers,” Meas. Sci. Technol. 14, 479–483(2003).
[CrossRef]

Mohammed, W.

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photonics Technol. Lett. 15, 1129–1131 (2003).
[CrossRef]

Nyce, D. S.

D. S. Nyce, Linear Position Sensors: Theory and Application (Wiley, 2003).
[CrossRef]

Obergfell, D.

C. Stampfer, A. Jungen, R. Linderman, D. Obergfell, S. Roth, and C. Hierold, “Nanoelectromechanical displacement sensing based on single-walled carbon nanotubes,” Nano Lett. 6, 1449–1453 (2006).
[CrossRef] [PubMed]

Peng, D.

J. Xu, D. Peng, W. Wan, and W. Yang, “New way of producing electrical traveling wave signal based on photoelectricity technology in design of time-grating displacement sensor,” Chin. J. Sens. Act. 20, 532–535 (2007).

Portilla, J.

V. Etxebarria, J. Lucas, J. Feuchtwanger, A. Sadeghzadeh, H. Hassanzadegan, N. Garmendia, and J. Portilla, “Very high-sensitivity displacement sensor based on resonant cavities,” IEEE Sens. J. 10, 1335–1336 (2010).
[CrossRef]

Quate, C. F.

G. G. Yaralioglu, A. Atalar, S. R. Manalis, and C. F. Quate, “Analysis and design of an interdigital cantilever as a displacement sensor,” J. Appl. Phys. 83, 7405–7414 (1998).
[CrossRef]

Roth, S.

C. Stampfer, A. Jungen, R. Linderman, D. Obergfell, S. Roth, and C. Hierold, “Nanoelectromechanical displacement sensing based on single-walled carbon nanotubes,” Nano Lett. 6, 1449–1453 (2006).
[CrossRef] [PubMed]

Sadeghzadeh, A.

V. Etxebarria, J. Lucas, J. Feuchtwanger, A. Sadeghzadeh, H. Hassanzadegan, N. Garmendia, and J. Portilla, “Very high-sensitivity displacement sensor based on resonant cavities,” IEEE Sens. J. 10, 1335–1336 (2010).
[CrossRef]

Sasaki, M.

Y. Li, X. Mi, M. Sasaki, and K. Hane, “Precision optical displacement sensor based on ultra-thin film photodiode-type optical interferometers,” Meas. Sci. Technol. 14, 479–483(2003).
[CrossRef]

Solgaard, O.

W. Suh, O. Solgaard, and S. Fan, “Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs,” J. Appl. Phys. 98, 033102 (2005).
[CrossRef]

Stampfer, C.

C. Stampfer, A. Jungen, R. Linderman, D. Obergfell, S. Roth, and C. Hierold, “Nanoelectromechanical displacement sensing based on single-walled carbon nanotubes,” Nano Lett. 6, 1449–1453 (2006).
[CrossRef] [PubMed]

Suh, W.

W. Suh, O. Solgaard, and S. Fan, “Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs,” J. Appl. Phys. 98, 033102 (2005).
[CrossRef]

Vj, L.

G. Zhou, L. Vj, and F. S. Chau, “An open-loop nanopositioning micromechanical digital-to-analog converter for grating light modulation,” IEEE Photonics Technol. Lett. 17, 1010–1012(2005).
[CrossRef]

Wan, W.

J. Xu, D. Peng, W. Wan, and W. Yang, “New way of producing electrical traveling wave signal based on photoelectricity technology in design of time-grating displacement sensor,” Chin. J. Sens. Act. 20, 532–535 (2007).

Wu, C.-C.

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

Wu, Y.

X. Zeng, Y. Wu, C. Hou, and G. Yang, “High-finesse displacement sensor and a theoretical accelerometer model based on a fiber Fabry–Perot interferometer,” J. Zhejiang Univ. Sci. A 10, 589–594 (2009).
[CrossRef]

Xu, J.

J. Xu, D. Peng, W. Wan, and W. Yang, “New way of producing electrical traveling wave signal based on photoelectricity technology in design of time-grating displacement sensor,” Chin. J. Sens. Act. 20, 532–535 (2007).

Yan, Y.

S. Yana, Z. Ji, Y. Yan, X. Ye, Z. Zhou, and W. Zhang, “Design and modeling of a novel microdisplacement sensor-based optical frequency comb,” Proc. SPIE 750875080G (2009).
[CrossRef]

Yana, S.

S. Yana, Z. Ji, Y. Yan, X. Ye, Z. Zhou, and W. Zhang, “Design and modeling of a novel microdisplacement sensor-based optical frequency comb,” Proc. SPIE 750875080G (2009).
[CrossRef]

Yang, G.

X. Zeng, Y. Wu, C. Hou, and G. Yang, “High-finesse displacement sensor and a theoretical accelerometer model based on a fiber Fabry–Perot interferometer,” J. Zhejiang Univ. Sci. A 10, 589–594 (2009).
[CrossRef]

Yang, W.

J. Xu, D. Peng, W. Wan, and W. Yang, “New way of producing electrical traveling wave signal based on photoelectricity technology in design of time-grating displacement sensor,” Chin. J. Sens. Act. 20, 532–535 (2007).

Yaralioglu, G. G.

G. G. Yaralioglu, A. Atalar, S. R. Manalis, and C. F. Quate, “Analysis and design of an interdigital cantilever as a displacement sensor,” J. Appl. Phys. 83, 7405–7414 (1998).
[CrossRef]

Ye, X.

S. Yana, Z. Ji, Y. Yan, X. Ye, Z. Zhou, and W. Zhang, “Design and modeling of a novel microdisplacement sensor-based optical frequency comb,” Proc. SPIE 750875080G (2009).
[CrossRef]

Zeng, X.

X. Zeng, Y. Wu, C. Hou, and G. Yang, “High-finesse displacement sensor and a theoretical accelerometer model based on a fiber Fabry–Perot interferometer,” J. Zhejiang Univ. Sci. A 10, 589–594 (2009).
[CrossRef]

Zhang, W.

S. Yana, Z. Ji, Y. Yan, X. Ye, Z. Zhou, and W. Zhang, “Design and modeling of a novel microdisplacement sensor-based optical frequency comb,” Proc. SPIE 750875080G (2009).
[CrossRef]

Zhou, G.

G. Zhou, L. Vj, and F. S. Chau, “An open-loop nanopositioning micromechanical digital-to-analog converter for grating light modulation,” IEEE Photonics Technol. Lett. 17, 1010–1012(2005).
[CrossRef]

Zhou, Z.

S. Yana, Z. Ji, Y. Yan, X. Ye, Z. Zhou, and W. Zhang, “Design and modeling of a novel microdisplacement sensor-based optical frequency comb,” Proc. SPIE 750875080G (2009).
[CrossRef]

W. Lee, N. A. Hall, Z. Zhou, and F. L. Degertekin, “Fabrication and characterization of a micromachined acoustic sensor with integrated optical readout,” IEEE J. Sel. Top. Quantum Electron. 10, 643–65 (2004).
[CrossRef]

Chin. J. Sens. Act. (1)

J. Xu, D. Peng, W. Wan, and W. Yang, “New way of producing electrical traveling wave signal based on photoelectricity technology in design of time-grating displacement sensor,” Chin. J. Sens. Act. 20, 532–535 (2007).

IEEE J. Sel. Top. Quantum Electron. (1)

W. Lee, N. A. Hall, Z. Zhou, and F. L. Degertekin, “Fabrication and characterization of a micromachined acoustic sensor with integrated optical readout,” IEEE J. Sel. Top. Quantum Electron. 10, 643–65 (2004).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

G. Zhou, L. Vj, and F. S. Chau, “An open-loop nanopositioning micromechanical digital-to-analog converter for grating light modulation,” IEEE Photonics Technol. Lett. 17, 1010–1012(2005).
[CrossRef]

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photonics Technol. Lett. 15, 1129–1131 (2003).
[CrossRef]

IEEE Sens. J. (1)

V. Etxebarria, J. Lucas, J. Feuchtwanger, A. Sadeghzadeh, H. Hassanzadegan, N. Garmendia, and J. Portilla, “Very high-sensitivity displacement sensor based on resonant cavities,” IEEE Sens. J. 10, 1335–1336 (2010).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

N. A. Hall, W. Lee, and F. L. Degertekin, “Capacitive micromachined ultrasonic transducers with diffraction-based integrated optical displacement detection,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1570–1580 (2003).
[CrossRef] [PubMed]

J. Appl. Phys. (3)

W. Suh, O. Solgaard, and S. Fan, “Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs,” J. Appl. Phys. 98, 033102 (2005).
[CrossRef]

G. G. Yaralioglu, A. Atalar, S. R. Manalis, and C. F. Quate, “Analysis and design of an interdigital cantilever as a displacement sensor,” J. Appl. Phys. 83, 7405–7414 (1998).
[CrossRef]

K.-S. Kim, R. J. Clifton, and P. Kumar, “A combined normal- and transverse- displacement interferometer with an application to impact of y-cut quartz,” J. Appl. Phys. 48, 4132–4139(1977).
[CrossRef]

J. Zhejiang Univ. Sci. A (1)

X. Zeng, Y. Wu, C. Hou, and G. Yang, “High-finesse displacement sensor and a theoretical accelerometer model based on a fiber Fabry–Perot interferometer,” J. Zhejiang Univ. Sci. A 10, 589–594 (2009).
[CrossRef]

Meas. Sci. Technol. (1)

Y. Li, X. Mi, M. Sasaki, and K. Hane, “Precision optical displacement sensor based on ultra-thin film photodiode-type optical interferometers,” Meas. Sci. Technol. 14, 479–483(2003).
[CrossRef]

Nano Lett. (1)

C. Stampfer, A. Jungen, R. Linderman, D. Obergfell, S. Roth, and C. Hierold, “Nanoelectromechanical displacement sensing based on single-walled carbon nanotubes,” Nano Lett. 6, 1449–1453 (2006).
[CrossRef] [PubMed]

Nature (1)

R. G. Knobel and A. N. Cleland, “Nanometer-scale displacement sensing using a single electron transistor,” Nature 424, 291–293 (2003).
[CrossRef] [PubMed]

Proc. SPIE (1)

S. Yana, Z. Ji, Y. Yan, X. Ye, Z. Zhou, and W. Zhang, “Design and modeling of a novel microdisplacement sensor-based optical frequency comb,” Proc. SPIE 750875080G (2009).
[CrossRef]

Sens. Actuators A (1)

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

Other (3)

D. S. Nyce, Linear Position Sensors: Theory and Application (Wiley, 2003).
[CrossRef]

P. Hariharan, Optical Interferometry, 2nd ed. (Elsevier, 2003).

Y.-Z. Lam, J. W. McBride, C. Maul, and J. K. Atkinson, “Displacement measurements at the connector contact interface employing a novel thick-film sensor,” in Proceedings of the Fifty-First IEEE Holm Conference on Electrical Contacts (IEEE, 2005), pp. 89–96.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic of the nanometer-scale displacement measuring principle.

Fig. 2
Fig. 2

Simulation diffraction intensities of the first three orders as a function of displacement between the integrated grating and the mirror (d).

Fig. 3
Fig. 3

Block diagram of experimental setup for the proposed displacement sensor.

Fig. 4
Fig. 4

(a) Simulated and fitting curves for the output voltage as a function of the displacement Δ d = d 0 d . (b) Fitting straight line in the linear region.

Fig. 5
Fig. 5

Three examples of output voltage- displacement curves, randomly chosen in 15 experimental data sets.

Equations (2)

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I 0 = I in cos 2 ( 2 π d λ ) I ± 1 = 4 I in π 2 sin 2 ( 2 π d λ ) I ± 3 = 4 I in 9 π 2 sin 2 ( 2 π d λ ) ,
i = R | I ± 1 α I ± 3 | .

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