Abstract

We study the control of coherent light propagation through multiple-scattering media in the presence of measurement noise. In our experiments, we use a two-step optimization procedure to find the optimal incident wavefront that generates a bright focal spot behind the medium. We conclude that the control of coherent light propagation through a multiple-scattering medium is only determined by the number of photoelectrons detected per optimized segment. The prediction of our model agrees well with the experimental results. Our results offer opportunities for imaging applications through scattering media such as biological tissue in the shot noise limit.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. Freund, “Looking through walls and around corners,” Physica A168, 49–65 (1990).
    [CrossRef]
  2. I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett.32, 2309–2311 (2007).
    [CrossRef] [PubMed]
  3. A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nature Photon.6, 283 (2012).
    [CrossRef]
  4. J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett.106, 103901 (2011).
    [CrossRef] [PubMed]
  5. O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nature Photon.5, 372–377 (2011).
    [CrossRef]
  6. D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nature Commun.2, 447 (2011).
    [CrossRef]
  7. I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nature Photon.4, 320–322 (2010).
    [CrossRef]
  8. E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett.106, 193905 (2011).
    [CrossRef] [PubMed]
  9. J. H. Park, C. Park, H. Yu, Y. H. Cho, and Y. Park, “Dynamic active wave plate using random nanoparticles,” Opt. Express20, 17010–17016 (2012).
    [CrossRef]
  10. Y. F. Guan, O. Katz, E. Small, J. Y. Zhou, and Y. Silberberg, “Polarization control of multiply scattered light through random media by wavefront shaping,” Opt. Lett.37, 4663–4665 (2012).
    [CrossRef] [PubMed]
  11. J. H. Park, C. Park, H. Yu, Y. Cho, and Y. H. Park, “Active spectral filtering through turbid media,” Opt. Lett.37, 3261–3263 (2012).
    [CrossRef] [PubMed]
  12. E. Small, O. Katz, Y. F. Guan, and Y. Silberberg, “Spectral control of broadband light through random media by wavefront shaping,” Opt. Lett.37, 3429–3431 (2012).
    [CrossRef]
  13. Y. M. Wang, B. Judkewitz, C. H. DiMarzio, and C. A. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nature Commun.3, 928 (2012).
    [CrossRef]
  14. K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation,” Nature Photon.6, 657–661 (2012).
    [CrossRef]
  15. J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491, 232–234 (2012).
    [CrossRef] [PubMed]
  16. I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun.281, 3071–3080 (2008).
    [CrossRef]
  17. 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] [PubMed]
  18. Z. Yaqoob, D. Psaltis, M. S. Feld, and C. H. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nature Photon.2, 110–115 (2008).
    [CrossRef]
  19. M. Cui and C. H. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express18, 3444–3455 (2010).
    [CrossRef] [PubMed]
  20. C. L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, “Digital phase conjugation of second harmonic radiation emitted by nanoparticles in turbid media,” Opt. Express18, 12283–12290 (2010).
    [CrossRef] [PubMed]
  21. D. Akbulut, T. J. Huisman, E. G. van Putten, W. L. Vos, and A. P. Mosk, “Focusing light through random photonic media by binary amplitude modulation,” Opt. Express19, 4017–4029 (2011).
    [CrossRef] [PubMed]
  22. M. Cui, “Parallel wavefront optimization method for focusing light through random scattering media,” Opt. Lett.36, 870–872 (2011).
    [CrossRef] [PubMed]
  23. D. B. Conkey, A. N. Brown, A. M. Caravaca-Aguirre, and R. Piestun, “Genetic algorithm optimization for focusing through turbid media in noisy environments,” Opt. Express20, 4840–4849 (2012).
    [CrossRef] [PubMed]
  24. D. B. Conkey, A. M. Caravaca-Aguirre, and R. Piestun, “High-speed scattering medium characterization with application to focusing light through turbid media,” Opt. Express20, 1733–1740 (2012).
    [CrossRef] [PubMed]
  25. C. Stockbridge, Y. Lu, J. Moore, S. Hoffman, R. Paxman, K. Toussaint, and T. Bifano, “Focusing through dynamic scattering media,” Opt. Express20, 15086–15092 (2012).
    [CrossRef] [PubMed]
  26. S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nature Commun.1, 81 (2010).
    [CrossRef]
  27. T. Weise, M. Zapf, R. Chiong, and A. J. Nebro, Nature-Inspired Algorithms for Optimisation (Springer, 2009).
  28. T. Weise, R. Chiong, and K. Tang, “Evolutionary optimization: Pitfalls and booby traps,” J. Comput. Sci.Technol.27, 907–936 (2012).
    [CrossRef]
  29. A. B. Parthasarathy, K. K. Chu, T. N. Ford, and J. Mertz, “Quantitative phase imaging using a partitioned detection aperture,” Opt. Lett.37, 4062–4064 (2012).
    [CrossRef] [PubMed]
  30. E. G. van Putten, I. M. Vellekoop, and A. P. Mosk, “Spatial amplitude and phase modulation using commercial twisted nematic LCDs,” Appl. Opt.47, 2076–2081 (2008).
    [CrossRef] [PubMed]
  31. S. A. Tretter, “Estimating the frequency of a noisy sinusoid by linear regression,” IEEE Trans. Inform. Theor.31, 832–835 (1985).
    [CrossRef]

2012

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nature Photon.6, 283 (2012).
[CrossRef]

Y. M. Wang, B. Judkewitz, C. H. DiMarzio, and C. A. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nature Commun.3, 928 (2012).
[CrossRef]

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation,” Nature Photon.6, 657–661 (2012).
[CrossRef]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491, 232–234 (2012).
[CrossRef] [PubMed]

T. Weise, R. Chiong, and K. Tang, “Evolutionary optimization: Pitfalls and booby traps,” J. Comput. Sci.Technol.27, 907–936 (2012).
[CrossRef]

D. B. Conkey, A. M. Caravaca-Aguirre, and R. Piestun, “High-speed scattering medium characterization with application to focusing light through turbid media,” Opt. Express20, 1733–1740 (2012).
[CrossRef] [PubMed]

D. B. Conkey, A. N. Brown, A. M. Caravaca-Aguirre, and R. Piestun, “Genetic algorithm optimization for focusing through turbid media in noisy environments,” Opt. Express20, 4840–4849 (2012).
[CrossRef] [PubMed]

C. Stockbridge, Y. Lu, J. Moore, S. Hoffman, R. Paxman, K. Toussaint, and T. Bifano, “Focusing through dynamic scattering media,” Opt. Express20, 15086–15092 (2012).
[CrossRef] [PubMed]

J. H. Park, C. Park, H. Yu, Y. H. Cho, and Y. Park, “Dynamic active wave plate using random nanoparticles,” Opt. Express20, 17010–17016 (2012).
[CrossRef]

J. H. Park, C. Park, H. Yu, Y. Cho, and Y. H. Park, “Active spectral filtering through turbid media,” Opt. Lett.37, 3261–3263 (2012).
[CrossRef] [PubMed]

E. Small, O. Katz, Y. F. Guan, and Y. Silberberg, “Spectral control of broadband light through random media by wavefront shaping,” Opt. Lett.37, 3429–3431 (2012).
[CrossRef]

A. B. Parthasarathy, K. K. Chu, T. N. Ford, and J. Mertz, “Quantitative phase imaging using a partitioned detection aperture,” Opt. Lett.37, 4062–4064 (2012).
[CrossRef] [PubMed]

Y. F. Guan, O. Katz, E. Small, J. Y. Zhou, and Y. Silberberg, “Polarization control of multiply scattered light through random media by wavefront shaping,” Opt. Lett.37, 4663–4665 (2012).
[CrossRef] [PubMed]

2011

D. Akbulut, T. J. Huisman, E. G. van Putten, W. L. Vos, and A. P. Mosk, “Focusing light through random photonic media by binary amplitude modulation,” Opt. Express19, 4017–4029 (2011).
[CrossRef] [PubMed]

M. Cui, “Parallel wavefront optimization method for focusing light through random scattering media,” Opt. Lett.36, 870–872 (2011).
[CrossRef] [PubMed]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett.106, 193905 (2011).
[CrossRef] [PubMed]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett.106, 103901 (2011).
[CrossRef] [PubMed]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nature Photon.5, 372–377 (2011).
[CrossRef]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nature Commun.2, 447 (2011).
[CrossRef]

2010

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nature Photon.4, 320–322 (2010).
[CrossRef]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nature Commun.1, 81 (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] [PubMed]

M. Cui and C. H. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express18, 3444–3455 (2010).
[CrossRef] [PubMed]

C. L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, “Digital phase conjugation of second harmonic radiation emitted by nanoparticles in turbid media,” Opt. Express18, 12283–12290 (2010).
[CrossRef] [PubMed]

2008

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. H. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nature Photon.2, 110–115 (2008).
[CrossRef]

E. G. van Putten, I. M. Vellekoop, and A. P. Mosk, “Spatial amplitude and phase modulation using commercial twisted nematic LCDs,” Appl. Opt.47, 2076–2081 (2008).
[CrossRef] [PubMed]

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun.281, 3071–3080 (2008).
[CrossRef]

2007

1990

I. Freund, “Looking through walls and around corners,” Physica A168, 49–65 (1990).
[CrossRef]

1985

S. A. Tretter, “Estimating the frequency of a noisy sinusoid by linear regression,” IEEE Trans. Inform. Theor.31, 832–835 (1985).
[CrossRef]

Akbulut, D.

D. Akbulut, T. J. Huisman, E. G. van Putten, W. L. Vos, and A. P. Mosk, “Focusing light through random photonic media by binary amplitude modulation,” Opt. Express19, 4017–4029 (2011).
[CrossRef] [PubMed]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett.106, 193905 (2011).
[CrossRef] [PubMed]

Aulbach, J.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett.106, 103901 (2011).
[CrossRef] [PubMed]

Austin, D. R.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nature Commun.2, 447 (2011).
[CrossRef]

Bertolotti, J.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491, 232–234 (2012).
[CrossRef] [PubMed]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett.106, 193905 (2011).
[CrossRef] [PubMed]

Bifano, T.

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491, 232–234 (2012).
[CrossRef] [PubMed]

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] [PubMed]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nature Commun.1, 81 (2010).
[CrossRef]

Bondareff, P.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nature Commun.2, 447 (2011).
[CrossRef]

Bromberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nature Photon.5, 372–377 (2011).
[CrossRef]

Brown, A. N.

Caravaca-Aguirre, A. M.

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] [PubMed]

Chatel, B.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nature Commun.2, 447 (2011).
[CrossRef]

Chiong, R.

T. Weise, R. Chiong, and K. Tang, “Evolutionary optimization: Pitfalls and booby traps,” J. Comput. Sci.Technol.27, 907–936 (2012).
[CrossRef]

T. Weise, M. Zapf, R. Chiong, and A. J. Nebro, Nature-Inspired Algorithms for Optimisation (Springer, 2009).

Cho, Y.

Cho, Y. H.

Chu, K. K.

Conkey, D. B.

Cui, M.

DiMarzio, C. H.

Y. M. Wang, B. Judkewitz, C. H. DiMarzio, and C. A. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nature Commun.3, 928 (2012).
[CrossRef]

Feld, M. S.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. H. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nature Photon.2, 110–115 (2008).
[CrossRef]

Fink, M.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nature Photon.6, 283 (2012).
[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] [PubMed]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nature Commun.1, 81 (2010).
[CrossRef]

Fiolka, R.

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation,” Nature Photon.6, 657–661 (2012).
[CrossRef]

Ford, T. N.

Freund, I.

I. Freund, “Looking through walls and around corners,” Physica A168, 49–65 (1990).
[CrossRef]

Gigan, S.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nature Commun.2, 447 (2011).
[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] [PubMed]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nature Commun.1, 81 (2010).
[CrossRef]

Gjonaj, B.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett.106, 103901 (2011).
[CrossRef] [PubMed]

Grange, R.

Guan, Y. F.

Hoffman, S.

Hsieh, C. L.

Huisman, T. J.

Johnson, P. M.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett.106, 103901 (2011).
[CrossRef] [PubMed]

Judkewitz, B.

Y. M. Wang, B. Judkewitz, C. H. DiMarzio, and C. A. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nature Commun.3, 928 (2012).
[CrossRef]

Katz, O.

Lagendijk, A.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491, 232–234 (2012).
[CrossRef] [PubMed]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nature Photon.6, 283 (2012).
[CrossRef]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett.106, 103901 (2011).
[CrossRef] [PubMed]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett.106, 193905 (2011).
[CrossRef] [PubMed]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nature Photon.4, 320–322 (2010).
[CrossRef]

Lerosey, G.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nature Photon.6, 283 (2012).
[CrossRef]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nature Commun.1, 81 (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] [PubMed]

Lu, Y.

McCabe, D. J.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nature Commun.2, 447 (2011).
[CrossRef]

Mertz, J.

Moore, J.

Mosk, A. P.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nature Photon.6, 283 (2012).
[CrossRef]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491, 232–234 (2012).
[CrossRef] [PubMed]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett.106, 103901 (2011).
[CrossRef] [PubMed]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett.106, 193905 (2011).
[CrossRef] [PubMed]

D. Akbulut, T. J. Huisman, E. G. van Putten, W. L. Vos, and A. P. Mosk, “Focusing light through random photonic media by binary amplitude modulation,” Opt. Express19, 4017–4029 (2011).
[CrossRef] [PubMed]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nature Photon.4, 320–322 (2010).
[CrossRef]

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun.281, 3071–3080 (2008).
[CrossRef]

E. G. van Putten, I. M. Vellekoop, and A. P. Mosk, “Spatial amplitude and phase modulation using commercial twisted nematic LCDs,” Appl. Opt.47, 2076–2081 (2008).
[CrossRef] [PubMed]

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett.32, 2309–2311 (2007).
[CrossRef] [PubMed]

Nebro, A. J.

T. Weise, M. Zapf, R. Chiong, and A. J. Nebro, Nature-Inspired Algorithms for Optimisation (Springer, 2009).

Park, C.

Park, J. H.

Park, Y.

Park, Y. H.

Parthasarathy, A. B.

Paxman, R.

Piestun, R.

Popoff, S.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nature Commun.1, 81 (2010).
[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] [PubMed]

Psaltis, D.

C. L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, “Digital phase conjugation of second harmonic radiation emitted by nanoparticles in turbid media,” Opt. Express18, 12283–12290 (2010).
[CrossRef] [PubMed]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. H. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nature Photon.2, 110–115 (2008).
[CrossRef]

Pu, Y.

Si, K.

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation,” Nature Photon.6, 657–661 (2012).
[CrossRef]

Silberberg, Y.

Small, E.

Stockbridge, C.

Tajalli, A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nature Commun.2, 447 (2011).
[CrossRef]

Tang, K.

T. Weise, R. Chiong, and K. Tang, “Evolutionary optimization: Pitfalls and booby traps,” J. Comput. Sci.Technol.27, 907–936 (2012).
[CrossRef]

Toussaint, K.

Tretter, S. A.

S. A. Tretter, “Estimating the frequency of a noisy sinusoid by linear regression,” IEEE Trans. Inform. Theor.31, 832–835 (1985).
[CrossRef]

van Putten, E. G.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491, 232–234 (2012).
[CrossRef] [PubMed]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett.106, 193905 (2011).
[CrossRef] [PubMed]

D. Akbulut, T. J. Huisman, E. G. van Putten, W. L. Vos, and A. P. Mosk, “Focusing light through random photonic media by binary amplitude modulation,” Opt. Express19, 4017–4029 (2011).
[CrossRef] [PubMed]

E. G. van Putten, I. M. Vellekoop, and A. P. Mosk, “Spatial amplitude and phase modulation using commercial twisted nematic LCDs,” Appl. Opt.47, 2076–2081 (2008).
[CrossRef] [PubMed]

Vellekoop, I. M.

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nature Photon.4, 320–322 (2010).
[CrossRef]

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun.281, 3071–3080 (2008).
[CrossRef]

E. G. van Putten, I. M. Vellekoop, and A. P. Mosk, “Spatial amplitude and phase modulation using commercial twisted nematic LCDs,” Appl. Opt.47, 2076–2081 (2008).
[CrossRef] [PubMed]

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett.32, 2309–2311 (2007).
[CrossRef] [PubMed]

Vos, W. L.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491, 232–234 (2012).
[CrossRef] [PubMed]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett.106, 193905 (2011).
[CrossRef] [PubMed]

D. Akbulut, T. J. Huisman, E. G. van Putten, W. L. Vos, and A. P. Mosk, “Focusing light through random photonic media by binary amplitude modulation,” Opt. Express19, 4017–4029 (2011).
[CrossRef] [PubMed]

Walmsley, I. A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nature Commun.2, 447 (2011).
[CrossRef]

Wang, Y. M.

Y. M. Wang, B. Judkewitz, C. H. DiMarzio, and C. A. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nature Commun.3, 928 (2012).
[CrossRef]

Weise, T.

T. Weise, R. Chiong, and K. Tang, “Evolutionary optimization: Pitfalls and booby traps,” J. Comput. Sci.Technol.27, 907–936 (2012).
[CrossRef]

T. Weise, M. Zapf, R. Chiong, and A. J. Nebro, Nature-Inspired Algorithms for Optimisation (Springer, 2009).

Yang, C. A.

Y. M. Wang, B. Judkewitz, C. H. DiMarzio, and C. A. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nature Commun.3, 928 (2012).
[CrossRef]

Yang, C. H.

M. Cui and C. H. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express18, 3444–3455 (2010).
[CrossRef] [PubMed]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. H. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nature Photon.2, 110–115 (2008).
[CrossRef]

Yaqoob, Z.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. H. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nature Photon.2, 110–115 (2008).
[CrossRef]

Yu, H.

Zapf, M.

T. Weise, M. Zapf, R. Chiong, and A. J. Nebro, Nature-Inspired Algorithms for Optimisation (Springer, 2009).

Zhou, J. Y.

Appl. Opt.

IEEE Trans. Inform. Theor.

S. A. Tretter, “Estimating the frequency of a noisy sinusoid by linear regression,” IEEE Trans. Inform. Theor.31, 832–835 (1985).
[CrossRef]

J. Comput. Sci.Technol.

T. Weise, R. Chiong, and K. Tang, “Evolutionary optimization: Pitfalls and booby traps,” J. Comput. Sci.Technol.27, 907–936 (2012).
[CrossRef]

Nature

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature491, 232–234 (2012).
[CrossRef] [PubMed]

Nature Commun.

Y. M. Wang, B. Judkewitz, C. H. DiMarzio, and C. A. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nature Commun.3, 928 (2012).
[CrossRef]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nature Commun.2, 447 (2011).
[CrossRef]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nature Commun.1, 81 (2010).
[CrossRef]

Nature Photon.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. H. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nature Photon.2, 110–115 (2008).
[CrossRef]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nature Photon.5, 372–377 (2011).
[CrossRef]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nature Photon.4, 320–322 (2010).
[CrossRef]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nature Photon.6, 283 (2012).
[CrossRef]

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation,” Nature Photon.6, 657–661 (2012).
[CrossRef]

Opt. Commun.

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun.281, 3071–3080 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

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] [PubMed]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett.106, 103901 (2011).
[CrossRef] [PubMed]

E. G. van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. P. Mosk, “Scattering lens resolves sub-100 nm structures with visible light,” Phys. Rev. Lett.106, 193905 (2011).
[CrossRef] [PubMed]

Physica A

I. Freund, “Looking through walls and around corners,” Physica A168, 49–65 (1990).
[CrossRef]

Other

T. Weise, M. Zapf, R. Chiong, and A. J. Nebro, Nature-Inspired Algorithms for Optimisation (Springer, 2009).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

The experimental setup for wavefront shaping. Laser light reflected by the SLM is focused on a white ZnO sample. The light transmitted through the sample is detected by a CCD camera. Abbreviations used, SLM: Spatial light modulator, PBS: polarizing beam splitter, λ/2: half-wave plate, CCD:charge coupled device, 20×: 20× beam expander.

Fig. 2
Fig. 2

Cartoon showing the effect of the noise on phase estimation. The target intensity I0 is shown versus the phase Δθ. The modulation signal S and the background B at the target position are shown during the phase modulation Δθ of a single segment. The standard deviation of the noise is represented by σ, and the standard deviation of the phase is represented by δθ. Yellow dots represent the measurements used to construct the quadratures.

Fig. 3
Fig. 3

Cartoon shows the phase map on the SLM after the pre-optimization (a), and after the second optimization (c). The focal spot at the target position after a pre-optimization (b), and after the second optimization (d).

Fig. 4
Fig. 4

Three contributions to the normalized noise to signal ratio versus the pre-enhancement factor at a fixed photon budget. The black curve shows the total noise to signal ratio. The dashed green curve represents the noise to signal ratio when there is only shot noise, the dashed blue curve the noise to signal ratio when there is only camera readout noise, and the dashed red curve the noise to signal ratio when there is only laser excess noise.

Fig. 5
Fig. 5

The final enhancement versus the pre-enhancement. The black dots show the experimental data. The red curve shows the enhancement according to Eq. (8) without adjustable parameters. The area between dashed red lines expresses the uncertainty region of the enhancement factor due to intensity drift at the target position during optimization.

Equations (12)

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

I 0 = I A + I B + 2 I A I B cos ( Δ θ + ϕ ) + σ = B + S cos ( Δ θ + ϕ ) + σ ,
S = 2 I A 1 N .
δ θ RMS = σ S .
η = π 4 N cos 2 δ θ ,
η = π 4 N ( 1 δ θ 2 ) .
η = π 4 N ( 1 σ 2 S 2 ) .
R = S N 1 / 2 σ .
η = π 4 N ( 1 N R 2 ) .
η max = π R 2 16 .
I 0 = B + 2 I A η pre N cos ( Δ θ + ϕ )
S = 2 I A η pre N .
η max = π I A 4 .

Metrics