Abstract

Theoretical analysis and experimental results of self-mixing speckle interference in a distributed feedback (DFB) laser are presented in this paper. Self-mixing speckle interference occurs when external optical feedback comes from a moving rough surface. Dynamic output variations in the DFB laser as well as their probability density functions (PDFs) are analyzed on the basis of speckle theory and self-mixing interference in the DFB laser. Numeric simulations and experiments are in agreement with each other. The both results show that self-mixing speckle interference in DFB laser can be used to measure velocity of target.

© 2006 Optical Society of America

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  1. T. Shibata, S. Shinohara et al. "Laser speckle velocimeter using self-mixing laser diode," IEEE Trans. Instrum. Meas. 45,499-503 (1996).
    [CrossRef]
  2. P. A. Porta, D. P. Curtin and J. G. McInerney, "Laser Doppler velocimetry by optical self-mixing in vertical-cavity surface-emitting lasers," IEEE Photonics Technol. Lett. 14, 1717-1721 (2002).
    [CrossRef]
  3. G. Giuliani, S. Bozzi-Pietra, S. Donati, "Self-mixing laser diode vibrometer" Meas. Sci. Tech. 14, 24-32 (2003).
    [CrossRef]
  4. M. Norgia, S. Donati, "A displacement-measuring instrument utilizing self-mixing interferometry", IEEE Trans. Instrum. Meas. 52, 1765-1770 (2003).
    [CrossRef]
  5. L. Scalise, Y. G. Yu, G. Giuliani,  et al. "Self-mixing laser diode velocimetry: Application to vibration and velocity measurement," IEEE Trans. Instrum. Meas. 53, 223-232 (2004).
    [CrossRef]
  6. J. W. Choi, M. J. Yu, M. Kopica, "Photoacoustic laser Doppler velocimetry using the self-mixing effect of CO2 laser," Proc. Soc. Photo-Opt.Instrum. 5240, 230-234 (2004).
  7. M. Laroche, L. Kervevan, H. Gilles, S. Girard, J.K. Sahu, "Doppler velocimetry using self-mixing effect in a short Er-Yb-doped phosphate glass fiber laser," Appl. Phys. B 80, 603-607 (2005).
    [CrossRef]
  8. T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, "Automatic measurement of velocity and length of moving plate using self-mixing laser diode", IEEE Trans. Instrum. Meas. 48, 1062-1067 (1999).
    [CrossRef]
  9. Sahin Kaya zdemir, S. Ito, S. Shinohara, H. Yoshida, M . Sumi, "Correlation-based speckle velocimeter with self-mixing interference in a semiconductor laser diode," Appl. Opt. 38, 6859-6865(1999).
    [CrossRef]
  10. M. Norgi, S. Donati, D. D’Alessandro, "Interferometric measurements of displacement on a diffusing target by a speckle tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
    [CrossRef]
  11. H. Huan, M. Wang, D. Guo et al. "Self-mixing interference effect of DFB semiconductor lasers," Appl. Phys. B 79,1554-1559 (2004).
    [CrossRef]
  12. J. Zhou, M. Wang, "Effects of self-mixing interference on gain-coupled distributed-feedback lasers," Opt. Express 13,1848-1854 (2005).
    [CrossRef] [PubMed]
  13. Max Born and Emil Worlf, Principles of Optics, Pergamon press, (1975).
  14. E. I. Thorsos, "The validity of the kirchoff approximation for rough surface scattering using a Gaussian roughness spectrum," J. Acous. Soc. Am. 83, 78-92 (1988).
    [CrossRef]
  15. A. K. Fung, M. F. Chen, "Numerical simulation of scattering from simple and composite random surfaces," J. Opt. Soc. Am. A 2, 2274-2284 (1985).
    [CrossRef]
  16. F. Favre, "Theoretical analysis of external optical feedback on DFB semiconductor lasers," IEEE J. Quantum Electron. 23, 81-88 (1987).
    [CrossRef]

2005

M. Laroche, L. Kervevan, H. Gilles, S. Girard, J.K. Sahu, "Doppler velocimetry using self-mixing effect in a short Er-Yb-doped phosphate glass fiber laser," Appl. Phys. B 80, 603-607 (2005).
[CrossRef]

J. Zhou, M. Wang, "Effects of self-mixing interference on gain-coupled distributed-feedback lasers," Opt. Express 13,1848-1854 (2005).
[CrossRef] [PubMed]

2004

H. Huan, M. Wang, D. Guo et al. "Self-mixing interference effect of DFB semiconductor lasers," Appl. Phys. B 79,1554-1559 (2004).
[CrossRef]

L. Scalise, Y. G. Yu, G. Giuliani,  et al. "Self-mixing laser diode velocimetry: Application to vibration and velocity measurement," IEEE Trans. Instrum. Meas. 53, 223-232 (2004).
[CrossRef]

J. W. Choi, M. J. Yu, M. Kopica, "Photoacoustic laser Doppler velocimetry using the self-mixing effect of CO2 laser," Proc. Soc. Photo-Opt.Instrum. 5240, 230-234 (2004).

2003

G. Giuliani, S. Bozzi-Pietra, S. Donati, "Self-mixing laser diode vibrometer" Meas. Sci. Tech. 14, 24-32 (2003).
[CrossRef]

M. Norgia, S. Donati, "A displacement-measuring instrument utilizing self-mixing interferometry", IEEE Trans. Instrum. Meas. 52, 1765-1770 (2003).
[CrossRef]

2002

P. A. Porta, D. P. Curtin and J. G. McInerney, "Laser Doppler velocimetry by optical self-mixing in vertical-cavity surface-emitting lasers," IEEE Photonics Technol. Lett. 14, 1717-1721 (2002).
[CrossRef]

2001

M. Norgi, S. Donati, D. D’Alessandro, "Interferometric measurements of displacement on a diffusing target by a speckle tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
[CrossRef]

1999

T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, "Automatic measurement of velocity and length of moving plate using self-mixing laser diode", IEEE Trans. Instrum. Meas. 48, 1062-1067 (1999).
[CrossRef]

Sahin Kaya zdemir, S. Ito, S. Shinohara, H. Yoshida, M . Sumi, "Correlation-based speckle velocimeter with self-mixing interference in a semiconductor laser diode," Appl. Opt. 38, 6859-6865(1999).
[CrossRef]

1996

T. Shibata, S. Shinohara et al. "Laser speckle velocimeter using self-mixing laser diode," IEEE Trans. Instrum. Meas. 45,499-503 (1996).
[CrossRef]

1988

E. I. Thorsos, "The validity of the kirchoff approximation for rough surface scattering using a Gaussian roughness spectrum," J. Acous. Soc. Am. 83, 78-92 (1988).
[CrossRef]

1987

F. Favre, "Theoretical analysis of external optical feedback on DFB semiconductor lasers," IEEE J. Quantum Electron. 23, 81-88 (1987).
[CrossRef]

1985

Bozzi-Pietra, S.

G. Giuliani, S. Bozzi-Pietra, S. Donati, "Self-mixing laser diode vibrometer" Meas. Sci. Tech. 14, 24-32 (2003).
[CrossRef]

Chen, M. F.

Choi, J. W.

J. W. Choi, M. J. Yu, M. Kopica, "Photoacoustic laser Doppler velocimetry using the self-mixing effect of CO2 laser," Proc. Soc. Photo-Opt.Instrum. 5240, 230-234 (2004).

Curtin, D. P.

P. A. Porta, D. P. Curtin and J. G. McInerney, "Laser Doppler velocimetry by optical self-mixing in vertical-cavity surface-emitting lasers," IEEE Photonics Technol. Lett. 14, 1717-1721 (2002).
[CrossRef]

D’Alessandro, D.

M. Norgi, S. Donati, D. D’Alessandro, "Interferometric measurements of displacement on a diffusing target by a speckle tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
[CrossRef]

Donati, S.

G. Giuliani, S. Bozzi-Pietra, S. Donati, "Self-mixing laser diode vibrometer" Meas. Sci. Tech. 14, 24-32 (2003).
[CrossRef]

M. Norgia, S. Donati, "A displacement-measuring instrument utilizing self-mixing interferometry", IEEE Trans. Instrum. Meas. 52, 1765-1770 (2003).
[CrossRef]

M. Norgi, S. Donati, D. D’Alessandro, "Interferometric measurements of displacement on a diffusing target by a speckle tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
[CrossRef]

Favre, F.

F. Favre, "Theoretical analysis of external optical feedback on DFB semiconductor lasers," IEEE J. Quantum Electron. 23, 81-88 (1987).
[CrossRef]

Fung, A. K.

Giuliani, G.

L. Scalise, Y. G. Yu, G. Giuliani,  et al. "Self-mixing laser diode velocimetry: Application to vibration and velocity measurement," IEEE Trans. Instrum. Meas. 53, 223-232 (2004).
[CrossRef]

G. Giuliani, S. Bozzi-Pietra, S. Donati, "Self-mixing laser diode vibrometer" Meas. Sci. Tech. 14, 24-32 (2003).
[CrossRef]

Guo, D.

H. Huan, M. Wang, D. Guo et al. "Self-mixing interference effect of DFB semiconductor lasers," Appl. Phys. B 79,1554-1559 (2004).
[CrossRef]

Huan, H.

H. Huan, M. Wang, D. Guo et al. "Self-mixing interference effect of DFB semiconductor lasers," Appl. Phys. B 79,1554-1559 (2004).
[CrossRef]

Ikeda, H.

T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, "Automatic measurement of velocity and length of moving plate using self-mixing laser diode", IEEE Trans. Instrum. Meas. 48, 1062-1067 (1999).
[CrossRef]

Ito, S.

Kaya zdemir, Sahin

Kopica, M.

J. W. Choi, M. J. Yu, M. Kopica, "Photoacoustic laser Doppler velocimetry using the self-mixing effect of CO2 laser," Proc. Soc. Photo-Opt.Instrum. 5240, 230-234 (2004).

Laroche, M.

M. Laroche, L. Kervevan, H. Gilles, S. Girard, J.K. Sahu, "Doppler velocimetry using self-mixing effect in a short Er-Yb-doped phosphate glass fiber laser," Appl. Phys. B 80, 603-607 (2005).
[CrossRef]

McInerney, J. G.

P. A. Porta, D. P. Curtin and J. G. McInerney, "Laser Doppler velocimetry by optical self-mixing in vertical-cavity surface-emitting lasers," IEEE Photonics Technol. Lett. 14, 1717-1721 (2002).
[CrossRef]

Norgi, M.

M. Norgi, S. Donati, D. D’Alessandro, "Interferometric measurements of displacement on a diffusing target by a speckle tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
[CrossRef]

Norgia, M.

M. Norgia, S. Donati, "A displacement-measuring instrument utilizing self-mixing interferometry", IEEE Trans. Instrum. Meas. 52, 1765-1770 (2003).
[CrossRef]

Porta, P. A.

P. A. Porta, D. P. Curtin and J. G. McInerney, "Laser Doppler velocimetry by optical self-mixing in vertical-cavity surface-emitting lasers," IEEE Photonics Technol. Lett. 14, 1717-1721 (2002).
[CrossRef]

Scalise, L.

L. Scalise, Y. G. Yu, G. Giuliani,  et al. "Self-mixing laser diode velocimetry: Application to vibration and velocity measurement," IEEE Trans. Instrum. Meas. 53, 223-232 (2004).
[CrossRef]

Shibata, T.

T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, "Automatic measurement of velocity and length of moving plate using self-mixing laser diode", IEEE Trans. Instrum. Meas. 48, 1062-1067 (1999).
[CrossRef]

T. Shibata, S. Shinohara et al. "Laser speckle velocimeter using self-mixing laser diode," IEEE Trans. Instrum. Meas. 45,499-503 (1996).
[CrossRef]

Shinohara, S.

T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, "Automatic measurement of velocity and length of moving plate using self-mixing laser diode", IEEE Trans. Instrum. Meas. 48, 1062-1067 (1999).
[CrossRef]

Sahin Kaya zdemir, S. Ito, S. Shinohara, H. Yoshida, M . Sumi, "Correlation-based speckle velocimeter with self-mixing interference in a semiconductor laser diode," Appl. Opt. 38, 6859-6865(1999).
[CrossRef]

T. Shibata, S. Shinohara et al. "Laser speckle velocimeter using self-mixing laser diode," IEEE Trans. Instrum. Meas. 45,499-503 (1996).
[CrossRef]

Sumi, M

Sumi, M.

T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, "Automatic measurement of velocity and length of moving plate using self-mixing laser diode", IEEE Trans. Instrum. Meas. 48, 1062-1067 (1999).
[CrossRef]

Thorsos, E. I.

E. I. Thorsos, "The validity of the kirchoff approximation for rough surface scattering using a Gaussian roughness spectrum," J. Acous. Soc. Am. 83, 78-92 (1988).
[CrossRef]

Wang, M.

J. Zhou, M. Wang, "Effects of self-mixing interference on gain-coupled distributed-feedback lasers," Opt. Express 13,1848-1854 (2005).
[CrossRef] [PubMed]

H. Huan, M. Wang, D. Guo et al. "Self-mixing interference effect of DFB semiconductor lasers," Appl. Phys. B 79,1554-1559 (2004).
[CrossRef]

Yoshida, H.

T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, "Automatic measurement of velocity and length of moving plate using self-mixing laser diode", IEEE Trans. Instrum. Meas. 48, 1062-1067 (1999).
[CrossRef]

Sahin Kaya zdemir, S. Ito, S. Shinohara, H. Yoshida, M . Sumi, "Correlation-based speckle velocimeter with self-mixing interference in a semiconductor laser diode," Appl. Opt. 38, 6859-6865(1999).
[CrossRef]

Yu, M. J.

J. W. Choi, M. J. Yu, M. Kopica, "Photoacoustic laser Doppler velocimetry using the self-mixing effect of CO2 laser," Proc. Soc. Photo-Opt.Instrum. 5240, 230-234 (2004).

Yu, Y. G.

L. Scalise, Y. G. Yu, G. Giuliani,  et al. "Self-mixing laser diode velocimetry: Application to vibration and velocity measurement," IEEE Trans. Instrum. Meas. 53, 223-232 (2004).
[CrossRef]

Zhou, J.

Appl. Opt.

Appl. Phys. B

M. Laroche, L. Kervevan, H. Gilles, S. Girard, J.K. Sahu, "Doppler velocimetry using self-mixing effect in a short Er-Yb-doped phosphate glass fiber laser," Appl. Phys. B 80, 603-607 (2005).
[CrossRef]

H. Huan, M. Wang, D. Guo et al. "Self-mixing interference effect of DFB semiconductor lasers," Appl. Phys. B 79,1554-1559 (2004).
[CrossRef]

IEEE J. Quantum Electron.

F. Favre, "Theoretical analysis of external optical feedback on DFB semiconductor lasers," IEEE J. Quantum Electron. 23, 81-88 (1987).
[CrossRef]

M. Norgi, S. Donati, D. D’Alessandro, "Interferometric measurements of displacement on a diffusing target by a speckle tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
[CrossRef]

IEEE Photonics Technol. Lett.

P. A. Porta, D. P. Curtin and J. G. McInerney, "Laser Doppler velocimetry by optical self-mixing in vertical-cavity surface-emitting lasers," IEEE Photonics Technol. Lett. 14, 1717-1721 (2002).
[CrossRef]

IEEE Trans. Instrum. Meas.

M. Norgia, S. Donati, "A displacement-measuring instrument utilizing self-mixing interferometry", IEEE Trans. Instrum. Meas. 52, 1765-1770 (2003).
[CrossRef]

L. Scalise, Y. G. Yu, G. Giuliani,  et al. "Self-mixing laser diode velocimetry: Application to vibration and velocity measurement," IEEE Trans. Instrum. Meas. 53, 223-232 (2004).
[CrossRef]

T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, "Automatic measurement of velocity and length of moving plate using self-mixing laser diode", IEEE Trans. Instrum. Meas. 48, 1062-1067 (1999).
[CrossRef]

T. Shibata, S. Shinohara et al. "Laser speckle velocimeter using self-mixing laser diode," IEEE Trans. Instrum. Meas. 45,499-503 (1996).
[CrossRef]

Instrum.

J. W. Choi, M. J. Yu, M. Kopica, "Photoacoustic laser Doppler velocimetry using the self-mixing effect of CO2 laser," Proc. Soc. Photo-Opt.Instrum. 5240, 230-234 (2004).

J. Acous. Soc. Am.

E. I. Thorsos, "The validity of the kirchoff approximation for rough surface scattering using a Gaussian roughness spectrum," J. Acous. Soc. Am. 83, 78-92 (1988).
[CrossRef]

J. Opt. Soc. Am. A

Meas. Sci. Tech.

G. Giuliani, S. Bozzi-Pietra, S. Donati, "Self-mixing laser diode vibrometer" Meas. Sci. Tech. 14, 24-32 (2003).
[CrossRef]

Opt. Express

Other

Max Born and Emil Worlf, Principles of Optics, Pergamon press, (1975).

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Figures (7)

Fig. 1.
Fig. 1.

the schematics of self-mixing speckle interference system

Fig. 2.
Fig. 2.

Schematic configuration of experimental system

Fig. 3.
Fig. 3.

The waveform of output variations from (a) simulation and (b) experiment (v= 167mm/s)

Fig. 4.
Fig. 4.

The PDFs of output variations from experiment and simulation (v=167mm/s)

Fig. 5.
Fig. 5.

Simulation results showing the effect of external cavity length on the PDF of output variations from a DFB laser

Fig. 6.
Fig. 6.

The results of experiment showing the PDFs of output variation vary with velocities of surface

Fig. 7.
Fig. 7.

The linear dependence between mean speckle frequencies and velocities of surface in experiment

Equations (10)

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

U ( X , Y ) = E r e i ω τ t A ( x , y ) exp ( i 4 π h ( x , y ) λ ) exp ( i 2 π ( x X + y Y ) λ L E ) dxdy
E r = ρ r E r + ξ t U ( X , Y )
ρ req = ρ r + ξ t U ( X , Y ) E r
ρ req = ρ r + ( 1 ρ ̂ r 2 ) R e j ϕ
Δ ρ r = ( 1 ρ ̂ r 2 ) R e j ϕ
R e j ϕ = ξ t U ( X , Y ) ( ( 1 ρ ̂ 2 ) E r )
( 1 ρ req ρ ) ( 1 ρ l ρ ) = ( ρ req ρ ) ( ρ l ρ ) e 2 γ L
ρ = γ + ( a j δ ) j κ
Δ α r L j Δ δ r L = C r R e j ϕ
Δ G = 2 c C r R η L cos ( ϕ arg ( C r ) arg ( R ) )

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