Abstract

The use of wavelength-modulated light incorporated into an optical-path-difference speckle interferometer is demonstrated as a heterodyne technique for measuring the in-plane displacement of a rough object. The in-plane displacement can be determined from the measured phase variation of the heterodyne speckle signal. We also improved the optical configuration to create a high-contrast interference pattern. Experimental results reveal that the proposed method can detect displacement up to a long range of 220 μm and displacement variation down to the nanometer range. Moreover, the sensitivity can reach up to 0.8°/nm. The performance of the system is discussed.

© 2012 Optical Society of America

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References

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  1. 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. Express 19, 9770–9782 (2011).
    [CrossRef]
  2. G. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75, 962–969 (2004).
    [CrossRef]
  3. 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]
  4. D. C. Su, M. H. Chiu, and C. D. Chen, “A heterodyne interferometer using an electro-optic modulator for measuring small displacements,” J. Opt. 27, 19–23 (1996).
    [CrossRef]
  5. H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
    [CrossRef]
  6. D. C. Williams, Optical Methods in Engineering Metrology (Chapman & Hall, 1993).
  7. Y. Zhong, G. Zhang, C. Leng, and T. Zhang, “A differential laser Doppler system for one-dimensional in-plane motion measurement of MEMS,” Measurement 40, 623–627 (2007).
    [CrossRef]
  8. X. Wang, X. Dong, J. Guo, and T. Xie, “Two-dimensional displacement sensing using a cross diffraction grating scheme,” J. Opt. A 6, 106–111 (2004).
    [CrossRef]
  9. Y. Wang, Q. Wang, P. Li, J. Lan, and K. Guo, “Photorefractive holographic interferometry for the measurement of object tilt and in-plane displacement,” Proc. SPIE 4292, 230–238 (2002).
    [CrossRef]
  10. S. T. Lin, “Three-dimensional displacement measurement using a newly designed moiré interferometer,” Opt. Eng. 40, 822–826 (2001).
    [CrossRef]
  11. N. K. Mohan and P. Rastogi, “Phase-shifting whole-field speckle photography technique for the measurement of in-plane deformations in real time,” Opt. Lett. 27, 565–567 (2002).
    [CrossRef]
  12. C. F. Kao, C. C. Chang, and M. H. Lu, “Double-diffraction planar encoder by conjugate optics,” Opt. Eng. 44, 023603 (2005).
    [CrossRef]
  13. G. Zhou and F. S. Chau, “Grating-assisted optical microprobing of in-plane and out-of-plane displacements of microelectromechanical devices,” J. Microelectromech. Syst. 15, 388–395 (2006).
    [CrossRef]
  14. R. Dandliker and J. F. Willemin, “Measuring microvibrations by heterodyne speckle interferometry,” Opt. Lett. 6, 165–167 (1981).
    [CrossRef]
  15. J. F. Willemin and R. Dandliker, “Measuring amplitude and phase of microvibrations by heterodyne speckle interferometry,” Opt. Lett. 8, 102–104 (1983).
    [CrossRef]
  16. F. Dong, K. Atherton, G. Pierce, and B. Culshaw, “Measurement of in-plane and out-of-plane displacements for ultrasonic flaw detection,” Proc. SPIE 4073, 324–331 (2000).
    [CrossRef]
  17. M. L. Jakobsen, H. E. Larsen, and S. G. Hanson, “Optical spatial filtering velocimetry sensor for sub-micron, in-plane vibration measurements,” J. Opt. A 7, S303–S307 (2005).
    [CrossRef]
  18. J. Y. Lee, K. Y. Lin, and S. H. Huang, “Wavelength-modulated heterodyne speckle interferometry for displacement measurement,” Proc. SPIE 7389, 73892G (2009).
    [CrossRef]
  19. J. Zheng, “Optical frequency-modulated continuous-wave interferometers,” Appl. Opt. 45, 2723–2730 (2006).
    [CrossRef]
  20. P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57–69 (2008).
    [CrossRef]
  21. J. H. Song, K. C. Kim, and S. H. Kim, “Reducing tilt errors in moiré linear encoders using phase-modulated grating,” Rev. Sci. Instrum. 71, 2296–2300 (2000).
    [CrossRef]

2011

2010

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
[CrossRef]

2009

J. Y. Lee, K. Y. Lin, and S. H. Huang, “Wavelength-modulated heterodyne speckle interferometry for displacement measurement,” Proc. SPIE 7389, 73892G (2009).
[CrossRef]

2008

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57–69 (2008).
[CrossRef]

2007

Y. Zhong, G. Zhang, C. Leng, and T. Zhang, “A differential laser Doppler system for one-dimensional in-plane motion measurement of MEMS,” Measurement 40, 623–627 (2007).
[CrossRef]

2006

J. Zheng, “Optical frequency-modulated continuous-wave interferometers,” Appl. Opt. 45, 2723–2730 (2006).
[CrossRef]

G. Zhou and F. S. Chau, “Grating-assisted optical microprobing of in-plane and out-of-plane displacements of microelectromechanical devices,” J. Microelectromech. Syst. 15, 388–395 (2006).
[CrossRef]

2005

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

M. L. Jakobsen, H. E. Larsen, and S. G. Hanson, “Optical spatial filtering velocimetry sensor for sub-micron, in-plane vibration measurements,” J. Opt. A 7, S303–S307 (2005).
[CrossRef]

2004

X. Wang, X. Dong, J. Guo, and T. Xie, “Two-dimensional displacement sensing using a cross diffraction grating scheme,” J. Opt. A 6, 106–111 (2004).
[CrossRef]

G. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75, 962–969 (2004).
[CrossRef]

2002

Y. Wang, Q. Wang, P. Li, J. Lan, and K. Guo, “Photorefractive holographic interferometry for the measurement of object tilt and in-plane displacement,” Proc. SPIE 4292, 230–238 (2002).
[CrossRef]

N. K. Mohan and P. Rastogi, “Phase-shifting whole-field speckle photography technique for the measurement of in-plane deformations in real time,” Opt. Lett. 27, 565–567 (2002).
[CrossRef]

2001

S. T. Lin, “Three-dimensional displacement measurement using a newly designed moiré interferometer,” Opt. Eng. 40, 822–826 (2001).
[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]

2000

F. Dong, K. Atherton, G. Pierce, and B. Culshaw, “Measurement of in-plane and out-of-plane displacements for ultrasonic flaw detection,” Proc. SPIE 4073, 324–331 (2000).
[CrossRef]

J. H. Song, K. C. Kim, and S. H. Kim, “Reducing tilt errors in moiré linear encoders using phase-modulated grating,” Rev. Sci. Instrum. 71, 2296–2300 (2000).
[CrossRef]

1996

D. C. Su, M. H. Chiu, and C. D. Chen, “A heterodyne interferometer using an electro-optic modulator for measuring small displacements,” J. Opt. 27, 19–23 (1996).
[CrossRef]

1983

1981

Atherton, K.

F. Dong, K. Atherton, G. Pierce, and B. Culshaw, “Measurement of in-plane and out-of-plane displacements for ultrasonic flaw detection,” Proc. SPIE 4073, 324–331 (2000).
[CrossRef]

Chang, C. C.

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

Chau, F. S.

G. Zhou and F. S. Chau, “Grating-assisted optical microprobing of in-plane and out-of-plane displacements of microelectromechanical devices,” J. Microelectromech. Syst. 15, 388–395 (2006).
[CrossRef]

Chen, C. D.

D. C. Su, M. H. Chiu, and C. D. Chen, “A heterodyne interferometer using an electro-optic modulator for measuring small displacements,” J. Opt. 27, 19–23 (1996).
[CrossRef]

Chen, J. C.

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. Express 19, 9770–9782 (2011).
[CrossRef]

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
[CrossRef]

Chiu, M. H.

D. C. Su, M. H. Chiu, and C. D. Chen, “A heterodyne interferometer using an electro-optic modulator for measuring small displacements,” J. Opt. 27, 19–23 (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]

Culshaw, B.

F. Dong, K. Atherton, G. Pierce, and B. Culshaw, “Measurement of in-plane and out-of-plane displacements for ultrasonic flaw detection,” Proc. SPIE 4073, 324–331 (2000).
[CrossRef]

Dai, G.

G. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75, 962–969 (2004).
[CrossRef]

Dandliker, R.

Danzebrink, H. U.

G. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75, 962–969 (2004).
[CrossRef]

Deturche, R.

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
[CrossRef]

Dong, F.

F. Dong, K. Atherton, G. Pierce, and B. Culshaw, “Measurement of in-plane and out-of-plane displacements for ultrasonic flaw detection,” Proc. SPIE 4073, 324–331 (2000).
[CrossRef]

Dong, X.

X. Wang, X. Dong, J. Guo, and T. Xie, “Two-dimensional displacement sensing using a cross diffraction grating scheme,” J. Opt. A 6, 106–111 (2004).
[CrossRef]

Guo, J.

X. Wang, X. Dong, J. Guo, and T. Xie, “Two-dimensional displacement sensing using a cross diffraction grating scheme,” J. Opt. A 6, 106–111 (2004).
[CrossRef]

Guo, K.

Y. Wang, Q. Wang, P. Li, J. Lan, and K. Guo, “Photorefractive holographic interferometry for the measurement of object tilt and in-plane displacement,” Proc. SPIE 4292, 230–238 (2002).
[CrossRef]

Hanson, S. G.

M. L. Jakobsen, H. E. Larsen, and S. G. Hanson, “Optical spatial filtering velocimetry sensor for sub-micron, in-plane vibration measurements,” J. Opt. A 7, S303–S307 (2005).
[CrossRef]

Hasche, K.

G. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75, 962–969 (2004).
[CrossRef]

Hsieh, H. L.

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. Express 19, 9770–9782 (2011).
[CrossRef]

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
[CrossRef]

Huang, S. H.

J. Y. Lee, K. Y. Lin, and S. H. Huang, “Wavelength-modulated heterodyne speckle interferometry for displacement measurement,” Proc. SPIE 7389, 73892G (2009).
[CrossRef]

Jacquot, P.

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57–69 (2008).
[CrossRef]

Jakobsen, M. L.

M. L. Jakobsen, H. E. Larsen, and S. G. Hanson, “Optical spatial filtering velocimetry sensor for sub-micron, in-plane vibration measurements,” J. Opt. A 7, S303–S307 (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, 023603 (2005).
[CrossRef]

Kim, K. C.

J. H. Song, K. C. Kim, and S. H. Kim, “Reducing tilt errors in moiré linear encoders using phase-modulated grating,” Rev. Sci. Instrum. 71, 2296–2300 (2000).
[CrossRef]

Kim, S. H.

J. H. Song, K. C. Kim, and S. H. Kim, “Reducing tilt errors in moiré linear encoders using phase-modulated grating,” Rev. Sci. Instrum. 71, 2296–2300 (2000).
[CrossRef]

Lan, J.

Y. Wang, Q. Wang, P. Li, J. Lan, and K. Guo, “Photorefractive holographic interferometry for the measurement of object tilt and in-plane displacement,” Proc. SPIE 4292, 230–238 (2002).
[CrossRef]

Larsen, H. E.

M. L. Jakobsen, H. E. Larsen, and S. G. Hanson, “Optical spatial filtering velocimetry sensor for sub-micron, in-plane vibration measurements,” J. Opt. A 7, S303–S307 (2005).
[CrossRef]

Lee, J. Y.

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. Express 19, 9770–9782 (2011).
[CrossRef]

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
[CrossRef]

J. Y. Lee, K. Y. Lin, and S. H. Huang, “Wavelength-modulated heterodyne speckle interferometry for displacement measurement,” Proc. SPIE 7389, 73892G (2009).
[CrossRef]

Leng, C.

Y. Zhong, G. Zhang, C. Leng, and T. Zhang, “A differential laser Doppler system for one-dimensional in-plane motion measurement of MEMS,” Measurement 40, 623–627 (2007).
[CrossRef]

Lerondel, G.

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. Express 19, 9770–9782 (2011).
[CrossRef]

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
[CrossRef]

Li, P.

Y. Wang, Q. Wang, P. Li, J. Lan, and K. Guo, “Photorefractive holographic interferometry for the measurement of object tilt and in-plane displacement,” Proc. SPIE 4292, 230–238 (2002).
[CrossRef]

Lin, K. Y.

J. Y. Lee, K. Y. Lin, and S. H. Huang, “Wavelength-modulated heterodyne speckle interferometry for displacement measurement,” Proc. SPIE 7389, 73892G (2009).
[CrossRef]

Lin, S. T.

S. T. Lin, “Three-dimensional displacement measurement using a newly designed moiré interferometer,” Opt. Eng. 40, 822–826 (2001).
[CrossRef]

Lu, M. H.

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

Pierce, G.

F. Dong, K. Atherton, G. Pierce, and B. Culshaw, “Measurement of in-plane and out-of-plane displacements for ultrasonic flaw detection,” Proc. SPIE 4073, 324–331 (2000).
[CrossRef]

Pohlenz, F.

G. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75, 962–969 (2004).
[CrossRef]

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]

Song, J. H.

J. H. Song, K. C. Kim, and S. H. Kim, “Reducing tilt errors in moiré linear encoders using phase-modulated grating,” Rev. Sci. Instrum. 71, 2296–2300 (2000).
[CrossRef]

Su, D. C.

D. C. Su, M. H. Chiu, and C. D. Chen, “A heterodyne interferometer using an electro-optic modulator for measuring small displacements,” J. Opt. 27, 19–23 (1996).
[CrossRef]

Wang, Q.

Y. Wang, Q. Wang, P. Li, J. Lan, and K. Guo, “Photorefractive holographic interferometry for the measurement of object tilt and in-plane displacement,” Proc. SPIE 4292, 230–238 (2002).
[CrossRef]

Wang, X.

X. Wang, X. Dong, J. Guo, and T. Xie, “Two-dimensional displacement sensing using a cross diffraction grating scheme,” J. Opt. A 6, 106–111 (2004).
[CrossRef]

Wang, Y.

Y. Wang, Q. Wang, P. Li, J. Lan, and K. Guo, “Photorefractive holographic interferometry for the measurement of object tilt and in-plane displacement,” Proc. SPIE 4292, 230–238 (2002).
[CrossRef]

Wilkening, G.

G. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75, 962–969 (2004).
[CrossRef]

Willemin, J. F.

Williams, D. C.

D. C. Williams, Optical Methods in Engineering Metrology (Chapman & Hall, 1993).

Wu, W. T.

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
[CrossRef]

Xie, T.

X. Wang, X. Dong, J. Guo, and T. Xie, “Two-dimensional displacement sensing using a cross diffraction grating scheme,” J. Opt. A 6, 106–111 (2004).
[CrossRef]

Xu, M.

G. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75, 962–969 (2004).
[CrossRef]

Zhang, G.

Y. Zhong, G. Zhang, C. Leng, and T. Zhang, “A differential laser Doppler system for one-dimensional in-plane motion measurement of MEMS,” Measurement 40, 623–627 (2007).
[CrossRef]

Zhang, T.

Y. Zhong, G. Zhang, C. Leng, and T. Zhang, “A differential laser Doppler system for one-dimensional in-plane motion measurement of MEMS,” Measurement 40, 623–627 (2007).
[CrossRef]

Zheng, J.

Zhong, Y.

Y. Zhong, G. Zhang, C. Leng, and T. Zhang, “A differential laser Doppler system for one-dimensional in-plane motion measurement of MEMS,” Measurement 40, 623–627 (2007).
[CrossRef]

Zhou, G.

G. Zhou and F. S. Chau, “Grating-assisted optical microprobing of in-plane and out-of-plane displacements of microelectromechanical devices,” J. Microelectromech. Syst. 15, 388–395 (2006).
[CrossRef]

Appl. Opt.

J. Microelectromech. Syst.

G. Zhou and F. S. Chau, “Grating-assisted optical microprobing of in-plane and out-of-plane displacements of microelectromechanical devices,” J. Microelectromech. Syst. 15, 388–395 (2006).
[CrossRef]

J. Opt.

D. C. Su, M. H. Chiu, and C. D. Chen, “A heterodyne interferometer using an electro-optic modulator for measuring small displacements,” J. Opt. 27, 19–23 (1996).
[CrossRef]

J. Opt. A

X. Wang, X. Dong, J. Guo, and T. Xie, “Two-dimensional displacement sensing using a cross diffraction grating scheme,” J. Opt. A 6, 106–111 (2004).
[CrossRef]

M. L. Jakobsen, H. E. Larsen, and S. G. Hanson, “Optical spatial filtering velocimetry sensor for sub-micron, in-plane vibration measurements,” J. Opt. A 7, S303–S307 (2005).
[CrossRef]

Meas. Sci. Technol.

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]

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21, 115304 (2010).
[CrossRef]

Measurement

Y. Zhong, G. Zhang, C. Leng, and T. Zhang, “A differential laser Doppler system for one-dimensional in-plane motion measurement of MEMS,” Measurement 40, 623–627 (2007).
[CrossRef]

Opt. Eng.

S. T. Lin, “Three-dimensional displacement measurement using a newly designed moiré interferometer,” Opt. Eng. 40, 822–826 (2001).
[CrossRef]

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

Opt. Express

Opt. Lett.

Proc. SPIE

F. Dong, K. Atherton, G. Pierce, and B. Culshaw, “Measurement of in-plane and out-of-plane displacements for ultrasonic flaw detection,” Proc. SPIE 4073, 324–331 (2000).
[CrossRef]

J. Y. Lee, K. Y. Lin, and S. H. Huang, “Wavelength-modulated heterodyne speckle interferometry for displacement measurement,” Proc. SPIE 7389, 73892G (2009).
[CrossRef]

Y. Wang, Q. Wang, P. Li, J. Lan, and K. Guo, “Photorefractive holographic interferometry for the measurement of object tilt and in-plane displacement,” Proc. SPIE 4292, 230–238 (2002).
[CrossRef]

Rev. Sci. Instrum.

G. Dai, F. Pohlenz, H. U. Danzebrink, M. Xu, K. Hasche, and G. Wilkening, “Metrological large range scanning probe microscope,” Rev. Sci. Instrum. 75, 962–969 (2004).
[CrossRef]

J. H. Song, K. C. Kim, and S. H. Kim, “Reducing tilt errors in moiré linear encoders using phase-modulated grating,” Rev. Sci. Instrum. 71, 2296–2300 (2000).
[CrossRef]

Strain

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57–69 (2008).
[CrossRef]

Other

D. C. Williams, Optical Methods in Engineering Metrology (Chapman & Hall, 1993).

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Figures (8)

Fig. 1.
Fig. 1.

Schematic diagram of the wavelength-modulated heterodyne speckle interferometer, where LD is the laser diode, FG is the function generator, BS is the beam splitter, TM is the triangular mirror, M is the mirror, S is the roughness surface, L is the lens, A is the aperture, PD is the photodetector, and DAQ is the data acquisition card.

Fig. 2.
Fig. 2.

Signal process diagram for calculating the phase variation.

Fig. 3.
Fig. 3.

Measurement results for long in-plane displacement of about 220 μm.

Fig. 4.
Fig. 4.

Observed nonlinear motion of the stage.

Fig. 5.
Fig. 5.

Measurement results for forward and backward in-plane displacement with amplitudes of about (a) 30 μm and 10 μm and (b) 5 μm and 1 μm.

Fig. 6.
Fig. 6.

Measurement results for the step-by-step in-plane motion.

Fig. 7.
Fig. 7.

Measurement results for in-plane displacement with steps of 10 nm.

Fig. 8.
Fig. 8.

Calculated displacement noise, including high and low frequency.

Equations (7)

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

I = I 0 [ 1 + γ cos ( 2 π Δ l / λ 0 + Φ ) ] .
Φ = 0 Γ 4 π Δ ν · d t = 4 π sin θ λ 0 0 Γ u d t = 4 π sin θ λ 0 d .
I ( t ) = I m ( t ) · [ 1 + γ cos ( ω t ϕ Φ ) ] .
d = λ 0 4 π sin θ × Φ .
Φ / d = 4 π sin θ / λ 0 .
Φ d n = 4 π d i sin θ λ 0 ± ( ϕ H + ϕ L ) ,
d c = λ 0 4 π sin θ × Φ d n = d i λ 0 × ( ϕ H + ϕ L ) 4 π sin θ .

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