Abstract

Ghost imaging produced by pseudothermal light is commonly obtained by correlating the intensities of two separate beams, neither of which conveys information about the shape of the object to be imaged. The single-beam experiment discussed here, while not exploitable for the practical purpose of reconstructing the shape of a real mask, uses the same mathematical machinery as two-beam experiments; it also suggests that image retrieval by classical light ghost imaging is only a product of normal signal processing and does not involve any “ghost”. In addition, the single-beam setup allows simpler calibration procedures in systematic investigations of the efficiency of coincidence imaging.

© 2007 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, "Optical imaging by means of two-photon quantum entanglement," Phys. Rev. A 52, R3429 (1995).
  2. R. S. Bennink, S. J. Bentley and R. W. Boyd, "two-photon coincidence imaging with a classical source," Phys. Rev. Lett. 89, 113601 (2002).
    [CrossRef] [PubMed]
  3. A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato," Ghost Imaging with Thermal Light: Comparing Entanglement and Classical Correlation," Phys. Rev. Lett. 93, 093602 (2004).
    [CrossRef] [PubMed]
  4. F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, "High-resolution ghost image and ghost diffraction experiments with thermal light," Phys. Rev. Lett. 94, 183602 (2005).
    [CrossRef] [PubMed]
  5. A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, "Two-photon imaging with thermal light," Phys. Rev. Lett. 94, 063601 (2005).
    [CrossRef] [PubMed]
  6. A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko and M. C. Teich, "Role of entanglement in Two-Photon Imaging," Phys. Rev. Lett. 87, 123602 (2001).
    [CrossRef] [PubMed]
  7. G. Scarcelli, V. Berardi, and Y. Shih, "Can Two-Photon Correlation of Chaotic Light be considered as Correlation of Intensity Fluctuations?," Phys. Rev. Lett. 96, 063602 (2006). Comment by A. Gatti, M. Bondani, L. A.Lugiato, M. G. A. Paris and C. Fabre, Phys. Rev. Lett. 98, 039301 (2007), and Scarcelli, Berardi, and Shih, Reply, Phys. Rev. Lett. 98, 039302 (2007).
    [CrossRef]
  8. W. Martienssen and E. Spiller, "Coherence and fluctuations in light beams," Am. J. Phys. 32, 919 (1964).
    [CrossRef]
  9. L. Basano, and P. Ottonello, "Ghost imaging: open secrets and puzzles for undergraduates," Am. J. Phys. 75, 343 (2007).
    [CrossRef]
  10. In this paper we make reference only to ghost imaging and not to ghost interference or diffraction
  11. The term "correlation" commonly employed in ghost imaging actually means "zero-delay cross-correlation"; in other words, two sequences are being "correlated" when they are multiplied term by term (without relative shift) and summed.

2007 (2)

G. Scarcelli, V. Berardi, and Y. Shih, "Can Two-Photon Correlation of Chaotic Light be considered as Correlation of Intensity Fluctuations?," Phys. Rev. Lett. 96, 063602 (2006). Comment by A. Gatti, M. Bondani, L. A.Lugiato, M. G. A. Paris and C. Fabre, Phys. Rev. Lett. 98, 039301 (2007), and Scarcelli, Berardi, and Shih, Reply, Phys. Rev. Lett. 98, 039302 (2007).
[CrossRef]

L. Basano, and P. Ottonello, "Ghost imaging: open secrets and puzzles for undergraduates," Am. J. Phys. 75, 343 (2007).
[CrossRef]

2005 (2)

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, "High-resolution ghost image and ghost diffraction experiments with thermal light," Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef] [PubMed]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, "Two-photon imaging with thermal light," Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef] [PubMed]

2004 (1)

A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato," Ghost Imaging with Thermal Light: Comparing Entanglement and Classical Correlation," Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef] [PubMed]

2002 (1)

R. S. Bennink, S. J. Bentley and R. W. Boyd, "two-photon coincidence imaging with a classical source," Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef] [PubMed]

2001 (1)

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko and M. C. Teich, "Role of entanglement in Two-Photon Imaging," Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef] [PubMed]

1995 (1)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, "Optical imaging by means of two-photon quantum entanglement," Phys. Rev. A 52, R3429 (1995).

1964 (1)

W. Martienssen and E. Spiller, "Coherence and fluctuations in light beams," Am. J. Phys. 32, 919 (1964).
[CrossRef]

Am. J. Phys. (2)

W. Martienssen and E. Spiller, "Coherence and fluctuations in light beams," Am. J. Phys. 32, 919 (1964).
[CrossRef]

L. Basano, and P. Ottonello, "Ghost imaging: open secrets and puzzles for undergraduates," Am. J. Phys. 75, 343 (2007).
[CrossRef]

Phys. Rev. A (1)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, "Optical imaging by means of two-photon quantum entanglement," Phys. Rev. A 52, R3429 (1995).

Phys. Rev. Lett. (6)

R. S. Bennink, S. J. Bentley and R. W. Boyd, "two-photon coincidence imaging with a classical source," Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef] [PubMed]

A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato," Ghost Imaging with Thermal Light: Comparing Entanglement and Classical Correlation," Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef] [PubMed]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, "High-resolution ghost image and ghost diffraction experiments with thermal light," Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef] [PubMed]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, "Two-photon imaging with thermal light," Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef] [PubMed]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko and M. C. Teich, "Role of entanglement in Two-Photon Imaging," Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef] [PubMed]

G. Scarcelli, V. Berardi, and Y. Shih, "Can Two-Photon Correlation of Chaotic Light be considered as Correlation of Intensity Fluctuations?," Phys. Rev. Lett. 96, 063602 (2006). Comment by A. Gatti, M. Bondani, L. A.Lugiato, M. G. A. Paris and C. Fabre, Phys. Rev. Lett. 98, 039301 (2007), and Scarcelli, Berardi, and Shih, Reply, Phys. Rev. Lett. 98, 039302 (2007).
[CrossRef]

Other (2)

In this paper we make reference only to ghost imaging and not to ghost interference or diffraction

The term "correlation" commonly employed in ghost imaging actually means "zero-delay cross-correlation"; in other words, two sequences are being "correlated" when they are multiplied term by term (without relative shift) and summed.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the two-beam setup. GGD: ground glass disk; BS: 50% beam splitter; B1: reference beam; CCD: ccd camera; B2: object beam passing through the mask M; BD: bucket detector for measuring the total intensity crossing the mask. The two-beam correlation is done by first multiplying (⊗) the outputs and then cumulating (∑) the results

Fig. 2.
Fig. 2.

Schematic of the single-beam setup. Only one beam (upper part of figure) impinges on the CCD camera, whose front side is shown enlarged in the lower part. F stands for the matrix whose elements are the speckle intensities recorded by the whole ccd array A. W is the numerical sum of the speckle intensities belonging to the subset M

Fig. 3.
Fig. 3.

(a). Result of two-beam correlation, measured according to the procedure explained in Sect. 2. Note the pair of prominent hills that represent the mask transparency function described in Sect. 4 are smoothed by the convolution operator. b) Result of single beam correlation, determined according to the procedure explained in Sects. 3–4. Also in this case, the image of the (software) mask is smoothed by the convolution operator.

Fig. 4.
Fig. 4.

The plotted values of visibility are the differences [R(in)-R(out)] properly normalized, i.e. divided by [R(in)+R(out)]

Fig. 5.
Fig. 5.

Values of the experimental variances of: (a) R(in) and: (b) R(out) plotted vs the ratio: (subset M area)/(coherence area). The continuous lines represent the theoretical functions (variances) given in Table I

Tables (1)

Tables Icon

Table I. Summary of statistical variables

Equations (13)

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Γ ( i , j ; k , l ; s , s ) = < F S ( i , j ) F S ( k , l ) > = Γ ( i k ; j 1 ; s s )
W ( s ) = Σ kl χ M ( k , l ) F S ( k , l ) ( s = 1 , 2 , S )
Φ S ( i , j ) = W ( s ) F S ( i , j ) ( s = 1 , 2 , S )
R ( i , j ) = Σ s Φ S ( i , j ) = Σ s W ( s ) F S ( i , j ) = Σ s [ Σ k , 1 χ M ( k , l ) F S ( k , l ) ] F S ( i , j )
R ( i , j ) = Σ k , 1 χ M ( k , l ) [ Σ s F S ( k , l ) F S ( i , j ) ]
[ s F S ( k , l )    F S    ( i , j ) ] = C F ( i k , j 1 )
R ( i , j ) = Σ k , l [ χ M ( k , l ) C F ( i k , j 1 ) ] = χ M * C F
C F ( i k , j l ) δ ( i k , j l )
W ( s ) = k = 1 T I s ( k ) ( s = 1 . . . . N )
Φ s ( k ) = W ( s ) · I s ( k ) weighted pattern on the s th trial
R ( k ) = s = 1 N Φ s ( k ) final image sum : of N weighted patterns .
< XY > = < X > < Y > + cov ( X , Y )
var ( XY ) = var ( X ) var ( Y ) + < X > 2 var ( Y ) + < Y > 2 var ( X ) + 2 < X > < Y > cov ( X , Y )

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