Abstract

We demonstrate feedback-optimized focusing of spatially coherent polychromatic light after transmission through strongly scattering media, and describe the relationship between optimized focus intensity and initial far-field speckle contrast. Optimization is performed using a MEMS spatial light modulator with camera-based or spectrometer-based feedback. We observe that the spectral bandwidth of the optimized focus depends on characteristics of the feedback signal. We interpret this dependence as a modification in the number of independent frequency components, or spectral correlations, transmitted by the sample, and introduce a simple model for polychromatic focus enhancement that is corroborated by experiment with calibrated samples.

© 2013 OSA

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  7. 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(10), 100601 (2010).
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  31. J. Tang, R. N. Germain, and M. Cui, “Superpenetration optical microscopy by iterative multiphoton adaptive compensation technique,” Proc. Natl. Acad. Sci. U.S.A.109(22), 8434–8439 (2012).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2012 (9)

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics6(5), 283–292 (2012).
[CrossRef]

C. Stockbridge, Y. Lu, J. Moore, S. Hoffman, R. Paxman, K. Toussaint, and T. Bifano, “Focusing through dynamic scattering media,” Opt. Express20(14), 15086–15092 (2012).
[CrossRef] [PubMed]

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. Express20(14), 16067–16076 (2012).
[CrossRef] [PubMed]

D. B. Conkey and R. Piestun, “Color image projection through a strongly scattering wall,” Opt. Express20(25), 27312–27318 (2012).
[CrossRef] [PubMed]

E. Small, O. Katz, Y. Guan, and Y. Silberberg, “Spectral control of broadband light through random media by wavefront shaping,” Opt. Lett.37(16), 3429–3431 (2012).
[CrossRef] [PubMed]

F. Lemoult, M. Fink, and G. Lerosey, “A polychromatic approach to far-field superlensing at visible wavelengths,” Nat Commun3, 889 (2012).
[CrossRef] [PubMed]

M. Davy, Z. Shi, and A. Z. Genack, “Focusing through random media: Eigenchannel participation number and intensity correlation,” Phys. Rev. B85(3), 035105 (2012).
[CrossRef]

J. Tang, R. N. Germain, and M. Cui, “Superpenetration optical microscopy by iterative multiphoton adaptive compensation technique,” Proc. Natl. Acad. Sci. U.S.A.109(22), 8434–8439 (2012).
[CrossRef] [PubMed]

J. Aulbach, B. Gjonaj, P. Johnson, and A. Lagendijk, “Spatiotemporal focusing in opaque scattering media by wave front shaping with nonlinear feedback,” Opt. Express20(28), 29237–29251 (2012).
[CrossRef] [PubMed]

2011 (7)

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics5(3), 154–157 (2011).
[CrossRef] [PubMed]

N. Curry, P. Bondareff, M. Leclercq, N. F. van Hulst, R. Sapienza, S. Gigan, and S. Grésillon, “Direct determination of Diffusion Properties of Random Media from Speckle Contrast,” Opt. Lett.36(17), 3332–3334 (2011).
[CrossRef] [PubMed]

F. van Beijnum, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Frequency bandwidth of light focused through turbid media,” Opt. Lett.36(3), 373–375 (2011).
[CrossRef] [PubMed]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett.106(10), 103901 (2011).
[CrossRef] [PubMed]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics5(6), 372–377 (2011).
[CrossRef]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat Commun2, 447 (2011).
[CrossRef] [PubMed]

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light though optical disordered media: transmission matrix approach,” New J. Phys.13(12), 123021 (2011).
[CrossRef]

2010 (3)

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics4(5), 320–322 (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(10), 100601 (2010).
[CrossRef] [PubMed]

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (1)

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun.281(11), 3071–3080 (2008).
[CrossRef]

2007 (2)

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett.32(16), 2309–2311 (2007).
[CrossRef] [PubMed]

M. J. Booth, “Adaptive optics in microscopy,” Philos. Transact. A. Math. Phys. Eng. Sci. 365(1861), 2829–2843 (2007).

2005 (1)

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods2(12), 932–940 (2005).
[CrossRef] [PubMed]

2003 (1)

2000 (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929 (2000).
[CrossRef]

1997 (1)

1992 (1)

J. F. D. Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev. B Condens. Matter45(2), 658–666 (1992).

1990 (1)

A. Z. Genack and J. M. Drake, “Relationship between optical intensity, fluctuations and pulse propagation in random media,” Europhys. Lett.11(4), 331–336 (1990).
[CrossRef]

1989 (1)

R. Pnini and B. Shapiro, “Fluctuations in transmission of waves through disordered slabs,” Phys. Rev. B Condens. Matter39(10), 6986–6994 (1989).
[CrossRef] [PubMed]

1977 (2)

D. J. Thouless, “Maximum Metallic Resistance in Thin Wires,” Phys. Rev. Lett.39(18), 1167–1169 (1977).
[CrossRef]

S. T. Hong, I. Sreenivasiah, and A. Ishimaru, “Plane wave pulse propagation though random media,” IEEE Trans. Antenn. Propag.25(6), 822–828 (1977).
[CrossRef]

Aulbach, J.

J. Aulbach, B. Gjonaj, P. Johnson, and A. Lagendijk, “Spatiotemporal focusing in opaque scattering media by wave front shaping with nonlinear feedback,” Opt. Express20(28), 29237–29251 (2012).
[CrossRef] [PubMed]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett.106(10), 103901 (2011).
[CrossRef] [PubMed]

Austin, D. R.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat Commun2, 447 (2011).
[CrossRef] [PubMed]

Betzig, E.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
[CrossRef] [PubMed]

Bifano, T.

Boccara, A. C.

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light though optical disordered media: transmission matrix approach,” New J. Phys.13(12), 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(10), 100601 (2010).
[CrossRef] [PubMed]

Boer, J. F. D.

J. F. D. Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev. B Condens. Matter45(2), 658–666 (1992).

Bondareff, P.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat Commun2, 447 (2011).
[CrossRef] [PubMed]

N. Curry, P. Bondareff, M. Leclercq, N. F. van Hulst, R. Sapienza, S. Gigan, and S. Grésillon, “Direct determination of Diffusion Properties of Random Media from Speckle Contrast,” Opt. Lett.36(17), 3332–3334 (2011).
[CrossRef] [PubMed]

Booth, M. J.

Botcherby, E. J.

Bromberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics5(6), 372–377 (2011).
[CrossRef]

Cao, H.

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(10), 100601 (2010).
[CrossRef] [PubMed]

Chatel, B.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat Commun2, 447 (2011).
[CrossRef] [PubMed]

Conkey, D. B.

Cui, M.

J. Tang, R. N. Germain, and M. Cui, “Superpenetration optical microscopy by iterative multiphoton adaptive compensation technique,” Proc. Natl. Acad. Sci. U.S.A.109(22), 8434–8439 (2012).
[CrossRef] [PubMed]

Curry, N.

Davy, M.

M. Davy, Z. Shi, and A. Z. Genack, “Focusing through random media: Eigenchannel participation number and intensity correlation,” Phys. Rev. B85(3), 035105 (2012).
[CrossRef]

Débarre, D.

Denk, W.

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods2(12), 932–940 (2005).
[CrossRef] [PubMed]

Drake, J. M.

A. Z. Genack and J. M. Drake, “Relationship between optical intensity, fluctuations and pulse propagation in random media,” Europhys. Lett.11(4), 331–336 (1990).
[CrossRef]

Fink, M.

F. Lemoult, M. Fink, and G. Lerosey, “A polychromatic approach to far-field superlensing at visible wavelengths,” Nat Commun3, 889 (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,” Nat. Photonics6(5), 283–292 (2012).
[CrossRef]

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light though optical disordered media: transmission matrix approach,” New J. Phys.13(12), 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(10), 100601 (2010).
[CrossRef] [PubMed]

Genack, A. Z.

M. Davy, Z. Shi, and A. Z. Genack, “Focusing through random media: Eigenchannel participation number and intensity correlation,” Phys. Rev. B85(3), 035105 (2012).
[CrossRef]

A. Z. Genack and J. M. Drake, “Relationship between optical intensity, fluctuations and pulse propagation in random media,” Europhys. Lett.11(4), 331–336 (1990).
[CrossRef]

Germain, R. N.

J. Tang, R. N. Germain, and M. Cui, “Superpenetration optical microscopy by iterative multiphoton adaptive compensation technique,” Proc. Natl. Acad. Sci. U.S.A.109(22), 8434–8439 (2012).
[CrossRef] [PubMed]

Gigan, S.

N. Curry, P. Bondareff, M. Leclercq, N. F. van Hulst, R. Sapienza, S. Gigan, and S. Grésillon, “Direct determination of Diffusion Properties of Random Media from Speckle Contrast,” Opt. Lett.36(17), 3332–3334 (2011).
[CrossRef] [PubMed]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat Commun2, 447 (2011).
[CrossRef] [PubMed]

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light though optical disordered media: transmission matrix approach,” New J. Phys.13(12), 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(10), 100601 (2010).
[CrossRef] [PubMed]

Gjonaj, B.

J. Aulbach, B. Gjonaj, P. Johnson, and A. Lagendijk, “Spatiotemporal focusing in opaque scattering media by wave front shaping with nonlinear feedback,” Opt. Express20(28), 29237–29251 (2012).
[CrossRef] [PubMed]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett.106(10), 103901 (2011).
[CrossRef] [PubMed]

Grésillon, S.

Guan, Y.

Helmchen, F.

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods2(12), 932–940 (2005).
[CrossRef] [PubMed]

Hoffman, S.

Hong, S. T.

S. T. Hong, I. Sreenivasiah, and A. Ishimaru, “Plane wave pulse propagation though random media,” IEEE Trans. Antenn. Propag.25(6), 822–828 (1977).
[CrossRef]

Ishimaru, A.

S. T. Hong, I. Sreenivasiah, and A. Ishimaru, “Plane wave pulse propagation though random media,” IEEE Trans. Antenn. Propag.25(6), 822–828 (1977).
[CrossRef]

Ji, N.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
[CrossRef] [PubMed]

Johnson, P.

Johnson, P. M.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett.106(10), 103901 (2011).
[CrossRef] [PubMed]

Katz, O.

E. Small, O. Katz, Y. Guan, and Y. Silberberg, “Spectral control of broadband light through random media by wavefront shaping,” Opt. Lett.37(16), 3429–3431 (2012).
[CrossRef] [PubMed]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics5(6), 372–377 (2011).
[CrossRef]

Lagendijk, A.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics6(5), 283–292 (2012).
[CrossRef]

J. Aulbach, B. Gjonaj, P. Johnson, and A. Lagendijk, “Spatiotemporal focusing in opaque scattering media by wave front shaping with nonlinear feedback,” Opt. Express20(28), 29237–29251 (2012).
[CrossRef] [PubMed]

F. van Beijnum, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Frequency bandwidth of light focused through turbid media,” Opt. Lett.36(3), 373–375 (2011).
[CrossRef] [PubMed]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett.106(10), 103901 (2011).
[CrossRef] [PubMed]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics4(5), 320–322 (2010).
[CrossRef]

J. F. D. Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev. B Condens. Matter45(2), 658–666 (1992).

Leclercq, M.

Lemoult, F.

F. Lemoult, M. Fink, and G. Lerosey, “A polychromatic approach to far-field superlensing at visible wavelengths,” Nat Commun3, 889 (2012).
[CrossRef] [PubMed]

Lerosey, G.

F. Lemoult, M. Fink, and G. Lerosey, “A polychromatic approach to far-field superlensing at visible wavelengths,” Nat Commun3, 889 (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,” Nat. Photonics6(5), 283–292 (2012).
[CrossRef]

S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light though optical disordered media: transmission matrix approach,” New J. Phys.13(12), 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(10), 100601 (2010).
[CrossRef] [PubMed]

Liu, H.

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics5(3), 154–157 (2011).
[CrossRef] [PubMed]

Lu, Y.

McCabe, D. J.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat Commun2, 447 (2011).
[CrossRef] [PubMed]

Milkie, D. E.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
[CrossRef] [PubMed]

Moore, J.

Mosk, A. P.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics6(5), 283–292 (2012).
[CrossRef]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett.106(10), 103901 (2011).
[CrossRef] [PubMed]

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J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett.106(10), 103901 (2011).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Schematic of the experimental setup. The spectrum (top right inset) of a fiber-delivered broadband SLD is adjusted using a grating and variable-width slit before being reflected from a MEMS spatial light modulator (SLM) and focused onto the surface of a strongly scattering sample. Transmitted light produces a speckle pattern that is sensed by either a camera or a spectrometer (bottom right inset). Focus optimization is based on a coordinate descent optimization algorithm [8]. SM = single mode; L1-L7 = lenses; PBS = polarizing beamsplitter; QWP = quarter-wave plate; P = polarizer.

Fig. 2
Fig. 2

Measured contrast (C) as a function of illumination spectral bandwidth (Δνl) for four samples of thicknesses L = 5.2l*, 2.1l*, 1.1l* and 0.8l*. The plots are fits to the experimental data based the model Eq. (3).

Fig. 3
Fig. 3

Optimized focus intensity enhancement (E) versus measured initial speckle contrast (C) for combinations of samples and illumination bandwidths. The red dashed trace shows E = E0C2, for reference.

Fig. 4
Fig. 4

Spectral profiles of a single speckle grain before (black) and after focus optimization using first a narrowband feedback signal (red) and then a full bandwidth feedback signal (blue). The feedback signal bandwidths were 0.4 THz and 11.8 THz, respectively. The resulting optimized speckle bandwidths were 2.6 THz and 5.3 THz, respectively. The sample thickness was L = 1.1l*. From the black curve, we observe that a single un-optimized spatial speckle grain contains several spectral speckles. From Eq. (3), the bandwidth of these spectral speckles, or, equivalently, the bandwidth of the independent frequency components transmitted by the sample, was calculated to be Δνs = 1.6 THz.

Fig. 5
Fig. 5

(a) Spectral bandwidth of the optimized focus as a function of increasing feedback signal bandwidth B, for different values of the nonlinearity parameter α. (b) Spectral profile of representative optimized foci for full bandwidth feedback and different values of α.

Fig. 6
Fig. 6

Enhancement (E) versus contrast (C) plots. Filled circles are enhancements obtained using camera-based feedback with α = 1 and full B (same as Fig. 2). Filled diamonds are enhancements obtained under the same experimental condition using spectrometer-based feedback with α = 1 and small B (less than Δνs). Corresponding plots are derived from Eq. (5) (i.e. they are not fits).

Equations (5)

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Δ ν l = ( S 0 (ν)dν ) 2 S 0 2 (ν)dν ,
C= 1 M .
C= Δ ν s Δ ν l +Δ ν s
J= B S α (ν)dν
M eff = 1 ξ (M1)+1= 1 ξ ( C 2 1)+1,

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