Abstract

Optical time-reversal techniques are being actively developed to focus light through or inside opaque scattering media. When applied to biological tissue, these techniques promise to revolutionize biophotonics by enabling deep-tissue non-invasive optical imaging, optogenetics, optical tweezing, and phototherapy. In all previous optical time-reversal experiments, the scattered light field was well-sampled during wavefront measurement and wavefront reconstruction, following the Nyquist sampling criterion. Here, we overturn this conventional practice by demonstrating that even when the scattered field is under-sampled, light can still be focused through or inside scattering media. Even more surprisingly, we show both theoretically and experimentally that the focus achieved by under-sampling can be one order of magnitude brighter than that achieved under the well-sampling conditions used in previous works, where 3×3 to 5×5 pixels were used to sample one speckle grain on average. Moreover, sub-Nyquist sampling improves the signal-to-noise ratio and the collection efficiency of the scattered light. We anticipate that this newly explored under-sampling scheme will transform the understanding of optical time reversal and boost the performance of optical imaging, manipulation, and communication through opaque scattering media.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2016 (4)

2015 (9)

D. Wang, E. H. 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).
[Crossref]

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).
[Crossref]

C. Ma, F. Zhou, Y. Liu, and L. V. Wang, “Single-exposure optical focusing inside scattering media using binarized time-reversed adapted perturbation,” Optica 2, 869–876 (2015).
[Crossref]

H. Ruan, M. Jang, and C. Yang, “Optical focusing inside scattering media with time-reversed ultrasound microbubble encoded light,” Nat. Commun. 6, 8968 (2015).
[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]

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. Rep. 5, 13289 (2015).
[Crossref]

E. E. Morales-Delgado, S. Farahi, I. N. Papadopoulos, D. Psaltis, and C. Moser, “Delivery of focused short pulses through a multimode fiber,” Opt. Express 23, 9109–9120 (2015).
[Crossref]

P. Lai, L. Wang, J. W. Tay, and L. V. Wang, “Photoacoustically guided wavefront shaping for enhanced optical focusing in scattering media,” Nat. Photonics 9, 126–132 (2015).
[Crossref]

M. Kim, W. Choi, Y. Choi, C. Yoon, and W. Choi, “Transmission matrix of a scattering medium and its applications in biophotonics,” Opt. Express 23, 12648–12668 (2015).
[Crossref]

2014 (7)

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

X. Hao, L. Martin-Rouault, and M. Cui, “A self-adaptive method for creating high efficiency communication channels through random scattering media,” Sci. Rep. 4, 5874 (2014).
[Crossref]

C. Ma, X. Xu, Y. Liu, and L. V. Wang, “Time-reversed adapted-perturbation (TRAP) optical focusing onto dynamic objects inside scattering media,” Nat. Photonics 8, 931–936 (2014).
[Crossref]

E. H. Zhou, H. Ruan, C. Yang, and B. Judkewitz, “Focusing on moving targets through scattering samples,” Optica 1, 227–232 (2014).
[Crossref]

M. Jang, H. Ruan, H. Zhou, B. Judkewitz, and C. Yang, “Method for auto-alignment of digital optical phase conjugation systems based on digital propagation,” Opt. Express 22, 14054–14071 (2014).
[Crossref]

H. Ruan, M. Jang, B. Judkewitz, and C. Yang, “Iterative time-reversed ultrasonically encoded light focusing in backscattering mode,” Sci. Rep. 4, 7156 (2014).
[Crossref]

M. Jang, H. Ruan, B. Judkewitz, and C. Yang, “Model for estimating the penetration depth limit of the time-reversed ultrasonically encoded optical focusing technique,” Opt. Express 22, 5787–5807 (2014).
[Crossref]

2013 (2)

B. Judkewitz, Y. M. Wang, R. Horstmeyer, A. Mathy, and C. Yang, “Speckle-scale focusing in the diffusive regime with time-reversal of variance-encoded light (TROVE),” Nat. Photonics 7, 300–305 (2013).
[Crossref]

T. Hillman, T. Yamauchi, W. Choi, R. Dasari, Z. Yaqoob, and Y. Park, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3, 1909 (2013).
[Crossref]

2012 (9)

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, 10583–10590 (2012).
[Crossref]

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).
[Crossref]

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

C. Stockbridge, Y. Lu, J. Moore, S. Hoffman, R. Paxman, K. Toussaint, and T. Bifano, “Focusing through dynamic scattering media,” Opt. Express 20, 15086–15092 (2012).
[Crossref]

I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett. 101, 081108 (2012).
[Crossref]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

Y. Liu, C. Zhang, and L. V. Wang, “Effects of light scattering on optical-resolution photoacoustic microscopy,” J. Biomed. Opt. 17, 126014 (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]

S. Tripathi, R. Paxman, T. Bifano, and K. C. Toussaint, “Vector transmission matrix for the polarization behavior of light propagation in highly scattering media,” Opt. Express 20, 16067–16076 (2012).
[Crossref]

2011 (3)

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]

M. Cui, “A high speed wavefront determination method based on spatial frequency modulations for focusing light through random scattering media,” Opt. Express 19, 2989–2995 (2011).
[Crossref]

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5, 154–157 (2011).
[Crossref]

2010 (5)

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]

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).
[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]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 1–5 (2010).
[Crossref]

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7, 603–614 (2010).
[Crossref]

2009 (1)

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7, 141–147 (2009).
[Crossref]

2008 (2)

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]

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
[Crossref]

2007 (1)

2002 (1)

G. S. He, “Optical phase conjugation: principles, techniques, and applications,” Prog. Quantum Electron. 26, 131–191 (2002).
[Crossref]

2000 (2)

F. Le Clerc, L. Collot, and M. Gross, “Numerical heterodyne holography with two-dimensional photodetector arrays,” Opt. Lett. 25, 716–718 (2000).
[Crossref]

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J. L. Thomas, and F. Wu, “Time-reversed acoustics,” Rep. Prog. Phys. 63, 1933–1995 (2000).
[Crossref]

1999 (1)

M. Fink, “Time-reversed acoustics,” Sci. Am. 281, 91–97 (1999).
[Crossref]

1997 (2)

Z. Ficek and P. D. Drummond, “Time reversed acoustics,” Phys. Today 50(9), 34–38 (1997).
[Crossref]

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[Crossref]

1995 (1)

A. Derode, P. Roux, and M. Fink, “Robust acoustic time reversal with high-order multiple scattering,” Phys. Rev. Lett. 101, 4206 (1995).
[Crossref]

1991 (1)

C. Prada, F. Wu, and M. Fink, “The iterative time reversal mirror: a solution to self-focusing in the pulse echo mode,” J. Acoust. Soc. Am. 90, 1119–1129 (1991).
[Crossref]

1987 (1)

1979 (1)

1978 (1)

A. Yariv, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. 14, 650–660 (1978).
[Crossref]

Atry, F.

Azimipour, M.

Beckwith, P. H.

Bertolotti, J.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

Betzig, E.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7, 141–147 (2009).
[Crossref]

Bifano, T.

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

Boccara, A. C.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 1–5 (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]

Brake, J.

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]

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]

Cassereau, D.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J. L. Thomas, and F. Wu, “Time-reversed acoustics,” Rep. Prog. Phys. 63, 1933–1995 (2000).
[Crossref]

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. Rep. 5, 13289 (2015).
[Crossref]

Choi, W.

Choi, Y.

Collot, L.

Conkey, D. B.

Cui, M.

X. Hao, L. Martin-Rouault, and M. Cui, “A self-adaptive method for creating high efficiency communication channels through random scattering media,” Sci. Rep. 4, 5874 (2014).
[Crossref]

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

I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett. 101, 081108 (2012).
[Crossref]

M. Cui, “A high speed wavefront determination method based on spatial frequency modulations for focusing light through random scattering media,” Opt. Express 19, 2989–2995 (2011).
[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]

Dasari, R.

T. Hillman, T. Yamauchi, W. Choi, R. Dasari, Z. Yaqoob, and Y. Park, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3, 1909 (2013).
[Crossref]

Derode, A.

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J. L. Thomas, and F. Wu, “Time-reversed acoustics,” Rep. Prog. Phys. 63, 1933–1995 (2000).
[Crossref]

A. Derode, P. Roux, and M. Fink, “Robust acoustic time reversal with high-order multiple scattering,” Phys. Rev. Lett. 101, 4206 (1995).
[Crossref]

DiMarzio, C. A.

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Supplementary Material (1)

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Figures (5)

Fig. 1.
Fig. 1. Sampling of speckle grains in optical time-reversal experiments. (a) Phase map of the scattered light on the rear surface of a scattering medium. (b) Phase map of the under-sampled speckle grains, which looks different from the real one in (a). (c) Phase map of the 400× magnified speckle grains. (d) Phase map of the well-sampled speckle grains. (e) Magnifying the speckle size by an iris and a lens. (f) Magnifying the speckle size by two objective lenses.
Fig. 2.
Fig. 2. Physical meaning of the reconstructed quantity in phase-shifting holography when speckle grains are under-sampled. (a) An illustration of 16 speckle grains occupying one digital PCM pixel. A phasor expression is used to represent the electric field of each speckle grain. (b) The reconstructed quantity (the large gray arrow) is a vector sum of the 16 independent phasors (the small black arrows).
Fig. 3.
Fig. 3. Schematic of the experimental setup for time-reversal-based optical focusing through scattering media. AOM, acousto-optic modulator; BS, beam splitter; CL, camera lens; HWP, half-wave plate; L, lens; M, mirror; MS, mechanical shutter; PBS, polarizing beam splitter; R, reference beam; S, sample beam; SLM, spatial light modulator; SM, scattering medium.
Fig. 4.
Fig. 4. Experimental results obtained by varying the pixel size of a PCM while fixing the speckle size on the PCM. (a) Plot of normalized PBR/NP as a function of the under-sampling factor F. The error bars show the standard deviations obtained from three realizations of the scattering medium. The blue dashed line indicates the theoretical prediction based on Eqs. (1) and (4). (b) Image of the achieved focus captured by Camera2 when the under-sampling factor F was 19. The experimental PBR is 1100 (theoretical PBR is πNP/4/(15×15)7200). Scale bar, 200 μm. (c) No focus was observed when a random phase map was displayed on the SLM.
Fig. 5.
Fig. 5. Experimental results obtained by varying the speckle size on a PCM while fixing the pixel size. (a) Plot of normalized PBR as a function of speckle area. The horizontal and vertical axes are shown in the log scale. The blue dashed line indicates the theoretical prediction based on Eqs. (1) and (4). The error bars show the standard deviations obtained from three realizations of the scattering medium. (b) Image of the achieved focus when the speckle area was 0.48× the pixel area. The PBR is 9100. Scale bar, 200 μm. (c) No focus was observed when a random phase map was displayed on the SLM.

Equations (7)

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PBR=NS,
ES=TEin=(t11t12t1NIt21t22t2NItNS1tNS2tNSNI)NS×NI(100)NI×1=(t11t21tNS1)NS×1.
ES,under-sampled=(t11+t21++tF1t11+t21++tF1t11+t21++tF1}F  rowstNSF+1,1+tNSF+2,1++tNS,1tNSF+1,1+tNSF+2,1++tNS,1tNSF+1,1+tNSF+2,1++tNS,1}F  rows)NS×1.
PBR=|Epeak|2|Ebackground|2=(NS)2+((F1)×NS)2(F×NS)2NSF=NP.
PBR=αNP,
SNRunder-sampled=2NPS,
SNRwell-sampled=2NPP=2NPS/G.

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