Abstract

In autodyne interferometry, the beating between the reference beam and the signal beam takes place inside the laser cavity and therefore the laser fulfills simultaneously the roles of the emitter and the detector of photons. In these conditions, the laser relaxation oscillations play a leading role, both in the laser quantum noise that determines the signal-to-noise ratio (SNR) and also in the laser dynamics that determine the response time of the interferometer. In the present study, we have theoretically analyzed the SNR and the response time of a laser optical feedback imaging (LOFI) setup based on an autodyne interferometer. More precisely, we have compared the image quality of two lasers having the same output power and the same relaxation frequency, but having two different values of the LOFI gain induced by two different values of the laser response time. From this study, we have finally determined the best laser dynamical parameters and the best experimental conditions for high-speed imaging at the shot-noise limit. Finally, we conclude that a laser diode with a very short response time (in the nanosecond range) seems to be an interesting candidate compared to solid-state microchip laser with a response time of several tens of microseconds. Analytical predictions are confirmed by numerical simulations.

© 2012 Optical Society of America

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References

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  1. T. Yoshizawa, ed., Handbook of Optical Metrology: Principles and Applications (CRC, 2009).
  2. K. Otsuka, “Effects of external perturbations on LiNdP4O12lasers,” IEEE J. Quantum Electron. QE-15, 655–663 (1979).
    [CrossRef]
  3. K. Otsuka, “Self-mixing thin-slice solids-state laser metrology,” Sensors 11, 2195–2245 (2011).
    [CrossRef]
  4. K. Otsuka, “Highly sensitive measurement of Doppler-shift with a microchip solid-state laser,” Jpn. J. Appl. Phys. 31, L1546–L1548 (1992).
    [CrossRef]
  5. S. Okamoto, H. Takeda, and F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
    [CrossRef]
  6. R. Kawai, Y. Asakawa, and K. Otsuka, “Ultrahigh-sensitivity self-mixing laser Doppler velocimetry with laser-diode-pumped microchip LiNdP4O12 lasers,” IEEE Photon. Technol. Lett. 11, 706–708 (1999).
    [CrossRef]
  7. S. Suddo, T. Ohtomo, Y. Takahascvhi, T. Oishi, and K. Otsuka, “Determination of velocity of self-mobile phytoplankton using a self thin-slice solid-state laser,” Appl. Opt. 48, 4049–4055 (2009).
    [CrossRef]
  8. K. Otsuka, K. Abe, J. Y. Ko, and T. S. Lim, “Real-time nanometer vibration measurement with self-mixing microchip solid-state laser,” Opt. Lett. 27, 1339–1341 (2002).
    [CrossRef]
  9. V. Muzet, E. Lacot, O. Hugon, and Y. Gaillard, “Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures,” Proc. SPIE 5856, 793–799 (2005).
    [CrossRef]
  10. E. Lacot and O. Hugon, “Phase-sensitive laser detection by frequency-shifted optical feedback,” Phys. Rev. A 70, 053824 (2004).
    [CrossRef]
  11. H. Gilles, S. Girard, M. Laroche, and A. Belarouci, “Near-field amplitude and phase measurements using heterodyne optical feedback on solid-state lasers,” Opt. Lett. 33, 1–3 (2008).
    [CrossRef]
  12. S. Blaize, B. Bérenguier, I. Stéfanon, A. Bruyant, G. Lerondel, P. Royer, O. Hugon, O. Jacquin, and E. Lacot, “Phase sensitive optical near-field mapping using frequency-shifted laser optical feedback interferometry,” Opt. Express 16, 11718–11726 (2008).
    [CrossRef]
  13. E. Lacot, R. Day, and F. Stoeckel, “Laser optical feedback tomography,” Opt. Lett. 24, 744–746 (1999).
    [CrossRef]
  14. A. Witomski, E. Lacot, O. Hugon, and O. Jacquin, “Synthetic aperture laser optical feedback imaging using galvanometric scanning,” Opt. Lett. 31, 3031–3033 (2006).
    [CrossRef]
  15. O. Hugon, I. A. Paun, C. Ricard, B. van der Sanden, E. Lacot, O. Jacquin, and A. Witomski, “Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser,” Ultramicroscopy 108, 523–528 (2008).
    [CrossRef]
  16. O. Hugon, F. Joud, E. Lacot, O. Jacquin, and H. Guillet de Chatellus, “Coherent microscopy by laser optical feedback imaging (LOFI) technique,” Ultramicroscopy 111, 1557–1563 (2011).
    [CrossRef]
  17. E. Lacot, R. Day, and F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815 (2001).
    [CrossRef]
  18. E. Lacot, O. Jacquin, G. Roussely, O. Hugon, and H. Guillet de Chatellus, “Comparative study of autodyne and heterodyne laser interferometry for imaging,” J. Opt. Soc. Am. A 27, 2450–2458 (2010).
    [CrossRef]
  19. O. Jacquin, E. Lacot, W. Glastre, O. Hugon, and H. Guillet de Chatellus, “Expérimetal comparison of autodyne and heterodyne laser interferometry using an Nd:YVO4 microchip laser,” J. Opt. Soc. Am. A 28, 1741–1746 (2011).
    [CrossRef]
  20. J. J. Zaykowski and A. Mooradian, “Single-frequency microchip Nd lasers,” Opt. Lett. 14, 24–26 (1989).
    [CrossRef]
  21. M. I. Kolobov, L. Davidovich, E. Giacobino, and C. Fabre, “Role of pumping statistics and dynamics of atomic polarization in quantum fluctuations of laser sources,” Phys. Rev. A 47, 1431–1446 (1993).
    [CrossRef]
  22. A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D. 6, 513–521 (1999).
    [CrossRef]
  23. Y. I. Khanin, Principles of Laser Dynamics (Elsevier, 1995).
  24. The saturation effect observed numerically cannot be obtained analytically, because Eq. (2) was obtained after a linearization of the set of Eqs. (1), i.e., far away from the saturation conditions.
  25. To observe the SNR amplification predicted by Eq. (21), one could imagine decreasing the LOFI gain by decreasing the laser time response, but in this case, the amplification effect that is proportional to laser time response then falls to a very small value hidden by the laser quantum fluctuations.

2011 (3)

K. Otsuka, “Self-mixing thin-slice solids-state laser metrology,” Sensors 11, 2195–2245 (2011).
[CrossRef]

O. Hugon, F. Joud, E. Lacot, O. Jacquin, and H. Guillet de Chatellus, “Coherent microscopy by laser optical feedback imaging (LOFI) technique,” Ultramicroscopy 111, 1557–1563 (2011).
[CrossRef]

O. Jacquin, E. Lacot, W. Glastre, O. Hugon, and H. Guillet de Chatellus, “Expérimetal comparison of autodyne and heterodyne laser interferometry using an Nd:YVO4 microchip laser,” J. Opt. Soc. Am. A 28, 1741–1746 (2011).
[CrossRef]

2010 (1)

2009 (1)

2008 (3)

2006 (1)

2005 (1)

V. Muzet, E. Lacot, O. Hugon, and Y. Gaillard, “Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures,” Proc. SPIE 5856, 793–799 (2005).
[CrossRef]

2004 (1)

E. Lacot and O. Hugon, “Phase-sensitive laser detection by frequency-shifted optical feedback,” Phys. Rev. A 70, 053824 (2004).
[CrossRef]

2002 (1)

2001 (1)

E. Lacot, R. Day, and F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815 (2001).
[CrossRef]

1999 (3)

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D. 6, 513–521 (1999).
[CrossRef]

E. Lacot, R. Day, and F. Stoeckel, “Laser optical feedback tomography,” Opt. Lett. 24, 744–746 (1999).
[CrossRef]

R. Kawai, Y. Asakawa, and K. Otsuka, “Ultrahigh-sensitivity self-mixing laser Doppler velocimetry with laser-diode-pumped microchip LiNdP4O12 lasers,” IEEE Photon. Technol. Lett. 11, 706–708 (1999).
[CrossRef]

1995 (1)

S. Okamoto, H. Takeda, and F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
[CrossRef]

1993 (1)

M. I. Kolobov, L. Davidovich, E. Giacobino, and C. Fabre, “Role of pumping statistics and dynamics of atomic polarization in quantum fluctuations of laser sources,” Phys. Rev. A 47, 1431–1446 (1993).
[CrossRef]

1992 (1)

K. Otsuka, “Highly sensitive measurement of Doppler-shift with a microchip solid-state laser,” Jpn. J. Appl. Phys. 31, L1546–L1548 (1992).
[CrossRef]

1989 (1)

1979 (1)

K. Otsuka, “Effects of external perturbations on LiNdP4O12lasers,” IEEE J. Quantum Electron. QE-15, 655–663 (1979).
[CrossRef]

Abe, K.

Asakawa, Y.

R. Kawai, Y. Asakawa, and K. Otsuka, “Ultrahigh-sensitivity self-mixing laser Doppler velocimetry with laser-diode-pumped microchip LiNdP4O12 lasers,” IEEE Photon. Technol. Lett. 11, 706–708 (1999).
[CrossRef]

Aubert, J. J.

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D. 6, 513–521 (1999).
[CrossRef]

Belarouci, A.

Bérenguier, B.

Blaize, S.

Bramati, A.

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D. 6, 513–521 (1999).
[CrossRef]

Bruyant, A.

Davidovich, L.

M. I. Kolobov, L. Davidovich, E. Giacobino, and C. Fabre, “Role of pumping statistics and dynamics of atomic polarization in quantum fluctuations of laser sources,” Phys. Rev. A 47, 1431–1446 (1993).
[CrossRef]

Day, R.

E. Lacot, R. Day, and F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815 (2001).
[CrossRef]

E. Lacot, R. Day, and F. Stoeckel, “Laser optical feedback tomography,” Opt. Lett. 24, 744–746 (1999).
[CrossRef]

Fabre, C.

M. I. Kolobov, L. Davidovich, E. Giacobino, and C. Fabre, “Role of pumping statistics and dynamics of atomic polarization in quantum fluctuations of laser sources,” Phys. Rev. A 47, 1431–1446 (1993).
[CrossRef]

Fulbert, L.

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D. 6, 513–521 (1999).
[CrossRef]

Gaillard, Y.

V. Muzet, E. Lacot, O. Hugon, and Y. Gaillard, “Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures,” Proc. SPIE 5856, 793–799 (2005).
[CrossRef]

Giacobino, E.

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D. 6, 513–521 (1999).
[CrossRef]

M. I. Kolobov, L. Davidovich, E. Giacobino, and C. Fabre, “Role of pumping statistics and dynamics of atomic polarization in quantum fluctuations of laser sources,” Phys. Rev. A 47, 1431–1446 (1993).
[CrossRef]

Gilles, H.

Girard, S.

Glastre, W.

Guillet de Chatellus, H.

Hermier, J. P.

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D. 6, 513–521 (1999).
[CrossRef]

Hugon, O.

O. Hugon, F. Joud, E. Lacot, O. Jacquin, and H. Guillet de Chatellus, “Coherent microscopy by laser optical feedback imaging (LOFI) technique,” Ultramicroscopy 111, 1557–1563 (2011).
[CrossRef]

O. Jacquin, E. Lacot, W. Glastre, O. Hugon, and H. Guillet de Chatellus, “Expérimetal comparison of autodyne and heterodyne laser interferometry using an Nd:YVO4 microchip laser,” J. Opt. Soc. Am. A 28, 1741–1746 (2011).
[CrossRef]

E. Lacot, O. Jacquin, G. Roussely, O. Hugon, and H. Guillet de Chatellus, “Comparative study of autodyne and heterodyne laser interferometry for imaging,” J. Opt. Soc. Am. A 27, 2450–2458 (2010).
[CrossRef]

S. Blaize, B. Bérenguier, I. Stéfanon, A. Bruyant, G. Lerondel, P. Royer, O. Hugon, O. Jacquin, and E. Lacot, “Phase sensitive optical near-field mapping using frequency-shifted laser optical feedback interferometry,” Opt. Express 16, 11718–11726 (2008).
[CrossRef]

O. Hugon, I. A. Paun, C. Ricard, B. van der Sanden, E. Lacot, O. Jacquin, and A. Witomski, “Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser,” Ultramicroscopy 108, 523–528 (2008).
[CrossRef]

A. Witomski, E. Lacot, O. Hugon, and O. Jacquin, “Synthetic aperture laser optical feedback imaging using galvanometric scanning,” Opt. Lett. 31, 3031–3033 (2006).
[CrossRef]

V. Muzet, E. Lacot, O. Hugon, and Y. Gaillard, “Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures,” Proc. SPIE 5856, 793–799 (2005).
[CrossRef]

E. Lacot and O. Hugon, “Phase-sensitive laser detection by frequency-shifted optical feedback,” Phys. Rev. A 70, 053824 (2004).
[CrossRef]

Jacquin, O.

Jost, V.

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D. 6, 513–521 (1999).
[CrossRef]

Joud, F.

O. Hugon, F. Joud, E. Lacot, O. Jacquin, and H. Guillet de Chatellus, “Coherent microscopy by laser optical feedback imaging (LOFI) technique,” Ultramicroscopy 111, 1557–1563 (2011).
[CrossRef]

Kannari, F.

S. Okamoto, H. Takeda, and F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
[CrossRef]

Kawai, R.

R. Kawai, Y. Asakawa, and K. Otsuka, “Ultrahigh-sensitivity self-mixing laser Doppler velocimetry with laser-diode-pumped microchip LiNdP4O12 lasers,” IEEE Photon. Technol. Lett. 11, 706–708 (1999).
[CrossRef]

Khanin, Y. I.

Y. I. Khanin, Principles of Laser Dynamics (Elsevier, 1995).

Ko, J. Y.

Kolobov, M. I.

M. I. Kolobov, L. Davidovich, E. Giacobino, and C. Fabre, “Role of pumping statistics and dynamics of atomic polarization in quantum fluctuations of laser sources,” Phys. Rev. A 47, 1431–1446 (1993).
[CrossRef]

Lacot, E.

O. Jacquin, E. Lacot, W. Glastre, O. Hugon, and H. Guillet de Chatellus, “Expérimetal comparison of autodyne and heterodyne laser interferometry using an Nd:YVO4 microchip laser,” J. Opt. Soc. Am. A 28, 1741–1746 (2011).
[CrossRef]

O. Hugon, F. Joud, E. Lacot, O. Jacquin, and H. Guillet de Chatellus, “Coherent microscopy by laser optical feedback imaging (LOFI) technique,” Ultramicroscopy 111, 1557–1563 (2011).
[CrossRef]

E. Lacot, O. Jacquin, G. Roussely, O. Hugon, and H. Guillet de Chatellus, “Comparative study of autodyne and heterodyne laser interferometry for imaging,” J. Opt. Soc. Am. A 27, 2450–2458 (2010).
[CrossRef]

O. Hugon, I. A. Paun, C. Ricard, B. van der Sanden, E. Lacot, O. Jacquin, and A. Witomski, “Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser,” Ultramicroscopy 108, 523–528 (2008).
[CrossRef]

S. Blaize, B. Bérenguier, I. Stéfanon, A. Bruyant, G. Lerondel, P. Royer, O. Hugon, O. Jacquin, and E. Lacot, “Phase sensitive optical near-field mapping using frequency-shifted laser optical feedback interferometry,” Opt. Express 16, 11718–11726 (2008).
[CrossRef]

A. Witomski, E. Lacot, O. Hugon, and O. Jacquin, “Synthetic aperture laser optical feedback imaging using galvanometric scanning,” Opt. Lett. 31, 3031–3033 (2006).
[CrossRef]

V. Muzet, E. Lacot, O. Hugon, and Y. Gaillard, “Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures,” Proc. SPIE 5856, 793–799 (2005).
[CrossRef]

E. Lacot and O. Hugon, “Phase-sensitive laser detection by frequency-shifted optical feedback,” Phys. Rev. A 70, 053824 (2004).
[CrossRef]

E. Lacot, R. Day, and F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815 (2001).
[CrossRef]

E. Lacot, R. Day, and F. Stoeckel, “Laser optical feedback tomography,” Opt. Lett. 24, 744–746 (1999).
[CrossRef]

Laroche, M.

Lerondel, G.

Lim, T. S.

Molva, E.

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D. 6, 513–521 (1999).
[CrossRef]

Mooradian, A.

Muzet, V.

V. Muzet, E. Lacot, O. Hugon, and Y. Gaillard, “Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures,” Proc. SPIE 5856, 793–799 (2005).
[CrossRef]

Ohtomo, T.

Oishi, T.

Okamoto, S.

S. Okamoto, H. Takeda, and F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
[CrossRef]

Otsuka, K.

K. Otsuka, “Self-mixing thin-slice solids-state laser metrology,” Sensors 11, 2195–2245 (2011).
[CrossRef]

S. Suddo, T. Ohtomo, Y. Takahascvhi, T. Oishi, and K. Otsuka, “Determination of velocity of self-mobile phytoplankton using a self thin-slice solid-state laser,” Appl. Opt. 48, 4049–4055 (2009).
[CrossRef]

K. Otsuka, K. Abe, J. Y. Ko, and T. S. Lim, “Real-time nanometer vibration measurement with self-mixing microchip solid-state laser,” Opt. Lett. 27, 1339–1341 (2002).
[CrossRef]

R. Kawai, Y. Asakawa, and K. Otsuka, “Ultrahigh-sensitivity self-mixing laser Doppler velocimetry with laser-diode-pumped microchip LiNdP4O12 lasers,” IEEE Photon. Technol. Lett. 11, 706–708 (1999).
[CrossRef]

K. Otsuka, “Highly sensitive measurement of Doppler-shift with a microchip solid-state laser,” Jpn. J. Appl. Phys. 31, L1546–L1548 (1992).
[CrossRef]

K. Otsuka, “Effects of external perturbations on LiNdP4O12lasers,” IEEE J. Quantum Electron. QE-15, 655–663 (1979).
[CrossRef]

Paun, I. A.

O. Hugon, I. A. Paun, C. Ricard, B. van der Sanden, E. Lacot, O. Jacquin, and A. Witomski, “Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser,” Ultramicroscopy 108, 523–528 (2008).
[CrossRef]

Ricard, C.

O. Hugon, I. A. Paun, C. Ricard, B. van der Sanden, E. Lacot, O. Jacquin, and A. Witomski, “Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser,” Ultramicroscopy 108, 523–528 (2008).
[CrossRef]

Roussely, G.

Royer, P.

Stéfanon, I.

Stoeckel, F.

E. Lacot, R. Day, and F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815 (2001).
[CrossRef]

E. Lacot, R. Day, and F. Stoeckel, “Laser optical feedback tomography,” Opt. Lett. 24, 744–746 (1999).
[CrossRef]

Suddo, S.

Takahascvhi, Y.

Takeda, H.

S. Okamoto, H. Takeda, and F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
[CrossRef]

van der Sanden, B.

O. Hugon, I. A. Paun, C. Ricard, B. van der Sanden, E. Lacot, O. Jacquin, and A. Witomski, “Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser,” Ultramicroscopy 108, 523–528 (2008).
[CrossRef]

Witomski, A.

O. Hugon, I. A. Paun, C. Ricard, B. van der Sanden, E. Lacot, O. Jacquin, and A. Witomski, “Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser,” Ultramicroscopy 108, 523–528 (2008).
[CrossRef]

A. Witomski, E. Lacot, O. Hugon, and O. Jacquin, “Synthetic aperture laser optical feedback imaging using galvanometric scanning,” Opt. Lett. 31, 3031–3033 (2006).
[CrossRef]

Zaykowski, J. J.

Appl. Opt. (1)

Eur. Phys. J. D. (1)

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D. 6, 513–521 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Otsuka, “Effects of external perturbations on LiNdP4O12lasers,” IEEE J. Quantum Electron. QE-15, 655–663 (1979).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

R. Kawai, Y. Asakawa, and K. Otsuka, “Ultrahigh-sensitivity self-mixing laser Doppler velocimetry with laser-diode-pumped microchip LiNdP4O12 lasers,” IEEE Photon. Technol. Lett. 11, 706–708 (1999).
[CrossRef]

J. Opt. Soc. Am. A (2)

Jpn. J. Appl. Phys. (1)

K. Otsuka, “Highly sensitive measurement of Doppler-shift with a microchip solid-state laser,” Jpn. J. Appl. Phys. 31, L1546–L1548 (1992).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Phys. Rev. A (3)

E. Lacot and O. Hugon, “Phase-sensitive laser detection by frequency-shifted optical feedback,” Phys. Rev. A 70, 053824 (2004).
[CrossRef]

E. Lacot, R. Day, and F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815 (2001).
[CrossRef]

M. I. Kolobov, L. Davidovich, E. Giacobino, and C. Fabre, “Role of pumping statistics and dynamics of atomic polarization in quantum fluctuations of laser sources,” Phys. Rev. A 47, 1431–1446 (1993).
[CrossRef]

Proc. SPIE (1)

V. Muzet, E. Lacot, O. Hugon, and Y. Gaillard, “Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures,” Proc. SPIE 5856, 793–799 (2005).
[CrossRef]

Rev. Sci. Instrum. (1)

S. Okamoto, H. Takeda, and F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
[CrossRef]

Sensors (1)

K. Otsuka, “Self-mixing thin-slice solids-state laser metrology,” Sensors 11, 2195–2245 (2011).
[CrossRef]

Ultramicroscopy (2)

O. Hugon, I. A. Paun, C. Ricard, B. van der Sanden, E. Lacot, O. Jacquin, and A. Witomski, “Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser,” Ultramicroscopy 108, 523–528 (2008).
[CrossRef]

O. Hugon, F. Joud, E. Lacot, O. Jacquin, and H. Guillet de Chatellus, “Coherent microscopy by laser optical feedback imaging (LOFI) technique,” Ultramicroscopy 111, 1557–1563 (2011).
[CrossRef]

Other (4)

Y. I. Khanin, Principles of Laser Dynamics (Elsevier, 1995).

The saturation effect observed numerically cannot be obtained analytically, because Eq. (2) was obtained after a linearization of the set of Eqs. (1), i.e., far away from the saturation conditions.

To observe the SNR amplification predicted by Eq. (21), one could imagine decreasing the LOFI gain by decreasing the laser time response, but in this case, the amplification effect that is proportional to laser time response then falls to a very small value hidden by the laser quantum fluctuations.

T. Yoshizawa, ed., Handbook of Optical Metrology: Principles and Applications (CRC, 2009).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram of the LOFI interferometer setup for scanning microscopy. L1, L2, and L3, lenses; BS, beam splitter with a power reflectivity Rbs; GS, galvanometric scanner; FS, frequency shifter with a round-trip frequency shift Fe; PD, photodiode with a white-noise spectrum. The lock-in amplifier is characterized by its integration time Tint. The laser is characterized by its output power pout (photons/s), its relaxation frequency FR, and its dynamical response time τR. The target is characterized by its effective reflectivity Re1.

Fig. 2.
Fig. 2.

Stationary LOFI SNR (SLOFI/NLaser) versus the normalized shift frequency (Fe/FR) for different values of the lock-in integration time: (a) Tint=10×τR, (b) Tint=τR, and (c) Tint=τR/10. The experimental conditions are Re=2×1011 and Rbs=1/2. The laser is a class-B laser with pout=3.2×1017photons/s (Pout=60mW at λ=1064nm), FR=356kHz, and FRτR14 (r=1.02, γc=5×109s1, γ1=5×103s1). For each integration time, the continuous curve shows the exact value of the LOFI SNR [Eq. (11)], while the dashed line shows the corresponding LOFI shot-noise limit [Eq. (13)].

Fig. 3.
Fig. 3.

SNR (SLOFI/NLaser) of a class-B laser (Pout=60mW; FR=356kHz, Re=4×1010 Rbs=0.5) versus the normalized shift-frequency (Fe/FR) for different values of the lock-in integration time: (squares) Tint=600μs, (diamonds) Tint=200μs, (triangles) Tint=60μs, (inverted triangles) Tint=20μs, (circles) Tint=6μs. Upper graph, G(FR)=1×104 and τR=4μs (γc/γ1=104, r=1.002); lower graph, G(FR)=8×105 and τR=333μs (γc/γ1=106, r=1.2).

Fig. 4.
Fig. 4.

Normalized (Re,2/C=1) ratio between the stationary and the transient LOFI signals (SLOFI/TLOFI) versus the normalized shift frequency (Fe/FR) for different values of the lock-in integration time (Tint) compared to the transient time (τR): (a) Tint=10×τR, (b) Tint=τR, and (c) Tint=τR/10. The laser is a class-B laser with FRτR14.

Fig. 5.
Fig. 5.

Numerical 1D scan obtained from the measured laser output power MC of a LOFI setup, when the laser is scanned on a symmetric reflectivity pyramid composed of four levels. Experimental conditions: Pout=60mW (i.e., pout=3.2×1017photons/s at λ=1064nm), FR=356kHz, Tint=20μs. Level 1 (pixels 1–10 and 61–70), Re=0; level 2 (pixels 11–20 and 51–60), Re=4×1012; level 3 (pixels 21–30 and 41–50), Re=1×1010; level 4 (pixels 31–40), Re=4×1010. Top row, G(FR)=1×104 with τR=4μs; bottom row, G(FR)=8×105 with τR=330μs; left column, Fe=FR; right column, Fe=1.5×FR. Curves with circles: results with laser quantum noise; solid curves: results without laser quantum noise.

Tables (3)

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Table 1. LOFI SNR [Eq. (13)] Obtained with the Laser Output Power Pout=60mW (i.e., pout=3.2×1017photons/s at λ=1064nm), a Target Effective Reflectivity Re=4×1010, and a Beam-Splitter Reflectivity Rbs=0.5

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Table 2. MC and SNR of the LOFI Images [Figs. 5(a) and 5(b)] Obtained with the Laser having the Lower Value LOFI Gain (G(FR)=1×104)a

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Table 3. MC and SNR of the LOFI Images [Figs. 5(c) and 5(d)] Obtained with the Laser having the Higher Value LOFI Gain (G(FR)=8×105)a

Equations (42)

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dNdt=γ1N0γ1NBN|Ec|2+FN(t),
dEcdt=12(BNγc)Ec+γcRe(1Rbs)Eccos[2πFet+ϕe]+FEc(t),
pout(t,Fe,Re)=pout+2G(Fe)(1Rbs)Repoutcos(2πFet+Φe),
G(Fe)=γc(2/τR)2+(2πFe)2[(2πFR)2(2πFe)2]2+(2/τR)2(2πFe)2FR1τRγc21(2πFR2πFe)2+(1/τR)2,
G(FR)=γcτR2.
MC(Fe,Re)=Δpout(Fe,Re)pout=2G(Fe)(1Rbs)Re.
RSat(Fe)=14×1G2(Fe)×1(1Rbs)2.
SLOFI(Fe,Re)=RbsΔpout(Fe,Re)2=Rbs2G(Fe)(1Rbs)Repout2.
PDLaser(F)=2poutγc2(2/τR)2+(2πF)2[(2πFR)2(2πF)2]2+(2/τR)2(2πF)2=2pout(t)G2(F).
NLaser2(Fe,Tint)=2Rbs+PDLaser(F)|Fint(FFe,Tint)|2dF,
|Fint(F,Tint)|2=1Tint211Tint2+(2πF)2
NLaser2(Fe,Tint)=Rbspout(t)12τRTint[1Tint+1τR]γc2[[1Tint+1τR]2+(2πFe2πFR)2],
SNR(Fe,Re,Tint)=SLOFI(Fe,Re)NLaser(Fe,Tint).
NLaser(Fe,TintτR)2Rbspout(t)γc21(2πFR2πFe)2+(1/τR)212Tint
NLaser(Fe,TintτR)2Rbspout(t)G(Fe)12Tint.
SNR(Fe,Re,TintτR)=Re(1Rbs)×RbspoutTint.
Re,min(1Rbs)2poutTint=1Rbs.
NLaser(Fe,TintτR)2Rbspout(t)γc(2Tint)2+4(2πFe2πFR)212TintτRTint.
NLaser(Fe,TintτR)2Rbspout(t)γc4|2πFe2πFR|12TintτRTint,
SLOFI(Fe,Re)Rbs2(1Rbs)Repout2γc212π|FeFR|,
SNR(Fe,Re,TintτR)Re(1Rbs)×RbspoutTintTintτR.
NLaser(FR,TintτR)2Rbspout(t)γcτR212τR,
SLOFI(FR,Re)=Rbs2(1Rbs)Repout2γcτR2,
SNR(FR,Re,TintτR)=Re(1Rbs)×RbspoutτR=Re(1Rbs)×RbspoutTintτRTint.
|FeFR|12πτRTint.
pout(t<0,Fe,re,1)=pout+2G(Fe)(1Rbs)Re,1poutcos(2πFet+Φe,1)
pout(t0,Fe,re,2)=pout+2G(Fe)(1Rbs)Re,2poutcos(2πFet+Φe,2)+exp(tτR)2G(Fe)(1Rbs)Cpoutcos(2πFRt+Φc),
Re,1cos(Φe,1)=Re,2cos(Φe,2)+Ccos(Φc),
Re,1FeFRsin(Φe,1)=Re,2FeFRsin(Φe,2)+Csin(Φc)12πτRFRCcos(Φc).
CRe,1+Re,22Re,1Re,2cos(Φe,2Φe,1)
|Re,2Re,1|C|Re,2+Re,1|.
TLOFI(Fe,C,Tint)=|1Tint0+exp(tTint)Rbs22G(Fe)(1Rbs)CpoutTR(t)exp(j2πFet)dt|
TLOFI(Fe,C,Tint)=Rbs2G(Fe)(1Rbs)Cpout21Tint1(1Tint+1τR)2+(2πFe2πFR)2,
TLOFI(Fe,C,Tint)=SLOFI(Fe,Re,2)CRe,21Tint1(1Tint+1τR)2+(2πFe2πFR)2.
SLOFI(Fe,Re,2)TLOFI(Fe,C,TintτR)TintτR1+(2πFe2πFR)2τR2,
SLOFI(Fe,Re,2)TLOFI(Fe,C,TintτR).
SLOFI(Fe,Re,2)TLOFI(Fe,C,TintτR)1+(2πFe2πFR)2Tint2,
SLOFI(FeFR,Re,2)TLOFI(FeFR,C,TintτR).
SLOFI(Fe,Re,2)TLOFI(Fe,C,TintτR)
G(Fe)TintτRG(FR).
Gopt(FR)=(γcγ1r)opt=12RbsNEP/(hc/λ)pout,
τR,opt=(2γ1r)opt=22RbsNEP/(hc/λ)γcpout.

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