Abstract

We present an experimental comparison between different iterative ghost imaging algorithms. Our experimental setup utilizes a spatial light modulator for generating known random light fields to illuminate a partially-transmissive object. We adapt the weighting factor used in the traditional ghost imaging algorithm to account for changes in the efficiency of the generated light field. We show that our normalized weighting algorithm can match the performance of differential ghost imaging.

© 2012 OSA

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References

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  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]
  2. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: Comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
    [CrossRef] [PubMed]
  3. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
    [CrossRef]
  4. A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
    [CrossRef] [PubMed]
  5. 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).
  6. J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008).
    [CrossRef]
  7. Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).
    [CrossRef]
  8. M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
    [CrossRef]
  9. F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
    [CrossRef] [PubMed]
  10. J. Goodman, Statistical Optics (Wiley, 2000).
  11. S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, 2004).
  12. D. L. Donoho and Y. Tsaig, “Fast solution of l1-norm minimization problems when the solution may be sparse,” IEEE Trans. Inf. Theory 54, 4789–4812 (2008).
    [CrossRef]
  13. O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
    [CrossRef]

2010 (1)

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef] [PubMed]

2009 (2)

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[CrossRef]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).
[CrossRef]

2008 (3)

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[CrossRef]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008).
[CrossRef]

D. L. Donoho and Y. Tsaig, “Fast solution of l1-norm minimization problems when the solution may be sparse,” IEEE Trans. Inf. Theory 54, 4789–4812 (2008).
[CrossRef]

2005 (1)

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 (2)

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: Comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

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]

1836 (1)

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).

Bache, M.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, 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).

Baraniuk, R.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[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]

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]

Boyd, S.

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, 2004).

Brambilla, E.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, 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).

Bromberg, Y.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).
[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[CrossRef]

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]

Davenport, M.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[CrossRef]

Donoho, D. L.

D. L. Donoho and Y. Tsaig, “Fast solution of l1-norm minimization problems when the solution may be sparse,” IEEE Trans. Inf. Theory 54, 4789–4812 (2008).
[CrossRef]

Duarte, M.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[CrossRef]

Ferri, F.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[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).

Gatti, A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: Comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

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).

Goodman, J.

J. Goodman, Statistical Optics (Wiley, 2000).

Katz, O.

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[CrossRef]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).
[CrossRef]

Kelly, K.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[CrossRef]

Laska, J.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[CrossRef]

Lugiato, L. A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: Comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[CrossRef] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

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).

Magatti, D.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[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).

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]

Shapiro, J. H.

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008).
[CrossRef]

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]

Silberberg, Y.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).
[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[CrossRef]

Sun, T.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[CrossRef]

Takhar, D.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[CrossRef]

Tsaig, Y.

D. L. Donoho and Y. Tsaig, “Fast solution of l1-norm minimization problems when the solution may be sparse,” IEEE Trans. Inf. Theory 54, 4789–4812 (2008).
[CrossRef]

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]

Vandenberghe, L.

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, 2004).

Appl. Phys. Lett. (1)

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[CrossRef]

IEEE Signal Processing Magazine (1)

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[CrossRef]

IEEE Trans. Inf. Theory (1)

D. L. Donoho and Y. Tsaig, “Fast solution of l1-norm minimization problems when the solution may be sparse,” IEEE Trans. Inf. Theory 54, 4789–4812 (2008).
[CrossRef]

Phys. Rev. A (3)

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008).
[CrossRef]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Phys. Rev. Lett. (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]

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).

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, E. Brambilla, M. Bache, 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, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef] [PubMed]

Other (2)

J. Goodman, Statistical Optics (Wiley, 2000).

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, 2004).

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Figures (5)

Fig. 1
Fig. 1

Computational ghost imaging setup used in the experiment. A spatial light modulator (SLM) is used to generate a random speckle field, as described in the text and a beam splitter (BS) is used to measure a reference signal R on a bucket detector before the object. The signal, S, is measured on a bucket detector which collects the light transmitted after the object.

Fig. 2
Fig. 2

(a) A typical speckle pattern hologram. (b) The measured intensity distribution of the speckle pattern (blue) and an exponential curve (red).

Fig. 3
Fig. 3

Experimental results (middle column) for TGI, DGI and NGI reconstruction algorithms as they evolve (10, 100, 1000 and 10000 iterations from left to right, respectively) with the corresponding simulated results (right column). The transmissive object is shown in the lower right. The bottom row shows the evolution for reconstructing the object with the NGI algorithm using a single detector and predicting the reference signal R, termed here the SNGI algorithm.

Fig. 4
Fig. 4

Signal-to-noise ratio’s for DGI, NGI, SNGI and TGI versus transmitting area. Transmitting ratio is defined as the ratio between the transmitting area of the object and the area of the speckle field.

Fig. 5
Fig. 5

(a) Experimental result of Normalized known vector reconstruction method (S/R) having SNR = 9.95. (b) Standard CGI reconstruction from S having SNR = 7.39.

Equations (18)

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S = A l I ( x S , y S ) T ( x S , y S ) d x S d y S ,
R = I ( x R , y R ) d x R d y R .
O i ( x , y ) = ( S S ) ( I ( x , y ) I ( x , y ) ) ,
O i ( x , y ) = ( S S R R ) ( I ( x , y ) I ( x , y ) ) .
O i ( x , y ) = ( S R S R ) ( I ( x , y ) I ( x , y ) ) ,
O ( x , y ) N G I = 1 R O ( x , y ) D G I .
O ( x , y ) D G I = A s ¯ I 2 δ T ( x , y ) ,
( Δ ( O D G I ) ) 2 = A s ¯ 2 I 4 ( Δ T ) 2 ,
( Δ O N G I ) 2 = A s ¯ 2 I 4 R 2 ( Δ T ) 2 .
δ O 2 ( x , y ) = O ( x , y ) 2 O ( x , y ) 2 ,
O D G I 2 A s A l I 4 δ T 2 ¯ ,
S R S R ( 1 + δ S S δ R R ) ,
O N G I 2 A s A l I 4 R 2 δ T 2 ¯ .
S N R N G I = S N R D G I = M N speckle Δ T 2 δ T 2 ¯ ,
S N R T G I = M N speckle Δ T 2 T 2 ¯ .
S N R N G I S N R T G I = 1 + T ¯ 2 T 2 ¯ T ¯ 2 .
[ S i S N ] = [ M × N ] × [ T ( x , y ) ] .
[ S i ' S N ' ] = [ M × N ] × [ T ( x , y ) ] .

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