Abstract

We demonstrate quantitative nonlinear recovery of images that have been hidden by the addition of partially coherent light. The method assumes a simple model for spatial nonlinearity that allows direct Laplacian inversion based on intensity transport.

© 2013 Optical Society of America

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References

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  1. D. V. Dylov and J. W. Fleischer, Nat. Photonics 4, 323 (2010).
    [CrossRef]
  2. D. Dylov, L. Waller, and J. Fleischer, Opt. Lett. 36, 3711 (2011).
    [CrossRef]
  3. D. V. Dylov, L. Waller, and J. W. Fleischer, IEEE J. Sel. Topics Quantum Electron. 18, 916 (2011).
  4. D. Christodoulides, T. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
    [CrossRef]
  5. A. Shiratori and M. Obara, Rev. Sci. Instrum. 69, 3741 (1998).
    [CrossRef]
  6. M. Teague, J. Opt. Soc. Am. 73, 1434 (1983).
    [CrossRef]
  7. A. Barty, K. Nugent, D. Paganin, and A. Roberts, Opt. Lett. 23, 817 (1998).
    [CrossRef]
  8. N. Streibl, Opt. Commun. 49, 6 (1984).
    [CrossRef]
  9. D. Paganin and K. Nugent, Opt. Lett. 27, 622 (2002).
    [CrossRef]
  10. T. Gureyev and K. Nugent, Opt. Commun. 4018, 339 (1997).
  11. N. Loomis, L. Waller, and G. Barbastathis, in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JMA7.
  12. L. Waller, L. Tian, and G. Barbastathis, Opt. Express 18, 12552 (2010).
    [CrossRef]
  13. C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
    [CrossRef]
  14. A. Zysk, R. Schoonover, P. S. Carney, and M. Anastasio, Opt. Lett. 35, 2239 (2010).
    [CrossRef]
  15. M. Soljacic, M. Segev, T. Coskun, D. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
    [CrossRef]

2011 (2)

D. Dylov, L. Waller, and J. Fleischer, Opt. Lett. 36, 3711 (2011).
[CrossRef]

D. V. Dylov, L. Waller, and J. W. Fleischer, IEEE J. Sel. Topics Quantum Electron. 18, 916 (2011).

2010 (3)

2009 (1)

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
[CrossRef]

2002 (1)

2000 (1)

M. Soljacic, M. Segev, T. Coskun, D. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

1998 (2)

A. Barty, K. Nugent, D. Paganin, and A. Roberts, Opt. Lett. 23, 817 (1998).
[CrossRef]

A. Shiratori and M. Obara, Rev. Sci. Instrum. 69, 3741 (1998).
[CrossRef]

1997 (2)

D. Christodoulides, T. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

T. Gureyev and K. Nugent, Opt. Commun. 4018, 339 (1997).

1984 (1)

N. Streibl, Opt. Commun. 49, 6 (1984).
[CrossRef]

1983 (1)

Anastasio, M.

Barbastathis, G.

L. Waller, L. Tian, and G. Barbastathis, Opt. Express 18, 12552 (2010).
[CrossRef]

N. Loomis, L. Waller, and G. Barbastathis, in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JMA7.

Barsi, C.

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
[CrossRef]

Barty, A.

Carney, P. S.

Christodoulides, D.

M. Soljacic, M. Segev, T. Coskun, D. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

D. Christodoulides, T. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Coskun, T.

M. Soljacic, M. Segev, T. Coskun, D. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

D. Christodoulides, T. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Dylov, D.

Dylov, D. V.

D. V. Dylov, L. Waller, and J. W. Fleischer, IEEE J. Sel. Topics Quantum Electron. 18, 916 (2011).

D. V. Dylov and J. W. Fleischer, Nat. Photonics 4, 323 (2010).
[CrossRef]

Fleischer, J.

Fleischer, J. W.

D. V. Dylov, L. Waller, and J. W. Fleischer, IEEE J. Sel. Topics Quantum Electron. 18, 916 (2011).

D. V. Dylov and J. W. Fleischer, Nat. Photonics 4, 323 (2010).
[CrossRef]

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
[CrossRef]

Gureyev, T.

T. Gureyev and K. Nugent, Opt. Commun. 4018, 339 (1997).

Loomis, N.

N. Loomis, L. Waller, and G. Barbastathis, in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JMA7.

Mitchell, M.

D. Christodoulides, T. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Nugent, K.

Obara, M.

A. Shiratori and M. Obara, Rev. Sci. Instrum. 69, 3741 (1998).
[CrossRef]

Paganin, D.

Roberts, A.

Schoonover, R.

Segev, M.

M. Soljacic, M. Segev, T. Coskun, D. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

D. Christodoulides, T. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Shiratori, A.

A. Shiratori and M. Obara, Rev. Sci. Instrum. 69, 3741 (1998).
[CrossRef]

Soljacic, M.

M. Soljacic, M. Segev, T. Coskun, D. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

Streibl, N.

N. Streibl, Opt. Commun. 49, 6 (1984).
[CrossRef]

Teague, M.

Tian, L.

Vishwanath, A.

M. Soljacic, M. Segev, T. Coskun, D. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

Waller, L.

D. Dylov, L. Waller, and J. Fleischer, Opt. Lett. 36, 3711 (2011).
[CrossRef]

D. V. Dylov, L. Waller, and J. W. Fleischer, IEEE J. Sel. Topics Quantum Electron. 18, 916 (2011).

L. Waller, L. Tian, and G. Barbastathis, Opt. Express 18, 12552 (2010).
[CrossRef]

N. Loomis, L. Waller, and G. Barbastathis, in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JMA7.

Wan, W.

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
[CrossRef]

Zysk, A.

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

D. V. Dylov, L. Waller, and J. W. Fleischer, IEEE J. Sel. Topics Quantum Electron. 18, 916 (2011).

J. Opt. Soc. Am. (1)

Nat. Photonics (2)

D. V. Dylov and J. W. Fleischer, Nat. Photonics 4, 323 (2010).
[CrossRef]

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
[CrossRef]

Opt. Commun. (2)

T. Gureyev and K. Nugent, Opt. Commun. 4018, 339 (1997).

N. Streibl, Opt. Commun. 49, 6 (1984).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. Lett. (2)

D. Christodoulides, T. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

M. Soljacic, M. Segev, T. Coskun, D. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

Rev. Sci. Instrum. (1)

A. Shiratori and M. Obara, Rev. Sci. Instrum. 69, 3741 (1998).
[CrossRef]

Other (1)

N. Loomis, L. Waller, and G. Barbastathis, in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JMA7.

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup. A weak signal beam is corrupted by additive partially coherent noise and passed through a photorefractive nonlinear crystal.

Fig. 2.
Fig. 2.

Input to the nonlinear crystal. The signal is added to a noise beam, whose intensity is the incoherent sum of many random speckle fields (colored curves).

Fig. 3.
Fig. 3.

Simulated intensity images of a weak signal being recovered quantitatively by nonlinear propagation.

Fig. 4.
Fig. 4.

Experimental demonstration of quantitative recovery of a low-level signal.

Fig. 5.
Fig. 5.

Simulated results. (Top) Input signal, nonlinear output intensity and Laplacian solution for γ=0.8×104. (Middle) One-dimensional cross-sections as nonlinearity is increased. (Bottom) Correlations with the input signal.

Equations (6)

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kIz=·(Iϕ),
ϕ(x,y)=kδzγ(Is+In),
Iz=γδz[(Is)2+(Is+In)2Is].
Iz=γδzIn2Is.
Ioutγ(δz)2In2Is,
Is=2(Iout/γ)(δz)2In.

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