Abstract

Wavefront shaping makes it possible to form a focus through opaque scattering materials. In some cases, this focus may be scanned over a small distance using the optical memory effect. However, in many cases of interest, the optical memory effect has a limited range or is even too small to be measured. In such cases, one often resorts to measuring the full transmission matrix (TM) of the sample to completely control the light transmission. However, this process is time-consuming and may not always be possible. We introduce a new method, to the best of our knowledge, for focusing and scanning the focus at any arbitrary position behind the medium by measuring only a subset of the TM, called sparse field focusing (SFF). With SFF, the scan range is not limited to the memory effect, and there is no need to measure the full TM. Our experimental results agree well with our theoretical model. We expect that this method will find applications in imaging through scattering media, especially when the optical memory effect range is small.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  2. J. Kubby, S. Gigan, and M. Cui, Wavefront Shaping for Biomedical Imaging, Advances in Microscopy and Microanalysis (Cambridge University, 2019).
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    [Crossref]
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    [Crossref]
  5. S. Schott, J. Bertolotti, J.-F. Léger, L. Bourdieu, and S. Gigan, Opt. Express 23, 13505 (2015).
    [Crossref]
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    [Crossref]
  7. G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, Optica 4, 886 (2017).
    [Crossref]
  8. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  19. I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, Opt. Express 16, 67 (2008).
    [Crossref]
  20. C.-L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, Opt. Express 18, 12283 (2010).
    [Crossref]
  21. J. Aulbach, B. Gjonaj, P. Johnson, and A. Lagendijk, Opt. Express 20, 29237 (2012).
    [Crossref]
  22. O. Katz, E. Small, Y. Guan, and Y. Silberberg, Optica 1, 170 (2014).
    [Crossref]
  23. J. Goodman, Introduction to Fourier Optics, McGraw-Hill Physical and Quantum Electronics Series (W. H. Freeman, 2005).

2017 (1)

2015 (6)

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, Nat. Phys. 11, 684 (2015).
[Crossref]

J.-H. Park, W. Sun, and M. Cui, Proc. Natl. Acad. Sci. USA 112, 9236 (2015).
[Crossref]

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, Nat. Commun. 6, 7276 (2015).
[Crossref]

I. M. Vellekoop, Opt. Express 23, 12189 (2015).
[Crossref]

M. Kim, W. Choi, Y. Choi, C. Yoon, and W. Choi, Opt. Express 23, 12648 (2015).
[Crossref]

S. Schott, J. Bertolotti, J.-F. Léger, L. Bourdieu, and S. Gigan, Opt. Express 23, 13505 (2015).
[Crossref]

2014 (1)

2013 (2)

H. Yilmaz, W. L. Vos, and A. P. Mosk, Biomed. Opt. Express 4, 1759 (2013).
[Crossref]

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, Phys. Rev. Lett. 111, 153902 (2013).
[Crossref]

2012 (2)

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[Crossref]

J. Aulbach, B. Gjonaj, P. Johnson, and A. Lagendijk, Opt. Express 20, 29237 (2012).
[Crossref]

2010 (4)

I. M. Vellekoop and C. M. Aegerter, Opt. Lett. 35, 1245 (2010).
[Crossref]

C.-L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, Opt. Express 18, 12283 (2010).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Nat. Commun. 1, 81 (2010).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

2008 (2)

2007 (1)

Aegerter, C. M.

Aulbach, J.

Bertolotti, J.

Betzig, E.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, Nat. Commun. 6, 7276 (2015).
[Crossref]

Boccara, A. C.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Nat. Commun. 1, 81 (2010).
[Crossref]

Bourdieu, L.

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Choi, W.

Choi, Y.

Cui, M.

J.-H. Park, W. Sun, and M. Cui, Proc. Natl. Acad. Sci. USA 112, 9236 (2015).
[Crossref]

J. Kubby, S. Gigan, and M. Cui, Wavefront Shaping for Biomedical Imaging, Advances in Microscopy and Microanalysis (Cambridge University, 2019).

Dasari, R. R.

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, Phys. Rev. Lett. 111, 153902 (2013).
[Crossref]

Feld, M. S.

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, Phys. Rev. Lett. 111, 153902 (2013).
[Crossref]

Fink, M.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Nat. Commun. 1, 81 (2010).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Gigan, S.

S. Schott, J. Bertolotti, J.-F. Léger, L. Bourdieu, and S. Gigan, Opt. Express 23, 13505 (2015).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Nat. Commun. 1, 81 (2010).
[Crossref]

J. Kubby, S. Gigan, and M. Cui, Wavefront Shaping for Biomedical Imaging, Advances in Microscopy and Microanalysis (Cambridge University, 2019).

Gjonaj, B.

Goodman, J.

J. Goodman, Introduction to Fourier Optics, McGraw-Hill Physical and Quantum Electronics Series (W. H. Freeman, 2005).

Grange, R.

Guan, Y.

Harvey, B. K.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, Nat. Commun. 6, 7276 (2015).
[Crossref]

Hillman, T. R.

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, Phys. Rev. Lett. 111, 153902 (2013).
[Crossref]

Horstmeyer, R.

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, Optica 4, 886 (2017).
[Crossref]

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, Nat. Phys. 11, 684 (2015).
[Crossref]

Hsieh, C.-L.

Ji, N.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, Nat. Commun. 6, 7276 (2015).
[Crossref]

Johnson, P.

Judkewitz, B.

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, Optica 4, 886 (2017).
[Crossref]

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, Nat. Phys. 11, 684 (2015).
[Crossref]

Katz, O.

Kim, M.

Kubby, J.

J. Kubby, S. Gigan, and M. Cui, Wavefront Shaping for Biomedical Imaging, Advances in Microscopy and Microanalysis (Cambridge University, 2019).

Labouesse, S.

O. Tzang, E. Niv, S. Singh, S. Labouesse, G. Myatt, and R. Piestun, Nat. Photonics, 1 (2019).
[Crossref]

Lagendijk, A.

Lee, J. O.

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, Phys. Rev. Lett. 111, 153902 (2013).
[Crossref]

Léger, J.-F.

Lerosey, G.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Nat. Commun. 1, 81 (2010).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Mosk, A. P.

Myatt, G.

O. Tzang, E. Niv, S. Singh, S. Labouesse, G. Myatt, and R. Piestun, Nat. Photonics, 1 (2019).
[Crossref]

Niv, E.

O. Tzang, E. Niv, S. Singh, S. Labouesse, G. Myatt, and R. Piestun, Nat. Photonics, 1 (2019).
[Crossref]

Osnabrugge, G.

Papadopoulos, I. N.

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, Optica 4, 886 (2017).
[Crossref]

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, Nat. Phys. 11, 684 (2015).
[Crossref]

Park, J.-H.

J.-H. Park, W. Sun, and M. Cui, Proc. Natl. Acad. Sci. USA 112, 9236 (2015).
[Crossref]

Park, Y.

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, Phys. Rev. Lett. 111, 153902 (2013).
[Crossref]

Piestun, R.

O. Tzang, E. Niv, S. Singh, S. Labouesse, G. Myatt, and R. Piestun, Nat. Photonics, 1 (2019).
[Crossref]

Popoff, S.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Nat. Commun. 1, 81 (2010).
[Crossref]

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Psaltis, D.

Pu, Y.

Richie, C. T.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, Nat. Commun. 6, 7276 (2015).
[Crossref]

Schott, S.

Silberberg, Y.

Singh, S.

O. Tzang, E. Niv, S. Singh, S. Labouesse, G. Myatt, and R. Piestun, Nat. Photonics, 1 (2019).
[Crossref]

Small, E.

Sun, W.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, Nat. Commun. 6, 7276 (2015).
[Crossref]

J.-H. Park, W. Sun, and M. Cui, Proc. Natl. Acad. Sci. USA 112, 9236 (2015).
[Crossref]

Tzang, O.

O. Tzang, E. Niv, S. Singh, S. Labouesse, G. Myatt, and R. Piestun, Nat. Photonics, 1 (2019).
[Crossref]

van Putten, E. G.

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, Opt. Express 16, 67 (2008).
[Crossref]

E. G. van Putten, “Disorder-enhanced imaging with spatially controlled light,” Ph.D. thesis (University of Twente, 2011).

Vellekoop, I. M.

Vos, W. L.

Wang, K.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, Nat. Commun. 6, 7276 (2015).
[Crossref]

Yang, C.

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, Nat. Phys. 11, 684 (2015).
[Crossref]

Yilmaz, H.

Yoon, C.

Yu, H.

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, Phys. Rev. Lett. 111, 153902 (2013).
[Crossref]

Biomed. Opt. Express (1)

Nat. Commun. (2)

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, Nat. Commun. 6, 7276 (2015).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Nat. Commun. 1, 81 (2010).
[Crossref]

Nat. Photonics (1)

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[Crossref]

Nat. Phys. (1)

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, Nat. Phys. 11, 684 (2015).
[Crossref]

Opt. Commun. (1)

I. M. Vellekoop and A. P. Mosk, Opt. Commun. 281, 3071 (2008).
[Crossref]

Opt. Express (6)

Opt. Lett. (2)

Optica (2)

Phys. Rev. Lett. (2)

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, Phys. Rev. Lett. 111, 153902 (2013).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

J.-H. Park, W. Sun, and M. Cui, Proc. Natl. Acad. Sci. USA 112, 9236 (2015).
[Crossref]

Other (4)

J. Kubby, S. Gigan, and M. Cui, Wavefront Shaping for Biomedical Imaging, Advances in Microscopy and Microanalysis (Cambridge University, 2019).

J. Goodman, Introduction to Fourier Optics, McGraw-Hill Physical and Quantum Electronics Series (W. H. Freeman, 2005).

O. Tzang, E. Niv, S. Singh, S. Labouesse, G. Myatt, and R. Piestun, Nat. Photonics, 1 (2019).
[Crossref]

E. G. van Putten, “Disorder-enhanced imaging with spatially controlled light,” Ph.D. thesis (University of Twente, 2011).

Supplementary Material (1)

NameDescription
» Visualization 1       Scanning the focus through the scattering medium using sparse field focusing.

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Figures (3)

Fig. 1.
Fig. 1. Focusing and scanning via (a), (b) conventional methods and (c), (d) SFF. (a) Focusing scattered light through a turbid medium. (b) Shifting the incident wavefront destroys the focus. (c) Discrete set of shaped waves illuminates the medium. The focus is formed by the superposition of the resulting plane waves in the image plane. (d) Changing the relative phase (solid line) between wavefronts makes the focus move. Note: for clarity, only three non-overlapping incident waves are drawn. In the experiment, several hundreds of overlapping incident waves are used.
Fig. 2.
Fig. 2. Schematic of the experimental setup. HWP, half-wave plate; M, mirror; BS, 50% non-polarizing beam splitter; P, polarizer; CMOS, complementary metal oxide semiconductor camera; obj, microscope objective lens; L1, L2, L3, L4, and L5, lenses with focal lengths of 150, 75, 100, 150, and 200 mm. The inset shows the distribution of 500 targets on CMOS1, and the circle around the targets corresponds to the back pupil of obj2.
Fig. 3.
Fig. 3. Intensity at the image plane (a) with a non-shaped incident beam and (b) when combining 500 optimized plane waves. The acquired focus is 47 times brighter than the original speckle pattern. (c) Intensity profile of the formed focus at the image plane. The dashed line is the intensity profile of the theoretical diffraction-limited focus. (d) Measured intensity enhancement as a function of the displacement from the center for the vertical scanning (blue circles). The predicted value for the enhancement, as given by Eq. (2), is represented by the red solid line.

Equations (11)

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E ( x , y ) = m = 1 M A m ( x , y ) exp ( i k m x x + i k m y y + i φ m ) + E bg ,
η ( x , y ) = | γ | 2 M ( N 1 ) N s F ( x , y ) + 1 ,
A = n M .
E b = a = 1 N t b a E a ,
E k m b E b exp ( i k m b ) ,
E ^ a = D γ m = 1 M b t b a * exp ( i k m b ) + m = 1 M 1 | γ | 2 N M ζ a m ,
| γ | 2 = π 4 SNR 1 + SNR ,
E ^ b = a = 1 N t b a D γ m = 1 M b t b a * exp ( i k m b ) + a = 1 N t b a m = 1 M 1 | γ | 2 N M ζ a m ,
| E ^ b | 2 = | γ | 2 M ( N 1 ) | t b a | 2 2 b | t b a | 2 + | t b a | 2 ,
η ( β ) = | γ | 2 M ( N 1 ) | t β a | 2 b | t b a | 2 + 1 ,
η ( β ) = | γ | 2 M ( N 1 ) N s | t β a | 2 max | t b a | 2 + 1 .

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