Abstract

We present a machine-learning-based method for light focusing through scattering media. In this method, the optical process in a scattering medium is computationally inverted based on a nonlinear regression algorithm with a number of training input–output pairs through the medium, and an input optimized for a target output is calculated. We experimentally demonstrate focusing via a process involving randomness due to a scattering medium and nonlinearity due to double modulation with a spatial light modulator. Our approach realizes model-free control of optical fields, where optical processes or models are unknown.

© 2017 Optical Society of America

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References

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  1. A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
    [Crossref]
  2. R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
    [Crossref]
  3. M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. USA 103, 17137–17142 (2006).
    [Crossref]
  4. D. Débarre, E. J. Botcherby, T. Watanabe, S. Srinivas, M. J. Booth, and T. Wilson, “Image-based adaptive optics for two-photon microscopy,” Opt. Lett. 34, 2495–2497 (2009).
    [Crossref]
  5. E. R. Andresen, S. Sivankutty, V. Tsvirkun, G. Bouwmans, and H. Rigneault, “Ultrathin endoscopes based on multicore fibers and adaptive optics: a status review and perspectives,” J. Biomed. Opt. 21, 121506 (2016).
    [Crossref]
  6. O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
    [Crossref]
  7. Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20, 6800213 (2014).
    [Crossref]
  8. T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
    [Crossref]
  9. S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12, 635–639 (2012).
    [Crossref]
  10. K. Deisseroth, “Optogenetics,” Nat. Methods 8, 26–29 (2011).
    [Crossref]
  11. I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
    [Crossref]
  12. O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
    [Crossref]
  13. I. M. Vellekoop, “Feedback-based wavefront shaping,” Opt. Express 23, 12189–12206 (2015).
    [Crossref]
  14. 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. Express 20, 4840–4849 (2012).
    [Crossref]
  15. 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]
  16. S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
    [Crossref]
  17. T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
    [Crossref]
  18. A. Drémeau, A. Liutkus, D. Martina, O. Katz, C. Schülke, F. Krzakala, S. Gigan, and L. Daudet, “Reference-less measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques,” Opt. Express 23, 11898–11911 (2015).
    [Crossref]
  19. T. Nakamura, R. Horisaki, and J. Tanida, “Compact wide-field-of-view imager with a designed disordered medium,” Opt. Rev. 22, 19–24 (2015).
    [Crossref]
  20. Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
    [Crossref]
  21. M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18, 3444–3455 (2010).
    [Crossref]
  22. G. New, Introduction to Nonlinear Optics (Cambridge University, 2011).
  23. R. Horisaki, R. Takagi, and J. Tanida, “Learning-based imaging through scattering media,” Opt. Express 24, 13738–13743 (2016).
    [Crossref]
  24. T. Ando, R. Horisaki, and J. Tanida, “Speckle-learning-based object recognition through scattering media,” Opt. Express 23, 33902–33910 (2015).
    [Crossref]
  25. R. Takagi, R. Horisaki, and J. Tanida, “Object recognition through a multi-mode fiber,” Opt. Rev. 24, 117–120 (2017).
    [Crossref]
  26. C. M. Bishop, Pattern Recognition and Machine Learning (Springer-Verlag, 2006).
  27. V. N. Vapnik, The Nature of Statistical Learning Theory (Springer-Verlag, 1995).
  28. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  29. M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
    [Crossref]
  30. T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
    [Crossref]
  31. E. Bossy and S. Gigan, “Photoacoustics with coherent light,” Photoacoustics 4, 22–35 (2016).
    [Crossref]

2017 (1)

R. Takagi, R. Horisaki, and J. Tanida, “Object recognition through a multi-mode fiber,” Opt. Rev. 24, 117–120 (2017).
[Crossref]

2016 (4)

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

E. Bossy and S. Gigan, “Photoacoustics with coherent light,” Photoacoustics 4, 22–35 (2016).
[Crossref]

R. Horisaki, R. Takagi, and J. Tanida, “Learning-based imaging through scattering media,” Opt. Express 24, 13738–13743 (2016).
[Crossref]

E. R. Andresen, S. Sivankutty, V. Tsvirkun, G. Bouwmans, and H. Rigneault, “Ultrathin endoscopes based on multicore fibers and adaptive optics: a status review and perspectives,” J. Biomed. Opt. 21, 121506 (2016).
[Crossref]

2015 (5)

2014 (1)

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20, 6800213 (2014).
[Crossref]

2013 (1)

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
[Crossref]

2012 (5)

T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref]

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

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. Express 20, 4840–4849 (2012).
[Crossref]

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12, 635–639 (2012).
[Crossref]

2011 (3)

K. Deisseroth, “Optogenetics,” Nat. Methods 8, 26–29 (2011).
[Crossref]

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

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
[Crossref]

2010 (3)

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]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18, 3444–3455 (2010).
[Crossref]

2009 (1)

2008 (1)

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

2007 (1)

2006 (1)

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. USA 103, 17137–17142 (2006).
[Crossref]

Ando, T.

Andreoli, D.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

Andresen, E. R.

E. R. Andresen, S. Sivankutty, V. Tsvirkun, G. Bouwmans, and H. Rigneault, “Ultrathin endoscopes based on multicore fibers and adaptive optics: a status review and perspectives,” J. Biomed. Opt. 21, 121506 (2016).
[Crossref]

Bianchi, S.

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12, 635–639 (2012).
[Crossref]

Bishop, C. M.

C. M. Bishop, Pattern Recognition and Machine Learning (Springer-Verlag, 2006).

Boccara, A. C.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
[Crossref]

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (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]

Booth, M. J.

Bossy, E.

E. Bossy and S. Gigan, “Photoacoustics with coherent light,” Photoacoustics 4, 22–35 (2016).
[Crossref]

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
[Crossref]

Botcherby, E. J.

Bouwmans, G.

E. R. Andresen, S. Sivankutty, V. Tsvirkun, G. Bouwmans, and H. Rigneault, “Ultrathin endoscopes based on multicore fibers and adaptive optics: a status review and perspectives,” J. Biomed. Opt. 21, 121506 (2016).
[Crossref]

Bromberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 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]

Chaigne, T.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
[Crossref]

Choi, W.

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20, 6800213 (2014).
[Crossref]

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20, 6800213 (2014).
[Crossref]

Choi, Y.

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20, 6800213 (2014).
[Crossref]

Cižmár, T.

T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

Conkey, D. B.

Cui, M.

Daudet, L.

Débarre, D.

Defienne, H.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

Deisseroth, K.

K. Deisseroth, “Optogenetics,” Nat. Methods 8, 26–29 (2011).
[Crossref]

Denk, W.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. USA 103, 17137–17142 (2006).
[Crossref]

Dholakia, K.

T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

Di Leonardo, R.

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12, 635–639 (2012).
[Crossref]

Drémeau, A.

Feld, M. S.

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

Fink, M.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (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]

Gigan, S.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

E. Bossy and S. Gigan, “Photoacoustics with coherent light,” Photoacoustics 4, 22–35 (2016).
[Crossref]

A. Drémeau, A. Liutkus, D. Martina, O. Katz, C. Schülke, F. Krzakala, S. Gigan, and L. Daudet, “Reference-less measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques,” Opt. Express 23, 11898–11911 (2015).
[Crossref]

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
[Crossref]

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (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]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Grésillon, S.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

Horisaki, R.

R. Takagi, R. Horisaki, and J. Tanida, “Object recognition through a multi-mode fiber,” Opt. Rev. 24, 117–120 (2017).
[Crossref]

R. Horisaki, R. Takagi, and J. Tanida, “Learning-based imaging through scattering media,” Opt. Express 24, 13738–13743 (2016).
[Crossref]

T. Ando, R. Horisaki, and J. Tanida, “Speckle-learning-based object recognition through scattering media,” Opt. Express 23, 33902–33910 (2015).
[Crossref]

T. Nakamura, R. Horisaki, and J. Tanida, “Compact wide-field-of-view imager with a designed disordered medium,” Opt. Rev. 22, 19–24 (2015).
[Crossref]

Horstmeyer, R.

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
[Crossref]

Katz, O.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

A. Drémeau, A. Liutkus, D. Martina, O. Katz, C. Schülke, F. Krzakala, S. Gigan, and L. Daudet, “Reference-less measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques,” Opt. Express 23, 11898–11911 (2015).
[Crossref]

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
[Crossref]

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

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

Kim, M.

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20, 6800213 (2014).
[Crossref]

Krzakala, F.

Lagendijk, A.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[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,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (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]

Liutkus, A.

Mack-Bucher, J. A.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. USA 103, 17137–17142 (2006).
[Crossref]

Martina, D.

Mazilu, M.

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

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,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

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

Mounaix, M.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

Nakamura, T.

T. Nakamura, R. Horisaki, and J. Tanida, “Compact wide-field-of-view imager with a designed disordered medium,” Opt. Rev. 22, 19–24 (2015).
[Crossref]

New, G.

G. New, Introduction to Nonlinear Optics (Cambridge University, 2011).

Piestun, R.

Popoff, S. M.

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (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]

Psaltis, D.

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

Rigneault, H.

E. R. Andresen, S. Sivankutty, V. Tsvirkun, G. Bouwmans, and H. Rigneault, “Ultrathin endoscopes based on multicore fibers and adaptive optics: a status review and perspectives,” J. Biomed. Opt. 21, 121506 (2016).
[Crossref]

Ruan, H.

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
[Crossref]

Rueckel, M.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. USA 103, 17137–17142 (2006).
[Crossref]

Schülke, C.

Silberberg, Y.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

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

Sivankutty, S.

E. R. Andresen, S. Sivankutty, V. Tsvirkun, G. Bouwmans, and H. Rigneault, “Ultrathin endoscopes based on multicore fibers and adaptive optics: a status review and perspectives,” J. Biomed. Opt. 21, 121506 (2016).
[Crossref]

Small, E.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

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

Srinivas, S.

Takagi, R.

R. Takagi, R. Horisaki, and J. Tanida, “Object recognition through a multi-mode fiber,” Opt. Rev. 24, 117–120 (2017).
[Crossref]

R. Horisaki, R. Takagi, and J. Tanida, “Learning-based imaging through scattering media,” Opt. Express 24, 13738–13743 (2016).
[Crossref]

Tanida, J.

R. Takagi, R. Horisaki, and J. Tanida, “Object recognition through a multi-mode fiber,” Opt. Rev. 24, 117–120 (2017).
[Crossref]

R. Horisaki, R. Takagi, and J. Tanida, “Learning-based imaging through scattering media,” Opt. Express 24, 13738–13743 (2016).
[Crossref]

T. Ando, R. Horisaki, and J. Tanida, “Speckle-learning-based object recognition through scattering media,” Opt. Express 23, 33902–33910 (2015).
[Crossref]

T. Nakamura, R. Horisaki, and J. Tanida, “Compact wide-field-of-view imager with a designed disordered medium,” Opt. Rev. 22, 19–24 (2015).
[Crossref]

Tsvirkun, V.

E. R. Andresen, S. Sivankutty, V. Tsvirkun, G. Bouwmans, and H. Rigneault, “Ultrathin endoscopes based on multicore fibers and adaptive optics: a status review and perspectives,” J. Biomed. Opt. 21, 121506 (2016).
[Crossref]

Vapnik, V. N.

V. N. Vapnik, The Nature of Statistical Learning Theory (Springer-Verlag, 1995).

Vellekoop, I. M.

Volpe, G.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

Watanabe, T.

Wilson, T.

Yang, C.

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
[Crossref]

M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18, 3444–3455 (2010).
[Crossref]

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

Yaqoob, Z.

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

Yoon, C.

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20, 6800213 (2014).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20, 6800213 (2014).
[Crossref]

J. Biomed. Opt. (1)

E. R. Andresen, S. Sivankutty, V. Tsvirkun, G. Bouwmans, and H. Rigneault, “Ultrathin endoscopes based on multicore fibers and adaptive optics: a status review and perspectives,” J. Biomed. Opt. 21, 121506 (2016).
[Crossref]

Lab Chip (1)

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12, 635–639 (2012).
[Crossref]

Nat. Commun. (1)

T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref]

Nat. Methods (1)

K. Deisseroth, “Optogenetics,” Nat. Methods 8, 26–29 (2011).
[Crossref]

Nat. Photonics (7)

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
[Crossref]

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

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

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8, 58–64 (2013).
[Crossref]

New J. Phys. (1)

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
[Crossref]

Opt. Express (6)

Opt. Lett. (2)

Opt. Rev. (2)

T. Nakamura, R. Horisaki, and J. Tanida, “Compact wide-field-of-view imager with a designed disordered medium,” Opt. Rev. 22, 19–24 (2015).
[Crossref]

R. Takagi, R. Horisaki, and J. Tanida, “Object recognition through a multi-mode fiber,” Opt. Rev. 24, 117–120 (2017).
[Crossref]

Photoacoustics (1)

E. Bossy and S. Gigan, “Photoacoustics with coherent light,” Photoacoustics 4, 22–35 (2016).
[Crossref]

Phys. Rev. Lett. (2)

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[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]

Proc. Natl. Acad. Sci. USA (1)

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. USA 103, 17137–17142 (2006).
[Crossref]

Other (4)

G. New, Introduction to Nonlinear Optics (Cambridge University, 2011).

C. M. Bishop, Pattern Recognition and Machine Learning (Springer-Verlag, 2006).

V. N. Vapnik, The Nature of Statistical Learning Theory (Springer-Verlag, 1995).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (4)

Fig. 1.
Fig. 1. Schematic diagram of the inverse operator for a scattering process.
Fig. 2.
Fig. 2. Experimental demonstration for focusing through a scattering medium. (a) Optical setup and (b) diffuser.
Fig. 3.
Fig. 3. Experimental result of focusing at a single pixel. The optimized input patterns for focusing at (a) (1, 1)-th pixel, (b) (2, 2)-th pixel, (c) (3, 3)-th pixel, (d) (4, 4)-th pixel, and (e) (5, 5)-th pixel. (f)–(j) Output patterns captured through the scattering medium, from the input patterns in (a)–(e). The pixel indices are in column-major order.
Fig. 4.
Fig. 4. Experimental results of focusing at multiple pixels. The optimized input patterns for focusing at the (a) (1, 5)-th and (5, 1)-th pixels, (b) (2, 3)-th and (4, 3)-th pixels, (c) (1, 3)-th, (5, 1)-th, and (5, 5)-th pixels, (d) (1, 1)-th, (1, 5)-th, and (5, 3)-th pixels, (e) (2, 3)-th, (3, 2)-th, (3, 4), and (4, 3)-th pixels. (f)–(j) Output patterns captured through the scattering medium, from the input patterns in (a)–(e). The pixel indices are in column-major order.

Tables (1)

Tables Icon

Table 1. Experimental Performance, in Terms of (a) PBR and (b) PSNR (dB), of Single-Pixel Focusing

Equations (10)

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

y=F[x],
x=F1[y],
x^=F1[y^].
y^=F[F1[y^]]=F[x^].
x^(k)=Fk1[y^],
Fk1[y^]=m=1M(αm(k)αm*(k))exp(||y^yˇm||22  h2)+b(k),
y=F[x]=|Pzd[S[Pzs[xP2zm[x]]]]|2,
xP2zm[x]=DxP2zmx,
PBR=y^(p)(||y^||y^(p))/(Ny1),
PSNR=10log10max(y^)2||y^y^||2/Ny,

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