Abstract

Based on the nature of self-mixing signals, we propose the use of the multiple signal classification (MUSIC) algorithm in place of the fast Fourier transform (FFT) for processing signals obtained from self-mixing interferometry (SMI). We apply this algorithm to two representative SMI measurement techniques: range finding and velocimetry. Applying MUSIC to SMI range finding, we find its signal-to-noise ratio performance to be significantly better than that of the FFT, allowing for more robust, longer-range measurement systems. We further demonstrate that MUSIC enables a fundamental change in how SMI Doppler velocity measurement is approached, letting one discard the complex fitting procedure and allowing for a real-time frequency estimation process.

© 2013 Optical Society of America

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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 4, S283–S294 (2002).
    [CrossRef]
  2. T. Bosch, N. Servagent, and S. Donati, “Optical feedback interferometry for sensing application,” Opt. Eng. 40, 20–27 (2001).
    [CrossRef]
  3. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
    [CrossRef]
  4. C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
    [CrossRef]
  5. P. Protter, Stochastic Integration and Differential Equations (Springer, 2005).
  6. U. Küchler and E. Platen, “Weak discrete time approximation of stochastic differential equations with time delay,” Math. Comput. Simul. 59, 497–507 (2002).
    [CrossRef]
  7. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer, 1999).
  8. R. O. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antennas Propag. 34, 276–280(1986).
    [CrossRef]
  9. M. Norgia, A. Magnani, and A. Pesatori, “High resolution self-mixing laser rangefinder,” Rev. Sci. Instrum. 83, 045113 (2012).
    [CrossRef]
  10. F. Gouaux, N. Servagent, and T. Bosch, “Absolute distance measurement with an optical feedback interferometer,” Appl. Opt. 37, 6684–6689 (1998).
    [CrossRef]
  11. J. Tucker, Y. L. Lim, and A. D. Rakic, “Laser range finding using the self-mixing effect in a vertical-cavity surface-emitting laser,” in Conference on Optoelectronic and Microelectronic Materials and Devices, M. Gal, ed. (IEEE, 2002), pp. 583–586.
  12. Y. L. Lim, M. Nikolic, K. Bertling, R. Kliese, and A. D. Rakic, “Self-mixing imaging sensor using a monolithic VCSEL array with parallel readout,” Opt. Express 17, 5517–5525 (2009).
    [CrossRef]
  13. J. R. Tucker, A. D. Rakic, C. J. O’Brien, and A. V. Zvyagin, “Effect of multiple transverse modes in self-mixing sensors based on vertical-cavity surface-emitting lasers,” Appl. Opt. 46, 611–619 (2007).
    [CrossRef]
  14. M. Wang and G. Lai, “Displacement measurement based on Fourier transform method with external laser cavity modulation,” Rev. Sci. Instrum. 72, 3440–3445 (2001).
    [CrossRef]
  15. M. Wang, “Fourier transform method for self-mixing interference signal analysis,” Opt. Laser Technol. 33, 409–416 (2001).
    [CrossRef]
  16. A. Sakamoto, N. Tsuda, and J. Yamada, “Characteristic of self-coupling distance meter using VCSEL,” IEEJ Trans. EIS 126, 1454–1459 (2006).
    [CrossRef]
  17. R. Kliese and A. D. Rakic, “Spectral broadening caused by dynamic speckle in self-mixing velocimetry sensors,” Opt. Express 20, 18757–18771 (2012).
    [CrossRef]
  18. K. Meigas, H. Hinrikus, R. Kattai, and J. Lass, “Self-mixing in a diode laser as a method for cardiovascular diagnostics,” J. Biomed. Opt. 8, 152–160 (2003).
    [CrossRef]
  19. L. Campagnolo, M. Nikolic, J. Perchoux, Y. L. Lim, K. Bertling, K. Loubière, L. Prat, A. D. Rakic, and T. Bosch, “Flow profile measurement in microchannel using the optical feedback interferometry sensing technique,” Microfluid. Nanofluid. 14, 113–119 (2013).
    [CrossRef]
  20. F. F. M. de Mul, L. Scalise, A. L. Petoukhova, M. van Herwijnen, P. Moes, and W. Steenbergen, “Glass-fiber self-mixing intra-arterial laser doppler velocimetry: signal stability and feedback analysis,” Appl. Opt. 41, 658–667 (2002).
    [CrossRef]
  21. S. M. Kay, Modern Spectral Estimation: Theory and Application (Prentice Hall, 1988).
  22. L. C. Godara, “Application of antenna arrays to mobile communications, part II: beam-forming and direction-of-arrival considerations,” Proc. IEEE 85, 1195–1245 (1997).
    [CrossRef]
  23. M. Hamalainen, R. Hari, R. J. Ilmoniemi, J. Knuutila, and O. V. Lounasmaa, “Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain,” Rev. Mod. Phys. 65, 413–497 (1993).
    [CrossRef]
  24. P. Stoica and A. Nehorai, “MUSIC, maximum likelihood, and Cramer–Rao bound,” IEEE Trans. Acoust. Speech Signal Process. 37, 720–741 (1989).
    [CrossRef]
  25. S. Donati and S. Merlo, “Applications of diode laser feedback interferometry,” J. Opt. 29, 156–161 (1998).
    [CrossRef]
  26. H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer-Verlag, 2003).

2013

L. Campagnolo, M. Nikolic, J. Perchoux, Y. L. Lim, K. Bertling, K. Loubière, L. Prat, A. D. Rakic, and T. Bosch, “Flow profile measurement in microchannel using the optical feedback interferometry sensing technique,” Microfluid. Nanofluid. 14, 113–119 (2013).
[CrossRef]

2012

M. Norgia, A. Magnani, and A. Pesatori, “High resolution self-mixing laser rangefinder,” Rev. Sci. Instrum. 83, 045113 (2012).
[CrossRef]

R. Kliese and A. D. Rakic, “Spectral broadening caused by dynamic speckle in self-mixing velocimetry sensors,” Opt. Express 20, 18757–18771 (2012).
[CrossRef]

2009

2007

2006

A. Sakamoto, N. Tsuda, and J. Yamada, “Characteristic of self-coupling distance meter using VCSEL,” IEEJ Trans. EIS 126, 1454–1459 (2006).
[CrossRef]

2003

K. Meigas, H. Hinrikus, R. Kattai, and J. Lass, “Self-mixing in a diode laser as a method for cardiovascular diagnostics,” J. Biomed. Opt. 8, 152–160 (2003).
[CrossRef]

2002

F. F. M. de Mul, L. Scalise, A. L. Petoukhova, M. van Herwijnen, P. Moes, and W. Steenbergen, “Glass-fiber self-mixing intra-arterial laser doppler velocimetry: signal stability and feedback analysis,” Appl. Opt. 41, 658–667 (2002).
[CrossRef]

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

U. Küchler and E. Platen, “Weak discrete time approximation of stochastic differential equations with time delay,” Math. Comput. Simul. 59, 497–507 (2002).
[CrossRef]

2001

T. Bosch, N. Servagent, and S. Donati, “Optical feedback interferometry for sensing application,” Opt. Eng. 40, 20–27 (2001).
[CrossRef]

M. Wang and G. Lai, “Displacement measurement based on Fourier transform method with external laser cavity modulation,” Rev. Sci. Instrum. 72, 3440–3445 (2001).
[CrossRef]

M. Wang, “Fourier transform method for self-mixing interference signal analysis,” Opt. Laser Technol. 33, 409–416 (2001).
[CrossRef]

1998

S. Donati and S. Merlo, “Applications of diode laser feedback interferometry,” J. Opt. 29, 156–161 (1998).
[CrossRef]

F. Gouaux, N. Servagent, and T. Bosch, “Absolute distance measurement with an optical feedback interferometer,” Appl. Opt. 37, 6684–6689 (1998).
[CrossRef]

1997

L. C. Godara, “Application of antenna arrays to mobile communications, part II: beam-forming and direction-of-arrival considerations,” Proc. IEEE 85, 1195–1245 (1997).
[CrossRef]

1993

M. Hamalainen, R. Hari, R. J. Ilmoniemi, J. Knuutila, and O. V. Lounasmaa, “Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain,” Rev. Mod. Phys. 65, 413–497 (1993).
[CrossRef]

1989

P. Stoica and A. Nehorai, “MUSIC, maximum likelihood, and Cramer–Rao bound,” IEEE Trans. Acoust. Speech Signal Process. 37, 720–741 (1989).
[CrossRef]

1986

R. O. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antennas Propag. 34, 276–280(1986).
[CrossRef]

1982

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
[CrossRef]

1980

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

Albrecht, H.-E.

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer-Verlag, 2003).

Bertling, K.

L. Campagnolo, M. Nikolic, J. Perchoux, Y. L. Lim, K. Bertling, K. Loubière, L. Prat, A. D. Rakic, and T. Bosch, “Flow profile measurement in microchannel using the optical feedback interferometry sensing technique,” Microfluid. Nanofluid. 14, 113–119 (2013).
[CrossRef]

Y. L. Lim, M. Nikolic, K. Bertling, R. Kliese, and A. D. Rakic, “Self-mixing imaging sensor using a monolithic VCSEL array with parallel readout,” Opt. Express 17, 5517–5525 (2009).
[CrossRef]

Borys, M.

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer-Verlag, 2003).

Bosch, T.

L. Campagnolo, M. Nikolic, J. Perchoux, Y. L. Lim, K. Bertling, K. Loubière, L. Prat, A. D. Rakic, and T. Bosch, “Flow profile measurement in microchannel using the optical feedback interferometry sensing technique,” Microfluid. Nanofluid. 14, 113–119 (2013).
[CrossRef]

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

T. Bosch, N. Servagent, and S. Donati, “Optical feedback interferometry for sensing application,” Opt. Eng. 40, 20–27 (2001).
[CrossRef]

F. Gouaux, N. Servagent, and T. Bosch, “Absolute distance measurement with an optical feedback interferometer,” Appl. Opt. 37, 6684–6689 (1998).
[CrossRef]

Campagnolo, L.

L. Campagnolo, M. Nikolic, J. Perchoux, Y. L. Lim, K. Bertling, K. Loubière, L. Prat, A. D. Rakic, and T. Bosch, “Flow profile measurement in microchannel using the optical feedback interferometry sensing technique,” Microfluid. Nanofluid. 14, 113–119 (2013).
[CrossRef]

Damaschke, N.

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer-Verlag, 2003).

de Mul, F. F. M.

Donati, S.

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

T. Bosch, N. Servagent, and S. Donati, “Optical feedback interferometry for sensing application,” Opt. Eng. 40, 20–27 (2001).
[CrossRef]

S. Donati and S. Merlo, “Applications of diode laser feedback interferometry,” J. Opt. 29, 156–161 (1998).
[CrossRef]

Giuliani, G.

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

Godara, L. C.

L. C. Godara, “Application of antenna arrays to mobile communications, part II: beam-forming and direction-of-arrival considerations,” Proc. IEEE 85, 1195–1245 (1997).
[CrossRef]

Gouaux, F.

Hamalainen, M.

M. Hamalainen, R. Hari, R. J. Ilmoniemi, J. Knuutila, and O. V. Lounasmaa, “Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain,” Rev. Mod. Phys. 65, 413–497 (1993).
[CrossRef]

Hari, R.

M. Hamalainen, R. Hari, R. J. Ilmoniemi, J. Knuutila, and O. V. Lounasmaa, “Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain,” Rev. Mod. Phys. 65, 413–497 (1993).
[CrossRef]

Henry, C. H.

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
[CrossRef]

Hinrikus, H.

K. Meigas, H. Hinrikus, R. Kattai, and J. Lass, “Self-mixing in a diode laser as a method for cardiovascular diagnostics,” J. Biomed. Opt. 8, 152–160 (2003).
[CrossRef]

Ilmoniemi, R. J.

M. Hamalainen, R. Hari, R. J. Ilmoniemi, J. Knuutila, and O. V. Lounasmaa, “Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain,” Rev. Mod. Phys. 65, 413–497 (1993).
[CrossRef]

Kattai, R.

K. Meigas, H. Hinrikus, R. Kattai, and J. Lass, “Self-mixing in a diode laser as a method for cardiovascular diagnostics,” J. Biomed. Opt. 8, 152–160 (2003).
[CrossRef]

Kay, S. M.

S. M. Kay, Modern Spectral Estimation: Theory and Application (Prentice Hall, 1988).

Kliese, R.

Kloeden, P. E.

P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer, 1999).

Knuutila, J.

M. Hamalainen, R. Hari, R. J. Ilmoniemi, J. Knuutila, and O. V. Lounasmaa, “Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain,” Rev. Mod. Phys. 65, 413–497 (1993).
[CrossRef]

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]

Küchler, U.

U. Küchler and E. Platen, “Weak discrete time approximation of stochastic differential equations with time delay,” Math. Comput. Simul. 59, 497–507 (2002).
[CrossRef]

Lai, G.

M. Wang and G. Lai, “Displacement measurement based on Fourier transform method with external laser cavity modulation,” Rev. Sci. Instrum. 72, 3440–3445 (2001).
[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]

Lass, J.

K. Meigas, H. Hinrikus, R. Kattai, and J. Lass, “Self-mixing in a diode laser as a method for cardiovascular diagnostics,” J. Biomed. Opt. 8, 152–160 (2003).
[CrossRef]

Lim, Y. L.

L. Campagnolo, M. Nikolic, J. Perchoux, Y. L. Lim, K. Bertling, K. Loubière, L. Prat, A. D. Rakic, and T. Bosch, “Flow profile measurement in microchannel using the optical feedback interferometry sensing technique,” Microfluid. Nanofluid. 14, 113–119 (2013).
[CrossRef]

Y. L. Lim, M. Nikolic, K. Bertling, R. Kliese, and A. D. Rakic, “Self-mixing imaging sensor using a monolithic VCSEL array with parallel readout,” Opt. Express 17, 5517–5525 (2009).
[CrossRef]

J. Tucker, Y. L. Lim, and A. D. Rakic, “Laser range finding using the self-mixing effect in a vertical-cavity surface-emitting laser,” in Conference on Optoelectronic and Microelectronic Materials and Devices, M. Gal, ed. (IEEE, 2002), pp. 583–586.

Loubière, K.

L. Campagnolo, M. Nikolic, J. Perchoux, Y. L. Lim, K. Bertling, K. Loubière, L. Prat, A. D. Rakic, and T. Bosch, “Flow profile measurement in microchannel using the optical feedback interferometry sensing technique,” Microfluid. Nanofluid. 14, 113–119 (2013).
[CrossRef]

Lounasmaa, O. V.

M. Hamalainen, R. Hari, R. J. Ilmoniemi, J. Knuutila, and O. V. Lounasmaa, “Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain,” Rev. Mod. Phys. 65, 413–497 (1993).
[CrossRef]

Magnani, A.

M. Norgia, A. Magnani, and A. Pesatori, “High resolution self-mixing laser rangefinder,” Rev. Sci. Instrum. 83, 045113 (2012).
[CrossRef]

Meigas, K.

K. Meigas, H. Hinrikus, R. Kattai, and J. Lass, “Self-mixing in a diode laser as a method for cardiovascular diagnostics,” J. Biomed. Opt. 8, 152–160 (2003).
[CrossRef]

Merlo, S.

S. Donati and S. Merlo, “Applications of diode laser feedback interferometry,” J. Opt. 29, 156–161 (1998).
[CrossRef]

Moes, P.

Nehorai, A.

P. Stoica and A. Nehorai, “MUSIC, maximum likelihood, and Cramer–Rao bound,” IEEE Trans. Acoust. Speech Signal Process. 37, 720–741 (1989).
[CrossRef]

Nikolic, M.

L. Campagnolo, M. Nikolic, J. Perchoux, Y. L. Lim, K. Bertling, K. Loubière, L. Prat, A. D. Rakic, and T. Bosch, “Flow profile measurement in microchannel using the optical feedback interferometry sensing technique,” Microfluid. Nanofluid. 14, 113–119 (2013).
[CrossRef]

Y. L. Lim, M. Nikolic, K. Bertling, R. Kliese, and A. D. Rakic, “Self-mixing imaging sensor using a monolithic VCSEL array with parallel readout,” Opt. Express 17, 5517–5525 (2009).
[CrossRef]

Norgia, M.

M. Norgia, A. Magnani, and A. Pesatori, “High resolution self-mixing laser rangefinder,” Rev. Sci. Instrum. 83, 045113 (2012).
[CrossRef]

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

O’Brien, C. J.

Perchoux, J.

L. Campagnolo, M. Nikolic, J. Perchoux, Y. L. Lim, K. Bertling, K. Loubière, L. Prat, A. D. Rakic, and T. Bosch, “Flow profile measurement in microchannel using the optical feedback interferometry sensing technique,” Microfluid. Nanofluid. 14, 113–119 (2013).
[CrossRef]

Pesatori, A.

M. Norgia, A. Magnani, and A. Pesatori, “High resolution self-mixing laser rangefinder,” Rev. Sci. Instrum. 83, 045113 (2012).
[CrossRef]

Petoukhova, A. L.

Platen, E.

U. Küchler and E. Platen, “Weak discrete time approximation of stochastic differential equations with time delay,” Math. Comput. Simul. 59, 497–507 (2002).
[CrossRef]

P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer, 1999).

Prat, L.

L. Campagnolo, M. Nikolic, J. Perchoux, Y. L. Lim, K. Bertling, K. Loubière, L. Prat, A. D. Rakic, and T. Bosch, “Flow profile measurement in microchannel using the optical feedback interferometry sensing technique,” Microfluid. Nanofluid. 14, 113–119 (2013).
[CrossRef]

Protter, P.

P. Protter, Stochastic Integration and Differential Equations (Springer, 2005).

Rakic, A. D.

L. Campagnolo, M. Nikolic, J. Perchoux, Y. L. Lim, K. Bertling, K. Loubière, L. Prat, A. D. Rakic, and T. Bosch, “Flow profile measurement in microchannel using the optical feedback interferometry sensing technique,” Microfluid. Nanofluid. 14, 113–119 (2013).
[CrossRef]

R. Kliese and A. D. Rakic, “Spectral broadening caused by dynamic speckle in self-mixing velocimetry sensors,” Opt. Express 20, 18757–18771 (2012).
[CrossRef]

Y. L. Lim, M. Nikolic, K. Bertling, R. Kliese, and A. D. Rakic, “Self-mixing imaging sensor using a monolithic VCSEL array with parallel readout,” Opt. Express 17, 5517–5525 (2009).
[CrossRef]

J. R. Tucker, A. D. Rakic, C. J. O’Brien, and A. V. Zvyagin, “Effect of multiple transverse modes in self-mixing sensors based on vertical-cavity surface-emitting lasers,” Appl. Opt. 46, 611–619 (2007).
[CrossRef]

J. Tucker, Y. L. Lim, and A. D. Rakic, “Laser range finding using the self-mixing effect in a vertical-cavity surface-emitting laser,” in Conference on Optoelectronic and Microelectronic Materials and Devices, M. Gal, ed. (IEEE, 2002), pp. 583–586.

Sakamoto, A.

A. Sakamoto, N. Tsuda, and J. Yamada, “Characteristic of self-coupling distance meter using VCSEL,” IEEJ Trans. EIS 126, 1454–1459 (2006).
[CrossRef]

Scalise, L.

Schmidt, R. O.

R. O. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antennas Propag. 34, 276–280(1986).
[CrossRef]

Servagent, N.

T. Bosch, N. Servagent, and S. Donati, “Optical feedback interferometry for sensing application,” Opt. Eng. 40, 20–27 (2001).
[CrossRef]

F. Gouaux, N. Servagent, and T. Bosch, “Absolute distance measurement with an optical feedback interferometer,” Appl. Opt. 37, 6684–6689 (1998).
[CrossRef]

Steenbergen, W.

Stoica, P.

P. Stoica and A. Nehorai, “MUSIC, maximum likelihood, and Cramer–Rao bound,” IEEE Trans. Acoust. Speech Signal Process. 37, 720–741 (1989).
[CrossRef]

Tropea, C.

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer-Verlag, 2003).

Tsuda, N.

A. Sakamoto, N. Tsuda, and J. Yamada, “Characteristic of self-coupling distance meter using VCSEL,” IEEJ Trans. EIS 126, 1454–1459 (2006).
[CrossRef]

Tucker, J.

J. Tucker, Y. L. Lim, and A. D. Rakic, “Laser range finding using the self-mixing effect in a vertical-cavity surface-emitting laser,” in Conference on Optoelectronic and Microelectronic Materials and Devices, M. Gal, ed. (IEEE, 2002), pp. 583–586.

Tucker, J. R.

van Herwijnen, M.

Wang, M.

M. Wang and G. Lai, “Displacement measurement based on Fourier transform method with external laser cavity modulation,” Rev. Sci. Instrum. 72, 3440–3445 (2001).
[CrossRef]

M. Wang, “Fourier transform method for self-mixing interference signal analysis,” Opt. Laser Technol. 33, 409–416 (2001).
[CrossRef]

Yamada, J.

A. Sakamoto, N. Tsuda, and J. Yamada, “Characteristic of self-coupling distance meter using VCSEL,” IEEJ Trans. EIS 126, 1454–1459 (2006).
[CrossRef]

Zvyagin, A. V.

Appl. Opt.

IEEE J. Quantum Electron.

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

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process.

P. Stoica and A. Nehorai, “MUSIC, maximum likelihood, and Cramer–Rao bound,” IEEE Trans. Acoust. Speech Signal Process. 37, 720–741 (1989).
[CrossRef]

IEEE Trans. Antennas Propag.

R. O. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antennas Propag. 34, 276–280(1986).
[CrossRef]

IEEJ Trans. EIS

A. Sakamoto, N. Tsuda, and J. Yamada, “Characteristic of self-coupling distance meter using VCSEL,” IEEJ Trans. EIS 126, 1454–1459 (2006).
[CrossRef]

J. Biomed. Opt.

K. Meigas, H. Hinrikus, R. Kattai, and J. Lass, “Self-mixing in a diode laser as a method for cardiovascular diagnostics,” J. Biomed. Opt. 8, 152–160 (2003).
[CrossRef]

J. Opt.

S. Donati and S. Merlo, “Applications of diode laser feedback interferometry,” J. Opt. 29, 156–161 (1998).
[CrossRef]

J. Opt. A

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

Math. Comput. Simul.

U. Küchler and E. Platen, “Weak discrete time approximation of stochastic differential equations with time delay,” Math. Comput. Simul. 59, 497–507 (2002).
[CrossRef]

Microfluid. Nanofluid.

L. Campagnolo, M. Nikolic, J. Perchoux, Y. L. Lim, K. Bertling, K. Loubière, L. Prat, A. D. Rakic, and T. Bosch, “Flow profile measurement in microchannel using the optical feedback interferometry sensing technique,” Microfluid. Nanofluid. 14, 113–119 (2013).
[CrossRef]

Opt. Eng.

T. Bosch, N. Servagent, and S. Donati, “Optical feedback interferometry for sensing application,” Opt. Eng. 40, 20–27 (2001).
[CrossRef]

Opt. Express

Opt. Laser Technol.

M. Wang, “Fourier transform method for self-mixing interference signal analysis,” Opt. Laser Technol. 33, 409–416 (2001).
[CrossRef]

Proc. IEEE

L. C. Godara, “Application of antenna arrays to mobile communications, part II: beam-forming and direction-of-arrival considerations,” Proc. IEEE 85, 1195–1245 (1997).
[CrossRef]

Rev. Mod. Phys.

M. Hamalainen, R. Hari, R. J. Ilmoniemi, J. Knuutila, and O. V. Lounasmaa, “Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain,” Rev. Mod. Phys. 65, 413–497 (1993).
[CrossRef]

Rev. Sci. Instrum.

M. Norgia, A. Magnani, and A. Pesatori, “High resolution self-mixing laser rangefinder,” Rev. Sci. Instrum. 83, 045113 (2012).
[CrossRef]

M. Wang and G. Lai, “Displacement measurement based on Fourier transform method with external laser cavity modulation,” Rev. Sci. Instrum. 72, 3440–3445 (2001).
[CrossRef]

Other

P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer, 1999).

P. Protter, Stochastic Integration and Differential Equations (Springer, 2005).

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer-Verlag, 2003).

S. M. Kay, Modern Spectral Estimation: Theory and Application (Prentice Hall, 1988).

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Figures (8)

Fig. 1.
Fig. 1.

Experimental setup for distance measurement showing the laser light focused through a single lens onto the stationary target at a distance L from the laser.

Fig. 2.
Fig. 2.

Distance measurement results for a target at 30 cm showing (a) time-domain signal with bounds indicating the window used for subsequent processing, (b) filtered and amplified time-domain signal exhibiting periodicity, and (c) FFT spectrum (bold red line) and MUSIC pseudospectrum (blue line) normalized such that the peaks correspond to 0 dB.

Fig. 3.
Fig. 3.

SNR of FFT (red crosses) and MUSIC (blue circles) methods versus target distance.

Fig. 4.
Fig. 4.

Distance measurement results versus distance to target showing (a) performance of FFT (red crosses) and MUSIC (blue circles) versus expected values (black line), (b) FFT error from expected, and (c) MUSIC error from expected.

Fig. 5.
Fig. 5.

Variation in MUSIC’s frequency estimation due to the parameter p for distance measurement, with shading to indicate instances of unsuccessful frequency estimation. Light gray shading indicates frequency estimation failure at one out of five distances, whereas dark gray shading indicates failure at two out of five distances. The mean difference in the estimated frequencies (for all distances at which frequency estimation was successful) for each value of p is given relative to the frequencies produced for the optimal p=18.

Fig. 6.
Fig. 6.

Experimental setup for Doppler velocity measurement, showing (a) the top view and (b) the front view. θ is the angle between the lasing axis and the target velocity vector, r is the length from the center of the rotating disk to the measurement point, and ω denotes the disk’s angular velocity.

Fig. 7.
Fig. 7.

Doppler measurement results showing (a) sample time domain exhibiting clear periodicity, (b) FFT spectrum (red solid line) and corresponding fit (black dashed line), and (c) MUSIC pseudospectrum.

Fig. 8.
Fig. 8.

Doppler measurement results versus target velocity showing (a) performance of FFT (red crosses) and MUSIC (blue circles) versus expected values (black line), (b) FFT error from expected, and (c) MUSIC error from expected.

Tables (1)

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Table 1. Underlying Dimension of the Signal Without Noise, p, for Doppler Frequency

Equations (3)

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fb=2ipkpkΩfmLc,
fD=2vcos(θ)λ,
Fit(f)=a+bfc+d×exp((ffDg)2),

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