Abstract

A sinusoidal phase-modulating He–Ne laser subject to weak optical feedback has been used to develop an interferometer that is capable of performing real-time displacement measurement with nanometer accuracy. The principle and the signal processing method are introduced. A commercial dual-frequency interferometer is included in the displacement measurement in both small and large ranges to evaluate the performance of the developed interferometer. Experimental results show that the average errors and standard deviations of the interferometer are in good agreement with data obtained from the commercial interferometer. The resolution and the multiple feedback effect of the interferometer are discussed in detail. These results show that the development of the interferometer is reasonable and feasible.

© 2013 Optical Society of America

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  1. H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, “Dimensional micro and nano metrology,” CIRP Ann. 55, 721–743 (2006).
    [CrossRef]
  2. H. Martinussen, A. Aksnes, and H. E. Engan, “Wide frequency range measurements of absolute phase and amplitude of vibrations in micro- and nanostructures by optical interferometry,” Opt. Express 15, 11370–11384 (2007).
    [CrossRef]
  3. L. Chassagne, M. Wakim, S. Xu, S. Topçu, P. Ruaux, P. Juncar, and Y. Alayli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimetre displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
    [CrossRef]
  4. B. Bodermann, E. Bhur, G. Ehret, F. Scholze, and M. Wurm, “Optical metrology of micro- and nanostructures at PTB: status and future developments,” Proc. SPIE 7155, 71550V (2008).
    [CrossRef]
  5. C. D. Frank, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9, 1024–1030 (1998).
    [CrossRef]
  6. L. Xinqun, W. Clegg, D. F. L. Jenkins, and L. Bo, “Polarization interferometer for measuring small displacement,” IEEE Trans. Instrum. Meas. 50, 868–871 (2001).
    [CrossRef]
  7. K. Falaggis, D. P. Towers, and C. E. Towers, “Multiwavelength interferometry: extended range metrology,” Opt. Lett. 34, 950–952 (2009).
    [CrossRef]
  8. K. Falaggis and C. E. Towers, “Absolute metrology by phase and frequency modulation for multiwavelength interferometry,” Opt. Lett. 36, 2928–2930 (2011).
    [CrossRef]
  9. M. Suematsu and M. Takeda, “Wavelength-shift interferometry for distance measurements using the Fourier transform technique for fringe analysis,” Appl. Opt. 30, 4046–4055 (1991).
    [CrossRef]
  10. G. Guido, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A 4, S283–S294 (2002).
    [CrossRef]
  11. G. Guido, B.-P. Simone, and D. Silvano, “Self-mixing laser diode vibrometer,” Meas. Sci. Technol. 14, 24–32 (2003).
    [CrossRef]
  12. U. Zabit, O. D. Bernal, T. Bosch, and F. Bony, “MEMS accelerometer embedded in a self-mixing displacement sensor for parasitic vibration compensation,” Opt. Lett. 36, 612–614 (2011).
    [CrossRef]
  13. P. de Groot, “Design of error-compensating algorithms for sinusoidal phase shifting interferometry,” Appl. Opt. 48, 6788–6796 (2009).
    [CrossRef]
  14. D. Guo, M. Wang, and S. Tan, “Self-mixing interferometer based on sinusoidal phase modulating technique,” Opt. Express 13, 1537–1543 (2005).
    [CrossRef]
  15. O. Sasaki and H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
    [CrossRef]
  16. T. Suzuki, M. Matsuda, O. Sasaki, and T. Maruyama, “Laser-diode interferometer with a photothermal modulation,” Appl. Opt. 38, 7069–7075 (1999).
    [CrossRef]
  17. X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoidal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
    [CrossRef]
  18. N. Servagent, T. Bosch, and M. Lescure, “Design of a phase-shifting optical feedback interferometer using an electrooptic modulator,” IEEE J. Sel. Top. Quantum Electron. 6, 798–802 (2000).
    [CrossRef]
  19. D. Guo and M. Wang, “Self-mixing interferometer based on temporal-carrier phase-shifting technique for micro-displacement reconstruction,” Opt. Commun. 263, 91–97 (2006).
    [CrossRef]
  20. K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
    [CrossRef]
  21. B. Ovryn and J. H. Andrews, “Phase-shifted laser feedback interferometry,” Opt. Lett. 23, 1078–1080 (1998).
    [CrossRef]

2011 (2)

K. Falaggis and C. E. Towers, “Absolute metrology by phase and frequency modulation for multiwavelength interferometry,” Opt. Lett. 36, 2928–2930 (2011).
[CrossRef]

U. Zabit, O. D. Bernal, T. Bosch, and F. Bony, “MEMS accelerometer embedded in a self-mixing displacement sensor for parasitic vibration compensation,” Opt. Lett. 36, 612–614 (2011).
[CrossRef]

2009 (2)

P. de Groot, “Design of error-compensating algorithms for sinusoidal phase shifting interferometry,” Appl. Opt. 48, 6788–6796 (2009).
[CrossRef]

K. Falaggis, D. P. Towers, and C. E. Towers, “Multiwavelength interferometry: extended range metrology,” Opt. Lett. 34, 950–952 (2009).
[CrossRef]

2008 (1)

B. Bodermann, E. Bhur, G. Ehret, F. Scholze, and M. Wurm, “Optical metrology of micro- and nanostructures at PTB: status and future developments,” Proc. SPIE 7155, 71550V (2008).
[CrossRef]

2007 (2)

H. Martinussen, A. Aksnes, and H. E. Engan, “Wide frequency range measurements of absolute phase and amplitude of vibrations in micro- and nanostructures by optical interferometry,” Opt. Express 15, 11370–11384 (2007).
[CrossRef]

L. Chassagne, M. Wakim, S. Xu, S. Topçu, P. Ruaux, P. Juncar, and Y. Alayli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimetre displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

2006 (2)

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, “Dimensional micro and nano metrology,” CIRP Ann. 55, 721–743 (2006).
[CrossRef]

D. Guo and M. Wang, “Self-mixing interferometer based on temporal-carrier phase-shifting technique for micro-displacement reconstruction,” Opt. Commun. 263, 91–97 (2006).
[CrossRef]

2005 (1)

D. Guo, M. Wang, and S. Tan, “Self-mixing interferometer based on sinusoidal phase modulating technique,” Opt. Express 13, 1537–1543 (2005).
[CrossRef]

2003 (1)

G. Guido, B.-P. Simone, and D. Silvano, “Self-mixing laser diode vibrometer,” Meas. Sci. Technol. 14, 24–32 (2003).
[CrossRef]

2002 (1)

G. Guido, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A 4, S283–S294 (2002).
[CrossRef]

2001 (1)

L. Xinqun, W. Clegg, D. F. L. Jenkins, and L. Bo, “Polarization interferometer for measuring small displacement,” IEEE Trans. Instrum. Meas. 50, 868–871 (2001).
[CrossRef]

2000 (1)

N. Servagent, T. Bosch, and M. Lescure, “Design of a phase-shifting optical feedback interferometer using an electrooptic modulator,” IEEE J. Sel. Top. Quantum Electron. 6, 798–802 (2000).
[CrossRef]

1999 (2)

T. Suzuki, M. Matsuda, O. Sasaki, and T. Maruyama, “Laser-diode interferometer with a photothermal modulation,” Appl. Opt. 38, 7069–7075 (1999).
[CrossRef]

X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoidal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
[CrossRef]

1998 (2)

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

B. Ovryn and J. H. Andrews, “Phase-shifted laser feedback interferometry,” Opt. Lett. 23, 1078–1080 (1998).
[CrossRef]

1993 (1)

K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

1991 (1)

M. Suematsu and M. Takeda, “Wavelength-shift interferometry for distance measurements using the Fourier transform technique for fringe analysis,” Appl. Opt. 30, 4046–4055 (1991).
[CrossRef]

1986 (1)

O. Sasaki and H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
[CrossRef]

Aksnes, A.

H. Martinussen, A. Aksnes, and H. E. Engan, “Wide frequency range measurements of absolute phase and amplitude of vibrations in micro- and nanostructures by optical interferometry,” Opt. Express 15, 11370–11384 (2007).
[CrossRef]

Alayli, Y.

L. Chassagne, M. Wakim, S. Xu, S. Topçu, P. Ruaux, P. Juncar, and Y. Alayli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimetre displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

Andrews, J. H.

B. Ovryn and J. H. Andrews, “Phase-shifted laser feedback interferometry,” Opt. Lett. 23, 1078–1080 (1998).
[CrossRef]

Bernal, O. D.

U. Zabit, O. D. Bernal, T. Bosch, and F. Bony, “MEMS accelerometer embedded in a self-mixing displacement sensor for parasitic vibration compensation,” Opt. Lett. 36, 612–614 (2011).
[CrossRef]

Bhur, E.

B. Bodermann, E. Bhur, G. Ehret, F. Scholze, and M. Wurm, “Optical metrology of micro- and nanostructures at PTB: status and future developments,” Proc. SPIE 7155, 71550V (2008).
[CrossRef]

Birch, K. P.

K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

Bo, L.

L. Xinqun, W. Clegg, D. F. L. Jenkins, and L. Bo, “Polarization interferometer for measuring small displacement,” IEEE Trans. Instrum. Meas. 50, 868–871 (2001).
[CrossRef]

Bodermann, B.

B. Bodermann, E. Bhur, G. Ehret, F. Scholze, and M. Wurm, “Optical metrology of micro- and nanostructures at PTB: status and future developments,” Proc. SPIE 7155, 71550V (2008).
[CrossRef]

Bony, F.

U. Zabit, O. D. Bernal, T. Bosch, and F. Bony, “MEMS accelerometer embedded in a self-mixing displacement sensor for parasitic vibration compensation,” Opt. Lett. 36, 612–614 (2011).
[CrossRef]

Bosch, T.

U. Zabit, O. D. Bernal, T. Bosch, and F. Bony, “MEMS accelerometer embedded in a self-mixing displacement sensor for parasitic vibration compensation,” Opt. Lett. 36, 612–614 (2011).
[CrossRef]

G. Guido, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A 4, S283–S294 (2002).
[CrossRef]

N. Servagent, T. Bosch, and M. Lescure, “Design of a phase-shifting optical feedback interferometer using an electrooptic modulator,” IEEE J. Sel. Top. Quantum Electron. 6, 798–802 (2000).
[CrossRef]

Carneiro, K.

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, “Dimensional micro and nano metrology,” CIRP Ann. 55, 721–743 (2006).
[CrossRef]

Chassagne, L.

L. Chassagne, M. Wakim, S. Xu, S. Topçu, P. Ruaux, P. Juncar, and Y. Alayli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimetre displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

Chen, G.

X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoidal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
[CrossRef]

X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoidal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
[CrossRef]

Clegg, W.

L. Xinqun, W. Clegg, D. F. L. Jenkins, and L. Bo, “Polarization interferometer for measuring small displacement,” IEEE Trans. Instrum. Meas. 50, 868–871 (2001).
[CrossRef]

De Chiffre, L.

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, “Dimensional micro and nano metrology,” CIRP Ann. 55, 721–743 (2006).
[CrossRef]

de Groot, P.

P. de Groot, “Design of error-compensating algorithms for sinusoidal phase shifting interferometry,” Appl. Opt. 48, 6788–6796 (2009).
[CrossRef]

Donati, S.

G. Guido, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A 4, S283–S294 (2002).
[CrossRef]

Downs, M. J.

K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

Ehret, G.

B. Bodermann, E. Bhur, G. Ehret, F. Scholze, and M. Wurm, “Optical metrology of micro- and nanostructures at PTB: status and future developments,” Proc. SPIE 7155, 71550V (2008).
[CrossRef]

Engan, H. E.

H. Martinussen, A. Aksnes, and H. E. Engan, “Wide frequency range measurements of absolute phase and amplitude of vibrations in micro- and nanostructures by optical interferometry,” Opt. Express 15, 11370–11384 (2007).
[CrossRef]

Falaggis, K.

K. Falaggis and C. E. Towers, “Absolute metrology by phase and frequency modulation for multiwavelength interferometry,” Opt. Lett. 36, 2928–2930 (2011).
[CrossRef]

K. Falaggis, D. P. Towers, and C. E. Towers, “Multiwavelength interferometry: extended range metrology,” Opt. Lett. 34, 950–952 (2009).
[CrossRef]

Fang, Z.

X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoidal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
[CrossRef]

Frank, C. D.

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

Guido, G.

G. Guido, B.-P. Simone, and D. Silvano, “Self-mixing laser diode vibrometer,” Meas. Sci. Technol. 14, 24–32 (2003).
[CrossRef]

G. Guido, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A 4, S283–S294 (2002).
[CrossRef]

Guo, D.

D. Guo and M. Wang, “Self-mixing interferometer based on temporal-carrier phase-shifting technique for micro-displacement reconstruction,” Opt. Commun. 263, 91–97 (2006).
[CrossRef]

D. Guo, M. Wang, and S. Tan, “Self-mixing interferometer based on sinusoidal phase modulating technique,” Opt. Express 13, 1537–1543 (2005).
[CrossRef]

Haitjema, H.

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, “Dimensional micro and nano metrology,” CIRP Ann. 55, 721–743 (2006).
[CrossRef]

Hansen, H. N.

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, “Dimensional micro and nano metrology,” CIRP Ann. 55, 721–743 (2006).
[CrossRef]

Jenkins, D. F. L.

L. Xinqun, W. Clegg, D. F. L. Jenkins, and L. Bo, “Polarization interferometer for measuring small displacement,” IEEE Trans. Instrum. Meas. 50, 868–871 (2001).
[CrossRef]

Juncar, P.

L. Chassagne, M. Wakim, S. Xu, S. Topçu, P. Ruaux, P. Juncar, and Y. Alayli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimetre displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

Lescure, M.

N. Servagent, T. Bosch, and M. Lescure, “Design of a phase-shifting optical feedback interferometer using an electrooptic modulator,” IEEE J. Sel. Top. Quantum Electron. 6, 798–802 (2000).
[CrossRef]

Martinussen, H.

H. Martinussen, A. Aksnes, and H. E. Engan, “Wide frequency range measurements of absolute phase and amplitude of vibrations in micro- and nanostructures by optical interferometry,” Opt. Express 15, 11370–11384 (2007).
[CrossRef]

Maruyama, T.

T. Suzuki, M. Matsuda, O. Sasaki, and T. Maruyama, “Laser-diode interferometer with a photothermal modulation,” Appl. Opt. 38, 7069–7075 (1999).
[CrossRef]

Matsuda, M.

T. Suzuki, M. Matsuda, O. Sasaki, and T. Maruyama, “Laser-diode interferometer with a photothermal modulation,” Appl. Opt. 38, 7069–7075 (1999).
[CrossRef]

Norgia, M.

G. Guido, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A 4, S283–S294 (2002).
[CrossRef]

Okazaki, H.

O. Sasaki and H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
[CrossRef]

Ovryn, B.

B. Ovryn and J. H. Andrews, “Phase-shifted laser feedback interferometry,” Opt. Lett. 23, 1078–1080 (1998).
[CrossRef]

Qian, F.

X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoidal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
[CrossRef]

Ruaux, P.

L. Chassagne, M. Wakim, S. Xu, S. Topçu, P. Ruaux, P. Juncar, and Y. Alayli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimetre displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

Sasaki, O.

T. Suzuki, M. Matsuda, O. Sasaki, and T. Maruyama, “Laser-diode interferometer with a photothermal modulation,” Appl. Opt. 38, 7069–7075 (1999).
[CrossRef]

O. Sasaki and H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
[CrossRef]

Scholze, F.

B. Bodermann, E. Bhur, G. Ehret, F. Scholze, and M. Wurm, “Optical metrology of micro- and nanostructures at PTB: status and future developments,” Proc. SPIE 7155, 71550V (2008).
[CrossRef]

Servagent, N.

N. Servagent, T. Bosch, and M. Lescure, “Design of a phase-shifting optical feedback interferometer using an electrooptic modulator,” IEEE J. Sel. Top. Quantum Electron. 6, 798–802 (2000).
[CrossRef]

Silvano, D.

G. Guido, B.-P. Simone, and D. Silvano, “Self-mixing laser diode vibrometer,” Meas. Sci. Technol. 14, 24–32 (2003).
[CrossRef]

Simone, B.-P.

G. Guido, B.-P. Simone, and D. Silvano, “Self-mixing laser diode vibrometer,” Meas. Sci. Technol. 14, 24–32 (2003).
[CrossRef]

Suematsu, M.

M. Suematsu and M. Takeda, “Wavelength-shift interferometry for distance measurements using the Fourier transform technique for fringe analysis,” Appl. Opt. 30, 4046–4055 (1991).
[CrossRef]

Suzuki, T.

T. Suzuki, M. Matsuda, O. Sasaki, and T. Maruyama, “Laser-diode interferometer with a photothermal modulation,” Appl. Opt. 38, 7069–7075 (1999).
[CrossRef]

Takeda, M.

M. Suematsu and M. Takeda, “Wavelength-shift interferometry for distance measurements using the Fourier transform technique for fringe analysis,” Appl. Opt. 30, 4046–4055 (1991).
[CrossRef]

Tan, S.

D. Guo, M. Wang, and S. Tan, “Self-mixing interferometer based on sinusoidal phase modulating technique,” Opt. Express 13, 1537–1543 (2005).
[CrossRef]

Topçu, S.

L. Chassagne, M. Wakim, S. Xu, S. Topçu, P. Ruaux, P. Juncar, and Y. Alayli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimetre displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

Towers, C. E.

K. Falaggis and C. E. Towers, “Absolute metrology by phase and frequency modulation for multiwavelength interferometry,” Opt. Lett. 36, 2928–2930 (2011).
[CrossRef]

K. Falaggis, D. P. Towers, and C. E. Towers, “Multiwavelength interferometry: extended range metrology,” Opt. Lett. 34, 950–952 (2009).
[CrossRef]

Towers, D. P.

K. Falaggis, D. P. Towers, and C. E. Towers, “Multiwavelength interferometry: extended range metrology,” Opt. Lett. 34, 950–952 (2009).
[CrossRef]

Wakim, M.

L. Chassagne, M. Wakim, S. Xu, S. Topçu, P. Ruaux, P. Juncar, and Y. Alayli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimetre displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

Wang, M.

D. Guo and M. Wang, “Self-mixing interferometer based on temporal-carrier phase-shifting technique for micro-displacement reconstruction,” Opt. Commun. 263, 91–97 (2006).
[CrossRef]

D. Guo, M. Wang, and S. Tan, “Self-mixing interferometer based on sinusoidal phase modulating technique,” Opt. Express 13, 1537–1543 (2005).
[CrossRef]

Wang, X.

X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoidal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
[CrossRef]

X. Wang, X. Wang, F. Qian, G. Chen, G. Chen, and Z. Fang, “Photothermal modulation of laser diode wavelength: application to sinusoidal phase-modulating interferometer for displacement measurements,” Opt. Laser Technol. 31, 559–564 (1999).
[CrossRef]

Wurm, M.

B. Bodermann, E. Bhur, G. Ehret, F. Scholze, and M. Wurm, “Optical metrology of micro- and nanostructures at PTB: status and future developments,” Proc. SPIE 7155, 71550V (2008).
[CrossRef]

Xinqun, L.

L. Xinqun, W. Clegg, D. F. L. Jenkins, and L. Bo, “Polarization interferometer for measuring small displacement,” IEEE Trans. Instrum. Meas. 50, 868–871 (2001).
[CrossRef]

Xu, S.

L. Chassagne, M. Wakim, S. Xu, S. Topçu, P. Ruaux, P. Juncar, and Y. Alayli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimetre displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

Zabit, U.

U. Zabit, O. D. Bernal, T. Bosch, and F. Bony, “MEMS accelerometer embedded in a self-mixing displacement sensor for parasitic vibration compensation,” Opt. Lett. 36, 612–614 (2011).
[CrossRef]

Appl. Opt. (4)

M. Suematsu and M. Takeda, “Wavelength-shift interferometry for distance measurements using the Fourier transform technique for fringe analysis,” Appl. Opt. 30, 4046–4055 (1991).
[CrossRef]

P. de Groot, “Design of error-compensating algorithms for sinusoidal phase shifting interferometry,” Appl. Opt. 48, 6788–6796 (2009).
[CrossRef]

O. Sasaki and H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
[CrossRef]

T. Suzuki, M. Matsuda, O. Sasaki, and T. Maruyama, “Laser-diode interferometer with a photothermal modulation,” Appl. Opt. 38, 7069–7075 (1999).
[CrossRef]

CIRP Ann. (1)

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, “Dimensional micro and nano metrology,” CIRP Ann. 55, 721–743 (2006).
[CrossRef]

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

N. Servagent, T. Bosch, and M. Lescure, “Design of a phase-shifting optical feedback interferometer using an electrooptic modulator,” IEEE J. Sel. Top. Quantum Electron. 6, 798–802 (2000).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

L. Xinqun, W. Clegg, D. F. L. Jenkins, and L. Bo, “Polarization interferometer for measuring small displacement,” IEEE Trans. Instrum. Meas. 50, 868–871 (2001).
[CrossRef]

J. Opt. A (1)

G. Guido, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A 4, S283–S294 (2002).
[CrossRef]

Meas. Sci. Technol. (3)

G. Guido, B.-P. Simone, and D. Silvano, “Self-mixing laser diode vibrometer,” Meas. Sci. Technol. 14, 24–32 (2003).
[CrossRef]

L. Chassagne, M. Wakim, S. Xu, S. Topçu, P. Ruaux, P. Juncar, and Y. Alayli, “A 2D nano-positioning system with sub-nanometric repeatability over the millimetre displacement range,” Meas. Sci. Technol. 18, 3267–3272 (2007).
[CrossRef]

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

Metrologia (1)

K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

Opt. Commun. (1)

D. Guo and M. Wang, “Self-mixing interferometer based on temporal-carrier phase-shifting technique for micro-displacement reconstruction,” Opt. Commun. 263, 91–97 (2006).
[CrossRef]

Opt. Express (2)

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[CrossRef]

H. Martinussen, A. Aksnes, and H. E. Engan, “Wide frequency range measurements of absolute phase and amplitude of vibrations in micro- and nanostructures by optical interferometry,” Opt. Express 15, 11370–11384 (2007).
[CrossRef]

Opt. Laser Technol. (1)

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[CrossRef]

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K. Falaggis, D. P. Towers, and C. E. Towers, “Multiwavelength interferometry: extended range metrology,” Opt. Lett. 34, 950–952 (2009).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Schematic diagram of the sinusoidal phase-modulating SMI.

Fig. 2.
Fig. 2.

Realization of interference signal processing: (a) simulated phase modulating SMI signal, (b) frequency spectrum of SMI signal, (c) intensities of the first and second harmonics, and (d) wrapped measured phase.

Fig. 3.
Fig. 3.

Schematic diagram of the signal processing of a sinusoidal phase-modulating SMI. LP, low-pass filter; FFT, fast Fourier transform; IFFT, inverse fast Fourier transform.

Fig. 4.
Fig. 4.

Photo of experimental setup. PBS, polarized beam splitter.

Fig. 5.
Fig. 5.

Comparison of displacement measurements in the millimeter range.

Fig. 6.
Fig. 6.

Comparison of displacement measurements in the micrometer range.

Fig. 7.
Fig. 7.

Comparison of displacement measurements in the nanometer range.

Fig. 8.
Fig. 8.

Measurement results for displacement amplitude of about (a) 100 nm (curve A) and 400 nm (curve B) and (b) 10 μm (curve C) and 20 μm (curve D).

Fig. 9.
Fig. 9.

Standard deviation of displacement measurement versus fringe visibility.

Fig. 10.
Fig. 10.

Noises in the displacement measurement.

Tables (4)

Tables Icon

Table 1. Displacement Measurement Results in the Millimeter Range

Tables Icon

Table 2. Displacement Measurement Results in the Micrometer Range

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Table 3. Displacement Measurement Results in the Nanometer Range

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Table 4. Displacement Amplitude Measured by Our System and the Agilent 5529A Interferometer

Equations (11)

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I(t)=I0{1+mcos[φ(t)+ψ(t)]}
φ(t)=4πnL(t)/λ0,
I(t)=I0[1+mcosφ(t)J0(2a)]+2mI0cosφ(t)n=1J2n(2a)cos(2n)(wMt+β)2mI0sinφ(t)n=1J2n1(2a)cos[(2n1)(wMt+β)],
φ(t)=arctan[J2(2a)J1(2a)·A1(t)A2(t)],
δΔL=(ΔLnδn)2+(ΔLλ0δλ)2+(λ04πnδΔφ)2,
Δntpf=[0.00268(PP0)0.929(TT0)0.00042(ff0)]×106,
δλ=λ02cδν0.9492×106μm.
s(t)=mI0cos{φ(t)+[a+δa(t)]sin(wmt+β)}.
Δφa=4πnΔLλ0+δasin(wmt+β),
δΔφ=ΔφaΔφ=Δφa4πnΔLλ0=δasin(wmt+β)|δa|.
I=I0[1+mcos(ϕ)j=0(η)jcos(jϕ)],

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