Abstract

In this paper we study the origin and the effect of amplitude and phase noise on laser optical feedback imaging associated with a synthetic aperture (SA) imaging system. Amplitude noise corresponds to photon noise and acts as an additive noise; it can be reduced by increasing the global measurement time. Phase noise can be divided in three families: random, sinusoidal, and drift phase noise; we show that it acts as a multiplicative noise. We explain how we can reduce phase noise by making oversampling or multiple measurements depending on its type. This work can easily be extended to all SA systems (radar, laser, or terahertz), especially when raw holograms are acquired point by point.

© 2012 Optical Society of America

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  1. 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]
  2. 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]
  3. I. M. Vellekoop and C. M. Aegerter, “Scattered light fluorescence microscopy: imaging through turbid layers,” Opt. Lett. 35, 1245–1247 (2010).
    [CrossRef]
  4. A. Dubois and C. Boccara, “L’OCT plein champ,” Med. Sci. 22, 859–864 (2006), in French.
  5. 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]
  6. M. Minsky, “Memoir on inventing the confocal scanning microscope,” Scanning 10, 128–138 (1988).
    [CrossRef]
  7. S. Vertu, J. Flugge, J. J. Delaunay, and O. Haeberle, “Improved and isotropic resolution in tomographic diffractive microscopy combining sample and illumination rotation,” Central Eur. J. Phys. 44, 969–974 (2011).
    [CrossRef]
  8. E. Lacot, R. Day, and F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815 (2001).
    [CrossRef]
  9. K. Otsuka, “Self-mixing thin-slice solid-state laser metrology,” Sensors 11, 2195–2245 (2011).
    [CrossRef]
  10. E. Lacot, R. Day, and F. Stoeckel, “Laser optical feedback tomography,” Opt. Lett. 24, 744–746 (1999).
    [CrossRef]
  11. O. Hugon, F. Joud, E. Lacot, O. Jacquin, and H. de Chatellus Guillet, “Coherent microscopy by laser optical feedback imaging (LOFI) technique,” Ultramicroscopy 111, 1557–1563 (2011).
    [CrossRef]
  12. E. Lacot, O. Jacquin, G. Roussely, O. Hugon, and H. de Chatellus Guillet, “Comparative study of autodyne and heterodyne laser interferometry for imaging,” J. Opt. Soc. Am. A 27, 2450–2458 (2010).
    [CrossRef]
  13. O. Jacquin, E. Lacot, W. Glastre, O. Hugon, and H. de Chatellus Guillet, “Experimental comparison of autodyne and heterodyne laser interferometry using Nd:YVO4 microchip laser,” J. Opt. Soc. Am. A 28, 1741–1746 (2011).
    [CrossRef]
  14. W. Glastre, O. Jacquin, O. Hugon, H. de Chatellus Guillet, and E. Lacot, “Synthetic aperture laser optical feedback imaging using a translational scanning with galvanometric mirrors,” J. Opt. Soc. Am. A 29, 1639–1647 (2012).
    [CrossRef]
  15. W. Glastre, E. Lacot, O. Jacquin, and H. de Chatellus Guillet, “Sensitivity of synthetic aperture laser optical feedback imaging,” J. Opt. Soc. Am. A 29, 476–485 (2012).
    [CrossRef]
  16. 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]
  17. J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2006).
  18. J. C. Curlander and R. N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing (Wiley, 1991).
  19. A. Ja. Pasmurov and J. S. Zimoview, Radar Imaging and Holography (Institution of Electrical Engineers, 2005).
  20. C. C. Aleksoff, J. S. Accetta, L. M. Peterson, A. M. Tai, A. Klooster, K. S. Schroeder, R. M. Majewski, J. O. Abshier, and M. Fee, “Synthetic aperture imaging with a pulsed CO2 TEA laser,” Proc. SPIE 783, 29–40 (1987).
    [CrossRef]
  21. S. Markus, B. D. Colella, and T. J. Green, “Solid-state laser synthetic aperture radar,” Appl. Opt. 33, 960–964 (1994).
    [CrossRef]
  22. A. Bandyopadhyay, A. Stepanov, B. Schulkin, M. D. Federici, A. Sengupta, D. Gary, and J. F. Federici, “Terahertz interferometric and synthetic aperture imaging,” J. Opt. Soc. Am. A 23, 1168–1178 (2006).
    [CrossRef]
  23. O. Jacquin, W. Glastre, E. Lacot, O. Hugon, H. de Chatellus Guillet, and F. Ramaz, “Acousto-optic laser optical feedback imaging,” Opt. Lett. 37, 2514–2516 (2012).
    [CrossRef]

2012 (3)

2011 (4)

S. Vertu, J. Flugge, J. J. Delaunay, and O. Haeberle, “Improved and isotropic resolution in tomographic diffractive microscopy combining sample and illumination rotation,” Central Eur. J. Phys. 44, 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. de Chatellus Guillet, “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. de Chatellus Guillet, “Experimental comparison of autodyne and heterodyne laser interferometry using Nd:YVO4 microchip laser,” J. Opt. Soc. Am. A 28, 1741–1746 (2011).
[CrossRef]

2010 (4)

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. de Chatellus Guillet, “Comparative study of autodyne and heterodyne laser interferometry for imaging,” J. Opt. Soc. Am. A 27, 2450–2458 (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]

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]

2008 (1)

2007 (1)

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 (2)

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 (1)

1994 (1)

1988 (1)

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

1987 (1)

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

Abshier, J. O.

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

Accetta, J. S.

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

Aegerter, C. M.

Aleksoff, C. C.

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

Bandyopadhyay, A.

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, “L’OCT plein champ,” Med. Sci. 22, 859–864 (2006), in French.

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]

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]

Colella, B. D.

Curlander, J. C.

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

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]

de Chatellus Guillet, H.

Delaunay, J. J.

S. Vertu, J. Flugge, J. J. Delaunay, and O. Haeberle, “Improved and isotropic resolution in tomographic diffractive microscopy combining sample and illumination rotation,” Central Eur. J. Phys. 44, 969–974 (2011).
[CrossRef]

Dubois, A.

A. Dubois and C. Boccara, “L’OCT plein champ,” Med. Sci. 22, 859–864 (2006), in French.

Federici, J. F.

Federici, M. D.

Fee, M.

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

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 diffractive microscopy combining sample and illumination rotation,” Central Eur. J. Phys. 44, 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]

Gary, D.

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.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2006).

Green, T. J.

Haeberle, O.

S. Vertu, J. Flugge, J. J. Delaunay, and O. Haeberle, “Improved and isotropic resolution in tomographic diffractive microscopy combining sample and illumination rotation,” Central Eur. J. Phys. 44, 969–974 (2011).
[CrossRef]

Hugon, O.

Jacquin, O.

Joud, F.

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

Klooster, A.

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

W. Glastre, E. Lacot, O. Jacquin, and H. de Chatellus Guillet, “Sensitivity of synthetic aperture laser optical feedback imaging,” J. Opt. Soc. Am. A 29, 476–485 (2012).
[CrossRef]

O. Jacquin, W. Glastre, E. Lacot, O. Hugon, H. de Chatellus Guillet, and F. Ramaz, “Acousto-optic laser optical feedback imaging,” Opt. Lett. 37, 2514–2516 (2012).
[CrossRef]

W. Glastre, O. Jacquin, O. Hugon, H. de Chatellus Guillet, and E. Lacot, “Synthetic aperture laser optical feedback imaging using a translational scanning with galvanometric mirrors,” J. Opt. Soc. Am. A 29, 1639–1647 (2012).
[CrossRef]

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

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]

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]

Majewski, R. M.

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

Otsuka, K.

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

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

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. Klooster, K. S. Schroeder, R. M. Majewski, J. O. Abshier, and M. Fee, “Synthetic aperture imaging with a pulsed CO2 TEA laser,” Proc. SPIE 783, 29–40 (1987).
[CrossRef]

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]

Ramaz, F.

Roussely, G.

Schroeder, K. S.

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

Schulkin, B.

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]

Sengupta, A.

Stepanov, A.

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]

Tai, A. M.

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

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]

Vellekoop, I. M.

Vertu, S.

S. Vertu, J. Flugge, J. J. Delaunay, and O. Haeberle, “Improved and isotropic resolution in tomographic diffractive microscopy combining sample and illumination rotation,” Central Eur. J. Phys. 44, 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]

Zimoview, J. S.

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

Appl. Opt. (2)

Central Eur. J. Phys. (1)

S. Vertu, J. Flugge, J. J. Delaunay, and O. Haeberle, “Improved and isotropic resolution in tomographic diffractive microscopy combining sample and illumination rotation,” Central Eur. J. Phys. 44, 969–974 (2011).
[CrossRef]

J. Neurosurg. (1)

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 (5)

Med. Sci. (1)

A. Dubois and C. Boccara, “L’OCT plein champ,” Med. Sci. 22, 859–864 (2006), in French.

Opt. Lett. (3)

Phys. Rev. A (1)

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

Phys. Rev. Lett. (1)

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 (1)

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 (1)

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

Scanning (1)

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

Sensors (1)

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

Ultramicroscopy (1)

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

Other (3)

J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2006).

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

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

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Figures (10)

Fig. 1.
Fig. 1.

Experimental setup of the SA LOFI-based imaging system. The laser is a cw Nd:YVO4 microchip collimated by lens L1. A beam splitter sends 10% of the beam on a photodiode connected to a lock-in amplifier, which gives access to the amplitude and phase of the signal. The frequency shifter is made of two acousto-optic modulators, which diffract respectively in orders 1 and 1 and give a net frequency shift of Fe/2=1.5MHz. X-Y plane is scanned by galvanometric mirrors MX (scan in the X direction) and MY (scan in the Y direction) conjugated by a telescope made by two identical lenses L3. f3 and f4 are the focal lengths of L3 and L4. αX and αY are the angular positions of MX and MY. r is the waist of the laser after L4.

Fig. 2.
Fig. 2.

Target used for the whole study: it is made 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).

Fig. 3.
Fig. 3.

Illustration of the effect of the spatial sampling on the Fourier content of the signal. The images are the amplitude of the Fourier transform of a simulated PSF with the following parameters: r=20μm, f=75mm, and L=2.5cm. For a constant field image of 2 mm, we have a sampling of (a) 128×128 pixels and (b) 1024×1024 pixels.

Fig. 4.
Fig. 4.

Amplitude of SA images of the setup of Fig. 2. Parameters are r=20μm, f=75mm, and L=2.5cm. (a), (c) Sampling of 128×128 pixels and (b), (d) sampling of 1024×1024 pixels. Figures are amplitude images after filtering (a), (b) by phase filter of Eq. (4) and (c), (d) adapted filter of Eq. (8).

Fig. 5.
Fig. 5.

Dependence of the power in a pixel of signal and noise (averaged) in the SA image with the acquisition time. The signal comes from the object of Fig. 2 with parameters r=20μm, f=75mm, and L=2.3cm. Acquisition time is increased via (a) the integration time in a pixel at constant sampling and field of view or (b) the sampling at constant integration time T and field of view. The power here is the mean of the square of the image amplitude. This power is normalized by the total number of pixels. The noise is measured in the absence of beads (see Fig. 4).

Fig. 6.
Fig. 6.

Propagation of a wavefront with phase noise over a distance L/2. In the final image plane, we have two contributions: a coherent one (solid line) and a random speckle (dashed line). The speckle and coherent contributions have relative intensities depending only on the density of probability of the random phase.

Fig. 7.
Fig. 7.

Effect of random Gaussian phase noise on SA operation. We use a simulated image of a punctual reflector. (a) Amplitude of raw image with L=4cm, (b) amplitude after numerical refocusing, without phase noise, (c) amplitude after numerical refocusing, σΦ=3π/5, and (d) amplitude after numerical refocusing, σΦ=π. Parameters are r=20μm, f=75mm, and the definition is 512×512 pixels; the numerical refocusing is made with the pure phase filter for all images.

Fig. 8.
Fig. 8.

Propagation of a wavefront with sinusoidal phase perturbations over a distance L/2. In the final image plane, there are two contributions: a coherent one (solid line) and several diffracted orders (dashed line). υ0 and μ0 are spatial frequencies of the perturbation in X and Y directions; the drawing is a projection along to the sinusoidal perturbation.

Fig. 9.
Fig. 9.

Effect of a mechanical sinusoidal phase perturbation on SA operation. Image parameters are 2048×2048 pixels, L=2.5cm, r=20μm, f=75mm, integration time T=150μs by pixel, and the target is the object of Fig. 2. Amplitude image after SA operation (a) without and (b) with the perturbation. The perturbation at 100 Hz is generated by a loud speaker localized near the target. This induces a phase perturbation of amplitude Φ0=1.2rad and of spatial frequencies υ0=10,000m1 and μ0=80,000m1. The SA operation is made with the pure phase filter of Eq. (4).

Fig. 10.
Fig. 10.

Effect of phase drifts during the raw acquisition on SA imaging. Parameters are r=13μm, f=25mm, L=2cm, and 512×512 pixels. The effect of the phase drift correction is illustrated too (here the correction is made on the image taken slowly along the Y direction). The target is still the object of Fig. 2. (a) Amplitude and (b) phase (white is π radians and the black is +π) of raw image of the target. (c) Phase difference between the two raw acquisitions acquired with different slow directions. (d) Phase correction to apply in the Y direction calculated from (c). Amplitudes of the synthetic image (pure phase filter is used) (e) before and (f) after phase correction.

Equations (18)

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hR(L,x,y)(exp(x2+y22RESR2)exp(jπx2+y22L2λ))2,RESR=λLπ2r.
HR(ν,μ)exp(υ2+μ2Δυ2)exp(jπLλ(ν2+μ2)2),Δυ=2πr.
|hSA(x,y)|=|FT1(HR(υ,μ)Hfilt(υ,μ))|exp(x2+y2RESSA2),RESSA=r2,
Hfilt(ν,μ)=exp(jπLλ(ν2+μ2)2).
TTot=NpixT.
SNRTTTot.
HFilt(ν,μ)=exp(υ2+μ2Δυ2)exp(jπLλ(ν2+μ2)2).
|hSA(x,y)|=|TF1(HR(x,y)Hfilt(x,y))|exp(x2+y2r2).
SNRAdaptFiltSNRPhFilt=SSSpectSNSpectSSSpectSNSpect=SSSpectSSSpectSNSpectSNSpect=128ΔυSh2πΔυ2=1πΔυ2δx2NPix.
SNRAdaptFiltSNRPhFiltNpixTTot.
hRPhN(x,y)=mPhN(x,y)hR(x,y),mPhN(x,y)=exp(jΦ(x,y)).
|hSAPhN(x,y)|2¯|hSA(x,y)|2*(|m¯PhN(x,y)|2δ(x,y)+(2λL)2DSPm(2xλL,2yλL)).
DSPm(υ,μ)=FT(COVm(x,y)),m¯PhN=+exp(jϕ)PΦ(ϕ)dϕ=P˜Φ(1)1σΦ22.
|m¯PhN(x,y)|Gauss2=|P˜Φ,Gauss(1)|2=exp(σΦ2).
|m¯PhN(x,y)|Uni2=|P˜Φ,Uni(1)|2=sinc2(12σΦ2).
hRSinPh(x,y)=mSinPh(x,y)hR(x,y),mSinPh(x,y)=exp(jΦ0sin(2π(υ0x+μ0y))).
hSASinPh(x,y)=n+Jn(Φ0)hSA(xnλυ0L2,ynλμ0L2).
hRPhDrift(x,y)=mPhDrift(y)hR(x,y),mPhDrift(y)=exp(jΦ(y)).

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