Abstract

The spatial longitudinal coherence length (SLCL), which is determined by the size of and the distance from the source, is introduced to investigate the longitudinal resolution of lensless ghost imaging. Its influence is discussed quantitatively by simulation. The discrepancy of position sensitivity between Scarcelli et al. [Appl. Phys. Lett. 88, 061106 (2006) ] and Basano and Ottonello [Appl. Phys. Lett. 88, 091109 (2006) ] is clarified.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. G. Scarcelli, V. Berardi, and Y. Shih, Phys. Rev. Lett. 96, 063602 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2007 (3)

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, Phys. Rev. A 75, 021803(R) (2007).
[CrossRef]

H. Liu, X. Shen, D.-M. Zhu, and S. Han, Phys. Rev. A 76, 053808 (2007).
[CrossRef]

H. Liu, J. Cheng, and S. Han, J. Appl. Phys. 102, 103102 (2007).
[CrossRef]

2006 (4)

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

G. Scarcelli, V. Berardi, and Y. Shih, Appl. Phys. Lett. 88, 061106 (2006).
[CrossRef]

L. Basano and P. Ottonello, Appl. Phys. Lett. 89, 091109 (2006).
[CrossRef]

Y. Cai and F. Wang, Opt. Lett. 31, 2278 (2006).
[CrossRef] [PubMed]

2005 (3)

D. Zhang, Y.-H. Zhai, L.-A. Wu, and X.-H. Chen, Opt. Lett. 30, 2354 (2005).
[CrossRef] [PubMed]

D. Z. Cao, J. Xiong, and K. Wang, Phys. Rev. A 71, 013801 (2005).
[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef] [PubMed]

2004 (4)

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef] [PubMed]

J. Cheng and S. Han, Phys. Rev. Lett. 92, 093903 (2004).
[CrossRef] [PubMed]

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

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef] [PubMed]

2002 (2)

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

C. Akcay, P. Parrein, and J. P. Rolland, Appl. Opt. 41, 5256 (2002).
[CrossRef] [PubMed]

1995 (1)

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

1987 (1)

Appl. Opt. (1)

Appl. Phys. Lett. (2)

G. Scarcelli, V. Berardi, and Y. Shih, Appl. Phys. Lett. 88, 061106 (2006).
[CrossRef]

L. Basano and P. Ottonello, Appl. Phys. Lett. 89, 091109 (2006).
[CrossRef]

J. Appl. Phys. (1)

H. Liu, J. Cheng, and S. Han, J. Appl. Phys. 102, 103102 (2007).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Lett. (2)

Phys. Rev. A (4)

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, Phys. Rev. A 75, 021803(R) (2007).
[CrossRef]

H. Liu, X. Shen, D.-M. Zhu, and S. Han, Phys. Rev. A 76, 053808 (2007).
[CrossRef]

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

D. Z. Cao, J. Xiong, and K. Wang, Phys. Rev. A 71, 013801 (2005).
[CrossRef]

Phys. Rev. Lett. (7)

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef] [PubMed]

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

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

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef] [PubMed]

J. Cheng and S. Han, Phys. Rev. Lett. 92, 093903 (2004).
[CrossRef] [PubMed]

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

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Figures (5)

Fig. 1
Fig. 1

Experimental setup. D 1 , bucket detector, lying close to the object to collect all the light passing through the object; D 2 , point detector, scanning along x 2 to collect the free propagating radiation; d A and d B , distances from the source along the two beams to D 1 and D 2 , respectively. A correlator is used to used to measure the intensity correlation function.

Fig. 2
Fig. 2

SLCL versus distance z for different source radii R, where λ = 0.632 μ m .

Fig. 3
Fig. 3

Computer simulation results for d A = 50 cm . (a) Variation of a typical speckle intensity profile along the x 2 coordinate in the image plane at d B = 50 cm . (b) Correlated true image over 10 4 frames when d B = 50 cm . (c) Variation of a typical speckle intensity profile at d B = 55 cm with the same source distribution as (a). (d) Correlated true image over the same 10 4 frames when d B = 55 cm with a magnification factor of d B d A = 1.1 .

Fig. 4
Fig. 4

Computer simulation results for d A = 10 cm , corresponding to Fig. 3. The image in (d) is totally blurred.

Fig. 5
Fig. 5

Simulation results of a diffraction image at d A = 50 cm with laser diameter D = 1.58 mm for selected values of d B ; 10 4 frames were used to build the statistics. The diffraction images of d B = 45 cm and d B = 55 cm are zoomed out 90% and in 110%, respectively. The diffraction image at d B = 30 cm , out of the SLCL, is blurred.

Equations (9)

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U ( x , y , z ) = e i k z i λ z d x d y U ( x , y ) exp { i k 2 z [ ( x x ) 2 + ( y y ) 2 ] } ,
U ( z ) = e i k z i λ z d x d y U ( x , y ) exp [ i k 2 z ( x 2 + y 2 ) ] .
U ( x , y ) U * ( x y ) = I ( x , y ) δ ( x x , y y ) ,
Δ I ( z ) Δ I ( z + Δ z ) = U ( z ) U * ( z + Δ z ) U ( z + Δ z ) U * ( z ) .
Δ I ( z ) Δ I ( z + Δ z ) = sinc 2 ( k Δ z R 2 2 z ( z + Δ z ) ) ,
z 1 = k R 2 k R 2 z + 0.886 π ,
z 2 = k R 2 k R 2 z 0.886 π ,
l SLCL = z 2 z 1 .
G ( x 1 , x 2 ) = T ( 2 π ( x 1 x 2 ) λ ( d A d O ) ) 2 ,

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