Abstract

This paper investigates experimental means of measuring the transmission matrix (TM) of a highly scattering medium, with the simplest optical setup. Spatial light modulation is performed by a digital micromirror device (DMD), allowing high rates and high pixel counts but only binary amplitude modulation. On the sensor side, without a reference beam, the CCD camera provides only intensity measurements. Within this framework, this paper shows that the TM can still be retrieved, through signal processing techniques of phase retrieval. This is experimentally validated on three criteria : quality of prediction, distribution of singular values, and quality of focusing.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]

2014 (4)

D. Kim, W. Choi, M. Kim, J. Moon, K. Seo, S. Ju, and W. Choi, “Implementing transmission eigenchannels of disordered media by a binary-control digital micromirror device,” Opt. Commun. 330, 35–39 (2014).
[Crossref]

J. W. Tay, J. Liang, and L. V. Wang, “Amplitude-masked photoacoustic wavefront shaping and application in flowmetry,” Opt. Lett. 39, 5499–5502 (2014).
[Crossref] [PubMed]

X. Zhang and P. Kner, “Binary wavefront optimization using a genetic algorithm,” Journal of Optics 16, 125704 (2014).
[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,” Nature Photonics 8, 58–64 (2014).
[Crossref]

2013 (2)

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “High-resolution, lensless endoscope based on digital scanning through a multimode optical fiber,” Biomed. Opt. Express 4, 260–270 (2013).
[Crossref] [PubMed]

E. Candès, T. Strohmer, and V. Voroninski, “Phaselift : exact and stable signal recovery from magnitude measurements via convex programming,” Commun. in Pure and Applied Mathematics 66, 1241–1274 (2013).
[Crossref]

2012 (6)

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab on a Chip 12, 635 (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. Express 20, 1733–1740 (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 Photonics 6, 283–292 (2012).
[Crossref]

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20, 10583 (2012).
[Crossref] [PubMed]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nature Photonics 6, 581–585 (2012).
[Crossref]

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109, 023902 (2012).
[Crossref]

2011 (4)

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. Express 19, 4017–4029 (2011).
[Crossref] [PubMed]

T. Čižmár and K. Dholakia, “Shaping the light transmission through a multimode optical fibre: complex transformation analysis and applications in biophotonics,” Opt. Express 19, 18871 (2011).
[Crossref] [PubMed]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref] [PubMed]

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New Journal of Physics 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] [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]

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] [PubMed]

2007 (1)

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Express 32, 2309 (2007).

1982 (1)

1972 (1)

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

1967 (1)

V. A. Marčenko and L. A. Pastur, “Distribution of eigenvalues for some sets of random matrices,” Mathematics of the USSR-Sbornik 1, 457–483 (1967).
[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. Express 19, 4017–4029 (2011).
[Crossref] [PubMed]

D. Akbulut, T. Strudley, J. Bertolotti, T. Zehender, E. Bakkers, A. Lagendijk, W. Vos, O. Muskens, and A. Mosk, “Measurements on the optical transmission matrices of strongly scattering nanowire layers,” in Proc. Conf. on Lasers and Electro-Optics Europe and International Quantum Electronics Conf. (CLEO EUROPE/IQEC), (2013).

Bakkers, E.

D. Akbulut, T. Strudley, J. Bertolotti, T. Zehender, E. Bakkers, A. Lagendijk, W. Vos, O. Muskens, and A. Mosk, “Measurements on the optical transmission matrices of strongly scattering nanowire layers,” in Proc. Conf. on Lasers and Electro-Optics Europe and International Quantum Electronics Conf. (CLEO EUROPE/IQEC), (2013).

Bertolotti, J.

D. Akbulut, T. Strudley, J. Bertolotti, T. Zehender, E. Bakkers, A. Lagendijk, W. Vos, O. Muskens, and A. Mosk, “Measurements on the optical transmission matrices of strongly scattering nanowire layers,” in Proc. Conf. on Lasers and Electro-Optics Europe and International Quantum Electronics Conf. (CLEO EUROPE/IQEC), (2013).

S. A. Goorden, J. Bertolotti, and A. P. Mosk, “Superpixel-based spatial amplitude and phase modulation using a digital micromirror device,” arXiv:1405.3893 [physics] (2014).

Bianchi, S.

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

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,” Nature Photonics 8, 58–64 (2014).
[Crossref]

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New Journal of Physics 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] [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]

Bossy, E.

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,” Nature Photonics 8, 58–64 (2014).
[Crossref]

Candès, E.

E. Candès, T. Strohmer, and V. Voroninski, “Phaselift : exact and stable signal recovery from magnitude measurements via convex programming,” Commun. in Pure and Applied Mathematics 66, 1241–1274 (2013).
[Crossref]

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]

Carron, I.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: Compressive imaging using a multiply scattering medium,” Sci. Rep.4 (2014).
[Crossref] [PubMed]

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,” Nature Photonics 8, 58–64 (2014).
[Crossref]

Chardon, G.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: Compressive imaging using a multiply scattering medium,” Sci. Rep.4 (2014).
[Crossref] [PubMed]

Choi, W.

D. Kim, W. Choi, M. Kim, J. Moon, K. Seo, S. Ju, and W. Choi, “Implementing transmission eigenchannels of disordered media by a binary-control digital micromirror device,” Opt. Commun. 330, 35–39 (2014).
[Crossref]

D. Kim, W. Choi, M. Kim, J. Moon, K. Seo, S. Ju, and W. Choi, “Implementing transmission eigenchannels of disordered media by a binary-control digital micromirror device,” Opt. Commun. 330, 35–39 (2014).
[Crossref]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nature Photonics 6, 581–585 (2012).
[Crossref]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nature Photonics 6, 581–585 (2012).
[Crossref]

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109, 023902 (2012).
[Crossref]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref] [PubMed]

Choi, Y.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nature Photonics 6, 581–585 (2012).
[Crossref]

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109, 023902 (2012).
[Crossref]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref] [PubMed]

Cižmár, T.

Conkey, D. B.

Cui, M.

d’Aspremont, A.

I. Waldspurger, A. d’Aspremont, and S. Mallat, “Phase recovery, maxcut and complex semidefinite programming,” Mathematical Programming Series A-Springer (2013).

Dasari, R. R.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109, 023902 (2012).
[Crossref]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref] [PubMed]

Daudet, L.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: Compressive imaging using a multiply scattering medium,” Sci. Rep.4 (2014).
[Crossref] [PubMed]

Dholakia, K.

Di Leonardo, R.

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

Drémeau, A.

A. Drémeau and F. Krzakala, “Phase recovery from a bayesian point of view: the variational approach,” in Proceedings of IEEE Trans. Acoust. Speech Signal Process. (2015).

Fang-Yen, C.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109, 023902 (2012).
[Crossref]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref] [PubMed]

Farahi, S.

Feld, M. S.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref] [PubMed]

Fienup, J. R.

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,” Nature Photonics 8, 58–64 (2014).
[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 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 Journal of Physics 13, 123021 (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]

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]

Gerchberg, R.

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Gigan, S.

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,” Nature Photonics 8, 58–64 (2014).
[Crossref]

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New Journal of Physics 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] [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]

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: Compressive imaging using a multiply scattering medium,” Sci. Rep.4 (2014).
[Crossref] [PubMed]

Goorden, S. A.

S. A. Goorden, J. Bertolotti, and A. P. Mosk, “Superpixel-based spatial amplitude and phase modulation using a digital micromirror device,” arXiv:1405.3893 [physics] (2014).

Huisman, T. J.

Ju, S.

D. Kim, W. Choi, M. Kim, J. Moon, K. Seo, S. Ju, and W. Choi, “Implementing transmission eigenchannels of disordered media by a binary-control digital micromirror device,” Opt. Commun. 330, 35–39 (2014).
[Crossref]

Kang, P.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref] [PubMed]

Katz, O.

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,” Nature Photonics 8, 58–64 (2014).
[Crossref]

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: Compressive imaging using a multiply scattering medium,” Sci. Rep.4 (2014).
[Crossref] [PubMed]

Kim, D.

D. Kim, W. Choi, M. Kim, J. Moon, K. Seo, S. Ju, and W. Choi, “Implementing transmission eigenchannels of disordered media by a binary-control digital micromirror device,” Opt. Commun. 330, 35–39 (2014).
[Crossref]

Kim, J.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nature Photonics 6, 581–585 (2012).
[Crossref]

Kim, M.

D. Kim, W. Choi, M. Kim, J. Moon, K. Seo, S. Ju, and W. Choi, “Implementing transmission eigenchannels of disordered media by a binary-control digital micromirror device,” Opt. Commun. 330, 35–39 (2014).
[Crossref]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nature Photonics 6, 581–585 (2012).
[Crossref]

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109, 023902 (2012).
[Crossref]

Kner, P.

X. Zhang and P. Kner, “Binary wavefront optimization using a genetic algorithm,” Journal of Optics 16, 125704 (2014).
[Crossref]

Krzakala, F.

A. Drémeau and F. Krzakala, “Phase recovery from a bayesian point of view: the variational approach,” in Proceedings of IEEE Trans. Acoust. Speech Signal Process. (2015).

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

D. Akbulut, T. Strudley, J. Bertolotti, T. Zehender, E. Bakkers, A. Lagendijk, W. Vos, O. Muskens, and A. Mosk, “Measurements on the optical transmission matrices of strongly scattering nanowire layers,” in Proc. Conf. on Lasers and Electro-Optics Europe and International Quantum Electronics Conf. (CLEO EUROPE/IQEC), (2013).

Lee, K. J.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109, 023902 (2012).
[Crossref]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref] [PubMed]

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 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 Journal of Physics 13, 123021 (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]

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]

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: Compressive imaging using a multiply scattering medium,” Sci. Rep.4 (2014).
[Crossref] [PubMed]

Liang, J.

Liutkus, A.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: Compressive imaging using a multiply scattering medium,” Sci. Rep.4 (2014).
[Crossref] [PubMed]

Mallat, S.

I. Waldspurger, A. d’Aspremont, and S. Mallat, “Phase recovery, maxcut and complex semidefinite programming,” Mathematical Programming Series A-Springer (2013).

Marcenko, V. A.

V. A. Marčenko and L. A. Pastur, “Distribution of eigenvalues for some sets of random matrices,” Mathematics of the USSR-Sbornik 1, 457–483 (1967).
[Crossref]

Martina, D.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: Compressive imaging using a multiply scattering medium,” Sci. Rep.4 (2014).
[Crossref] [PubMed]

Moon, J.

D. Kim, W. Choi, M. Kim, J. Moon, K. Seo, S. Ju, and W. Choi, “Implementing transmission eigenchannels of disordered media by a binary-control digital micromirror device,” Opt. Commun. 330, 35–39 (2014).
[Crossref]

Moser, C.

Mosk, A.

D. Akbulut, T. Strudley, J. Bertolotti, T. Zehender, E. Bakkers, A. Lagendijk, W. Vos, O. Muskens, and A. Mosk, “Measurements on the optical transmission matrices of strongly scattering nanowire layers,” in Proc. Conf. on Lasers and Electro-Optics Europe and International Quantum Electronics Conf. (CLEO EUROPE/IQEC), (2013).

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

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. Express 19, 4017–4029 (2011).
[Crossref] [PubMed]

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Express 32, 2309 (2007).

S. A. Goorden, J. Bertolotti, and A. P. Mosk, “Superpixel-based spatial amplitude and phase modulation using a digital micromirror device,” arXiv:1405.3893 [physics] (2014).

Muskens, O.

D. Akbulut, T. Strudley, J. Bertolotti, T. Zehender, E. Bakkers, A. Lagendijk, W. Vos, O. Muskens, and A. Mosk, “Measurements on the optical transmission matrices of strongly scattering nanowire layers,” in Proc. Conf. on Lasers and Electro-Optics Europe and International Quantum Electronics Conf. (CLEO EUROPE/IQEC), (2013).

Papadopoulos, I. N.

Park, Q.-H.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nature Photonics 6, 581–585 (2012).
[Crossref]

Pastur, L. A.

V. A. Marčenko and L. A. Pastur, “Distribution of eigenvalues for some sets of random matrices,” Mathematics of the USSR-Sbornik 1, 457–483 (1967).
[Crossref]

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]

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: Compressive imaging using a multiply scattering medium,” Sci. Rep.4 (2014).
[Crossref] [PubMed]

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 Journal of Physics 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] [PubMed]

Psaltis, D.

Rangan, S.

P. Schniter and S. Rangan, “Compressive phase retrieval via generalized approximate message passing,” in Proceedings of Communication, Control, and Computing (Allerton) (2012).

Sampsell, J. B.

J. B. Sampsell, “Dmd display system,” (1995). US Patent5,452,024.

Saxton, W.

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Schniter, P.

P. Schniter and S. Rangan, “Compressive phase retrieval via generalized approximate message passing,” in Proceedings of Communication, Control, and Computing (Allerton) (2012).

Sebbah, P.

P. Sebbah, Waves and Imaging Through Complex Media (Springer, 2001).
[Crossref]

Seo, K.

D. Kim, W. Choi, M. Kim, J. Moon, K. Seo, S. Ju, and W. Choi, “Implementing transmission eigenchannels of disordered media by a binary-control digital micromirror device,” Opt. Commun. 330, 35–39 (2014).
[Crossref]

Strohmer, T.

E. Candès, T. Strohmer, and V. Voroninski, “Phaselift : exact and stable signal recovery from magnitude measurements via convex programming,” Commun. in Pure and Applied Mathematics 66, 1241–1274 (2013).
[Crossref]

Strudley, T.

D. Akbulut, T. Strudley, J. Bertolotti, T. Zehender, E. Bakkers, A. Lagendijk, W. Vos, O. Muskens, and A. Mosk, “Measurements on the optical transmission matrices of strongly scattering nanowire layers,” in Proc. Conf. on Lasers and Electro-Optics Europe and International Quantum Electronics Conf. (CLEO EUROPE/IQEC), (2013).

Tay, J. W.

van Putten, E. G.

Vellekoop, I. M.

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Express 32, 2309 (2007).

Voroninski, V.

E. Candès, T. Strohmer, and V. Voroninski, “Phaselift : exact and stable signal recovery from magnitude measurements via convex programming,” Commun. in Pure and Applied Mathematics 66, 1241–1274 (2013).
[Crossref]

Vos, W.

D. Akbulut, T. Strudley, J. Bertolotti, T. Zehender, E. Bakkers, A. Lagendijk, W. Vos, O. Muskens, and A. Mosk, “Measurements on the optical transmission matrices of strongly scattering nanowire layers,” in Proc. Conf. on Lasers and Electro-Optics Europe and International Quantum Electronics Conf. (CLEO EUROPE/IQEC), (2013).

Vos, W. L.

Waldspurger, I.

I. Waldspurger, A. d’Aspremont, and S. Mallat, “Phase recovery, maxcut and complex semidefinite programming,” Mathematical Programming Series A-Springer (2013).

Wang, L. V.

Yang, C.

Yang, T. D.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109, 023902 (2012).
[Crossref]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref] [PubMed]

Yoon, C.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109, 023902 (2012).
[Crossref]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nature Photonics 6, 581–585 (2012).
[Crossref]

Zehender, T.

D. Akbulut, T. Strudley, J. Bertolotti, T. Zehender, E. Bakkers, A. Lagendijk, W. Vos, O. Muskens, and A. Mosk, “Measurements on the optical transmission matrices of strongly scattering nanowire layers,” in Proc. Conf. on Lasers and Electro-Optics Europe and International Quantum Electronics Conf. (CLEO EUROPE/IQEC), (2013).

Zhang, X.

X. Zhang and P. Kner, “Binary wavefront optimization using a genetic algorithm,” Journal of Optics 16, 125704 (2014).
[Crossref]

Appl. Opt. (1)

Biomed. Opt. Express (1)

Commun. in Pure and Applied Mathematics (1)

E. Candès, T. Strohmer, and V. Voroninski, “Phaselift : exact and stable signal recovery from magnitude measurements via convex programming,” Commun. in Pure and Applied Mathematics 66, 1241–1274 (2013).
[Crossref]

Journal of Optics (1)

X. Zhang and P. Kner, “Binary wavefront optimization using a genetic algorithm,” Journal of Optics 16, 125704 (2014).
[Crossref]

Lab on a Chip (1)

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

Mathematics of the USSR-Sbornik (1)

V. A. Marčenko and L. A. Pastur, “Distribution of eigenvalues for some sets of random matrices,” Mathematics of the USSR-Sbornik 1, 457–483 (1967).
[Crossref]

Nature Commun. (1)

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 Photonics (3)

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nature Photonics 6, 581–585 (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,” Nature Photonics 6, 283–292 (2012).
[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,” Nature Photonics 8, 58–64 (2014).
[Crossref]

New Journal of Physics (1)

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

Opt. Commun. (1)

D. Kim, W. Choi, M. Kim, J. Moon, K. Seo, S. Ju, and W. Choi, “Implementing transmission eigenchannels of disordered media by a binary-control digital micromirror device,” Opt. Commun. 330, 35–39 (2014).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

Optik (1)

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Phys. Rev. Lett. (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] [PubMed]

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109, 023902 (2012).
[Crossref]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref] [PubMed]

Other (8)

P. Sebbah, Waves and Imaging Through Complex Media (Springer, 2001).
[Crossref]

S. A. Goorden, J. Bertolotti, and A. P. Mosk, “Superpixel-based spatial amplitude and phase modulation using a digital micromirror device,” arXiv:1405.3893 [physics] (2014).

J. B. Sampsell, “Dmd display system,” (1995). US Patent5,452,024.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: Compressive imaging using a multiply scattering medium,” Sci. Rep.4 (2014).
[Crossref] [PubMed]

D. Akbulut, T. Strudley, J. Bertolotti, T. Zehender, E. Bakkers, A. Lagendijk, W. Vos, O. Muskens, and A. Mosk, “Measurements on the optical transmission matrices of strongly scattering nanowire layers,” in Proc. Conf. on Lasers and Electro-Optics Europe and International Quantum Electronics Conf. (CLEO EUROPE/IQEC), (2013).

A. Drémeau and F. Krzakala, “Phase recovery from a bayesian point of view: the variational approach,” in Proceedings of IEEE Trans. Acoust. Speech Signal Process. (2015).

I. Waldspurger, A. d’Aspremont, and S. Mallat, “Phase recovery, maxcut and complex semidefinite programming,” Mathematical Programming Series A-Springer (2013).

P. Schniter and S. Rangan, “Compressive phase retrieval via generalized approximate message passing,” in Proceedings of Communication, Control, and Computing (Allerton) (2012).

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Figures (7)

Fig. 1
Fig. 1

Different experimental approaches for measuring the complex-valued transmission matrix of a scattering medium with a binary DMD amplitude modulator: (a) using a reference arm for retrieving the phase of the output field by off-axis or phase-shifting holography; (b) using the DMD as a spatial phase modulator by displaying amplitude holograms, and using the unmodulated parts of the field as a phase-stable reference; (c) presented approach where only intensity values are measured.

Fig. 2
Fig. 2

Experimental scheme: A 532 nm CW laser is expanded through a telescope in order to obtain an homogeneous beam. Through a rectangular mask, it illuminates the DMD which acts as binary amplitude spatial light modulator. The DMD reflects the light in two different directions corresponding to either “ON” (unit transmission) or “OFF” (the light is deviated towards a beam dump). The transmitted pattern is focused by a first lens L1 on the scattering medium – here a white paint layer –, acting as a thick multiply scattering medium. The transmitted speckle pattern is collected by a microscope objective and is observed through a polarizer P on a CCD camera.

Fig. 3
Fig. 3

Prediction performance according to (a), the mean-square error (MSE), in log scale, and to (b), the normalized cross-correlation between observation predictions using the estimated TM, and actual measurements of the output moduli (square root of the camera intensity values), as a function of the number of calibration measurements (x-axis is α, such that p = αN calibration measurements are used).

Fig. 4
Fig. 4

Density of the normalized singular values for different γ = M/N. Stamped line: experimental results, continuous line: Marčenko-Pastur law.

Fig. 5
Fig. 5

Illustration of light focusing on 3 points. The circles mark the positions of the targets.

Fig. 6
Fig. 6

Single target experiment. Enhancement factor as a function of the number of measurements used to learn the TM (x-axis is α, such that p = αN calibration measurements are used). For the same estimation of the TM, 2 focusing techniques are compared: binary phase conjugation (blue boxes), and the Bayesian technique [23] (red boxes).

Fig. 7
Fig. 7

Multiple target experiment. (a) Average enhancement factor as a function of the number of measurements used to learn the TM (x-axis is α, such that p = αN calibration measurements are used), and the number of target points (y-axis). (b) Missed detection rate (same axis as in (a)).

Equations (29)

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

y μ = | D x μ | , μ { 1 , ... , P } ,
Y H = | X H D H | ,
M S E = y P p | X P p H d ^ | 2 2 y P p | | 2 2 ,
C o r r = y P p H | X P p H d ^ | y P p H y P p | | 2 d ^ H X P p X P p H d ^ | | 2 ,
η I foc I back ,
y μ = e j θ μ ( i = 1 N x μ i d i * + ω μ ) ,
p ( d ) = i = 1 N p ( d i ) with p ( d i ) = C N ( 0 , σ d 2 ) ,
and p ( θ ) = μ = 1 P p ( θ μ ) with p ( θ μ ) = 1 2 π .
d ^ = arg max p ( d | y ) ,
with p ( d | y ) = θ p ( d , θ | y ) .
q ( d i ) = C N ( m i , Σ i ) ,
m i = σ d 2 σ n 2 + σ d 2 x i H x i r i H x i , Σ i = σ n 2 σ d 2 σ n 2 + σ d 2 x i H x i , r i = y ¯ k i m k * x k ,
y ¯ = [ y μ e ( j arg ( y μ * z μ ) ) I 1 ( 2 σ n 2 | y μ * z μ | ) I 0 ( 2 σ n 2 | y μ * z μ | ) ] μ = { 1 P }
z μ = i = 1 N m i * x μ i .
p ( d | y ) = θ p ( d , θ | y ) ,
θ q ( d , θ ) ,
θ i q ( d i ) μ q ( θ μ ) ,
i q ( d i ) ,
y μ = e j θ μ ( i = 1 N d μ i x i + ω μ ) ,
p ( x ) = i = 1 N p ( x i ) with p ( x i ) = Ber ( p i ) { p i 1 p i if x i = 1 , if x i = 0 ,
x ^ = arg max x p ( x | y ) ,
with p ( x | y ) = θ p ( x , θ | y ) .
q ( x i ) = p ( x i ) exp ( x i 2 ( d i H r i ) d i H d i σ 2 ) ,
r i = y ¯ k i q ( x k = 1 ) d k ,
y ¯ = [ y μ e ( j arg ( y μ * z μ ) ) I 1 ( 2 σ 2 | y μ * z μ | ) I 0 ( 2 σ 2 | y μ * z μ | ) ] μ = { 1 M }
z μ = i q ( x i = 1 ) d μ i ,
p ( x | y ) = θ p ( x , θ | y ) ,
θ i q ( x i ) μ q ( θ μ ) ,
= i q ( x i ) .

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