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, Y. Shih, 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 (1)

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]

Abouraddy, A. F.

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]

Bache, M.

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. 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]

Basano, L.

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

Bennink, R. S.

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]

Bentley, S. J.

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]

Berardi, V.

G. Scarcelli, V. Berardi, Y. Shih, 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]

Bondani, M.

G. Scarcelli, V. Berardi, Y. Shih, 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]

Boyd, R. W.

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]

Brambilla, E.

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. 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]

D’Angelo, M.

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

Fabre, C.

G. Scarcelli, V. Berardi, Y. Shih, 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]

Ferri, F.

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]

Gatti, A.

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. 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]

G. Scarcelli, V. Berardi, Y. Shih, 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]

Lugiato, L. A.

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. 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]

G. Scarcelli, V. Berardi, Y. Shih, 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]

Magatti, D.

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]

Martienssen, W.

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

Ottonello, P.

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

Paris, M. G. A.

G. Scarcelli, V. Berardi, Y. Shih, 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]

Pittman, T. B.

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).

Saleh, B. E. A.

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]

Scarcelli, G.

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

G. Scarcelli, V. Berardi, Y. Shih, 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]

Sergienko, A. V.

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]

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).

Shih, Y.

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

G. Scarcelli, V. Berardi, Y. Shih, 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]

Shih, Y. H.

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).

Spiller, E.

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

Strekalov, D. V.

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).

Teich, M. C.

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]

Valencia, A.

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

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. (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. (5)

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]

Other (3)

G. Scarcelli, V. Berardi, Y. Shih, 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]

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

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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

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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.

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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)]

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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

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Tables (1)

Tables Icon

Table I. Summary of statistical variables

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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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