Abstract

The recovered image in ghost imaging (GI) contains an error term when the number of measurements M is limited. By iteratively calculating the high-order error term, the iterative ghost imaging (IGI) approach reconstructs a better image, compared to one recovered using a traditional GI approach, without adding complexity. We first propose an experimental scheme, for which IGI can be realized, namely the narrowed point spread function and exponentially increased signal-to-noise ratio (SNR) are realized. The exponentially increasing SNR when implementing IGI results from the replacement of M with Mk. Thus, a perfect recovery of the unknown object is demonstrated with M slightly bigger than the number of speckles in a typical light field. Based on our theoretical framework from the angle of high-order correlation Rk, the two critical behaviors of the iterative coefficients α and the measurements M are derived and well explained.

© 2014 Optical Society of America

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References

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  1. T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
    [CrossRef]
  2. O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013).
    [CrossRef]
  3. R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
    [CrossRef]
  4. A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, Phys. Rev. Lett. 94, 063601 (2005).
    [CrossRef]
  5. F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
    [CrossRef]
  6. B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
    [CrossRef]
  7. W. Gong and S. Han, Phys. Lett. A 376, 171519 (2012).
  8. W. Gong, P. Zhang, X. Shen, and S. Han, Appl. Phys. Lett. 95, 071110 (2009).
    [CrossRef]
  9. O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
    [CrossRef]
  10. K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, Opt. Lett. 34, 213343 (2009).
  11. J. H. Shapiro, D. Venkatraman, and F. N. C. Wong, Sci. Rep.3, 1849 (2013).
  12. J. H. Shapiro, Phys. Rev. A 78, 061802R (2008).
    [CrossRef]
  13. Y. Bromberg, O. Katz, and Y. Silberberg, Phys. Rev. A 79, 053840 (2009).
    [CrossRef]
  14. I. M. Vellekoop and A. P. Mosk, Phys. Rev. Lett. 101, 120601 (2008).
    [CrossRef]
  15. F. Lemoult, G. Lerosey, J. de Rosny, and M. Fink, Phys. Rev. Lett. 103, 173902 (2009).
    [CrossRef]
  16. J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2006), pp. 90–92.

2013 (2)

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013).
[CrossRef]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

2012 (1)

W. Gong and S. Han, Phys. Lett. A 376, 171519 (2012).

2010 (1)

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

2009 (5)

F. Lemoult, G. Lerosey, J. de Rosny, and M. Fink, Phys. Rev. Lett. 103, 173902 (2009).
[CrossRef]

Y. Bromberg, O. Katz, and Y. Silberberg, Phys. Rev. A 79, 053840 (2009).
[CrossRef]

W. Gong, P. Zhang, X. Shen, and S. Han, Appl. Phys. Lett. 95, 071110 (2009).
[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, Opt. Lett. 34, 213343 (2009).

2008 (2)

J. H. Shapiro, Phys. Rev. A 78, 061802R (2008).
[CrossRef]

I. M. Vellekoop and A. P. Mosk, Phys. Rev. Lett. 101, 120601 (2008).
[CrossRef]

2005 (1)

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

2002 (1)

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef]

1995 (1)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

Bennink, R. S.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef]

Bentley, S. J.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef]

Bowman, A.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Bowman, R.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Boyd, R. W.

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013).
[CrossRef]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, Opt. Lett. 34, 213343 (2009).

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef]

Bromberg, Y.

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Y. Bromberg, O. Katz, and Y. Silberberg, Phys. Rev. A 79, 053840 (2009).
[CrossRef]

Chan, K. W. C.

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, Opt. Lett. 34, 213343 (2009).

D’Angelo, M.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

de Rosny, J.

F. Lemoult, G. Lerosey, J. de Rosny, and M. Fink, Phys. Rev. Lett. 103, 173902 (2009).
[CrossRef]

Edgar, M. P.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Ferri, F.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

Fink, M.

F. Lemoult, G. Lerosey, J. de Rosny, and M. Fink, Phys. Rev. Lett. 103, 173902 (2009).
[CrossRef]

Gatti, A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

Gong, W.

W. Gong and S. Han, Phys. Lett. A 376, 171519 (2012).

W. Gong, P. Zhang, X. Shen, and S. Han, Appl. Phys. Lett. 95, 071110 (2009).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2006), pp. 90–92.

Han, S.

W. Gong and S. Han, Phys. Lett. A 376, 171519 (2012).

W. Gong, P. Zhang, X. Shen, and S. Han, Appl. Phys. Lett. 95, 071110 (2009).
[CrossRef]

Howell, J. C.

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013).
[CrossRef]

Howland, G. A.

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013).
[CrossRef]

Katz, O.

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Y. Bromberg, O. Katz, and Y. Silberberg, Phys. Rev. A 79, 053840 (2009).
[CrossRef]

Lemoult, F.

F. Lemoult, G. Lerosey, J. de Rosny, and M. Fink, Phys. Rev. Lett. 103, 173902 (2009).
[CrossRef]

Lerosey, G.

F. Lemoult, G. Lerosey, J. de Rosny, and M. Fink, Phys. Rev. Lett. 103, 173902 (2009).
[CrossRef]

Lugiato, L. A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

Magaña-Loaiza, O. S.

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013).
[CrossRef]

Magatti, D.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

Malik, M.

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013).
[CrossRef]

Mosk, A. P.

I. M. Vellekoop and A. P. Mosk, Phys. Rev. Lett. 101, 120601 (2008).
[CrossRef]

O’Sullivan, M. N.

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, Opt. Lett. 34, 213343 (2009).

Padgett, M. J.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

Scarcelli, G.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

Sergienko, A. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

Shapiro, J. H.

J. H. Shapiro, Phys. Rev. A 78, 061802R (2008).
[CrossRef]

J. H. Shapiro, D. Venkatraman, and F. N. C. Wong, Sci. Rep.3, 1849 (2013).

Shen, X.

W. Gong, P. Zhang, X. Shen, and S. Han, Appl. Phys. Lett. 95, 071110 (2009).
[CrossRef]

Shih, Y.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

Shih, Y. H.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

Silberberg, Y.

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Y. Bromberg, O. Katz, and Y. Silberberg, Phys. Rev. A 79, 053840 (2009).
[CrossRef]

Strekalov, D. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

Sun, B.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Valencia, A.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

Vellekoop, I. M.

I. M. Vellekoop and A. P. Mosk, Phys. Rev. Lett. 101, 120601 (2008).
[CrossRef]

Venkatraman, D.

J. H. Shapiro, D. Venkatraman, and F. N. C. Wong, Sci. Rep.3, 1849 (2013).

Vittert, L. E.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Welsh, S.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Wong, F. N. C.

J. H. Shapiro, D. Venkatraman, and F. N. C. Wong, Sci. Rep.3, 1849 (2013).

Zhang, P.

W. Gong, P. Zhang, X. Shen, and S. Han, Appl. Phys. Lett. 95, 071110 (2009).
[CrossRef]

Appl. Phys. Lett. (3)

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013).
[CrossRef]

W. Gong, P. Zhang, X. Shen, and S. Han, Appl. Phys. Lett. 95, 071110 (2009).
[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Opt. Lett. (1)

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, Opt. Lett. 34, 213343 (2009).

Phys. Lett. A (1)

W. Gong and S. Han, Phys. Lett. A 376, 171519 (2012).

Phys. Rev. A (3)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

J. H. Shapiro, Phys. Rev. A 78, 061802R (2008).
[CrossRef]

Y. Bromberg, O. Katz, and Y. Silberberg, Phys. Rev. A 79, 053840 (2009).
[CrossRef]

Phys. Rev. Lett. (5)

I. M. Vellekoop and A. P. Mosk, Phys. Rev. Lett. 101, 120601 (2008).
[CrossRef]

F. Lemoult, G. Lerosey, J. de Rosny, and M. Fink, Phys. Rev. Lett. 103, 173902 (2009).
[CrossRef]

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

Science (1)

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Other (2)

J. H. Shapiro, D. Venkatraman, and F. N. C. Wong, Sci. Rep.3, 1849 (2013).

J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2006), pp. 90–92.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram of the experimental setup used for demonstrating IGI. The computer controls the patterns (Am,φm) generated on the spatial light modulator (SLM) and subsequently reconstructs an image using the light intensities Sm collected by a bucket detector.

Fig. 2.
Fig. 2.

Flow sheet of IGI depending on the GI module.

Fig. 3.
Fig. 3.

(a) Normalized PSFs from simulation and IPSFs of IGI for α below the threshold. Acoh=5.3d2. (b) PSFs of IGI with different iterative numbers for Acoh=1.32d2. Overlapping green and red lines implies a final stable PSF. (c) Simulated PSF and theoretical IPSF for α beyond the threshold. (d) Mean-squared error of GI and IGI.

Fig. 4.
Fig. 4.

(a) Unknown object in detection. (b) Recovered images using IGI with different measurements M and iterative numbers N.

Fig. 5.
Fig. 5.

(a) Variances of Rk for three different values of λ2. Inset, the zoomed-in black line shows an uptrend caused by f(k,k1). (b) Demonstration of the linear relationship between Rk and ON. The variance of ON decreases although the SNR of Rk decreases. (c) Exponentially increasing SNR of ON for different λ2. (d) Nonlinear relationship between SNR and M. Enlarged black curve in the inset shows the upper limit of the improvement of SNR is around 1026.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

O(x)=AcohI¯2[Tγ](x),
ON(x)=O1+FO1FNO1=T(x)FNT,
IPSF(x)k=1N(α)kCNk(AcohI¯2)kkexp(x2kδx2).
SNR(ON(x))=OnN(x)¯2ΔOnN(x)2,
α2kM2k1dx2k2δSm2δIm2(x2k2)δIm2(x),
Var(Rk(x))=A11λ2k1k1=1kf(k,k1)(λ1)k11.

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