Abstract

In this paper, we compare the sensitivity of two imaging configurations, both based on laser optical feedback imaging (LOFI). The first one is direct imaging, which uses conventional optical focalization on target, and the second one is made by a synthetic aperture (SA) laser, which uses numerical focalization. We show that SA configuration allows us to obtain good resolutions with high working distance and that the drawback of SA imagery is that it has a worse photometric balance in comparison to a conventional microscope. This drawback is partially compensated by the important sensitivity of LOFI. Another interest of SA relies on the capacity of getting three-dimensional information in a single x-y scan.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. 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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    [CrossRef]
  18. V. Muzet, E. Lacot, O. Hugon, and Y. Guillard, “Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures,” Proc. SPIE 5856, 793–799 (2005).
    [CrossRef]
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    [CrossRef]
  28. 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]
  29. O. Jacquin, E. Lacot, C. Felix, and O. Hugon, “Laser optical feedback imaging insensitive to parasitic optical feedback,” Appl. Opt. 46, 6779–6782 (2007).
    [CrossRef]
  30. O. Jacquin, S. Heidmann, E. Lacot, and O. Hugon, “Self-aligned setup for laser optical feedback imaging insensitive to parasitic optical feedback,” Appl. Opt. 48, 64–68 (2009).
    [CrossRef]
  31. G. Liu, J. Li, Z. Xu, J. Wu, Q. Chen, H. Zhang, R. Zhang, H. Jia, and X. Luo, “Surface deformation associated with the 2008 Ms8.0 Wenchuan earthquake from ALOS L-band SAR interferometry,” Int. J. Appl. Earth Obs. Geoinf. 12, 496–505 (2010).

2011

S. Vertu, J. Flugge, J. J. Delaunay, and O. Haeberle, “Improved and isotropic resolution in tomographic driffractive microscopy combining sample and illumination rotation,” Central Eur. J. Phys. 9, 969–974 (2011).
[CrossRef]

K. Otsuka, “Self-mixing thin-slice solid-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, “Experimental comparison of autodyne and heterodyne laser interferometry using Nd:YVO4 microchip laser,” J. Opt. Soc. Am. A 28, 1741–1746 (2011).
[CrossRef]

2010

I. M. Vellekoop and C. M. Aegerter, “Scattered light fluorescence microscopy: imaging through turbid layers,” Opt. Lett. 35, 1245–1247 (2010).
[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]

G. Liu, J. Li, Z. Xu, J. Wu, Q. Chen, H. Zhang, R. Zhang, H. Jia, and X. Luo, “Surface deformation associated with the 2008 Ms8.0 Wenchuan earthquake from ALOS L-band SAR interferometry,” Int. J. Appl. Earth Obs. Geoinf. 12, 496–505 (2010).

P. Pantazis, J. Maloney, D. Wu, and S. E. Fraser, “Second harmonic generating (SHG) nanoprobes for in vivo imaging,” Proc. Natl. Acad. Sci. USA 107, 14535–14540 (2010).
[CrossRef]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

2009

2008

A. Witomski, E. Lacot, O. Hugon, and O. Jacquin, “Two dimensional synthetic aperture laser optical feedback imaging using galvanometric scanning,” Appl. Opt. 47, 860–869 (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]

2007

O. Jacquin, E. Lacot, C. Felix, and O. Hugon, “Laser optical feedback imaging insensitive to parasitic optical feedback,” Appl. Opt. 46, 6779–6782 (2007).
[CrossRef]

M. Pernot, J.-F. Aubry, M. Tanter, A.-L. Boch, F. Marquet, M. Kujas, D. Seilhean, and M. Fink, “In vivo transcranial brain surgery with an ultrasonic time reversal mirror,” J. Neurosurg. 106, 1061–1066 (2007).
[CrossRef]

2006

2005

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

2003

O. Hugon, E. Lacot, and F. Stoeckel, “Submicrometric displacement and vibration measurement using optical feedback in a fiber laser,” Fiber Integr. Opt. 22, 283–288 (2003).
[CrossRef]

2001

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

R. Day, E. Lacot, F. Stoeckel, and B. Berge, “Three-dimensional sensing based on a dynamically focused laser optical feedback imaging technique,” Appl. Opt. 40, 1921–1924 (2001).
[CrossRef]

1999

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

1994

1993

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]

1988

M. Minsky, “Memoir on inventing the confocal scanning microscope,” Scanning 10, 128–138 (1988).
[CrossRef]

1987

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, “Synthetic aperture imaging with a pulsed CO2 laser,” Proc. SPIE 783, 29–40 (1987).

Abshier, J. O.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, “Synthetic aperture imaging with a pulsed CO2 laser,” Proc. SPIE 783, 29–40 (1987).

Accetta, J. S.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, “Synthetic aperture imaging with a pulsed CO2 laser,” Proc. SPIE 783, 29–40 (1987).

Aegerter, C. M.

Aleksoff, C. C.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, “Synthetic aperture imaging with a pulsed CO2 laser,” Proc. SPIE 783, 29–40 (1987).

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]

Aubry, J.-F.

M. Pernot, J.-F. Aubry, M. Tanter, A.-L. Boch, F. Marquet, M. Kujas, D. Seilhean, and M. Fink, “In vivo transcranial brain surgery with an ultrasonic time reversal mirror,” J. Neurosurg. 106, 1061–1066 (2007).
[CrossRef]

Berge, B.

Boccara, A. C.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Boccara, C.

A. Dubois and C. Boccara, “Full-field OCT,” Med. Sci. (Paris) 22, 859–864 (2006).

Boch, A.-L.

M. Pernot, J.-F. Aubry, M. Tanter, A.-L. Boch, F. Marquet, M. Kujas, D. Seilhean, and M. Fink, “In vivo transcranial brain surgery with an ultrasonic time reversal mirror,” J. Neurosurg. 106, 1061–1066 (2007).
[CrossRef]

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]

Callens, N.

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Chen, Q.

G. Liu, J. Li, Z. Xu, J. Wu, Q. Chen, H. Zhang, R. Zhang, H. Jia, and X. Luo, “Surface deformation associated with the 2008 Ms8.0 Wenchuan earthquake from ALOS L-band SAR interferometry,” Int. J. Appl. Earth Obs. Geoinf. 12, 496–505 (2010).

Colella, B. D.

Curlander, J. C.

J. C. Curlander and R. N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing (Wiley, 1991).

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.

Delaunay, J. J.

S. Vertu, J. Flugge, J. J. Delaunay, and O. Haeberle, “Improved and isotropic resolution in tomographic driffractive microscopy combining sample and illumination rotation,” Central Eur. J. Phys. 9, 969–974 (2011).
[CrossRef]

Dubois, A.

A. Dubois and C. Boccara, “Full-field OCT,” Med. Sci. (Paris) 22, 859–864 (2006).

Dubois, F.

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]

Fee, M.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, “Synthetic aperture imaging with a pulsed CO2 laser,” Proc. SPIE 783, 29–40 (1987).

Felix, C.

Fink, M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

M. Pernot, J.-F. Aubry, M. Tanter, A.-L. Boch, F. Marquet, M. Kujas, D. Seilhean, and M. Fink, “In vivo transcranial brain surgery with an ultrasonic time reversal mirror,” J. Neurosurg. 106, 1061–1066 (2007).
[CrossRef]

Flugge, J.

S. Vertu, J. Flugge, J. J. Delaunay, and O. Haeberle, “Improved and isotropic resolution in tomographic driffractive microscopy combining sample and illumination rotation,” Central Eur. J. Phys. 9, 969–974 (2011).
[CrossRef]

Fraser, S. E.

P. Pantazis, J. Maloney, D. Wu, and S. E. Fraser, “Second harmonic generating (SHG) nanoprobes for in vivo imaging,” Proc. Natl. Acad. Sci. USA 107, 14535–14540 (2010).
[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]

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]

Gigan, S.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Glastre, W.

Green, T. J.

Guillard, Y.

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

Guillet de Chatellus, H.

Haeberle, O.

S. Vertu, J. Flugge, J. J. Delaunay, and O. Haeberle, “Improved and isotropic resolution in tomographic driffractive microscopy combining sample and illumination rotation,” Central Eur. J. Phys. 9, 969–974 (2011).
[CrossRef]

Heidmann, S.

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. Jacquin, E. Lacot, W. Glastre, O. Hugon, and H. Guillet de Chatellus, “Experimental comparison of autodyne and heterodyne laser interferometry using 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. Jacquin, S. Heidmann, E. Lacot, and O. Hugon, “Self-aligned setup for laser optical feedback imaging insensitive to parasitic optical feedback,” Appl. Opt. 48, 64–68 (2009).
[CrossRef]

A. Witomski, E. Lacot, O. Hugon, and O. Jacquin, “Two dimensional synthetic aperture laser optical feedback imaging using galvanometric scanning,” Appl. Opt. 47, 860–869 (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]

O. Jacquin, E. Lacot, C. Felix, and O. Hugon, “Laser optical feedback imaging insensitive to parasitic optical feedback,” Appl. Opt. 46, 6779–6782 (2007).
[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. Guillard, “Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures,” Proc. SPIE 5856, 793–799 (2005).
[CrossRef]

O. Hugon, E. Lacot, and F. Stoeckel, “Submicrometric displacement and vibration measurement using optical feedback in a fiber laser,” Fiber Integr. Opt. 22, 283–288 (2003).
[CrossRef]

Jacquin, 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, “Experimental comparison of autodyne and heterodyne laser interferometry using 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. Jacquin, S. Heidmann, E. Lacot, and O. Hugon, “Self-aligned setup for laser optical feedback imaging insensitive to parasitic optical feedback,” Appl. Opt. 48, 64–68 (2009).
[CrossRef]

A. Witomski, E. Lacot, O. Hugon, and O. Jacquin, “Two dimensional synthetic aperture laser optical feedback imaging using galvanometric scanning,” Appl. Opt. 47, 860–869 (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]

O. Jacquin, E. Lacot, C. Felix, and O. Hugon, “Laser optical feedback imaging insensitive to parasitic optical feedback,” Appl. Opt. 46, 6779–6782 (2007).
[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]

Jia, H.

G. Liu, J. Li, Z. Xu, J. Wu, Q. Chen, H. Zhang, R. Zhang, H. Jia, and X. Luo, “Surface deformation associated with the 2008 Ms8.0 Wenchuan earthquake from ALOS L-band SAR interferometry,” Int. J. Appl. Earth Obs. Geoinf. 12, 496–505 (2010).

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]

Klossler, A.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, “Synthetic aperture imaging with a pulsed CO2 laser,” Proc. SPIE 783, 29–40 (1987).

Ko, J.

K. Otsuka, T. Ohtomo, H. Makino, S. Sudo, and J. Ko, “Net motion of an ensemble of many Brownian particles captured with a self-mixing laser,” Appl. Phys. Lett. 94, 241117 (2009).
[CrossRef]

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]

Kujas, M.

M. Pernot, J.-F. Aubry, M. Tanter, A.-L. Boch, F. Marquet, M. Kujas, D. Seilhean, and M. Fink, “In vivo transcranial brain surgery with an ultrasonic time reversal mirror,” J. Neurosurg. 106, 1061–1066 (2007).
[CrossRef]

Lacot, E.

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, “Experimental comparison of autodyne and heterodyne laser interferometry using 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. Jacquin, S. Heidmann, E. Lacot, and O. Hugon, “Self-aligned setup for laser optical feedback imaging insensitive to parasitic optical feedback,” Appl. Opt. 48, 64–68 (2009).
[CrossRef]

A. Witomski, E. Lacot, O. Hugon, and O. Jacquin, “Two dimensional synthetic aperture laser optical feedback imaging using galvanometric scanning,” Appl. Opt. 47, 860–869 (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]

O. Jacquin, E. Lacot, C. Felix, and O. Hugon, “Laser optical feedback imaging insensitive to parasitic optical feedback,” Appl. Opt. 46, 6779–6782 (2007).
[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. Guillard, “Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures,” Proc. SPIE 5856, 793–799 (2005).
[CrossRef]

O. Hugon, E. Lacot, and F. Stoeckel, “Submicrometric displacement and vibration measurement using optical feedback in a fiber laser,” Fiber Integr. Opt. 22, 283–288 (2003).
[CrossRef]

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

R. Day, E. Lacot, F. Stoeckel, and B. Berge, “Three-dimensional sensing based on a dynamically focused laser optical feedback imaging technique,” Appl. Opt. 40, 1921–1924 (2001).
[CrossRef]

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

Lerosey, G.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Li, J.

G. Liu, J. Li, Z. Xu, J. Wu, Q. Chen, H. Zhang, R. Zhang, H. Jia, and X. Luo, “Surface deformation associated with the 2008 Ms8.0 Wenchuan earthquake from ALOS L-band SAR interferometry,” Int. J. Appl. Earth Obs. Geoinf. 12, 496–505 (2010).

Liu, G.

G. Liu, J. Li, Z. Xu, J. Wu, Q. Chen, H. Zhang, R. Zhang, H. Jia, and X. Luo, “Surface deformation associated with the 2008 Ms8.0 Wenchuan earthquake from ALOS L-band SAR interferometry,” Int. J. Appl. Earth Obs. Geoinf. 12, 496–505 (2010).

Luo, X.

G. Liu, J. Li, Z. Xu, J. Wu, Q. Chen, H. Zhang, R. Zhang, H. Jia, and X. Luo, “Surface deformation associated with the 2008 Ms8.0 Wenchuan earthquake from ALOS L-band SAR interferometry,” Int. J. Appl. Earth Obs. Geoinf. 12, 496–505 (2010).

Majwski, R. M.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, “Synthetic aperture imaging with a pulsed CO2 laser,” Proc. SPIE 783, 29–40 (1987).

Makino, H.

K. Otsuka, T. Ohtomo, H. Makino, S. Sudo, and J. Ko, “Net motion of an ensemble of many Brownian particles captured with a self-mixing laser,” Appl. Phys. Lett. 94, 241117 (2009).
[CrossRef]

Maloney, J.

P. Pantazis, J. Maloney, D. Wu, and S. E. Fraser, “Second harmonic generating (SHG) nanoprobes for in vivo imaging,” Proc. Natl. Acad. Sci. USA 107, 14535–14540 (2010).
[CrossRef]

Markus, S.

Marquet, F.

M. Pernot, J.-F. Aubry, M. Tanter, A.-L. Boch, F. Marquet, M. Kujas, D. Seilhean, and M. Fink, “In vivo transcranial brain surgery with an ultrasonic time reversal mirror,” J. Neurosurg. 106, 1061–1066 (2007).
[CrossRef]

McDonough, R. N.

J. C. Curlander and R. N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing (Wiley, 1991).

Minsky, M.

M. Minsky, “Memoir on inventing the confocal scanning microscope,” Scanning 10, 128–138 (1988).
[CrossRef]

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]

Muzet, V.

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

Ohtomo, T.

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

K. Otsuka, T. Ohtomo, H. Makino, S. Sudo, and J. Ko, “Net motion of an ensemble of many Brownian particles captured with a self-mixing laser,” Appl. Phys. Lett. 94, 241117 (2009).
[CrossRef]

Oishi, T.

Otsuka, K.

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

K. Otsuka, T. Ohtomo, H. Makino, S. Sudo, and J. Ko, “Net motion of an ensemble of many Brownian particles captured with a self-mixing laser,” Appl. Phys. Lett. 94, 241117 (2009).
[CrossRef]

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

Pantazis, P.

P. Pantazis, J. Maloney, D. Wu, and S. E. Fraser, “Second harmonic generating (SHG) nanoprobes for in vivo imaging,” Proc. Natl. Acad. Sci. USA 107, 14535–14540 (2010).
[CrossRef]

Pasmurov, A. J.

A. J. Pasmurov and J. S. Zimoview, Radar Imaging and Holography (Institution of Electrical Engineers, 2005).

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]

Pernot, M.

M. Pernot, J.-F. Aubry, M. Tanter, A.-L. Boch, F. Marquet, M. Kujas, D. Seilhean, and M. Fink, “In vivo transcranial brain surgery with an ultrasonic time reversal mirror,” J. Neurosurg. 106, 1061–1066 (2007).
[CrossRef]

Peterson, L. M.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, “Synthetic aperture imaging with a pulsed CO2 laser,” Proc. SPIE 783, 29–40 (1987).

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[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.

Schockaert, C.

Schroeder, K. S.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, “Synthetic aperture imaging with a pulsed CO2 laser,” Proc. SPIE 783, 29–40 (1987).

Seilhean, D.

M. Pernot, J.-F. Aubry, M. Tanter, A.-L. Boch, F. Marquet, M. Kujas, D. Seilhean, and M. Fink, “In vivo transcranial brain surgery with an ultrasonic time reversal mirror,” J. Neurosurg. 106, 1061–1066 (2007).
[CrossRef]

Stoeckel, F.

O. Hugon, E. Lacot, and F. Stoeckel, “Submicrometric displacement and vibration measurement using optical feedback in a fiber laser,” Fiber Integr. Opt. 22, 283–288 (2003).
[CrossRef]

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

R. Day, E. Lacot, F. Stoeckel, and B. Berge, “Three-dimensional sensing based on a dynamically focused laser optical feedback imaging technique,” Appl. Opt. 40, 1921–1924 (2001).
[CrossRef]

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

Sudo, S.

K. Otsuka, T. Ohtomo, H. Makino, S. Sudo, and J. Ko, “Net motion of an ensemble of many Brownian particles captured with a self-mixing laser,” Appl. Phys. Lett. 94, 241117 (2009).
[CrossRef]

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

Tai, A. M.

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, “Synthetic aperture imaging with a pulsed CO2 laser,” Proc. SPIE 783, 29–40 (1987).

Takahashi, Y.

Tanter, M.

M. Pernot, J.-F. Aubry, M. Tanter, A.-L. Boch, F. Marquet, M. Kujas, D. Seilhean, and M. Fink, “In vivo transcranial brain surgery with an ultrasonic time reversal mirror,” J. Neurosurg. 106, 1061–1066 (2007).
[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]

Vellekoop, I. M.

Vertu, S.

S. Vertu, J. Flugge, J. J. Delaunay, and O. Haeberle, “Improved and isotropic resolution in tomographic driffractive microscopy combining sample and illumination rotation,” Central Eur. J. Phys. 9, 969–974 (2011).
[CrossRef]

Witomski, A.

Wu, D.

P. Pantazis, J. Maloney, D. Wu, and S. E. Fraser, “Second harmonic generating (SHG) nanoprobes for in vivo imaging,” Proc. Natl. Acad. Sci. USA 107, 14535–14540 (2010).
[CrossRef]

Wu, J.

G. Liu, J. Li, Z. Xu, J. Wu, Q. Chen, H. Zhang, R. Zhang, H. Jia, and X. Luo, “Surface deformation associated with the 2008 Ms8.0 Wenchuan earthquake from ALOS L-band SAR interferometry,” Int. J. Appl. Earth Obs. Geoinf. 12, 496–505 (2010).

Xu, Z.

G. Liu, J. Li, Z. Xu, J. Wu, Q. Chen, H. Zhang, R. Zhang, H. Jia, and X. Luo, “Surface deformation associated with the 2008 Ms8.0 Wenchuan earthquake from ALOS L-band SAR interferometry,” Int. J. Appl. Earth Obs. Geoinf. 12, 496–505 (2010).

Yourassowsky, C.

Zhang, H.

G. Liu, J. Li, Z. Xu, J. Wu, Q. Chen, H. Zhang, R. Zhang, H. Jia, and X. Luo, “Surface deformation associated with the 2008 Ms8.0 Wenchuan earthquake from ALOS L-band SAR interferometry,” Int. J. Appl. Earth Obs. Geoinf. 12, 496–505 (2010).

Zhang, R.

G. Liu, J. Li, Z. Xu, J. Wu, Q. Chen, H. Zhang, R. Zhang, H. Jia, and X. Luo, “Surface deformation associated with the 2008 Ms8.0 Wenchuan earthquake from ALOS L-band SAR interferometry,” Int. J. Appl. Earth Obs. Geoinf. 12, 496–505 (2010).

Zimoview, J. S.

A. J. Pasmurov and J. S. Zimoview, Radar Imaging and Holography (Institution of Electrical Engineers, 2005).

Appl. Opt.

Appl. Phys. Lett.

K. Otsuka, T. Ohtomo, H. Makino, S. Sudo, and J. Ko, “Net motion of an ensemble of many Brownian particles captured with a self-mixing laser,” Appl. Phys. Lett. 94, 241117 (2009).
[CrossRef]

Central Eur. J. Phys.

S. Vertu, J. Flugge, J. J. Delaunay, and O. Haeberle, “Improved and isotropic resolution in tomographic driffractive microscopy combining sample and illumination rotation,” Central Eur. J. Phys. 9, 969–974 (2011).
[CrossRef]

Eur. Phys. J. D

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]

Fiber Integr. Opt.

O. Hugon, E. Lacot, and F. Stoeckel, “Submicrometric displacement and vibration measurement using optical feedback in a fiber laser,” Fiber Integr. Opt. 22, 283–288 (2003).
[CrossRef]

Int. J. Appl. Earth Obs. Geoinf.

G. Liu, J. Li, Z. Xu, J. Wu, Q. Chen, H. Zhang, R. Zhang, H. Jia, and X. Luo, “Surface deformation associated with the 2008 Ms8.0 Wenchuan earthquake from ALOS L-band SAR interferometry,” Int. J. Appl. Earth Obs. Geoinf. 12, 496–505 (2010).

J. Neurosurg.

M. Pernot, J.-F. Aubry, M. Tanter, A.-L. Boch, F. Marquet, M. Kujas, D. Seilhean, and M. Fink, “In vivo transcranial brain surgery with an ultrasonic time reversal mirror,” J. Neurosurg. 106, 1061–1066 (2007).
[CrossRef]

J. Opt. Soc. Am. A

Med. Sci. (Paris)

A. Dubois and C. Boccara, “Full-field OCT,” Med. Sci. (Paris) 22, 859–864 (2006).

Opt. Express

Opt. Lett.

Phys. Rev. A

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]

Phys. Rev. Lett.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Proc. Natl. Acad. Sci. USA

P. Pantazis, J. Maloney, D. Wu, and S. E. Fraser, “Second harmonic generating (SHG) nanoprobes for in vivo imaging,” Proc. Natl. Acad. Sci. USA 107, 14535–14540 (2010).
[CrossRef]

Proc. SPIE

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

C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klossler, K. S. Schroeder, R. M. Majwski, J. O. Abshier, and M. Fee, “Synthetic aperture imaging with a pulsed CO2 laser,” Proc. SPIE 783, 29–40 (1987).

Scanning

M. Minsky, “Memoir on inventing the confocal scanning microscope,” Scanning 10, 128–138 (1988).
[CrossRef]

Sensors

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

Ultramicroscopy

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

J. C. Curlander and R. N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing (Wiley, 1991).

A. J. Pasmurov and J. S. Zimoview, Radar Imaging and Holography (Institution of Electrical Engineers, 2005).

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Figures (8)

Fig. 1.
Fig. 1.

Description of the LOFI experimental setups. The target is located in the vertical plane (x,y,z=0). L1, L2, L3 are lenses; BS is a beam splitter (T=90%); Fe is the total optical frequency shift. Mx and My are the rotating mirrors that allow scanning of the target in the horizontal direction x and the vertical direction y, respectively. The angular orientations of the galvanometric mirrors are given by the angles αx and αy. (a) Conventional LOFI experiment where the laser is focused in the target plane. (b) SA LOFI experiment. The laser is focused in front of the target plane. l is the focal spot–Mx distance, d is the MxMy distance, L is the My–target plane distance, and SSA is the Gaussian laser beam surface in the target plane.

Fig. 2.
Fig. 2.

Sketch of the two configurations discussed in the paper. (a) Conventional LOFI: Wc is the beam waist before L3’, rc is the waist in the target plane, and θ is the numerical aperture. (b) SA LOFI : rSA is the beam waist before the galvanometric mirrors, l is the distance between them, and SSA is the surface of the beam in the object plane. L is the distance between the last optical element (the scanning mirror) of the setup and the target of surface S.

Fig. 3.
Fig. 3.

(a) Object under microscope. It is composed of reflective silica beads of 40 μm diameter behind a circular aperture of 1 mm diameter. The bright field transmission image is made through a Zeiss microscope objective with a magnification of 10 and a 0.25 numerical aperture (focal length of 20 mm). (b) LOFI amplitude image of the target (size: 512*512 pixels). The image is formed through the same Zeiss objective but with a laser beam input size of Wc=1.3mm; a resolution RESc of 7μm is expected, which is coherent with bead’s image size on the image. A laser power of 2 mW is sent on the target. (c) Raw image of the target (size: 2048*2048 pixels). Parameters are rSA=20μm, l=10cm, d=1cm, L=2.5cm. The power sent on the target is 1.5 mW. The beam size on the target plane is equal to 1.7 mm: beads are not resolved, and the size of raw image is enlarged compared to real image. (d) Synthetic image after filtering of the raw image. Predicted resolution is RESSA,x=5.7μm in X direction and RESSA,y=5.3μm in Y direction, which is coherent with bead’s image size on the image. We found the good focusing plane (so in the target plane) by using the detection criteria described by F. According to Dubois et al. [26], this algorithm will be used each time SA filtering is performed. The image in the lower right corner has the same size as the image in the lower left corner but is zoomed on the object to be comparable to the conventional image of the image in the upper right corner.

Fig. 4.
Fig. 4.

Image of a 3D object composed of one 350 μm width horizontal strip, which is 4 cm after My, and of three double slits spaced respectively by 400, 600, and 800 μm at a distance of nine cm after My. (a) Raw image; the beam size is 1.4 mm in the strip plane and 2.2 mm in the slits plane. Slits are not resolved. (b) The image numerically focused on the strip plane (double slits are not resolved); theoretical resolution is 20 μm. (c) The image numerically focused on double slits that are now resolved (theoretical resolution is 40 μm).

Fig. 5.
Fig. 5.

Experimental photometric comparison between conventional and SA LOFI with same resolutions. Parameters are Wc=0.9mm, WSA=1.3mm, rSA=20μm, l=5cm, d=1cm. The laser power after frequency shifter is 2 mW (the power sent on the beads is reduced comparede to the 50 mW available power to stay in weak reinjection conditions). For the conventional microscope, the focal length of L3’ (L) is varied from 5 to 30 cm. The conventional photometric balance is fitted with 1/(1+L)2L2, whereas the SA photometric balance is fitted to 1/L4.

Fig. 6.
Fig. 6.

Scheme of the experimental setup. (a) Conventional configuration, b) SA LOFI configuration. The object of Fig. 3 is placed in a tank filled with milk diluted in water. ΔL=4cm is the distance between the input face of the tank and the object (i.e., the distance travelled by the laser beam in the solution). Experimental parameters are Wc=0.9mm, WSA=1.3mm, Sc=5.6.109m2, Sc,tank=3.2.107m2, SSA=3.1.105m2, SSA,tank=1.88.105m2, rSA=20μm, l=5cm, f(L3)L=12cm; the power sent on the target is 2 mW. Milk concentrations are chosen from 0 to 2.5% in volume.

Fig. 7.
Fig. 7.

(a) Experimental results associated to setups of Fig. 6. Top: power reflected by the target (signal) and by the background (noise) in conventional and SA configurations versus the optical density (OD) of a diluted milk solution through 4 cm; concentrations evolve from 0 to 2.5% in volume. Bottom: plot of the SNR accessible in conventional and SA configurations versus the OD.

Fig. 8.
Fig. 8.

Power measurements from the target and from the background versus OD. The setup is the same as in Fig. 6 but with an attenuator before the acousto-optic deflectors. The setups are quantum noise limited. Again when the round trip density is increased by 1, the power is divided by 10, which is coherent with Beer–Lambert law.

Equations (32)

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

ΔPout(αx,αy)=2GR(Ωe)PoutiRe(αx,αy,xi,yi)cos(Ωet+Φ(αx,αy,xi,yi)+ΦR(Ωe)),
GR(Ωe)=γc(ηγ1)2+Ωe2(ΩR2Ωe2)2+(ηγ1Ωe)2,ΦR(Ωe)=arctan(Ωe(ΩR2Ωe2(ηγ1)2)ηγ1ΩR2),
I(αx,αy)=2GR(Ωe)PoutiRe(αx,αy,xi,yi)cos(Φ(αx,αy,xi,yi)),Q(αx,αy)=2GR(Ωe)PoutiRe(αx,αy,xi,yi)sin(Φ(αx,αy,xi,yi)),
h(αx,αy)=I(αx,αy)+jQ(αx,αy)=|h(αx,αy)|exp(jΦS(αx,αy)).
|hc(x,y)|exp[2(x2+y2RESc2)].
RESc=2rc=2λπWcfc,
|hSA(x,y)|exp[2(x2RESSA,x2+y2RESSA,y2)],
RESSA,x=rSA(d+L)landRESSA,y=rSALl+d.
RESc=2λπWcfc2λπWcL,RESSA=rSAlL=2λπ(2λlxπrSA)L=2λπWSAL.
Ec=Poutπrc2=PoutπWc2λ2L2,
Gc=Sπθ2=SπWc2L2,
Lc=ρEcπ.
Pc=GcLc=SπWc2L2ρPoutπWc2πλ2L2=ρPoutSπWc4λ2L4.
PSA=NpixelsPpixelSA2,
Npixels=SSASpixel=π(λπrSA(l+L))2π(rSALl)2=λ2(l+L)2l2π2rSA4L2.
PpixelSA=GSALSA
GSA=πrSA2S(l+L)2,
LSA=ρESAπ=ρπPoutπ(λπrSA(l+L))2=ρPoutrSA2λ2(l+L)2,
PSA=12λ2(l+L)2l2π2rSA4L2πrSA2S(l+L)2ρPoutrSA2λ2(l+L)2=ρPoutl2S2πL2(l+L)2.
PSA,lL=ρPoutl2S2πL4.
PcPSA,lL=2π2Wc4λ2l2.
Tacq,SA,lL=Npixels,lLTλ2l2π2rSA4T.
PSA,lL=ρPoutS2πL2.
PcPSA,lL=2π2Wc4λ2L2.
Tacq,SA,lL=Npixels,lLTλ2l4π2rSA4L2T.
Pc,tankPSA,tank=ρtankPoutScπWc4λ2L4ρtankScPoutl22πL4=2π2Wc4λ2l2.
Pc,tank=Lc,tankGc=ρtankEc,tankπGc=ρtankPoutπSc,tankSc,tankScΔL2=ρtankPoutScπΔL2.
Pc,tank=Lc,tankGc=ρtankEc,tankπGc=ρtankPoutπScScπθ2=ρtankPoutθ2.
π(λΔLπrc)2=Sc,tankΔL=Sc,tankπrc2λ2=Sc,tankScλ,θ=λπrc=λπSc.
Pc,tankPc,tank=Sc,tankSc.
PSA,tankPSA,tank=SSA,tankSSA.
SNRc=PcPc,tank=PcPc,tankSc,tankSc,SNRSA=PSAPSA,tank=PSAPSA,tankSSA,tankSSA,SNRcSNRSA=Sc,tankSSAScSSA,tank.

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