Abstract

In turbid materials it is impossible to concentrate light into a focus with conventional optics. Recently, it has been shown that the intensity on a dye-doped probe inside a turbid material can be enhanced by spatially shaping the wavefront of light before it enters a turbid medium. Here we show that this enhancement is due to concentration of light energy to a spot much smaller than a wavelength. We focus light on a dye-doped probe sphere that is hidden by an opaque layer. The light (λ=532nm) is optimally concentrated to a focal area smaller than 0.037μm2. The focus can be substantially smaller than the used probe. We use a comparison between the emission and excitation intensity to show the light is concentrated to a spot below the resolution of our oil-immersion objective. The results are in good agreement with an optimal concentration of linearly or elliptically polarized light.

© 2011 Optical Society of America

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2010 (7)

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photon. 4, 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, 100601 (2010).
[CrossRef] [PubMed]

I. M. Vellekoop and C. M. Aegerter, “Scattered light fluorescence microscopy: imaging through turbid layers,” Opt. Lett. 35, 1245–1247 (2010).
[CrossRef] [PubMed]

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]

C.-L. Hsieh, Y. Pu, R. Grange, G. Laporte, and Demetri Psaltis, “Imaging through turbid layers by scanning the phase conjugated second harmonic radiation from a nanoparticle,” Opt. Express 18, 20723–20731 (2010).
[CrossRef] [PubMed]

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

R. Carminati, “Subwavelength spatial correlations in near-field speckle patterns,” Phys. Rev. Lett. 81, 053804 (2010).

2008 (4)

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

O. L. Muskens and A. Lagendijk, “Broadband enhanced backscattering spectroscopy of strongly scattering media,” Opt. Express 16, 1222–1231 (2008).
[CrossRef] [PubMed]

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

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
[CrossRef] [PubMed]

2005 (1)

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2, 932–940 (2005).
[CrossRef] [PubMed]

2004 (1)

B. E. Henty and D. D. Stancil, “Multipath-enabled super- resolution for RF and microwave communication using phase- conjugate arrays,” Phys. Rev. Lett. 93, 243904 (2004).
[CrossRef]

2003 (3)

J. G. Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[CrossRef]

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
[CrossRef] [PubMed]

1999 (1)

J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
[CrossRef]

1997 (1)

C. Draeger and M. Fink, “One-channel time reversal of elastic waves in a chaotic 2D-silicon cavity,” Phys. Rev. Lett. 79, 407–410 (1997).
[CrossRef]

1996 (1)

M. U. Vera and D. J. Durian, “Angular distribution of diffusely transmitted light,” Phys. Rev. E 53, 3215–3224 (1996).
[CrossRef]

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1180 (1991).
[CrossRef] [PubMed]

1990 (1)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

1986 (1)

B. Shapiro, “Large intensity fluctuations for wave propagation in random media,” Phys. Rev. Lett. 57, 2168–2171 (1986).
[CrossRef] [PubMed]

1978 (1)

1966 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253, 358–379 (1959).
[CrossRef]

1938 (1)

F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica 5, 785–795 (1938).
[CrossRef]

1934 (1)

P. H. van Cittert, “Die wahrscheinliche Schwingungsverteilung in einer von einer Lichtquelle direkt oder mittels einer Linse beleuchteten Ebene,” Physica 1, 201–210 (1934).
[CrossRef]

Aegerter, C. M.

Aliev, F.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

Apostol, A.

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
[CrossRef] [PubMed]

Boccara, A. C.

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).
[CrossRef] [PubMed]

Bret, B. P. J.

J. G. Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[CrossRef]

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]

R. Carminati, “Subwavelength spatial correlations in near-field speckle patterns,” Phys. Rev. Lett. 81, 053804 (2010).

Cazayous, M.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1180 (1991).
[CrossRef] [PubMed]

Cižmár, T.

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

Colocci, M.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

Dau, D. H.

J. G. Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[CrossRef]

Denk, W.

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2, 932–940 (2005).
[CrossRef] [PubMed]

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Dholakia, K.

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

Dogariu, A.

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
[CrossRef] [PubMed]

Draeger, C.

C. Draeger and M. Fink, “One-channel time reversal of elastic waves in a chaotic 2D-silicon cavity,” Phys. Rev. Lett. 79, 407–410 (1997).
[CrossRef]

Durian, D. J.

M. U. Vera and D. J. Durian, “Angular distribution of diffusely transmitted light,” Phys. Rev. E 53, 3215–3224 (1996).
[CrossRef]

Emiliani, V.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

Feld, M. S.

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

Fink, M.

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,” Nat. Commun. 1, 81 (2010).
[CrossRef] [PubMed]

C. Draeger and M. Fink, “One-channel time reversal of elastic waves in a chaotic 2D-silicon cavity,” Phys. Rev. Lett. 79, 407–410 (1997).
[CrossRef]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1180 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1180 (1991).
[CrossRef] [PubMed]

Gigan, S.

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,” Nat. Commun. 1, 81 (2010).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 2000).

J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).

Grange, R.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1180 (1991).
[CrossRef] [PubMed]

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1180 (1991).
[CrossRef] [PubMed]

Helmchen, F.

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2, 932–940 (2005).
[CrossRef] [PubMed]

Henty, B. E.

B. E. Henty and D. D. Stancil, “Multipath-enabled super- resolution for RF and microwave communication using phase- conjugate arrays,” Phys. Rev. Lett. 93, 243904 (2004).
[CrossRef]

Hijmans, T. W.

J. G. Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[CrossRef]

Hsieh, C.-L.

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1180 (1991).
[CrossRef] [PubMed]

Imhof, A.

J. G. Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[CrossRef]

Intonti, F.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

Ishimaru, A.

Johnson, P. M.

J. G. Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[CrossRef]

Lagendijk, A.

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photon. 4, 320–322 (2010).
[CrossRef]

O. L. Muskens and A. Lagendijk, “Broadband enhanced backscattering spectroscopy of strongly scattering media,” Opt. Express 16, 1222–1231 (2008).
[CrossRef] [PubMed]

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
[CrossRef] [PubMed]

J. G. Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[CrossRef]

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

Laporte, G.

Leith, E. N.

Lerosey, G.

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,” Nat. Commun. 1, 81 (2010).
[CrossRef] [PubMed]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1180 (1991).
[CrossRef] [PubMed]

Mazilu, M.

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

Mosk, A. P.

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photon. 4, 320–322 (2010).
[CrossRef]

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

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
[CrossRef] [PubMed]

Muskens, O. L.

Popoff, S.

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]

Popoff, S. M.

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.

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

Psaltis, Demetri

Pu, Y.

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1180 (1991).
[CrossRef] [PubMed]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253, 358–379 (1959).
[CrossRef]

Rivas, J. G.

J. G. Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[CrossRef]

Schmitt, J. M.

J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
[CrossRef]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1180 (1991).
[CrossRef] [PubMed]

Sebbah, P.

P. Sebbah, Waves and Imaging through Complex Media (Kluwer Academic, 1999).

Shapiro, B.

B. Shapiro, “Large intensity fluctuations for wave propagation in random media,” Phys. Rev. Lett. 57, 2168–2171 (1986).
[CrossRef] [PubMed]

Sprik, R.

J. G. Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[CrossRef]

Stancil, D. D.

B. E. Henty and D. D. Stancil, “Multipath-enabled super- resolution for RF and microwave communication using phase- conjugate arrays,” Phys. Rev. Lett. 93, 243904 (2004).
[CrossRef]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1180 (1991).
[CrossRef] [PubMed]

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1180 (1991).
[CrossRef] [PubMed]

Upatnieks, J.

van Cittert, P. H.

P. H. van Cittert, “Die wahrscheinliche Schwingungsverteilung in einer von einer Lichtquelle direkt oder mittels einer Linse beleuchteten Ebene,” Physica 1, 201–210 (1934).
[CrossRef]

van Putten, E. G.

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[CrossRef]

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[CrossRef] [PubMed]

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

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
[CrossRef] [PubMed]

Vera, M. U.

M. U. Vera and D. J. Durian, “Angular distribution of diffusely transmitted light,” Phys. Rev. E 53, 3215–3224 (1996).
[CrossRef]

Webb, W. W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Wiersma, D. S.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

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B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253, 358–379 (1959).
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Yaqoob, Z.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photon. 2, 110–115 (2008).
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F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica 5, 785–795 (1938).
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Appl. Opt. (1)

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

J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

Nat. Commun. (1)

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]

Nat. Methods (1)

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2, 932–940 (2005).
[CrossRef] [PubMed]

Nat. Photon. (3)

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photon. 4, 320–322 (2010).
[CrossRef]

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

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

Opt. Commun. (2)

J. G. Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[CrossRef]

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

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. E (1)

M. U. Vera and D. J. Durian, “Angular distribution of diffusely transmitted light,” Phys. Rev. E 53, 3215–3224 (1996).
[CrossRef]

Phys. Rev. Lett. (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, 100601 (2010).
[CrossRef] [PubMed]

C. Draeger and M. Fink, “One-channel time reversal of elastic waves in a chaotic 2D-silicon cavity,” Phys. Rev. Lett. 79, 407–410 (1997).
[CrossRef]

B. E. Henty and D. D. Stancil, “Multipath-enabled super- resolution for RF and microwave communication using phase- conjugate arrays,” Phys. Rev. Lett. 93, 243904 (2004).
[CrossRef]

B. Shapiro, “Large intensity fluctuations for wave propagation in random media,” Phys. Rev. Lett. 57, 2168–2171 (1986).
[CrossRef] [PubMed]

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
[CrossRef] [PubMed]

R. Carminati, “Subwavelength spatial correlations in near-field speckle patterns,” Phys. Rev. Lett. 81, 053804 (2010).

Physica (2)

P. H. van Cittert, “Die wahrscheinliche Schwingungsverteilung in einer von einer Lichtquelle direkt oder mittels einer Linse beleuchteten Ebene,” Physica 1, 201–210 (1934).
[CrossRef]

F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica 5, 785–795 (1938).
[CrossRef]

Proc. R. Soc. Lond. A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253, 358–379 (1959).
[CrossRef]

Science (2)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1180 (1991).
[CrossRef] [PubMed]

Other (3)

J. W. Goodman, Statistical Optics (Wiley, 2000).

J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).

P. Sebbah, Waves and Imaging through Complex Media (Kluwer Academic, 1999).

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Figures (4)

Fig. 1
Fig. 1

Principle of the experiment. (a) A positive lens focuses a plane wave to a spot that is limited in size by the NA of the lens. (b) A strongly turbid material behind the lens scatters the light so that no focus is formed. By matching the incident wavefront to the scattering sample, we force constructive interference at a target position inside the sample. The light now arrives from all directions at the target position, significantly increasing the NA of the system.

Fig. 2
Fig. 2

(a), (c) Fluorescence and (b), (d) excitation images taken at the position of a probe sphere hidden under a layer of ZnO. The probe sphere has a radius of R = 150 nm . The images are taken at the back of the sample where the sphere is directly visible. In (a) and (b) we focus a plane wave onto the sample. Scattering creates a random specular pattern of excitation light resulting in a small amount of fluorescent response of the probe sphere. In (c) and (d) we illuminate the sample with a shaped wave that is created to maximize the fluorescent emission. Aside from the fluorescent emission enhancement, we see a sharp focus of excitation light. All intensities are in counts per second.

Fig. 3
Fig. 3

The measured radial intensity profile of the generated spot (squares), the SCFs of the illumination ( NA = 0.95 , triangles), and the imaging ( NA = 1.49 , circles) microscope objectives. We corrected the intensity profile of the focus by subtracting the speckle background (bg corrected) on which it resides.

Fig. 4
Fig. 4

Measured enhancements of the excitation and emission intensity for spheres with a radius of (a)  R = 80 nm and (b)  R = 150 nm . The solid curves indicate the linear regression of the data points. We show the expected regression for light that is optimally concentrated to the center of the probe using a vector theory (dashed curves) and a scalar approximation (dotted–dashed lines).

Equations (2)

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C ( Δ x , Δ y ) I ( x , y ) I ( x Δ x , y Δ y ) I ( x , y ) I ( x Δ x , y Δ y ) 1 ,
C R η em η ex = 1 V 0 R 0 π 0 2 π I ( ϕ , θ , r ) I peak r 2 sin θ d ϕ d θ d r ,

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