Abstract

Approaches that are, to our knowledge, novel, are proposed in this paper to improve the accuracy performance of self-mixing interferometry (SMI) for displacement measurement. First, the characteristics associated with signals observed in SMI systems are studied, based on which a new procedure is proposed for achieving accurate estimation of the laser phase. The studies also revealed the reasons for the inherent errors associated with the existing SMI-based techniques for displacement measurement. Then, this paper presents a new method for estimating the optical feedback level factor (denoted by C) in real time. Combining the new algorithms for estimating the laser phase and updating C value, the paper finally presents a novel technique for displacement measurement with improved accuracy performance in contrast to existing techniques. The proposed technique is verified by both simulation and experimental data.

© 2011 Optical Society of America

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References

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  1. G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
    [CrossRef]
  2. T. Bosch, “An overview of self-mixing sensing applications,” in Proceedings of IEEE Conference on Optoelectronic and Microelectronic Materials and Devices (IEEE, 2004), pp. 385–392.
    [CrossRef]
  3. L. Scalise, Y. Yanguang, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53, 223–232 (2004).
    [CrossRef]
  4. S. Donati, M. Norgia, and G. Giuliani, “A review of self-mixing techniques for sensing applications,” in Proceedings of the 17th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2004 (LEOS 2004), Vol.  261, pp. 260–261.
  5. S. Donati, “Laser interferometry by induced modulation of cavity field,” J. Appl. Phys. 49, 495–497 (1978).
    [CrossRef]
  6. S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31, 113–119(1995).
    [CrossRef]
  7. S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33, 527–531 (1997).
    [CrossRef]
  8. N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29, 168–173 (1998).
    [CrossRef]
  9. D. M. Guo, M. Wang, and S. Q. Tan, “Self-mixing interferometer based on sinusoidal phase modulating technique,” Opt. Express 13, 1537–1543 (2005).
    [CrossRef] [PubMed]
  10. G. Plantier, C. Bes, T. Bosch, and F. Bony, “Autoadaptive signal processing of a laser diode self-mixing displacement sensor,” in Proceedings of IEEE Conference on Instrumentation and Measurement Technology (IEEE, 2005), pp. 1013–1017.
    [CrossRef]
  11. C. Bes, G. Plantier, and T. Bosch, “Displacement measurements using a self-mixing laser diode under moderate feedback,” IEEE Trans. Instrum. Meas. 55, 1101–1105 (2006).
    [CrossRef]
  12. U. Zabit, T. Bosch, and F. Bony, “A fast derivative-less optimization of the feedback coupling coefficient for a self-mixing laser displacement sensor,” in Proceedings of IEEE North-East Workshop on Circuits and Systems and TAISA (IEEE, 2009), pp. 1–4.
    [CrossRef]
  13. U. Zabit, T. Bosch, and F. Bony, “Adaptive transition detection algorithm for a self-mixing displacement sensor,” IEEE Sens. J. 9, 1879–1886 (2009).
    [CrossRef]
  14. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
    [CrossRef]
  15. N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24, 1242–1247(1988).
    [CrossRef]
  16. Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16, 990–992 (2004).
    [CrossRef]
  17. J. Xi, Y. Yu, J. F. Chicharo, and T. Bosch, “Estimating the parameters of semiconductor lasers based on weak optical feedback self-mixing interferometry,” IEEE J. Quantum Electron. 41, 1058–1064 (2005).
    [CrossRef]
  18. Y. Yu, J. Xi, J. F. Chicharo, and T. M. Bosch, “Optical feedback self-mixing interferometry with a large feedback factor C: behavior studies,” IEEE J. Quantum Electron. 45, 840–848(2009).
    [CrossRef]
  19. Y. Yu, J. Xi, J. F. Chicharo, and T. Bosch, “Toward automatic measurement of the linewidth-enhancement factor using optical feedback self-mixing interferometry with weak optical feedback,” IEEE J. Quantum Electron. 43, 527–534 (2007).
    [CrossRef]

2009 (2)

U. Zabit, T. Bosch, and F. Bony, “Adaptive transition detection algorithm for a self-mixing displacement sensor,” IEEE Sens. J. 9, 1879–1886 (2009).
[CrossRef]

Y. Yu, J. Xi, J. F. Chicharo, and T. M. Bosch, “Optical feedback self-mixing interferometry with a large feedback factor C: behavior studies,” IEEE J. Quantum Electron. 45, 840–848(2009).
[CrossRef]

2007 (1)

Y. Yu, J. Xi, J. F. Chicharo, and T. Bosch, “Toward automatic measurement of the linewidth-enhancement factor using optical feedback self-mixing interferometry with weak optical feedback,” IEEE J. Quantum Electron. 43, 527–534 (2007).
[CrossRef]

2006 (1)

C. Bes, G. Plantier, and T. Bosch, “Displacement measurements using a self-mixing laser diode under moderate feedback,” IEEE Trans. Instrum. Meas. 55, 1101–1105 (2006).
[CrossRef]

2005 (2)

J. Xi, Y. Yu, J. F. Chicharo, and T. Bosch, “Estimating the parameters of semiconductor lasers based on weak optical feedback self-mixing interferometry,” IEEE J. Quantum Electron. 41, 1058–1064 (2005).
[CrossRef]

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

2004 (2)

L. Scalise, Y. Yanguang, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53, 223–232 (2004).
[CrossRef]

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16, 990–992 (2004).
[CrossRef]

2002 (1)

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

1998 (1)

N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29, 168–173 (1998).
[CrossRef]

1997 (1)

S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33, 527–531 (1997).
[CrossRef]

1995 (1)

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31, 113–119(1995).
[CrossRef]

1988 (1)

N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24, 1242–1247(1988).
[CrossRef]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
[CrossRef]

1978 (1)

S. Donati, “Laser interferometry by induced modulation of cavity field,” J. Appl. Phys. 49, 495–497 (1978).
[CrossRef]

Bes, C.

C. Bes, G. Plantier, and T. Bosch, “Displacement measurements using a self-mixing laser diode under moderate feedback,” IEEE Trans. Instrum. Meas. 55, 1101–1105 (2006).
[CrossRef]

G. Plantier, C. Bes, T. Bosch, and F. Bony, “Autoadaptive signal processing of a laser diode self-mixing displacement sensor,” in Proceedings of IEEE Conference on Instrumentation and Measurement Technology (IEEE, 2005), pp. 1013–1017.
[CrossRef]

Bony, F.

U. Zabit, T. Bosch, and F. Bony, “Adaptive transition detection algorithm for a self-mixing displacement sensor,” IEEE Sens. J. 9, 1879–1886 (2009).
[CrossRef]

U. Zabit, T. Bosch, and F. Bony, “A fast derivative-less optimization of the feedback coupling coefficient for a self-mixing laser displacement sensor,” in Proceedings of IEEE North-East Workshop on Circuits and Systems and TAISA (IEEE, 2009), pp. 1–4.
[CrossRef]

G. Plantier, C. Bes, T. Bosch, and F. Bony, “Autoadaptive signal processing of a laser diode self-mixing displacement sensor,” in Proceedings of IEEE Conference on Instrumentation and Measurement Technology (IEEE, 2005), pp. 1013–1017.
[CrossRef]

Bosch, T.

U. Zabit, T. Bosch, and F. Bony, “Adaptive transition detection algorithm for a self-mixing displacement sensor,” IEEE Sens. J. 9, 1879–1886 (2009).
[CrossRef]

Y. Yu, J. Xi, J. F. Chicharo, and T. Bosch, “Toward automatic measurement of the linewidth-enhancement factor using optical feedback self-mixing interferometry with weak optical feedback,” IEEE J. Quantum Electron. 43, 527–534 (2007).
[CrossRef]

C. Bes, G. Plantier, and T. Bosch, “Displacement measurements using a self-mixing laser diode under moderate feedback,” IEEE Trans. Instrum. Meas. 55, 1101–1105 (2006).
[CrossRef]

J. Xi, Y. Yu, J. F. Chicharo, and T. Bosch, “Estimating the parameters of semiconductor lasers based on weak optical feedback self-mixing interferometry,” IEEE J. Quantum Electron. 41, 1058–1064 (2005).
[CrossRef]

L. Scalise, Y. Yanguang, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53, 223–232 (2004).
[CrossRef]

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

N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29, 168–173 (1998).
[CrossRef]

T. Bosch, “An overview of self-mixing sensing applications,” in Proceedings of IEEE Conference on Optoelectronic and Microelectronic Materials and Devices (IEEE, 2004), pp. 385–392.
[CrossRef]

G. Plantier, C. Bes, T. Bosch, and F. Bony, “Autoadaptive signal processing of a laser diode self-mixing displacement sensor,” in Proceedings of IEEE Conference on Instrumentation and Measurement Technology (IEEE, 2005), pp. 1013–1017.
[CrossRef]

U. Zabit, T. Bosch, and F. Bony, “A fast derivative-less optimization of the feedback coupling coefficient for a self-mixing laser displacement sensor,” in Proceedings of IEEE North-East Workshop on Circuits and Systems and TAISA (IEEE, 2009), pp. 1–4.
[CrossRef]

Bosch, T. M.

Y. Yu, J. Xi, J. F. Chicharo, and T. M. Bosch, “Optical feedback self-mixing interferometry with a large feedback factor C: behavior studies,” IEEE J. Quantum Electron. 45, 840–848(2009).
[CrossRef]

Chicharo, J. F.

Y. Yu, J. Xi, J. F. Chicharo, and T. M. Bosch, “Optical feedback self-mixing interferometry with a large feedback factor C: behavior studies,” IEEE J. Quantum Electron. 45, 840–848(2009).
[CrossRef]

Y. Yu, J. Xi, J. F. Chicharo, and T. Bosch, “Toward automatic measurement of the linewidth-enhancement factor using optical feedback self-mixing interferometry with weak optical feedback,” IEEE J. Quantum Electron. 43, 527–534 (2007).
[CrossRef]

J. Xi, Y. Yu, J. F. Chicharo, and T. Bosch, “Estimating the parameters of semiconductor lasers based on weak optical feedback self-mixing interferometry,” IEEE J. Quantum Electron. 41, 1058–1064 (2005).
[CrossRef]

Donati, S.

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16, 990–992 (2004).
[CrossRef]

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

S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33, 527–531 (1997).
[CrossRef]

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31, 113–119(1995).
[CrossRef]

S. Donati, “Laser interferometry by induced modulation of cavity field,” J. Appl. Phys. 49, 495–497 (1978).
[CrossRef]

S. Donati, M. Norgia, and G. Giuliani, “A review of self-mixing techniques for sensing applications,” in Proceedings of the 17th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2004 (LEOS 2004), Vol.  261, pp. 260–261.

Giuliani, G.

L. Scalise, Y. Yanguang, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53, 223–232 (2004).
[CrossRef]

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16, 990–992 (2004).
[CrossRef]

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

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31, 113–119(1995).
[CrossRef]

S. Donati, M. Norgia, and G. Giuliani, “A review of self-mixing techniques for sensing applications,” in Proceedings of the 17th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2004 (LEOS 2004), Vol.  261, pp. 260–261.

Gouaux, F.

N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29, 168–173 (1998).
[CrossRef]

Guo, D. M.

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
[CrossRef]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
[CrossRef]

Merlo, S.

S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33, 527–531 (1997).
[CrossRef]

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31, 113–119(1995).
[CrossRef]

Norgia, M.

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

S. Donati, M. Norgia, and G. Giuliani, “A review of self-mixing techniques for sensing applications,” in Proceedings of the 17th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2004 (LEOS 2004), Vol.  261, pp. 260–261.

Petermann, K.

N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24, 1242–1247(1988).
[CrossRef]

Plantier, G.

C. Bes, G. Plantier, and T. Bosch, “Displacement measurements using a self-mixing laser diode under moderate feedback,” IEEE Trans. Instrum. Meas. 55, 1101–1105 (2006).
[CrossRef]

L. Scalise, Y. Yanguang, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53, 223–232 (2004).
[CrossRef]

G. Plantier, C. Bes, T. Bosch, and F. Bony, “Autoadaptive signal processing of a laser diode self-mixing displacement sensor,” in Proceedings of IEEE Conference on Instrumentation and Measurement Technology (IEEE, 2005), pp. 1013–1017.
[CrossRef]

Scalise, L.

L. Scalise, Y. Yanguang, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53, 223–232 (2004).
[CrossRef]

Schunk, N.

N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24, 1242–1247(1988).
[CrossRef]

Servagent, N.

N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29, 168–173 (1998).
[CrossRef]

Tan, S. Q.

Wang, M.

Xi, J.

Y. Yu, J. Xi, J. F. Chicharo, and T. M. Bosch, “Optical feedback self-mixing interferometry with a large feedback factor C: behavior studies,” IEEE J. Quantum Electron. 45, 840–848(2009).
[CrossRef]

Y. Yu, J. Xi, J. F. Chicharo, and T. Bosch, “Toward automatic measurement of the linewidth-enhancement factor using optical feedback self-mixing interferometry with weak optical feedback,” IEEE J. Quantum Electron. 43, 527–534 (2007).
[CrossRef]

J. Xi, Y. Yu, J. F. Chicharo, and T. Bosch, “Estimating the parameters of semiconductor lasers based on weak optical feedback self-mixing interferometry,” IEEE J. Quantum Electron. 41, 1058–1064 (2005).
[CrossRef]

Yanguang, Y.

L. Scalise, Y. Yanguang, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53, 223–232 (2004).
[CrossRef]

Yu, Y.

Y. Yu, J. Xi, J. F. Chicharo, and T. M. Bosch, “Optical feedback self-mixing interferometry with a large feedback factor C: behavior studies,” IEEE J. Quantum Electron. 45, 840–848(2009).
[CrossRef]

Y. Yu, J. Xi, J. F. Chicharo, and T. Bosch, “Toward automatic measurement of the linewidth-enhancement factor using optical feedback self-mixing interferometry with weak optical feedback,” IEEE J. Quantum Electron. 43, 527–534 (2007).
[CrossRef]

J. Xi, Y. Yu, J. F. Chicharo, and T. Bosch, “Estimating the parameters of semiconductor lasers based on weak optical feedback self-mixing interferometry,” IEEE J. Quantum Electron. 41, 1058–1064 (2005).
[CrossRef]

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16, 990–992 (2004).
[CrossRef]

Zabit, U.

U. Zabit, T. Bosch, and F. Bony, “Adaptive transition detection algorithm for a self-mixing displacement sensor,” IEEE Sens. J. 9, 1879–1886 (2009).
[CrossRef]

U. Zabit, T. Bosch, and F. Bony, “A fast derivative-less optimization of the feedback coupling coefficient for a self-mixing laser displacement sensor,” in Proceedings of IEEE North-East Workshop on Circuits and Systems and TAISA (IEEE, 2009), pp. 1–4.
[CrossRef]

IEEE J. Quantum Electron. (7)

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31, 113–119(1995).
[CrossRef]

S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33, 527–531 (1997).
[CrossRef]

J. Xi, Y. Yu, J. F. Chicharo, and T. Bosch, “Estimating the parameters of semiconductor lasers based on weak optical feedback self-mixing interferometry,” IEEE J. Quantum Electron. 41, 1058–1064 (2005).
[CrossRef]

Y. Yu, J. Xi, J. F. Chicharo, and T. M. Bosch, “Optical feedback self-mixing interferometry with a large feedback factor C: behavior studies,” IEEE J. Quantum Electron. 45, 840–848(2009).
[CrossRef]

Y. Yu, J. Xi, J. F. Chicharo, and T. Bosch, “Toward automatic measurement of the linewidth-enhancement factor using optical feedback self-mixing interferometry with weak optical feedback,” IEEE J. Quantum Electron. 43, 527–534 (2007).
[CrossRef]

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
[CrossRef]

N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24, 1242–1247(1988).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16, 990–992 (2004).
[CrossRef]

IEEE Sens. J. (1)

U. Zabit, T. Bosch, and F. Bony, “Adaptive transition detection algorithm for a self-mixing displacement sensor,” IEEE Sens. J. 9, 1879–1886 (2009).
[CrossRef]

IEEE Trans. Instrum. Meas. (2)

C. Bes, G. Plantier, and T. Bosch, “Displacement measurements using a self-mixing laser diode under moderate feedback,” IEEE Trans. Instrum. Meas. 55, 1101–1105 (2006).
[CrossRef]

L. Scalise, Y. Yanguang, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53, 223–232 (2004).
[CrossRef]

J. Appl. Phys. (1)

S. Donati, “Laser interferometry by induced modulation of cavity field,” J. Appl. Phys. 49, 495–497 (1978).
[CrossRef]

J. Opt. (1)

N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29, 168–173 (1998).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

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

Opt. Express (1)

Other (4)

U. Zabit, T. Bosch, and F. Bony, “A fast derivative-less optimization of the feedback coupling coefficient for a self-mixing laser displacement sensor,” in Proceedings of IEEE North-East Workshop on Circuits and Systems and TAISA (IEEE, 2009), pp. 1–4.
[CrossRef]

T. Bosch, “An overview of self-mixing sensing applications,” in Proceedings of IEEE Conference on Optoelectronic and Microelectronic Materials and Devices (IEEE, 2004), pp. 385–392.
[CrossRef]

S. Donati, M. Norgia, and G. Giuliani, “A review of self-mixing techniques for sensing applications,” in Proceedings of the 17th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2004 (LEOS 2004), Vol.  261, pp. 260–261.

G. Plantier, C. Bes, T. Bosch, and F. Bony, “Autoadaptive signal processing of a laser diode self-mixing displacement sensor,” in Proceedings of IEEE Conference on Instrumentation and Measurement Technology (IEEE, 2005), pp. 1013–1017.
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

SMI-based displacement sensing system and an SMS waveform. (a) Displacement L ( n ) generated by the moving target; (b) SMS waveform with C = 3 , α = 3 ; (c) SMI structure.

Fig. 2
Fig. 2

Classification of fringe shapes. (a) Displacement waveform L ( n ) ; (b) sinusoidal-like fringe (type 1) with C = 0.5 , α = 3 ; (c) left-inclined sawtoothlike fringe (type 2) and right-inclined sawtoothlike fringe (type 3) with C = 2 , α = 3 .

Fig. 3
Fig. 3

Characteristic points on an SMS ( C = 2 , α = 1.3 ).

Fig. 4
Fig. 4

Extracting reverse segments from an SMS. (a) SMS with C = 3 , α = 3 ; (b) pulse train e ( n ) ; (c) extracted reverse segments of the SMS.

Fig. 5
Fig. 5

Segmentation of an SMS with C = 3 , α = 3 .

Fig. 6
Fig. 6

Reconstruction result by using a preset C ^ with C ^ = 2 . (a) Displacement L ( n ) ; (b) SMS with C = 6 , α = 3 ; (c) reconstructed displacement L ^ ( n ) with C ^ = 2 ; (d) residual error between L ( n ) and L ^ ( n ) .

Fig. 7
Fig. 7

Displacement reconstruction results and their corresponding fluctuation signals using different C ^ . (a) Displacement reconstruction result L ^ ( n ) , (b) fluctuation signals D F ( n ) .

Fig. 8
Fig. 8

Reconstruction results under a weak feedback level. (a) Feedback phase ϕ F ( n ) ; (b) simulated SMS with C = 0.6 , α = 2 ; (c) reconstructed ϕ ^ F ( n ) ; (d) residual error between ϕ F ( n ) and ϕ ^ F ( n ) .

Fig. 9
Fig. 9

Reconstruction results under a moderate feedback level. (a) Feedback phase ϕ F ( n ) ; (b) simulated SMS with C = 2 , α = 3 ; (c) reconstructed ϕ ^ F ( n ) ; (d) residual error between ϕ F ( n ) and ϕ ^ F ( n ) .

Fig. 10
Fig. 10

Reconstruction results under a strong feedback level. (a) Feedback phase ϕ F ( n ) ; (b) simulated SMS with C = 5 , α = 1.3 ; (c) reconstructed ϕ ^ F ( n ) ; (d) residual error between ϕ F ( n ) and ϕ ^ F ( n ) .

Fig. 11
Fig. 11

Numerical simulation results when treating P and J as same point. (a) Displacement waveform L ( n ) ; (b) SMS with C = 2 , α = 4 ; (c) reconstructed displacement L ^ ( n ) from the SMS; (d) residual error between L ( n ) and L ^ ( n ) .

Fig. 12
Fig. 12

Displacement reconstruction results by using experimental data. (a) Three SMSs under different feedback levels, (b) displacement reconstruction results cooperating real-time C values, (c) displacement reconstruction results with a preset C ( C = 5 ).

Tables (2)

Tables Icon

Table 1 Meaning of Parameters in Equations (1, 2, 3, 4)

Tables Icon

Table 2 C Estimation Results

Equations (10)

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

ϕ 0 ( n ) = 4 π L ( n ) / λ 0 ,
ϕ F ( n ) = ϕ 0 ( n ) C sin [ ϕ F ( n ) + arctan ( α ) ] ,
g ( n ) = cos ( ϕ F ( n ) ) ,
p ( n ) = p 0 [ 1 + b · g ( n ) ] .
ϕ F r ( n ) = arccos ( g ( n ) ) .
ϕ F ( n ) = { ϕ F r ( n ) + 2 π ( k 1 ) , when v ( k ) n < p ( k ) ϕ F r ( n ) + 2 π ( k 1 ) , when p ( k ) n < v ( k + 1 ) ,
ϕ F ( n ) = { ϕ F r ( n ) 2 π ( K k + 1 ) , when v ( k ) n < p ( k ) ϕ F r ( n ) 2 π ( K k + 1 ) , when p ( k ) n < v ( k + 1 ) ,
ϕ F ( n ) = { ϕ F r ( n ) + 2 π ( k 1 ) , when v ( k ) n < p ( k ) ϕ F r ( n ) + 2 π ( k 1 ) , when p ( k ) n < j ( k ) ,
ϕ F ( n ) = { ϕ F r ( n ) 2 π ( K k + 1 ) , when v ( k ) n < p ( k ) + 1 ϕ F r ( n ) 2 π ( K k + 1 ) , when p ( k ) + 1 n < j ( k ) .
S = D F ( n ) .

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