Abstract

Ghost imaging has attracted much attention, in which the object can be reconstructed by using the correlation of intensity fluctuations. It is well known that a large number of realizations (such as 5000 or even 20,000) are usually required for object reconstructions in ghost imaging. In this Letter, we demonstrate, for the first time to our knowledge, how the reconstructed object can be authenticated using the significantly small number of realizations (i.e., less than 5% of Nyquist limit) in computational ghost imaging. The main objective for our study is to authenticate the object reconstructed by using the small number of realizations rather than to directly extract the high-fidelity object.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012 (2)

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, Phys. Rev. A 86, 041803 (2012).
[CrossRef]

K. W. C. Chan, Opt. Lett. 37, 2739 (2012).
[CrossRef]

2011 (2)

D. Venkatraman, N. D. Hardy, F. N. C. Wong, and J. H. Shapiro, Opt. Lett. 36, 3684 (2011).
[CrossRef]

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, Phys. Rev. A 84, 061804 (2011).
[CrossRef]

2010 (2)

B. I. Erkmen and J. H. Shapiro, Adv. Opt. Photon. 2, 405 (2010).
[CrossRef]

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

2009 (3)

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

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

Y. Cai, Q. Lin, and O. Korotkova, Opt. Express 17, 2453 (2009).
[CrossRef]

2008 (2)

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

R. Meyers, K. S. Deacon, and Y. Shih, Phys. Rev. A 77, 041801 (2008).
[CrossRef]

2006 (1)

G. Scarcelli, V. Berardi, and Y. Shih, Phys. Rev. Lett. 96, 063602 (2006).
[CrossRef]

2002 (1)

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

1995 (1)

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef]

1989 (1)

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]

Berardi, V.

G. Scarcelli, V. Berardi, and Y. Shih, Phys. Rev. Lett. 96, 063602 (2006).
[CrossRef]

Boyd, R. W.

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, Phys. Rev. A 84, 061804 (2011).
[CrossRef]

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]

Cai, Y.

Chan, K. W. C.

K. W. C. Chan, Opt. Lett. 37, 2739 (2012).
[CrossRef]

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, Phys. Rev. A 84, 061804 (2011).
[CrossRef]

Clemente, P.

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, Phys. Rev. A 86, 041803 (2012).
[CrossRef]

Deacon, K. S.

R. Meyers, K. S. Deacon, and Y. Shih, Phys. Rev. A 77, 041801 (2008).
[CrossRef]

Durán, V.

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, Phys. Rev. A 86, 041803 (2012).
[CrossRef]

Erkmen, B. I.

Ferri, F.

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

Gatti, A.

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

Hardy, N. D.

Howell, J. C.

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, Phys. Rev. A 84, 061804 (2011).
[CrossRef]

Javidi, B.

B. Javidi, Appl. Opt. 28, 2358 (1989).
[CrossRef]

F. Sadjadi and B. Javidi, Physics of Automatic Target Recognition (Springer, 2007).

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]

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef]

Korotkova, O.

Lancis, J.

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, Phys. Rev. A 86, 041803 (2012).
[CrossRef]

Lin, Q.

Lugiato, L. A.

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

Magatti, D.

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

Meyers, R.

R. Meyers, K. S. Deacon, and Y. Shih, Phys. Rev. A 77, 041801 (2008).
[CrossRef]

Sadjadi, F.

F. Sadjadi and B. Javidi, Physics of Automatic Target Recognition (Springer, 2007).

Scarcelli, G.

G. Scarcelli, V. Berardi, and Y. Shih, Phys. Rev. Lett. 96, 063602 (2006).
[CrossRef]

Sergienko, A. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef]

Shapiro, J. H.

Shih, Y.

R. Meyers, K. S. Deacon, and Y. Shih, Phys. Rev. A 77, 041801 (2008).
[CrossRef]

G. Scarcelli, V. Berardi, and Y. Shih, Phys. Rev. Lett. 96, 063602 (2006).
[CrossRef]

Shih, Y. H.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef]

Silberberg, Y.

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

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

Strekalov, D. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef]

Tajahuerce, E.

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, Phys. Rev. A 86, 041803 (2012).
[CrossRef]

Torres-Company, V.

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, Phys. Rev. A 86, 041803 (2012).
[CrossRef]

Venkatraman, D.

Wong, F. N. C.

Zerom, P.

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, Phys. Rev. A 84, 061804 (2011).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. Lett. (1)

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

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (5)

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, Phys. Rev. A 84, 061804 (2011).
[CrossRef]

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

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

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, Phys. Rev. A 86, 041803 (2012).
[CrossRef]

R. Meyers, K. S. Deacon, and Y. Shih, Phys. Rev. A 77, 041801 (2008).
[CrossRef]

Phys. Rev. Lett. (4)

G. Scarcelli, V. Berardi, and Y. Shih, Phys. Rev. Lett. 96, 063602 (2006).
[CrossRef]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef]

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

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

Other (1)

F. Sadjadi and B. Javidi, Physics of Automatic Target Recognition (Springer, 2007).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic experimental setup: SLM, spatial light modulator; BSC, nonpolarizing beam splitter cube; CCD, 2D charge-coupled device.

Fig. 2.
Fig. 2.

Flow chart for the optical object (information) authentication in computational ghost imaging using a significantly small number of realizations.

Fig. 3.
Fig. 3.

(a) Original object t(ξ,η), (b) reconstructed object (only 4.88% of Nyquist limit), (c) reconstructed object (7.32% of Nyquist limit), (d) and (e) nonlinear correlation maps (k=0.4), respectively corresponding to (b) and (c).

Fig. 4.
Fig. 4.

(a) Reconstructed object and (b) the nonlinear correlation map (k=0.4). 200 realizations are used.

Fig. 5.
Fig. 5.

(a) Similar object s(ξ,η), (b) the reconstructed object, and (c) the nonlinear correlation map between image in (b) and original object t(ξ,η). 200 realizations are used.

Equations (5)

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Ei(ξ,η)=exp[jφi(x,y)]*h(x,y,d),
h(x,y,d)=exp(j2πd/λ)jdλexp[jπdλ(x2+y2)],
Bi=dξdηIi(ξ,η)|t(ξ,η)|2,
ΔG(ξ,η)=BI(ξ,η)BI(ξ,η)=1Ni=1N(Bi{Bi})[Ii(ξ,η){Ii(ξ,η)}],
C(ξ,η)=|IFT(|{FT[ΔG(ξ,η)]}{FT[t(ξ,η)]}|k{FT[ΔG(ξ,η)]}{FT[t(ξ,η)]}|{FT[ΔG(ξ,η)]}{FT[t(ξ,η)]}|)|2,

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