Abstract

We show theoretically that high-order thermal ghost imaging has considerably higher visibility and contrast-to-noise ratio than conventional thermal ghost imaging, which utilizes the lowest-order intensity cross correlation of the object and the reference signal. We also deduce the optimal power order of the correlation that gives the best contrast-to-noise ratio.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
    [CrossRef] [PubMed]
  2. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
    [CrossRef]
  3. A. Valencia, G. Scarcelli, M. D'Angelo, and Y. H. Shih, Phys. Rev. Lett. 94, 063601 (2005).
    [CrossRef] [PubMed]
  4. K. W. C. Chan, M. N. O'Sullivan, and R. W. Boyd, Phys. Rev. A 79, 033808 (2009).
    [CrossRef]
  5. G. Scarcelli, V. Berardi, and Y. H. Shih, Phys. Rev. Lett. 96, 063602 (2006).
    [CrossRef] [PubMed]
  6. A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, Phys. Rev. Lett. 98, 039301 (2007).
    [CrossRef] [PubMed]
  7. B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 77, 043809 (2008).
    [CrossRef]
  8. L.-G. Wang, S. Qamar, S.-Y. Zhu, and M. S. Zubairy, Phys. Rev. A 79, 033835 (2009).
    [CrossRef]
  9. J. H. Shapiro, Phys. Rev. A 78, 061802 (2008).
    [CrossRef]
  10. Y. Bromberg, O. Katz, and Y. Silberberg, Phys. Rev. A 79, 053840 (2009).
    [CrossRef]
  11. L. Basano and P. Ottonello, Opt. Express 15, 12386 (2007).
    [CrossRef] [PubMed]
  12. D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
    [CrossRef]
  13. B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 79, 023833 (2009).
    [CrossRef]
  14. O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
    [CrossRef]

2009

K. W. C. Chan, M. N. O'Sullivan, and R. W. Boyd, Phys. Rev. A 79, 033808 (2009).
[CrossRef]

L.-G. Wang, S. Qamar, S.-Y. Zhu, and M. S. Zubairy, Phys. Rev. A 79, 033835 (2009).
[CrossRef]

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

B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 79, 023833 (2009).
[CrossRef]

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

2008

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 77, 043809 (2008).
[CrossRef]

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

2007

A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, Phys. Rev. Lett. 98, 039301 (2007).
[CrossRef] [PubMed]

L. Basano and P. Ottonello, Opt. Express 15, 12386 (2007).
[CrossRef] [PubMed]

2006

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

2005

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

2004

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

1995

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

Bache, M.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Basano, L.

Berardi, V.

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

Bondani, M.

A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, Phys. Rev. Lett. 98, 039301 (2007).
[CrossRef] [PubMed]

Boyd, R. W.

K. W. C. Chan, M. N. O'Sullivan, and R. W. Boyd, Phys. Rev. A 79, 033808 (2009).
[CrossRef]

Brambilla, E.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Bromberg, 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]

Cao, D.-Z.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Chan, K. W. C.

K. W. C. Chan, M. N. O'Sullivan, and R. W. Boyd, Phys. Rev. A 79, 033808 (2009).
[CrossRef]

D'Angelo, M.

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

Erkmen, B. I.

B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 79, 023833 (2009).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 77, 043809 (2008).
[CrossRef]

Fabre, C.

A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, Phys. Rev. Lett. 98, 039301 (2007).
[CrossRef] [PubMed]

Gao, L.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Gatti, A.

A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, Phys. Rev. Lett. 98, 039301 (2007).
[CrossRef] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Katz, O.

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]

Lin, L.-F.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Lugiato, L. A.

A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, Phys. Rev. Lett. 98, 039301 (2007).
[CrossRef] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

O'Sullivan, M. N.

K. W. C. Chan, M. N. O'Sullivan, and R. W. Boyd, Phys. Rev. A 79, 033808 (2009).
[CrossRef]

Ottonello, P.

Paris, M. G. A.

A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, Phys. Rev. Lett. 98, 039301 (2007).
[CrossRef] [PubMed]

Pittman, T. B.

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

Qamar, S.

L.-G. Wang, S. Qamar, S.-Y. Zhu, and M. S. Zubairy, Phys. Rev. A 79, 033835 (2009).
[CrossRef]

Scarcelli, G.

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

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

Sergienko, A. V.

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

Shapiro, J. H.

B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 79, 023833 (2009).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 77, 043809 (2008).
[CrossRef]

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

Shih, Y. H.

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

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

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

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] [PubMed]

Valencia, A.

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

Wang, K.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Wang, L.-G.

L.-G. Wang, S. Qamar, S.-Y. Zhu, and M. S. Zubairy, Phys. Rev. A 79, 033835 (2009).
[CrossRef]

Xiong, J.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Zhang, S.-H.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Zhu, S.-Y.

L.-G. Wang, S. Qamar, S.-Y. Zhu, and M. S. Zubairy, Phys. Rev. A 79, 033835 (2009).
[CrossRef]

Zubairy, M. S.

L.-G. Wang, S. Qamar, S.-Y. Zhu, and M. S. Zubairy, Phys. Rev. A 79, 033835 (2009).
[CrossRef]

Appl. Phys. Lett.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

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

Opt. Express

Phys. Rev. A

B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 79, 023833 (2009).
[CrossRef]

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

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

K. W. C. Chan, M. N. O'Sullivan, and R. W. Boyd, Phys. Rev. A 79, 033808 (2009).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 77, 043809 (2008).
[CrossRef]

L.-G. Wang, S. Qamar, S.-Y. Zhu, and M. S. Zubairy, Phys. Rev. A 79, 033835 (2009).
[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]

Phys. Rev. Lett.

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

A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, Phys. Rev. Lett. 98, 039301 (2007).
[CrossRef] [PubMed]

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

(a) Schematic representation of lensless thermal ghost imaging. (b) Simplified object model for analysis. The object plane (upper) and the reference detector plane (lower) are discretized by pixels of finite sizes. The light falling on a pixel is assumed to be statistically independent of that on other pixels.

Fig. 2
Fig. 2

(a) Plots of the visibility V m , n and the contrast-to-noise ratio CNR m , n N as functions of m and n using Eqs. (7a, 8) with T = 45 . (b) Plots of V m , n and CNR m , n N as functions of m and n for numerical simulations of a one-dimensional double slit using pseudothermal light. The field spatial correlation is given by E * ( x ) E ( x ) = μ exp ( ( x x ) 2 ( Δ x ) 2 ) with Δ x = 0.01 , which gives a CNR opt that corresponds to T 45 . The speckle size Δ speckle 2 ( Δ x 2 ) and the number of speckles covering the slits T speckle = 0.8 Δ speckle 57 . The simulation grid size is 0.001. The number of samplings is taken to be N = 500,000 to obtain good results for large n. (c) Reconstructed conventional ghost image G 1 , 1 ( x ) and optimal ghost image G 6 , 1 ( x ) with the background normalized to 1.

Fig. 3
Fig. 3

(a) Plot of the CNR as a function of T. The solid line shows the optimal CNR, whereas the dashed curve shows the CNR for conventional thermal ghost imaging. (b) Plots of the optimal bucket signal order m and reference signal order n for the CNR. The data points shown on the figures are from the numerical simulations using delta correlations (+) with T = 1 , 10, 20, 50, and 100, and Gaussian correlations E * ( x ) E ( x ) = μ exp ( ( x x ) 2 ( Δ x ) 2 ) (×) with Δ x = 0.05 , 0.02, 0.01, 0.002, and 0.001. The effective T s for the Gaussian cases are obtained by matching the calculated CNR opt with the theory and are found to be T 9 , 22, 45, 224, and 460. The number of speckles covering the slits T speckle 11 , 28, 57, 283, and 567 (see the caption of Fig. 2). The simulation grid size for the Gaussian correlation is 0.001, and that for the delta correlation is adjusted to give the desired values of T.

Equations (10)

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

G m , n ( x ) = 1 N s = 1 N [ I o ( s ) ] m [ I ( s ) ( x ) ] n ,
I o ( s ) = d y O ( y ) I ( s ) ( y )
I o ( s ) = y in T I ( s ) ( y in ) ,
G m , n ( x in ) = ( T + m + n 1 ) ! n ! ( T + n 1 ) ! μ m + n ,
G m , n ( x out ) = ( T + m 1 ) ! n ! ( T 1 ) ! μ m + n ,
[ y in T I ( s ) ( y in ) ] m = ( T + m 1 ) ! ( T 1 ) ! μ m
[ Δ G m , n ( x ) ] 2 = [ G m , n ( x ) ] 2 G m , n ( x ) 2 = [ G 2 m , 2 n ( x ) G m , n ( x ) 2 ] N .
V m , n = G m , n ( x in ) G m , n ( x out ) G m , n ( x in ) + G m , n ( x out ) = 1 2 [ 1 + ( T + m + n 1 ) ! ( T 1 ) ! ( T + m 1 ) ! ( T + n 1 ) ! ] 1
tanh ( m n 2 T ) , for T m , n .
CNR m , n = G m , n ( x in ) G m , n ( x out ) Δ G m , n ( x in ) + Δ G m , n ( x out ) = 2 V m , n ( 1 + V m , n SNR m , n ( in ) + 1 V m , n SNR m , n ( out ) ) ,

Metrics