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 emitter and detector of photons. In these conditions, the laser relaxation oscillations play a leading role, both in the laser quantum noise, which determines the signal-to-noise ratio (SNR), and also in the laser dynamics, which determines the response time of the interferometer. In the present study, we have experimentally analyzed the SNR and the response time of a laser optical feedback imaging (LOFI) interferometer based on a Nd3+ microchip laser, with a relaxation frequency in the megahertz range. More precisely, we have compared the image quality obtained when the laser dynamics is free and when it is controlled by a stabilizing electronic feedback loop using a differentiator. From this study, we can conclude that when the laser time response is shorter (i.e., the LOFI gain is lower), the image quality can be better (i.e., the LOFI SNR can be higher) and that the use of an adapted electronic feedback loop allows high-speed LOFI with a shot-noise limited sensitivity. Despite the critical stability of the electronic feedback loop, the obtained experimental results are in good agreement with the theoretical predictions.

© 2013 Optical Society of America

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  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).
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  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).
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  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). doi: 10.1016/j.ultramic.2011.08.004.
    [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]
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    [CrossRef]
  20. E. Lacot, W. Glastre, O. Jacquin, O. Hugon, and H. Guillet de Chatellus, “Optimization of an autodyne laser interferometer for high speed confocal imaging,” J. Opt. Soc. Am. A 30, 60–70 (2013).
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    [CrossRef]
  23. 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]
  24. Y. I. Khanin, Principles of Laser Dynamics (Elsevier, 1995).
  25. Experimentally, the minus sign comes directly from the fact that when the RF voltage applied on the AOM increases, the intensity of the zero order beam of the AOM decreases and therefore the pumping power decreases.
  26. On Fig. 1, this complex gain (amplitude and phase) is the ratio between the input voltage applied on the AOM, and the output voltage of the electronic differentiator when the link between these two component is open (i.e., no direct connection)
  27. A. Bramati, J.-P. Hermier, V. Jost, and E. Giacobino, “Feedback control and nonlinear intensity noise of Nd:YVO4 microchip lasers,” Phys. Rev. A 62, 043806 (2000).
    [CrossRef]
  28. C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
    [CrossRef]
  29. S. Bielawski, D. Derozier, and P. Glorieux, “Antiphase dynamics and polarization effects in the Nd-doped fiber laser,” Phys. Rev. A 46, 2812–2822 (1988).
  30. E. lacot and F. Stoeckel, “Nonlinear mode coupling in a microchip laser,” J. Opt. Soc. Am. B 13, 2034–2040 (1996).
    [CrossRef]

2013 (1)

2011 (3)

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

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). doi: 10.1016/j.ultramic.2011.08.004.
[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]

2000 (1)

A. Bramati, J.-P. Hermier, V. Jost, and E. Giacobino, “Feedback control and nonlinear intensity noise of Nd:YVO4 microchip lasers,” Phys. Rev. A 62, 043806 (2000).
[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]

1996 (1)

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]

1994 (1)

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[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)

1988 (1)

S. Bielawski, D. Derozier, and P. Glorieux, “Antiphase dynamics and polarization effects in the Nd-doped fiber laser,” Phys. Rev. A 46, 2812–2822 (1988).

1979 (1)

K. Otsuka, “Effects of external perturbations on LiNdP4012 Lasers,” 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]

Bachor, H.-A.

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[CrossRef]

Belarouci, A.

Bérenguier, B.

Bielawski, S.

S. Bielawski, D. Derozier, and P. Glorieux, “Antiphase dynamics and polarization effects in the Nd-doped fiber laser,” Phys. Rev. A 46, 2812–2822 (1988).

Blaize, S.

Bramati, A.

A. Bramati, J.-P. Hermier, V. Jost, and E. Giacobino, “Feedback control and nonlinear intensity noise of Nd:YVO4 microchip lasers,” Phys. Rev. A 62, 043806 (2000).
[CrossRef]

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]

Derozier, D.

S. Bielawski, D. Derozier, and P. Glorieux, “Antiphase dynamics and polarization effects in the Nd-doped fiber laser,” Phys. Rev. A 46, 2812–2822 (1988).

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]

Freitag, I.

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[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, and E. Giacobino, “Feedback control and nonlinear intensity noise of Nd:YVO4 microchip lasers,” Phys. Rev. A 62, 043806 (2000).
[CrossRef]

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.

Glorieux, P.

S. Bielawski, D. Derozier, and P. Glorieux, “Antiphase dynamics and polarization effects in the Nd-doped fiber laser,” Phys. Rev. A 46, 2812–2822 (1988).

Gray, M. B.

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[CrossRef]

Guillet de Chatellus, H.

Harb, C. C.

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[CrossRef]

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]

Hermier, J.-P.

A. Bramati, J.-P. Hermier, V. Jost, and E. Giacobino, “Feedback control and nonlinear intensity noise of Nd:YVO4 microchip lasers,” Phys. Rev. A 62, 043806 (2000).
[CrossRef]

Hugon, O.

E. Lacot, W. Glastre, O. Jacquin, O. Hugon, and H. Guillet de Chatellus, “Optimization of an autodyne laser interferometer for high speed confocal imaging,” J. Opt. Soc. Am. A 30, 60–70 (2013).
[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). doi: 10.1016/j.ultramic.2011.08.004.
[CrossRef]

O. Jacquin, E. Lacot, W. Glastre, O. Hugon, and H. Guillet de Chatellus, “Experimental 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]

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]

Jacquin, O.

E. Lacot, W. Glastre, O. Jacquin, O. Hugon, and H. Guillet de Chatellus, “Optimization of an autodyne laser interferometer for high speed confocal imaging,” J. Opt. Soc. Am. A 30, 60–70 (2013).
[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). doi: 10.1016/j.ultramic.2011.08.004.
[CrossRef]

O. Jacquin, E. Lacot, W. Glastre, O. Hugon, and H. Guillet de Chatellus, “Experimental 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]

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]

Jost, V.

A. Bramati, J.-P. Hermier, V. Jost, and E. Giacobino, “Feedback control and nonlinear intensity noise of Nd:YVO4 microchip lasers,” Phys. Rev. A 62, 043806 (2000).
[CrossRef]

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). doi: 10.1016/j.ultramic.2011.08.004.
[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.

E. Lacot, W. Glastre, O. Jacquin, O. Hugon, and H. Guillet de Chatellus, “Optimization of an autodyne laser interferometer for high speed confocal imaging,” J. Opt. Soc. Am. A 30, 60–70 (2013).
[CrossRef]

O. Jacquin, E. Lacot, W. Glastre, O. Hugon, and H. Guillet de Chatellus, “Experimental 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). doi: 10.1016/j.ultramic.2011.08.004.
[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]

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]

E. lacot and F. Stoeckel, “Nonlinear mode coupling in a microchip laser,” J. Opt. Soc. Am. B 13, 2034–2040 (1996).
[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).
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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 LiNdP4012 Lasers,” 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]

Rottengatter, P.

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[CrossRef]

Roussely, G.

Royer, P.

Schilling, R.

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[CrossRef]

Stéfanon, I.

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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]

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C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[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]

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Appl. Opt. (1)

Eur. Phys. J. D (1)

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[CrossRef]

IEEE J. Quantum Electron. (2)

K. Otsuka, “Effects of external perturbations on LiNdP4012 Lasers,” IEEE J. Quantum Electron. QE-15, 655–663 (1979).
[CrossRef]

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[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 (3)

J. Opt. Soc. Am. B (1)

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 (5)

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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). doi: 10.1016/j.ultramic.2011.08.004.
[CrossRef]

Other (4)

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

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

Experimentally, the minus sign comes directly from the fact that when the RF voltage applied on the AOM increases, the intensity of the zero order beam of the AOM decreases and therefore the pumping power decreases.

On Fig. 1, this complex gain (amplitude and phase) is the ratio between the input voltage applied on the AOM, and the output voltage of the electronic differentiator when the link between these two component is open (i.e., no direct connection)

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Figures (6)

Fig. 1.
Fig. 1.

Schematic diagram of the LOFI setup with an electronic feedback loop using a differentiator. L1, L2, L3, L4, and L5, Lenses; AOM, Acousto-Optic Modulator; BS, Beam Splitter with a power reflectivity Rbs; GS, Galvanometric Scanner; FS, Frequency Shifter with a round trip frequency-shift Fe; PD, Photodiode. The lock-in amplifier is characterized by its integration time Tint. The Nd3+ microchip-laser is characterized by its output power pout (photons/s), its relaxation frequency FR, and its dynamical response time τR. The optical feedback from the target is characterized by the 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=500μs, (b) Tint=50μs, (c) Tint=5μs. For each integration time, the dotted line and the solid line show the exact value of the LOFI SNR [Eq. (24)], when respectively τR=50μs and τR=3μs, while the dashed line shows the corresponding LOFI shot-noise limit [Eq. (25)]. The calculation conditions are Re=4×1010 and Rbs=1/2. The laser is a class-B laser with pout5×1016photons/s (Pout10mW at λ=1064nm) and FR=950kHz. The vertical dashed–dotted line (Fe=1.05×FR) corresponds to the working frequency for the remainder of this manuscript.

Fig. 3.
Fig. 3.

Open-loop transfer function [Gofl(Fe)]: (a) Bode diagram for the gain (i.e., the modulus) and (b) Bode diagram for the phase. (c) Nyquist diagram in the complex plane. (d) Zoom of the left part of the Nyquist diagram near the instability point [×(1,0)]. ○, experimental results. Solid lines, fitted transfer function. Dashed line, unity circle around the instability point.

Fig. 4.
Fig. 4.

Dynamical behavior of the free running laser [left column, (a) and (c)] and of the laser with the electronic feedback control [right column, (b) and (d)]. Top row, temporal behavior; bottom row, corresponding RF power spectra with FR950kHz.The RF power spectra are fitted by using Eq. (12) with Re=0. (c) Dashed line, Gofl=0, i.e., no feedback loop. τR50μs (d) Dashed line, Gofl0 and calculated with the parameter of the ideal feedback loop, τ˜R(g)3μs; dashed–dotted line, Gofl0 calculated with the parameter of the real feedback loop, i.e., experimentally determined [Eqs. (26)].

Fig. 5.
Fig. 5.

Numerical (left column) and experimental (right column) 1D LOFI scans, for different values of the lock-in integration time: (a) and (e) Tint=50μs, (b) and (f) Tint=20μs, (c) and (g) Tint=10μs, (d) and (h) Tint=5μs. Curves with circles (○), results obtained with the free running laser (i.e., τR50μs). Solid curve, results obtained with the electronic feedback control (i.e., τR3μs). Experimental conditions: Pout10mW (i.e., pout5×1016photons/s at λ=1064nm); FR950kHz; Fe1.05×FR; Rbs=0.5; the target is a reflectivity block with Re=0 (pixels 1–25 and 51–70) and Re4×1010 (pixels 26–50) with Re×(1Rbs)2×pout5×106photons/s0.06pW.

Fig. 6.
Fig. 6.

LOFI images of the edge of a metallic ruler. (a) Image obtained with the free running laser (i.e. τR50μs) and giving an SNR of: SNRa11dB. (b) Image obtained with the laser controlled by the electronic feedback loop (i.e., τR3μs) and giving SNRb17dB. Experimental conditions: Pout10mW (i.e., pout5×1016photons/s at λ=1064nm), FR950kHz; Fe1.05×FR; Rbs=0.5, and Tint=50μs. The SNR has been calculated by dividing the mean values of the measured signals on the ruler (right rectangle) and outside the ruler (left rectangle). The effective reflectivity of the ruler is estimated to be Re2×1010, which corresponds to the detection of: Re×(1Rbs)2×pout×50μs160photons for each pixel of the bright part of the ruler.

Tables (1)

Tables Icon

Table 1. LOFI SNR for the Free Running Laser (i.e., τR50μs) and for the Laser with the Electronic Feedback Control (i.e., τR3μs)a

Equations (38)

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dNdt=γ1N0+γ1ΔN0(t)γ1NBNI+FN(t),
dIdt=(BNγc)I+2γcRe(1Rbs)Icos[2πFet+ϕe]+FI(t),
Ns=γcB,
Is=γ1B(A1),
iΩΔN(Ω)=γ1AΔN(Ω)+γ1ΔN0(Ω)γcΔI(Ω)+FN(Ω)
iΩΔI(Ω)=BISΔN(Ω)+2γcRe(1Rbs)ISexp(iϕe)δ(ΩΩe)2+FI(Ω).
ΔI(Ω)=ΔILOFI(Ω)+ΔInoise(Ω)+ΔIpump(Ω),
ΔILOFI(Ω)=GLOFI(Ω)Re(1Rbs)ISδ(ΩΩe)exp(iϕe)
ΔIpump(Ω)=Gpump(Ω)ΔN0(Ω)
ΔInoise(Ω)=GLOFI(Ω)γc1FI(Ω)+Gpump(Ω)γ11FN(Ω),
GLOFI(Ω)=γc(iΩ+γ1A)ΩR2Ω2+iΩγ1A
Gpump(Ω)=γ1BISΩR2Ω2+iΩγ1A=γ1γcΩR2ΩR2Ω2+iΩγ1A,
ΔN0(Ω)=gRbsGAOM(Ω)GEFL(Ω)ΔI(Ω),
ΔI(Ω,g)=ΔILOFI(Ω)+ΔInoise(Ω)1+Gofl(Ω,g),
Gofl(Ω,g)=gRbsGAOM(Ω)GEFL(Ω)Gpump(Ω).
2πPSout(Ω,g)δ(Ω+Ω)=Δpout(Ω,g)Δpout(Ω,g).
PSout(Ω,g)=PSLOFI(Ω)+PSnoise(Ω)|1+Gofl(Ω,g)|2
PSLOFI(Ω)=Re(1Rbs)2pout2|GLOFI(Ω)|2δ(ΩΩe)
PSnoise(Ω)2pout|GLOFI(Ω)|2,
PSout(Ω,g)|GLOFI(Ω)|2|1+Gofl(Ω,g)|2[Repout2δ(ΩΩe)+2pout].
GAOM(Ω)=1
GEFL(Ω)=iΩΩc+iΩΩΩciΩΩc.
|G˜LOFI(Ω,g)|2=|GLOFI(Ω)|2|1+Gofl(Ω,g)|2ΩΩcγc2[Ω2+(γ1A)2](ΩR2Ω2)2+Ω2[γ1A+gRbsγ1γcΩR2Ωc]2.
|G˜LOFI(Ω,0)|2=|GLOFI(Ω)|2=γc2[Ω2+(γ1A)2](Ω2ΩR2)2+Ω2(γ1A)2ΩRγ1Aγc24(ΩΩR)2+(γ1A)2,
τR=(γ1A2)1.
τ˜R(g)=(γ1A+gRbsγ1γcΩR2Ωc2)1.
S˜LOFI2(Fe,Re,g)=2Rbs2+PSLOFI(2πF)|1+Gofl(2πF,g)|2|Fint[2π(FFe),Tint]|2dF
N˜LOFI2(Fe,Tint,g)=2Rbs+PSnoise(2πF)|1+Gofl(2πF,g)|2|Fint[2π(FFe),Tint]|2dF,
|Fint(Ω,Tint)|2=1Tint2+Ω2
S˜LOFI2(Fe,Re,g)=2Rbs2Re(1Rbs)2pout2|G˜LOFI(2πFe,g)|2
NLOFI2(Fe,Tint,g)=Rbspout12τ˜R(g)Tint(1Tint+1τ˜R(g))×γc2[1Tint+1τ˜R(g)]2+[2π(FeFR)]2.
SNR(Fe,Re,Tint,g)=SLOFI(Fe,Re,g)NLOFI(Fe,Tint,g).
SNR(Fe,Re,TintτR,g)=Re(1Rbs)×RbspoutTint.
Gpump(Ω)=γ1BISΩR2Ω2+iΩγ1A=γ1γcΩR2ΩR2Ω2+iΩγ1A
GAOM(Ω)=exp(iΩτA)
GEFL(Ω)=iΩΩc+iΩexp(iΩτE),
gRbs5×104.
τR,opt=(2γ1r)opt=22RbsNEP/(hc/λ)γcpout,

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