Abstract

We introduce a simple but practical method to measure the optical transmission matrix (TM) of complex media. The optical TM of a complex medium is obtained by modulating the wavefront of a beam impinging on the complex medium and imaging the transmitted full-field speckle intensity patterns. Using the retrieved TM, we demonstrate the generation and linear combination of multiple foci on demand through the complex medium. This method will be used as a versatile tool for coherence control of waves through turbid media.

© 2015 Optical Society of America

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References

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2015 (3)

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(2), 126–132 (2015).
[Crossref]

H. Yu, J. Park, K. Lee, J. Yoon, K. Kim, S. Lee, and Y. Park, “Recent advances in wavefront shaping techniques for biomedical applications,” Curr. Appl. Phys. 15(5), 632–641 (2015).
[Crossref]

J. Park, J.-H. Park, H. Yu, and Y. Park, “Focusing through turbid media by polarization modulation,” Opt. Lett. 40(8), 1667–1670 (2015).
[Crossref]

2014 (3)

2013 (6)

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8(1), 58–64 (2013).
[Crossref]

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(4), 300–305 (2013).
[Crossref] [PubMed]

J. Jang, J. Lim, H. Yu, H. Choi, J. Ha, J. H. Park, W. Y. Oh, W. Jang, S. Lee, and Y. Park, “Complex wavefront shaping for optimal depth-selective focusing in optical coherence tomography,” Opt. Express 21(3), 2890–2902 (2013).
[Crossref] [PubMed]

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–458 (2013).
[Crossref]

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref] [PubMed]

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. Rep. 3, 1909 (2013).
[Crossref] [PubMed]

2012 (9)

I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett. 101(8), 081108 (2012).
[Crossref] [PubMed]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

T. Cižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref] [PubMed]

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(2), 1733–1740 (2012).
[Crossref] [PubMed]

D. B. Conkey, A. N. Brown, A. M. Caravaca-Aguirre, and R. Piestun, “Genetic algorithm optimization for focusing through turbid media in noisy environments,” Opt. Express 20(5), 4840–4849 (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. Express 20(14), 16067–16076 (2012).
[Crossref] [PubMed]

J.-H. Park, C. Park, H. Yu, Y.-H. Cho, and Y. Park, “Dynamic active wave plate using random nanoparticles,” Opt. Express 20(15), 17010–17016 (2012).
[Crossref]

J. H. Park, C. Park, H. Yu, Y. H. Cho, and Y. Park, “Active spectral filtering through turbid media,” Opt. Lett. 37(15), 3261–3263 (2012).
[Crossref] [PubMed]

2011 (4)

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

M. Cui, “Parallel wavefront optimization method for focusing light through random scattering media,” Opt. Lett. 36(6), 870–872 (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]

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5(3), 154–157 (2011).
[Crossref] [PubMed]

2010 (4)

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]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1(6), 81 (2010).
[Crossref] [PubMed]

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18(4), 3444–3455 (2010).
[Crossref] [PubMed]

2008 (2)

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101(12), 120601 (2008).
[Crossref] [PubMed]

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

2007 (1)

1999 (1)

H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

1997 (1)

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[Crossref]

Aulbach, J.

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]

Bartolini, P.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[Crossref]

Bifano, T.

Boccara, A. C.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8(1), 58–64 (2013).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through 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]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1(6), 81 (2010).
[Crossref] [PubMed]

Bossy, E.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8(1), 58–64 (2013).
[Crossref]

Brown, A. N.

Cao, H.

H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[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(10), 100601 (2010).
[Crossref] [PubMed]

Chaigne, T.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8(1), 58–64 (2013).
[Crossref]

Chang, R.

H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Cho, Y. H.

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y. H. Lee, Y. H. Cho, and Y. Park, “Full-Field Subwavelength Imaging Using a Scattering Superlens,” Phys. Rev. Lett. 113(11), 113901 (2014).
[Crossref] [PubMed]

J. H. Park, C. Park, H. Yu, Y. H. Cho, and Y. Park, “Active spectral filtering through turbid media,” Opt. Lett. 37(15), 3261–3263 (2012).
[Crossref] [PubMed]

Cho, Y.-H.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–458 (2013).
[Crossref]

J.-H. Park, C. Park, H. Yu, Y.-H. Cho, and Y. Park, “Dynamic active wave plate using random nanoparticles,” Opt. Express 20(15), 17010–17016 (2012).
[Crossref]

Choi, H.

Choi, W.

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. Rep. 3, 1909 (2013).
[Crossref] [PubMed]

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref] [PubMed]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
[Crossref]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
[Crossref]

Choi, Y.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
[Crossref]

Cizmar, T.

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

Cižmár, T.

T. Cižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref] [PubMed]

Conkey, D. B.

Cui, M.

Dasari, R. R.

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. Rep. 3, 1909 (2013).
[Crossref] [PubMed]

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref] [PubMed]

Dholakia, K.

T. Cižmár 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 4(6), 388–394 (2010).
[Crossref]

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. Rep. 3, 1909 (2013).
[Crossref] [PubMed]

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref] [PubMed]

Fink, M.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8(1), 58–64 (2013).
[Crossref]

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(5), 283–292 (2012).
[Crossref]

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

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1(6), 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(10), 100601 (2010).
[Crossref] [PubMed]

Gigan, S.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8(1), 58–64 (2013).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through 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]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1(6), 81 (2010).
[Crossref] [PubMed]

Gjonaj, B.

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]

Goorden, S. A.

Ha, J.

Han, S.

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y. H. Lee, Y. H. Cho, and Y. Park, “Full-Field Subwavelength Imaging Using a Scattering Superlens,” Phys. Rev. Lett. 113(11), 113901 (2014).
[Crossref] [PubMed]

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–458 (2013).
[Crossref]

Hillman, T. R.

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref] [PubMed]

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. Rep. 3, 1909 (2013).
[Crossref] [PubMed]

Ho, S.

H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Horstmann, M.

Horstmeyer, R.

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(4), 300–305 (2013).
[Crossref] [PubMed]

Jang, J.

Jang, W.

Jin, K.

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y. H. Lee, Y. H. Cho, and Y. Park, “Full-Field Subwavelength Imaging Using a Scattering Superlens,” Phys. Rev. Lett. 113(11), 113901 (2014).
[Crossref] [PubMed]

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]

Judkewitz, B.

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(4), 300–305 (2013).
[Crossref] [PubMed]

Katz, O.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8(1), 58–64 (2013).
[Crossref]

Kim, J.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
[Crossref]

Kim, J.-Y.

Kim, K.

H. Yu, J. Park, K. Lee, J. Yoon, K. Kim, S. Lee, and Y. Park, “Recent advances in wavefront shaping techniques for biomedical applications,” Curr. Appl. Phys. 15(5), 632–641 (2015).
[Crossref]

Kim, M.

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y. H. Lee, Y. H. Cho, and Y. Park, “Full-Field Subwavelength Imaging Using a Scattering Superlens,” Phys. Rev. Lett. 113(11), 113901 (2014).
[Crossref] [PubMed]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
[Crossref]

Ko, S. H.

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y. H. Lee, Y. H. Cho, and Y. Park, “Full-Field Subwavelength Imaging Using a Scattering Superlens,” Phys. Rev. Lett. 113(11), 113901 (2014).
[Crossref] [PubMed]

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–458 (2013).
[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. Photonics 6(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]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[Crossref]

Lai, P.

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(2), 126–132 (2015).
[Crossref]

Lee, J. O.

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref] [PubMed]

Lee, K.

H. Yu, J. Park, K. Lee, J. Yoon, K. Kim, S. Lee, and Y. Park, “Recent advances in wavefront shaping techniques for biomedical applications,” Curr. Appl. Phys. 15(5), 632–641 (2015).
[Crossref]

Lee, S.

H. Yu, J. Park, K. Lee, J. Yoon, K. Kim, S. Lee, and Y. Park, “Recent advances in wavefront shaping techniques for biomedical applications,” Curr. Appl. Phys. 15(5), 632–641 (2015).
[Crossref]

J. Jang, J. Lim, H. Yu, H. Choi, J. Ha, J. H. Park, W. Y. Oh, W. Jang, S. Lee, and Y. Park, “Complex wavefront shaping for optimal depth-selective focusing in optical coherence tomography,” Opt. Express 21(3), 2890–2902 (2013).
[Crossref] [PubMed]

Lee, Y. H.

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y. H. Lee, Y. H. Cho, and Y. Park, “Full-Field Subwavelength Imaging Using a Scattering Superlens,” Phys. Rev. Lett. 113(11), 113901 (2014).
[Crossref] [PubMed]

Lerosey, G.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through 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]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1(6), 81 (2010).
[Crossref] [PubMed]

Lim, J.

Liu, H.

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5(3), 154–157 (2011).
[Crossref] [PubMed]

Mathy, A.

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(4), 300–305 (2013).
[Crossref] [PubMed]

Mazilu, M.

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

Mosk, A.

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

Mosk, A. P.

S. A. Goorden, M. Horstmann, A. P. Mosk, B. Škorić, and P. W. Pinkse, “Quantum-secure authentication of a physical unclonable key,” Optica 1(6), 421–424 (2014).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(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]

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101(12), 120601 (2008).
[Crossref] [PubMed]

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

Nam, K. T.

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y. H. Lee, Y. H. Cho, and Y. Park, “Full-Field Subwavelength Imaging Using a Scattering Superlens,” Phys. Rev. Lett. 113(11), 113901 (2014).
[Crossref] [PubMed]

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–458 (2013).
[Crossref]

Oh, W. Y.

Park, C.

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y. H. Lee, Y. H. Cho, and Y. Park, “Full-Field Subwavelength Imaging Using a Scattering Superlens,” Phys. Rev. Lett. 113(11), 113901 (2014).
[Crossref] [PubMed]

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–458 (2013).
[Crossref]

J. H. Park, C. Park, H. Yu, Y. H. Cho, and Y. Park, “Active spectral filtering through turbid media,” Opt. Lett. 37(15), 3261–3263 (2012).
[Crossref] [PubMed]

J.-H. Park, C. Park, H. Yu, Y.-H. Cho, and Y. Park, “Dynamic active wave plate using random nanoparticles,” Opt. Express 20(15), 17010–17016 (2012).
[Crossref]

Park, J.

H. Yu, J. Park, K. Lee, J. Yoon, K. Kim, S. Lee, and Y. Park, “Recent advances in wavefront shaping techniques for biomedical applications,” Curr. Appl. Phys. 15(5), 632–641 (2015).
[Crossref]

J. Park, J.-H. Park, H. Yu, and Y. Park, “Focusing through turbid media by polarization modulation,” Opt. Lett. 40(8), 1667–1670 (2015).
[Crossref]

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–458 (2013).
[Crossref]

Park, J. H.

Park, J.-H.

J. Park, J.-H. Park, H. Yu, and Y. Park, “Focusing through turbid media by polarization modulation,” Opt. Lett. 40(8), 1667–1670 (2015).
[Crossref]

H. Yu, J. Jang, J. Lim, J.-H. Park, W. Jang, J.-Y. Kim, and Y. Park, “Depth-enhanced 2-D optical coherence tomography using complex wavefront shaping,” Opt. Express 22(7), 7514–7523 (2014).
[PubMed]

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y. H. Lee, Y. H. Cho, and Y. Park, “Full-Field Subwavelength Imaging Using a Scattering Superlens,” Phys. Rev. Lett. 113(11), 113901 (2014).
[Crossref] [PubMed]

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–458 (2013).
[Crossref]

J.-H. Park, C. Park, H. Yu, Y.-H. Cho, and Y. Park, “Dynamic active wave plate using random nanoparticles,” Opt. Express 20(15), 17010–17016 (2012).
[Crossref]

Park, Q.-H.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
[Crossref]

Park, Y.

H. Yu, J. Park, K. Lee, J. Yoon, K. Kim, S. Lee, and Y. Park, “Recent advances in wavefront shaping techniques for biomedical applications,” Curr. Appl. Phys. 15(5), 632–641 (2015).
[Crossref]

J. Park, J.-H. Park, H. Yu, and Y. Park, “Focusing through turbid media by polarization modulation,” Opt. Lett. 40(8), 1667–1670 (2015).
[Crossref]

H. Yu, J. Jang, J. Lim, J.-H. Park, W. Jang, J.-Y. Kim, and Y. Park, “Depth-enhanced 2-D optical coherence tomography using complex wavefront shaping,” Opt. Express 22(7), 7514–7523 (2014).
[PubMed]

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y. H. Lee, Y. H. Cho, and Y. Park, “Full-Field Subwavelength Imaging Using a Scattering Superlens,” Phys. Rev. Lett. 113(11), 113901 (2014).
[Crossref] [PubMed]

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref] [PubMed]

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–458 (2013).
[Crossref]

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. Rep. 3, 1909 (2013).
[Crossref] [PubMed]

J. Jang, J. Lim, H. Yu, H. Choi, J. Ha, J. H. Park, W. Y. Oh, W. Jang, S. Lee, and Y. Park, “Complex wavefront shaping for optimal depth-selective focusing in optical coherence tomography,” Opt. Express 21(3), 2890–2902 (2013).
[Crossref] [PubMed]

J. H. Park, C. Park, H. Yu, Y. H. Cho, and Y. Park, “Active spectral filtering through turbid media,” Opt. Lett. 37(15), 3261–3263 (2012).
[Crossref] [PubMed]

J.-H. Park, C. Park, H. Yu, Y.-H. Cho, and Y. Park, “Dynamic active wave plate using random nanoparticles,” Opt. Express 20(15), 17010–17016 (2012).
[Crossref]

Paxman, R.

Piestun, R.

Pinkse, P. W.

Popoff, S.

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

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1(6), 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(10), 100601 (2010).
[Crossref] [PubMed]

Righini, R.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[Crossref]

Rodriguez, C.

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y. H. Lee, Y. H. Cho, and Y. Park, “Full-Field Subwavelength Imaging Using a Scattering Superlens,” Phys. Rev. Lett. 113(11), 113901 (2014).
[Crossref] [PubMed]

Seelig, E.

H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Shin, J.

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y. H. Lee, Y. H. Cho, and Y. Park, “Full-Field Subwavelength Imaging Using a Scattering Superlens,” Phys. Rev. Lett. 113(11), 113901 (2014).
[Crossref] [PubMed]

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–458 (2013).
[Crossref]

Škoric, B.

Tay, J. W.

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(2), 126–132 (2015).
[Crossref]

Toussaint, K. C.

Tripathi, S.

Vellekoop, I.

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

Vellekoop, I. M.

I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett. 101(8), 081108 (2012).
[Crossref] [PubMed]

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101(12), 120601 (2008).
[Crossref] [PubMed]

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

Wang, L.

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(2), 126–132 (2015).
[Crossref]

Wang, L. V.

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(2), 126–132 (2015).
[Crossref]

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5(3), 154–157 (2011).
[Crossref] [PubMed]

Wang, Q.

H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Wang, Y. M.

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(4), 300–305 (2013).
[Crossref] [PubMed]

Wiersma, D. S.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[Crossref]

Xu, X.

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5(3), 154–157 (2011).
[Crossref] [PubMed]

Yamauchi, T.

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. Rep. 3, 1909 (2013).
[Crossref] [PubMed]

Yang, C.

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(4), 300–305 (2013).
[Crossref] [PubMed]

I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett. 101(8), 081108 (2012).
[Crossref] [PubMed]

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(4), 3444–3455 (2010).
[Crossref] [PubMed]

Yaqoob, Z.

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. Rep. 3, 1909 (2013).
[Crossref] [PubMed]

Yoon, C.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
[Crossref]

Yoon, J.

H. Yu, J. Park, K. Lee, J. Yoon, K. Kim, S. Lee, and Y. Park, “Recent advances in wavefront shaping techniques for biomedical applications,” Curr. Appl. Phys. 15(5), 632–641 (2015).
[Crossref]

Yu, H.

H. Yu, J. Park, K. Lee, J. Yoon, K. Kim, S. Lee, and Y. Park, “Recent advances in wavefront shaping techniques for biomedical applications,” Curr. Appl. Phys. 15(5), 632–641 (2015).
[Crossref]

J. Park, J.-H. Park, H. Yu, and Y. Park, “Focusing through turbid media by polarization modulation,” Opt. Lett. 40(8), 1667–1670 (2015).
[Crossref]

H. Yu, J. Jang, J. Lim, J.-H. Park, W. Jang, J.-Y. Kim, and Y. Park, “Depth-enhanced 2-D optical coherence tomography using complex wavefront shaping,” Opt. Express 22(7), 7514–7523 (2014).
[PubMed]

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y. H. Lee, Y. H. Cho, and Y. Park, “Full-Field Subwavelength Imaging Using a Scattering Superlens,” Phys. Rev. Lett. 113(11), 113901 (2014).
[Crossref] [PubMed]

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–458 (2013).
[Crossref]

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref] [PubMed]

J. Jang, J. Lim, H. Yu, H. Choi, J. Ha, J. H. Park, W. Y. Oh, W. Jang, S. Lee, and Y. Park, “Complex wavefront shaping for optimal depth-selective focusing in optical coherence tomography,” Opt. Express 21(3), 2890–2902 (2013).
[Crossref] [PubMed]

J.-H. Park, C. Park, H. Yu, Y.-H. Cho, and Y. Park, “Dynamic active wave plate using random nanoparticles,” Opt. Express 20(15), 17010–17016 (2012).
[Crossref]

J. H. Park, C. Park, H. Yu, Y. H. Cho, and Y. Park, “Active spectral filtering through turbid media,” Opt. Lett. 37(15), 3261–3263 (2012).
[Crossref] [PubMed]

Zhao, Y.

H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Appl. Phys. Lett. (1)

I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett. 101(8), 081108 (2012).
[Crossref] [PubMed]

Curr. Appl. Phys. (1)

H. Yu, J. Park, K. Lee, J. Yoon, K. Kim, S. Lee, and Y. Park, “Recent advances in wavefront shaping techniques for biomedical applications,” Curr. Appl. Phys. 15(5), 632–641 (2015).
[Crossref]

Nat. Commun. (2)

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Figures (6)

Fig. 1
Fig. 1 Conceptual diagram of the optical system. The optical field is transferred from a SLM to a camera through a linear optical system (t).
Fig. 2
Fig. 2 Schematics for each step of the TM measurement algorithm. (a) Group1 measurement step. Individual pixels of Group 1 is modulated, while Group 2 stays still to provide a reference field. Required acquisitions are 4G. (b) Group2 measurement step. Identical with (a) but the role of groups are exchanged. Required acquisitions are 4(N-G). (c) Reference phase matching step. Each group rather than each pixel is modulated individually. Required acquisitions are 8.
Fig. 3
Fig. 3 Experimental setup. Used abbreviations are defined as followings: BD, beam dump; SLM, spatial light modulator; P, polarizer; L#, lens; M, mirror; Obj#, objective lens; S, scattering medium.
Fig. 4
Fig. 4 Retrieved optical TM of a turbid medium. (a) The phase information of the retrieved conjugated TM. Row and column correspond to the pixel indexes of the camera and SLM, respectively. (b) The reshaped 2-D map of the m-th row of the conjugated TM, which corresponds to the optimal phase information to be applied to the SLM in order to generate an optical focus at the m-th camera pixel.
Fig. 5
Fig. 5 Focusing through a turbid medium using retrieved TM information. (a) Diagonal focus movements by displaying the corresponding optimal phase map on the SLM. The numbers above each image indicate the (x, y) coordinate of target foci. (b) Multiple foci formation with a linear combination of optimal phase maps.
Fig. 6
Fig. 6 Controlling the intensities of generated foci. (a) Images of two optimized foci obtained with a different fraction value ��12. (b) the intensities of two optimized foci as a function of the fraction value.

Equations (11)

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|ψ= n=1 N t| x n ,
y m |ψ= n=1 N y m |t| x n .
|ψ=|R+|S= n=G+1 N t| x n + n=1 G t| x n e i ω n t ,
| y m |ψ | 2 = | y m |R | 2 + p,q=1 G t mp * t mq e i( ω q ω p )t + y m |R * p=1 G t mp e i ω p t + y m |R p=1 G t mp * e i ω p t .
Group 1 : ( r m0 + r m2 ) * ( t m1 , t m2 ,, t mG ) Group 2 : ( r m0 + r m1 ) * ( t m( G+1 ) , t m( G+2 ) ,, t mN )
|ψ=| R 0 +| R 1 e i ω 1 t +| R 2 e i ω 2 t ,
C= ( r m0 + r m2 ) * ( r m0 + r m1 )= | r m0 | 2 + r m0 * r m1 + r m2 * r m0 + r m2 * r m1 = ( r m0 * r m2 ) * ( r m0 * r m1 ) r m2 * r m1 + r m0 * r m1 + ( r m0 * r m2 ) * + r m2 * r m1 ,
Group 1 : | r m0 + r m2 | | r m0 + r m2 | ( r m0 + r m2 ) * ( t m1 , t m2 ,, t mG ) Group 2 : | r m0 + r m1 | | r m0 + r m2 | ( r m0 + r m2 ) * ( t m( G+1 ) , t m( G+2 ) ,, t mN ).
Group 1 : | r m0 + r m2 |( t m1 , t m2 ,, t mG ) Group 2 : | r m0 + r m1 |( t m( G+1 ) , t m( G+2 ) ,, t mN ).
| SL M opt =( m Y 1 Y t | y m ).
| SL M opt =( m Y α m t | y m ).

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