Abstract

Angular speckle correlations known as the “memory effect” have recently been exploited for noninvasive imaging through scattering layers. Here we show that the information obtained from speckle correlations can be used as a noninvasive feedback mechanism for wavefront shaping. We utilize this feedback to demonstrate noninvasive diffraction-limited focusing of coherent light through thin scattering layers.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

2017 (2)

S. Rotter and S. Gigan, Rev. Mod. Phys. 89, 015005 (2017).
[Crossref]

I. N. Papadopoulos, J. S. Jouhanneau, J. F. Poulet, and B. Judkewitz, Nat. Photonics 11, 116 (2017).
[Crossref]

2016 (1)

2015 (4)

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

P. Lai, L. Wang, J. W. Tay, and L. V. Wang, Nat. Photonics 9, 126 (2015).
[Crossref]

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

R. Horstmeyer, H. Ruan, and C. Yang, Nat. Photonics 9, 563 (2015).
[Crossref]

2014 (3)

2012 (5)

D. B. Conkey, A. M. Caravaca-Aguirre, and R. Piestun, Opt. Express 20, 1733 (2012).
[Crossref]

D. B. Conkey, A. N. Brown, A. M. Caravaca-Aguirre, and R. Piestun, Opt. Express 20, 4840 (2012).
[Crossref]

J. Tang, R. N. Germain, and M. Cui, Proc. Natl. Acad. Sci. USA 109, 8434 (2012).
[Crossref]

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

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, Nature 491, 232 (2012).
[Crossref]

2010 (1)

V. Ntziachristos, Nat. Methods 7, 603 (2010).
[Crossref]

2008 (1)

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

2007 (1)

1990 (1)

I. Freund, Phys. A 168, 49 (1990).
[Crossref]

1988 (2)

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[Crossref]

I. Freund, M. Rosenbluh, and S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
[Crossref]

Aegerter, C. M.

Bertolotti, J.

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, Nature 491, 232 (2012).
[Crossref]

Bourdieu, L.

Brasselet, S.

Brown, A. N.

Caravaca-Aguirre, A. M.

Chang, J.

J. Chang and G. Wetzstein, J. Biophotonics 11, e201700224 (2018).
[Crossref]

Conkey, D. B.

Cui, M.

J. Tang, R. N. Germain, and M. Cui, Proc. Natl. Acad. Sci. USA 109, 8434 (2012).
[Crossref]

Edrei, E.

Feng, S.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[Crossref]

I. Freund, M. Rosenbluh, and S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
[Crossref]

Fink, M.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, Nat. Photonics 8, 784 (2014).
[Crossref]

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

Freund, I.

I. Freund, Phys. A 168, 49 (1990).
[Crossref]

I. Freund, M. Rosenbluh, and S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
[Crossref]

Germain, R. N.

J. Tang, R. N. Germain, and M. Cui, Proc. Natl. Acad. Sci. USA 109, 8434 (2012).
[Crossref]

Ghielmetti, G.

Gigan, S.

S. Rotter and S. Gigan, Rev. Mod. Phys. 89, 015005 (2017).
[Crossref]

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

O. Katz, P. Heidmann, M. Fink, and S. Gigan, Nat. Photonics 8, 784 (2014).
[Crossref]

Goodman, J. W.

J. W. Goodman, Statistical Optics (2015).

Guan, Y.

Heidmann, P.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, Nat. Photonics 8, 784 (2014).
[Crossref]

Hofer, M.

Horstmeyer, R.

R. Horstmeyer, H. Ruan, and C. Yang, Nat. Photonics 9, 563 (2015).
[Crossref]

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

Jouhanneau, J. S.

I. N. Papadopoulos, J. S. Jouhanneau, J. F. Poulet, and B. Judkewitz, Nat. Photonics 11, 116 (2017).
[Crossref]

Judkewitz, B.

I. N. Papadopoulos, J. S. Jouhanneau, J. F. Poulet, and B. Judkewitz, Nat. Photonics 11, 116 (2017).
[Crossref]

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

Kane, C.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[Crossref]

Katz, O.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, Nat. Photonics 8, 784 (2014).
[Crossref]

O. Katz, E. Small, Y. Guan, and Y. Silberberg, Optica 1, 170 (2014).
[Crossref]

Lagendijk, A.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, Nature 491, 232 (2012).
[Crossref]

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

Lai, P.

P. Lai, L. Wang, J. W. Tay, and L. V. Wang, Nat. Photonics 9, 126 (2015).
[Crossref]

Lee, P. A.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[Crossref]

Léger, J.

Lerosey, G.

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

Mosk, A.

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

I. Vellekoop and A. Mosk, Opt. Lett. 32, 2309 (2007).
[Crossref]

Mosk, A. P.

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

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, Nature 491, 232 (2012).
[Crossref]

Ntziachristos, V.

V. Ntziachristos, Nat. Methods 7, 603 (2010).
[Crossref]

Papadopoulos, I. N.

I. N. Papadopoulos, J. S. Jouhanneau, J. F. Poulet, and B. Judkewitz, Nat. Photonics 11, 116 (2017).
[Crossref]

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

Piestun, R.

Poulet, J. F.

I. N. Papadopoulos, J. S. Jouhanneau, J. F. Poulet, and B. Judkewitz, Nat. Photonics 11, 116 (2017).
[Crossref]

Rosenbluh, M.

I. Freund, M. Rosenbluh, and S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
[Crossref]

Rotter, S.

S. Rotter and S. Gigan, Rev. Mod. Phys. 89, 015005 (2017).
[Crossref]

Ruan, H.

R. Horstmeyer, H. Ruan, and C. Yang, Nat. Photonics 9, 563 (2015).
[Crossref]

Scarcelli, G.

Schott, S.

Silberberg, Y.

Small, E.

Soeller, C.

Stone, A. D.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[Crossref]

Tang, J.

J. Tang, R. N. Germain, and M. Cui, Proc. Natl. Acad. Sci. USA 109, 8434 (2012).
[Crossref]

Tay, J. W.

P. Lai, L. Wang, J. W. Tay, and L. V. Wang, Nat. Photonics 9, 126 (2015).
[Crossref]

van Putten, E. G.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, Nature 491, 232 (2012).
[Crossref]

Vellekoop, I.

Vellekoop, I. M.

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

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

Vos, W. L.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, Nature 491, 232 (2012).
[Crossref]

Wang, L.

P. Lai, L. Wang, J. W. Tay, and L. V. Wang, Nat. Photonics 9, 126 (2015).
[Crossref]

Wang, L. V.

P. Lai, L. Wang, J. W. Tay, and L. V. Wang, Nat. Photonics 9, 126 (2015).
[Crossref]

Wetzstein, G.

J. Chang and G. Wetzstein, J. Biophotonics 11, e201700224 (2018).
[Crossref]

Yang, C.

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

R. Horstmeyer, H. Ruan, and C. Yang, Nat. Photonics 9, 563 (2015).
[Crossref]

J. Biophotonics (1)

J. Chang and G. Wetzstein, J. Biophotonics 11, e201700224 (2018).
[Crossref]

Nat. Methods (1)

V. Ntziachristos, Nat. Methods 7, 603 (2010).
[Crossref]

Nat. Photonics (5)

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

R. Horstmeyer, H. Ruan, and C. Yang, Nat. Photonics 9, 563 (2015).
[Crossref]

I. N. Papadopoulos, J. S. Jouhanneau, J. F. Poulet, and B. Judkewitz, Nat. Photonics 11, 116 (2017).
[Crossref]

P. Lai, L. Wang, J. W. Tay, and L. V. Wang, Nat. Photonics 9, 126 (2015).
[Crossref]

O. Katz, P. Heidmann, M. Fink, and S. Gigan, Nat. Photonics 8, 784 (2014).
[Crossref]

Nat. Phys. (1)

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

Nature (1)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, Nature 491, 232 (2012).
[Crossref]

Opt. Commun. (1)

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

Opt. Express (5)

Opt. Lett. (1)

Optica (2)

Phys. A (1)

I. Freund, Phys. A 168, 49 (1990).
[Crossref]

Phys. Rev. Lett. (2)

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[Crossref]

I. Freund, M. Rosenbluh, and S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
[Crossref]

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

J. Tang, R. N. Germain, and M. Cui, Proc. Natl. Acad. Sci. USA 109, 8434 (2012).
[Crossref]

Rev. Mod. Phys. (1)

S. Rotter and S. Gigan, Rev. Mod. Phys. 89, 015005 (2017).
[Crossref]

Other (1)

J. W. Goodman, Statistical Optics (2015).

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Figures (5)

Fig. 1.
Fig. 1. Setup for focusing between two scattering layers via speckle correlations: a laser beam is shaped by an SLM. The shaped beam passes through a first diffuser, reaches the target object (a transmission mask), and is scattered again by a second diffuser. The second diffuser’s surface is imaged on a camera to provide feedback for the focusing process ( u = 6    cm , v = 4    cm , and f 4 = 24    mm ). Inset, close-up view of the considered scenario: a target object with a diameter D obj is illuminated by a speckle field with a speckle grain size of d speckle < D obj . The target is located at a distance of L from the second diffuser. We aim at focusing the light on the target to the diffraction limit ( d speckle ).
Fig. 2.
Fig. 2. Retrieval of a hidden object field autocorrelation (e) from a camera image of the second diffuser’s surface (b)–(d), numerical example. Top row, evolution of the speckle intensity distribution diffracted from a hidden target object, as measured by a camera: (a) target object plane; (b)–(d) diffracted intensity distributions at increasing distances from the object. Bottom row, comparison between (e) the object’s field autocorrelation and (f)–(h) the Fourier transform of the camera images (b)–(d). (The autocorrelation coherent peak is removed for visualization.) The Fourier transform of the speckle intensity (f)–(h) provides an estimate for the object field autocorrelation and, thus, a measure of the illuminated area shape. To achieve focusing, a wavefront-shaping algorithm minimizes the width of this autocorrelation, concentrating light on the target.
Fig. 3.
Fig. 3. Experimental results with a round target object (75 μm diameter pinhole). Top row: initial images of (a) the object, (b) the camera image, and the Fourier transform of the camera image, which provides an estimate of the object autocorrelation, A ( x , y ) , after removing the speckle grain wide central coherent peak (c). (d)–(f) same as (a)–(c) after running the iterative optimization algorithm aimed at minimizing the width of (c) (red circle), resulting in sharp focusing on the object (d). Scale bars, 20 μm.
Fig. 4.
Fig. 4. Experimental results: comparison of the proposed approach and conventional optimization of the total intensity on a complex object. Top row: initial images of the object (a), camera image of the diffuser surface, I cam (b), and the log of the Fourier transform of I cam , providing the estimate for the object’s autocorrelation (c). (d)–(f) same as (a)–(c) after a conventional iterative optimization of the total intensity, (g)–(i) the same as (d)–(f) with the proposed approach, showing sharp focusing. Scale bars, 20 μm.
Fig. 5.
Fig. 5. Numerical comparison of the focus intensity enhancement ( η ) for different (circular) object sizes, averaged over 10 realizations of scatterers. The error bars are one standard deviation. The object size (horizontal axis) is given as the ratio between its diameter to the speckle grain diameter. Insets: final intensity distributions at the object plane.

Equations (2)

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I camera ( x , y ) | E ( x , y , L ) | 2 | F ( E object ( x , y ) ) | 2 ,
F ˜ ( I camera ( x , y ) ) E object E object = A ( x , y ) .

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