Abstract

Scattering often limits the controlled delivery of light in applications such as biomedical imaging, optogenetics, optical trapping, and fiber-optic communication or imaging. Such scattering can be controlled by appropriately shaping the light wavefront entering the material. Here, we develop a machine-learning approach for light control. Using pairs of binary intensity patterns and intensity measurements we train neural networks (NNs) to provide the wavefront corrections necessary to shape the beam after the scatterer. Additionally, we demonstrate that NNs can be used to find a functional relationship between transmitted and reflected speckle patterns. Establishing the validity of this relationship, we focus and scan in transmission through opaque media using reflected light. Our approach shows the versatility of NNs for light shaping, for efficiently and flexibly correcting for scattering, and in particular the feasibility of transmission control based on reflected light.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (11)

C. Deans, L. D. Griffin, L. Marmugi, and F. Renzoni, “Machine learning based localization and classification with atomic magnetometers,” Phys. Rev. Lett. 120, 033204 (2018).
[Crossref] [PubMed]

E. Nehme, L. E. Weiss, T. Michaeli, and Y. Shechtman, “Deep-storm: Super resolution single molecule microscopy by deep learning,” Optica 5, 458–464 (2018).
[Crossref]

N. Borhani, E. Kakkava, C. Moser, and D. Psaltis, “Learning to see through multimode fibers,” Optica 5, 960–966 (2018).
[Crossref]

S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5, 803–813 (2018).
[Crossref]

N. Fayard, A. Goetschy, R. Pierrat, and R. Carminati, “Mutual information between reflected and transmitted speckle images,” Phys. Rev. Lett. 120, 073901 (2018).
[Crossref] [PubMed]

M. Kadobianskyi, I. N. Papadopoulos, T. Chaigne, R. Horstmeyer, and B. Judkewitz, “Scattering correlations of time-gated light,” Optica 5, 389–394 (2018).
[Crossref]

I. Starshynov, A. M. Paniagua-Diaz, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti, “Non-gaussian correlations between reflected and transmitted intensity patterns emerging from opaque disordered media,” Phys. Rev. X 8, 021041 (2018).

S. Jeong, Y.-R. Lee, W. Choi, S. Kang, J. H. Hong, J.-S. Park, Y.-S. Lim, H.-G. Park, and W. Choi, “Focusing of light energy inside a scattering medium by controlling the time-gated multiple light scattering,” Nat. Photonics 12, 277–283 (2018).
[Crossref]

T. Zhao, L. Deng, W. Wang, D. S. Elson, and L. Su, “Bayes’ theorem-based binary algorithm for fast reference-less calibration of a multimode fiber,” Opt. Express 26, 20368-20378 (2018).
[Crossref] [PubMed]

B. Sun, P. S. Salter, C. Roider, A. Jesacher, J. Strauss, J. Heberle, M. Schmidt, and M. J. Booth, “Four-dimensional light shaping: manipulating ultrafast spatiotemporal foci in space and time,” Light. Sci. Appl. 7, 17117 (2018).
[Crossref]

R. Kuschmierz, E. Scharf, N. Koukourakis, and J. W. Czarske, “Self-calibration of lensless holographic endoscope using programmable guide stars,” Opt. Lett. 43, 2997–3000 (2018).
[Crossref] [PubMed]

2017 (15)

A. M. Caravaca-Aguirre and R. Piestun, “Single multimode fiber endoscope,” Opt. Express 25, 1656–1665 (2017).
[Crossref]

H. Frostig, E. Small, A. Daniel, P. Oulevey, S. Derevynko, and Y. Silberberg Mosk, “Focusing light by wavefront shaping through disorder and nonlinearity,” Optica 4, 1073–1079 (2017).
[Crossref]

S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K. D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
[Crossref] [PubMed]

R. Horisaki, R. Takagi, and J. Tanida, “Learning-based focusing through scattering media,” Appl. Opt. 56, 4358–4362 (2017).
[Crossref] [PubMed]

A. Sinha, J. L. S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4, 1117–1125 (2017).
[Crossref]

Y. Rivenson, Z. Göröcs, H. Günaydin, Y. Zhang, H. Wang, and A. Ozcan, “Deep learning microscopy,” Optica 4, 1437–1443 (2017).
[Crossref]

B. Zhang, Z. Zhang, Q. Feng, Z. Liu, C. Lin, and Y. Ding, “Focusing light through strongly scattering media using genetic algorithm with sbr discriminant,” J. Opt. 20, 025601 (2017).
[Crossref]

Y. Liu, C. Ma, Y. Shen, J. Shi, and L. V. Wang, “Focusing light inside dynamic scattering media with millisecond digital optical phase conjugation,” Optica 4, 280–288 (2017).
[Crossref] [PubMed]

A. Boniface, M. Mounaix, B. Blochet, R. Piestun, and S. Gigan, “Transmission-matrix-based point-spread-function engineering through a complex medium,” Optica 4, 54–59 (2017).
[Crossref]

B. Blochet, L. Bourdieu, and S. Gigan, “Focusing light through dynamical samples using fast continuous wavefront optimization,” Opt. Lett. 42, 4994–4997 (2017).
[Crossref] [PubMed]

S. Rotter and S. Gigan, “Light fields in complex media: Mesoscopic scattering meets wave control,” Rev. Mod. Phys. 89, 015005 (2017).
[Crossref]

N. Ji, “Adaptive optical fluorescence microscopy,” Nat. Methods 14, 374–380 (2017).
[Crossref] [PubMed]

H. W. Ruan, J. Brake, J. E. Robinson, Y. Liu, M. Jang, C. Xiao, C. Y. Zhou, Y. Gradinaru, and C. H. Yang, “Deep tissue optical focusing and optogenetic modulation with time-reversed ultrasonically encoded light,” Sci. Adv. 3, eaao5520 (2017).
[Crossref] [PubMed]

S. Turtaev, I. T. Leite, K. J. Mitchell, M. J. Padgett, D. B. Phillips, and T. Cizmar, “Comparison of nematic liquid-crystal and dmd based spatial light modulation in complex photonics,” Opt. Express 25(24), 29874–29884 (2017).
[Crossref] [PubMed]

H. Ruan, J. Brake, J. E. Robinson, Y. Liu, M. Jang, C. Xiao, C. Zhou, V. Gradinaru, and C. Yang, “Deep tissue optical focusing and optogenetic modulation with time-reversed ultrasonically encoded light,” Sci. Adv. 3, eaao5520 (2017).
[Crossref] [PubMed]

2016 (3)

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon 8, 200–227 (2016).
[Crossref]

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

A. Badon, D. Y. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2, e1600370 (2016).
[Crossref] [PubMed]

2015 (17)

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[Crossref]

N. Fayard, A. Caze, R. Pierrat, and R. Carminati, “Intensity correlations between reflected and transmitted speckle patterns,” Phys. Rev. A 92, 033827 (2015).
[Crossref]

H. Yu, J. H. Park, and Y. Park, “Measuring large optical reflection matrices of turbid media,” Opt. Commun. 352, 33–38 (2015).
[Crossref]

D. P. C. M. Damien Loterie, Salma Farahi, “Complex pattern projection through a multimode fiber,” Proc. SPIE 9335, 93350I (2015).
[Crossref]

K. F. Tehrani, J. Xu, Y. Zhang, P. Shen, and P. Kner, “Adaptive optics stochastic optical reconstruction microscopy (ao-storm) using a genetic algorithm,” Opt. Express 23, 13677–13692 (2015).
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Z. Liu, L. D. Lavis, and E. Betzig, “Imaging live-cell dynamics and structure at the single-molecule level,” Mol. Cell 58, 644–659 (2015).
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T. Ando, R. Horisaki, and J. Tanida, “Speckle learning-based object recognition through scattering media,” Opt. Express 23, 33902–33910 (2015).
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A. Dremeau, 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).
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M. I. Jordan and T. M. Mitchell, “Machine learning: Trends, perspectives, and prospects,” Science 349, 255–260 (2015).
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Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521, 436–444 (2015).
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L. Waller and L. Tian, “Machine learning for 3d microscopy,” Nature 523, 416–417 (2015).
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U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2, 517–522 (2015).
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J. Yoon, M. Lee, K. Lee, N. Kim, J. M. Kim, J. Park, H. Yu, C. Choi, W. D. Heo, and Y. Park, “Optogenetic control of cell signaling pathway through scattering skull using wavefront shaping,” Sci. Reports 3, 13289 (2015).
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D. Wang, E. Zhou, J. Brake, H. Ruan, M. Jang, and C. Yang, “Focusing through dynamic tissue with millisecond digital optical phase conjugation,” Optica 2, 728–735 (2015).
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Y. Liu, P. Lai, C. Ma, X. Xu, A. A. Grabar, and L. V. Wang, “Optical focusing deep inside dynamic scattering media with near infrared time-reversed ultrasonically encoded (true) light,” Nat. Commun. 6, 5904 (2015).
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I. M. Vellekoop, “Feedback-based wavefront shaping,” Opt. Express 23, 12189–12206 (2015).
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R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
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2014 (4)

D. Kim, J. Moon, M. Kim, T. D. Yang, J. Kim, E. Chung, and W. Choi, “Toward a miniature endomicroscope: pixelation-free and diffraction-limited imaging through a fiber bundle,” Opt. Express 39, 1291–1294 (2014).

X. Zhang and P. Kner, “Binary wavefront optimization using a genetic algorithm,” J. Opt. 17, 125704 (2014).
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J. Schmidhuber, “Deep learning in neural networks: An overview,” Neural Networks 61, 85–117 (2014).
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C. Jin, R. R. Nadakuditi, E. Michielssen, and S. C. Rand, “Backscatter analysis based algorithms for increasing transmission through highly scattering random media using phase-only-modulated wavefronts,” J. Opt. Soc. Am. A 31, 1788–1800 (2014).
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2013 (3)

C. Jin, R. R. Nadakuditi, E. Michielssen, and S. C. Rand, “Iterative, backscatter-analysis algorithms for increasing transmission and focusing light through highly scattering random media,” J. Opt. Soc. Am. A 30, 1592–1602 (2013).
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Y. Choi, T. R. Hillman, W. Choi, N. Lue, R. R. Dasari, P. T. C. So, W. Choi, and Z. Yaqoob, “Measurement of the time-resolved reflection matrix for enhancing light energy delivery into a scattering medium,” Phys. Rev. Lett. 111, 243901 (2013).
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T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Reports 3, 1909 (2013).
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2012 (8)

D. B. Conkey, A. N. Brown, A. M. Caravaca-Aguirre, and R. Piestun, “Genetic algorithm optimization for focusing through turbid media in noisy environments,” J. Opt. 20, 4840–4849 (2012).

R. Fiolka, K. Si, and M. Cui, “Parallel wavefront measurements in ultrasound pulse guided digital phase conjugation,” Opt. Express 20, 24827–24834 (2012).
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Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
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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).
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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).
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J. Tanga, R. N. Germain, and M. Cui, “Superpenetration optical microscopy by iterative multiphoton adaptive compensation technique,” Proc. Natl. Acad. Sci. 129, 8434–8439 (2012).
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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, 203901 (2012).
[Crossref] [PubMed]

T. Cizmar and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
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2011 (3)

2010 (5)

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).
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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).
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C.-L. Hsieh, Y. Pu, R. Grange, G. Laporte, and D. Psaltis, “Imaging through turbid layers by scanning the phase conjugated second harmonic radiation from a nanoparticle,” Opt. Express 18, 20723–20731 (2010).
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S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
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T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 3, 388–394 (2010).
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2009 (2)

K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose–Einstein condensates,” New J. Phys. 11, 043030 (2009).
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J. P. Rickgauer and D. W. Tank, “Two-photon excitation of channelrhodopsin-2 at saturation,” PNAS 106, 15025–15030 (2009).
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2007 (1)

2004 (1)

1990 (1)

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Akbulut, D.

Ando, T.

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Aubry, A.

A. Badon, D. Y. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2, e1600370 (2016).
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Badon, A.

A. Badon, D. Y. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2, e1600370 (2016).
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Baraniuk, R. G.

C. A. Metzler, M. K. Sharma, S. Nagesh, R. G. Baraniuk, O. Cossairt, and A. Veeraraghavan, “Coherent inverse scattering via transmission matrices: Efficient phase retrieval algorithms and a public dataset,” in 2017 IEEE International Conference on Computational Photography (ICCP) (2017), pp. 1–16.

Barbastathis, G.

Bengio, Y.

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521, 436–444 (2015).
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Bertolotti, J.

I. Starshynov, A. M. Paniagua-Diaz, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti, “Non-gaussian correlations between reflected and transmitted intensity patterns emerging from opaque disordered media,” Phys. Rev. X 8, 021041 (2018).

Betzig, E.

Z. Liu, L. D. Lavis, and E. Betzig, “Imaging live-cell dynamics and structure at the single-molecule level,” Mol. Cell 58, 644–659 (2015).
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Bianchi, S.

Blochet, B.

Boccara, A. C.

A. Badon, D. Y. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2, e1600370 (2016).
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S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
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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).
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Boniface, A.

Booth, M. J.

B. Sun, P. S. Salter, C. Roider, A. Jesacher, J. Strauss, J. Heberle, M. Schmidt, and M. J. Booth, “Four-dimensional light shaping: manipulating ultrafast spatiotemporal foci in space and time,” Light. Sci. Appl. 7, 17117 (2018).
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Borhani, N.

Boshier, M. G.

K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose–Einstein condensates,” New J. Phys. 11, 043030 (2009).
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Bourdieu, L.

Brake, J.

H. Ruan, J. Brake, J. E. Robinson, Y. Liu, M. Jang, C. Xiao, C. Zhou, V. Gradinaru, and C. Yang, “Deep tissue optical focusing and optogenetic modulation with time-reversed ultrasonically encoded light,” Sci. Adv. 3, eaao5520 (2017).
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H. W. Ruan, J. Brake, J. E. Robinson, Y. Liu, M. Jang, C. Xiao, C. Y. Zhou, Y. Gradinaru, and C. H. Yang, “Deep tissue optical focusing and optogenetic modulation with time-reversed ultrasonically encoded light,” Sci. Adv. 3, eaao5520 (2017).
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D. Wang, E. Zhou, J. Brake, H. Ruan, M. Jang, and C. Yang, “Focusing through dynamic tissue with millisecond digital optical phase conjugation,” Optica 2, 728–735 (2015).
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Brown, A. N.

D. B. Conkey, A. N. Brown, A. M. Caravaca-Aguirre, and R. Piestun, “Genetic algorithm optimization for focusing through turbid media in noisy environments,” J. Opt. 20, 4840–4849 (2012).

Caravaca-Aguirre, A. M.

A. M. Caravaca-Aguirre and R. Piestun, “Single multimode fiber endoscope,” Opt. Express 25, 1656–1665 (2017).
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D. B. Conkey, A. N. Brown, A. M. Caravaca-Aguirre, and R. Piestun, “Genetic algorithm optimization for focusing through turbid media in noisy environments,” J. Opt. 20, 4840–4849 (2012).

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).
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S. Ohayon, A. M. Caravaca-Aguirre, R. Piestun, and J. J. DiCarlo, “Deep brain fluorescence imaging with minimally invasive ultra-thin optical fibers,” arxiv preprint arXiv:1703.07633 (2017).

Carminati, R.

I. Starshynov, A. M. Paniagua-Diaz, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti, “Non-gaussian correlations between reflected and transmitted intensity patterns emerging from opaque disordered media,” Phys. Rev. X 8, 021041 (2018).

N. Fayard, A. Goetschy, R. Pierrat, and R. Carminati, “Mutual information between reflected and transmitted speckle images,” Phys. Rev. Lett. 120, 073901 (2018).
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N. Fayard, A. Caze, R. Pierrat, and R. Carminati, “Intensity correlations between reflected and transmitted speckle patterns,” Phys. Rev. A 92, 033827 (2015).
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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).
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Caze, A.

N. Fayard, A. Caze, R. Pierrat, and R. Carminati, “Intensity correlations between reflected and transmitted speckle patterns,” Phys. Rev. A 92, 033827 (2015).
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Chaigne, T.

Choi, C.

J. Yoon, M. Lee, K. Lee, N. Kim, J. M. Kim, J. Park, H. Yu, C. Choi, W. D. Heo, and Y. Park, “Optogenetic control of cell signaling pathway through scattering skull using wavefront shaping,” Sci. Reports 3, 13289 (2015).
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Choi, W.

S. Jeong, Y.-R. Lee, W. Choi, S. Kang, J. H. Hong, J.-S. Park, Y.-S. Lim, H.-G. Park, and W. Choi, “Focusing of light energy inside a scattering medium by controlling the time-gated multiple light scattering,” Nat. Photonics 12, 277–283 (2018).
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S. Jeong, Y.-R. Lee, W. Choi, S. Kang, J. H. Hong, J.-S. Park, Y.-S. Lim, H.-G. Park, and W. Choi, “Focusing of light energy inside a scattering medium by controlling the time-gated multiple light scattering,” Nat. Photonics 12, 277–283 (2018).
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S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K. D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
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S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J. S. Lee, Y. S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9, 253–258 (2015).
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S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J. S. Lee, Y. S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9, 253–258 (2015).
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D. Kim, J. Moon, M. Kim, T. D. Yang, J. Kim, E. Chung, and W. Choi, “Toward a miniature endomicroscope: pixelation-free and diffraction-limited imaging through a fiber bundle,” Opt. Express 39, 1291–1294 (2014).

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Reports 3, 1909 (2013).
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Y. Choi, T. R. Hillman, W. Choi, N. Lue, R. R. Dasari, P. T. C. So, W. Choi, and Z. Yaqoob, “Measurement of the time-resolved reflection matrix for enhancing light energy delivery into a scattering medium,” Phys. Rev. Lett. 111, 243901 (2013).
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Y. Choi, T. R. Hillman, W. Choi, N. Lue, R. R. Dasari, P. T. C. So, W. Choi, and Z. Yaqoob, “Measurement of the time-resolved reflection matrix for enhancing light energy delivery into a scattering medium,” Phys. Rev. Lett. 111, 243901 (2013).
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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, 203901 (2012).
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Choi, Y.

Y. Choi, T. R. Hillman, W. Choi, N. Lue, R. R. Dasari, P. T. C. So, W. Choi, and Z. Yaqoob, “Measurement of the time-resolved reflection matrix for enhancing light energy delivery into a scattering medium,” Phys. Rev. Lett. 111, 243901 (2013).
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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, 203901 (2012).
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Chung, E.

D. Kim, J. Moon, M. Kim, T. D. Yang, J. Kim, E. Chung, and W. Choi, “Toward a miniature endomicroscope: pixelation-free and diffraction-limited imaging through a fiber bundle,” Opt. Express 39, 1291–1294 (2014).

Cizmar, T.

S. Turtaev, I. T. Leite, K. J. Mitchell, M. J. Padgett, D. B. Phillips, and T. Cizmar, “Comparison of nematic liquid-crystal and dmd based spatial light modulation in complex photonics,” Opt. Express 25(24), 29874–29884 (2017).
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T. Cizmar and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref] [PubMed]

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 3, 388–394 (2010).
[Crossref]

Conkey, D. B.

D. B. Conkey, A. N. Brown, A. M. Caravaca-Aguirre, and R. Piestun, “Genetic algorithm optimization for focusing through turbid media in noisy environments,” J. Opt. 20, 4840–4849 (2012).

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]

Cossairt, O.

C. A. Metzler, M. K. Sharma, S. Nagesh, R. G. Baraniuk, O. Cossairt, and A. Veeraraghavan, “Coherent inverse scattering via transmission matrices: Efficient phase retrieval algorithms and a public dataset,” in 2017 IEEE International Conference on Computational Photography (ICCP) (2017), pp. 1–16.

Cui, M.

Czarske, J. W.

Damien Loterie, D. P. C. M.

D. P. C. M. Damien Loterie, Salma Farahi, “Complex pattern projection through a multimode fiber,” Proc. SPIE 9335, 93350I (2015).
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Daniel, A.

Dasari, R. R.

Y. Choi, T. R. Hillman, W. Choi, N. Lue, R. R. Dasari, P. T. C. So, W. Choi, and Z. Yaqoob, “Measurement of the time-resolved reflection matrix for enhancing light energy delivery into a scattering medium,” Phys. Rev. Lett. 111, 243901 (2013).
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T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Reports 3, 1909 (2013).
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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, 203901 (2012).
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Deng, L.

Deng, M.

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T. Cizmar and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
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T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 3, 388–394 (2010).
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DiCarlo, J. J.

S. Ohayon, A. M. Caravaca-Aguirre, R. Piestun, and J. J. DiCarlo, “Deep brain fluorescence imaging with minimally invasive ultra-thin optical fibers,” arxiv preprint arXiv:1703.07633 (2017).

DiMarzio, C. A.

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

B. Zhang, Z. Zhang, Q. Feng, Z. Liu, C. Lin, and Y. Ding, “Focusing light through strongly scattering media using genetic algorithm with sbr discriminant,” J. Opt. 20, 025601 (2017).
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W. Drexler and J. G. Fujimoto, Optical Coherence Tomography (Springer International Publishing, 2015).
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A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon 8, 200–227 (2016).
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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, 203901 (2012).
[Crossref] [PubMed]

Fayard, N.

N. Fayard, A. Goetschy, R. Pierrat, and R. Carminati, “Mutual information between reflected and transmitted speckle images,” Phys. Rev. Lett. 120, 073901 (2018).
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I. Starshynov, A. M. Paniagua-Diaz, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti, “Non-gaussian correlations between reflected and transmitted intensity patterns emerging from opaque disordered media,” Phys. Rev. X 8, 021041 (2018).

N. Fayard, A. Caze, R. Pierrat, and R. Carminati, “Intensity correlations between reflected and transmitted speckle patterns,” Phys. Rev. A 92, 033827 (2015).
[Crossref]

Feierabend, M.

Feld, M. S.

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Reports 3, 1909 (2013).
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Feng, Q.

B. Zhang, Z. Zhang, Q. Feng, Z. Liu, C. Lin, and Y. Ding, “Focusing light through strongly scattering media using genetic algorithm with sbr discriminant,” J. Opt. 20, 025601 (2017).
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Fink, M.

A. Badon, D. Y. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2, e1600370 (2016).
[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,” Nat. Photonics 6, 283–292 (2012).
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S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[Crossref] [PubMed]

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).
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Fiolka, R.

Forbes, A.

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon 8, 200–227 (2016).
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Fujimoto, J. G.

W. Drexler and J. G. Fujimoto, Optical Coherence Tomography (Springer International Publishing, 2015).
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J. Tanga, R. N. Germain, and M. Cui, “Superpenetration optical microscopy by iterative multiphoton adaptive compensation technique,” Proc. Natl. Acad. Sci. 129, 8434–8439 (2012).
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S. Rotter and S. Gigan, “Light fields in complex media: Mesoscopic scattering meets wave control,” Rev. Mod. Phys. 89, 015005 (2017).
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Supplementary Material (12)

NameDescription
» Visualization 1       movie 1 as described in paper.
» Visualization 2       movie 2 as described in paper.
» Visualization 3       movie 3 as described in paper.
» Visualization 4       movie 4 as described in paper.
» Visualization 5       movie 5 as described in paper.
» Visualization 6       movie 6 as described in paper.
» Visualization 7       movie 7 as described in paper.
» Visualization 8       movie 8 as described in paper.
» Visualization 9       movie 9 as described in paper.
» Visualization 10       movie 10 as described in paper.
» Visualization 11       movie 11 as described in paper.
» Visualization 12       movie 12 as described in paper.

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Figures (13)

Fig. 1
Fig. 1 Approach for light control through scattering media with NNs. A NN is trained with pairs of illumination and speckle patterns (illustration, see figures below for examples of actual illumination and speckle patterns), using the speckle patterns as input of the network and the illumination as output. Once the NN is trained, it is used to predict the illumination necessary to generate a target pattern after the scattering material. The predicted illumination is subsequently sent through the material resulting in the desired light pattern.
Fig. 2
Fig. 2 Sketch of the experimental setup (see text for details). A DMD generates pseudo-random binary illumination patterns that are projected onto the back aperture of a microscope objective. After passing through the scattering material, light is projected onto a CCD camera by using a second identical microscope objective. A beam splitter placed before the first objective and a CCD camera are used to retrieve speckle patterns reflected by the sample for experiments with combined transmission and reflection. Bottom-right insets depict illustrations of illumination and speckle patterns. (PH: pinhole, NPBS: non-polarizing beam splitter, MO: microscope objective, SM: scattering material.)
Fig. 3
Fig. 3 Focusing with neural networks. Top: Illustration of SLNN (a) or CNN (b) with speckle and illumination pattern. Bottom: Intensity distributions (first row) and intensity profiles through the foci along horizontal (second row) and vertical (third row) directions of Gaussian beams obtained at different positions after training (a) the SLNN and (b) the CNN. Red-dashed lines (- -) are the targeted intensity distributions that enter the NN, normalized to the corresponding experimental result. Scale bars = 2 µm. FCL: fully-connected layer; Conv n × m × p: convolutional layer of p kernels with dimensions n × m; MP: max pooling operation reducing the previous element size. Color bars: intensity (a.u.).
Fig. 4
Fig. 4 Light control through a glass diffuser with a SLNN. Normalized intensity patterns obtained after the glass diffuser with the SLNN: (a) five Gaussian foci; (b) a line at 45°; (c) the letter "E"; and (d) the number "5"; Insets show the desired light distribution. Scale bars = 2 µm. Color bar: intensity (a.u.) normalized for each image.
Fig. 5
Fig. 5 Neural networks focus light through multimode fibers. Normalized transverse maximum intensity projection of the light field (see Visualization 7, Visualization 8, Visualization 9 for further information) after a multimode fiber when (a) no correction is applied and when a single focus is scanned (maximum intensity projection) along (b) a circle, (c) a square, and (d) an array of 5 × 5 points. Scale bars = 2.3 µm. Color bar: intensity (a.u.) normalized for each image.
Fig. 6
Fig. 6 Neural networks find functional relationships between transmitted and reflected speckle patterns. (a) Histogram of the Pearson correlation coefficient ρr,p between the measured reflected and transmitted speckle patterns (in blue) and the measured and predicted reflected speckle patterns (orange). Number of bins: 30. Total number of pairs of samples used: 2000. Bottom: Examples of the normalized transverse intensity distributions of the light field of the (b) measured reflected speckle pattern, (c) predicted reflected speckle pattern, and (d) measured reflected speckle pattern while focusing in transmission (e).
Fig. 7
Fig. 7 Focusing and scanning in transmission using reflected light. Illustration of network approach to control transmitted light using reflected light. A SLNN is trained to learn the relationship between simultaneously recorded transmitted and reflected speckle patterns. After training of the network, it is sufficient to train a second SLNN to relate reflection to illumination for controlling light through the combined network. Bottom: Normalized transverse maximum intensity projection of the light field after a sheet of paper when a single focus is scanned (maximum intensity projection) along (a) a circle, (b) a square, and (c) an array of 5 × 5 points. Scale bars = 2.7 µm. Color bar: intensity (a.u.) normalized for each image.
Fig. 8
Fig. 8 Single-focus scanning allows time-averaged pattern projection. Patterns obtained when a single focus is scanned following (a/d) a circle (128/96 scanning points), (b/e) a square (256/256 scanning points), and (c/f) a grid of 5 × 5 points with the SLNN (first row) and the CNN (second row). Color bars: intensity (a.u.) normalized for each image. Scale bars: 2.3 µm
Fig. 9
Fig. 9 Single-focus scanning allows time-averaged pattern projection through paper. Maximum intensity projections of patterns obtained when a single focus is scanned following (a) a circle (128 scanning points), (b) a square (256 scanning points), and (c) a grid of 5 × 5 points with the SLNN and paper as scattering material. Color bars: intensity (a.u.) normalized for each image. Scale bars:2.7 µm
Fig. 10
Fig. 10 Light control over different fields of view. Normalized transverse intensity distributions of an example of speckle pattern (first column), a single focus (second column), the number “1" (fourth column), and the number “5" (6th column) for different fields of view: 256 × 256 pixels (first row), 128 × 128 pixels (second row), 96 × 96 pixels (third row), and 64 × 64 pixels (last row). Columns number 3, 5, and 7 are the actual DMD patterns used to generate the light distributions from columns number 2, 4, and 6, respectively. Color bars: intensity (a.u.) normalized for each image.
Fig. 11
Fig. 11 Scanning and corresponding enhancement for focusing across paper with the SLNN (a, b) and the CNN (c, d) with the 40× objective. (a) shows different scan patterns across the entire field of view (grid, circle and square) for the SLNN, and (b) shows the corresponding enhancement for each point in (a). (c) Same as (a) for the CNN. (d) same as (b) for the CNN. The width and height of the full field of view is 51 µm, the single pixel width and hight is 0.53 µm. Note the different scale bars for the enhancement for the SLNN and CNN.
Fig. 12
Fig. 12 Training performance of SLNN. Mean-square error (MSE) between the predicted and original illumination patterns for the single-layer neural network for different sizes of the dataset. Red-, green-, and blue-dashed curves correspond to illumination sizes of 64 × 64, 32 × 32, and 16 × 16, respectively. Insets below show the the predicted illumination at different stages of the training for the 16 × 16 case.
Fig. 13
Fig. 13 Speed of SLNN training and quality of focus. (a) Training time of the SLNN and (b) enhancement η of the generated foci with paper as scattering sample for different values of the number of image pairs used during training. The enhancement is defined as ηIfocus/⟨Ispeckle⟩, where Ifocus is the intensity at the generated foci and Ispeckle⟩ is the mean value of the background speckle [67]. Image in the lower part of the figure are examples of focusing with N samples used for training (with the number N of samples used for training at the top of each image.

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