Abstract

Using a classical source generating a field with an adjustable degree of spatial coherence, we propose and demonstrate a two-photon correlated Fourier imaging scheme in which both amplitude and phase information about the spatial frequencies of an object can be obtained. The effects of the incident field’s partial coherence are discussed in a geometrical optics approach.

© 2006 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, Phys. Rev. A 52, R3429 (1995).
    [CrossRef] [PubMed]
  2. D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
    [CrossRef] [PubMed]
  3. R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
    [CrossRef] [PubMed]
  4. A. Valencia, G. Scarcelli, M. D'Angelo, and Y. Shih, Phys. Rev. Lett. 94, 063601 (2005).
    [CrossRef] [PubMed]
  5. M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, Phys. Rev. A 70, 023823 (2004).
    [CrossRef]
  6. E. Baleine and A. Dogariu, Opt. Lett. 29, 1233 (2004).
    [CrossRef] [PubMed]
  7. E. Baleine and A. Dogariu, J. Opt. Soc. Am. A 21, 1917 (2004).
    [CrossRef]
  8. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  9. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
    [CrossRef]
  10. D. N. Klyshko, Photons and Nonlinear Optics (Gordon & Breach, 1988).
  11. J. Cheng and S. Han, Phys. Rev. Lett. 92, 093903 (2004).
    [CrossRef] [PubMed]
  12. B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
    [CrossRef]

2005

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

2004

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, Phys. Rev. A 70, 023823 (2004).
[CrossRef]

E. Baleine and A. Dogariu, Opt. Lett. 29, 1233 (2004).
[CrossRef] [PubMed]

E. Baleine and A. Dogariu, J. Opt. Soc. Am. A 21, 1917 (2004).
[CrossRef]

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

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

2002

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

2000

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

1995

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

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef] [PubMed]

Abouraddy, A. F.

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Bache, M.

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

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, Phys. Rev. A 70, 023823 (2004).
[CrossRef]

Baleine, E.

Bennink, R. S.

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

Bentley, S. J.

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

Boyd, R. W.

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

Brambilla, E.

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, Phys. Rev. A 70, 023823 (2004).
[CrossRef]

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

Cheng, J.

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

D'Angelo, M.

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

Dogariu, A.

Gatti, A.

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

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, Phys. Rev. A 70, 023823 (2004).
[CrossRef]

Han, S.

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

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef] [PubMed]

D. N. Klyshko, Photons and Nonlinear Optics (Gordon & Breach, 1988).

Lugiato, L. A.

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, Phys. Rev. A 70, 023823 (2004).
[CrossRef]

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

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Pittman, T. B.

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

Saleh, B. E. A.

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Scarcelli, G.

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

Sergienko, A. V.

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef] [PubMed]

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

Shih, Y.

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

Shih, Y. H.

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

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef] [PubMed]

Strekalov, D. V.

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

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef] [PubMed]

Teich, M. C.

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Valencia, A.

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

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

J. Opt. Soc. Am. A

Opt. Lett.

Phys. Rev. A

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, Phys. Rev. A 70, 023823 (2004).
[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]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Phys. Rev. Lett.

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

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef] [PubMed]

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

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

Other

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

D. N. Klyshko, Photons and Nonlinear Optics (Gordon & Breach, 1988).

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Figures (3)

Fig. 1
Fig. 1

Unfolded representation of the imaging setup.

Fig. 2
Fig. 2

Coincidence counts G ( 2 ) and intensities in the object arm ( I 1 ) and the reference arm ( I 2 ) measured as a function of the source parameter Δ r 0 for ϕ = 0 (solid curves) and ϕ = π (dotted curves) when the grating is in the position T ( 0 ) = 0 . The intensities are normalized with respect to the values obtained without the object and for Δ r 0 200 μ m .

Fig. 3
Fig. 3

(a1) Analytic Fourier transform of the grating’s transmittance for the case T ( 0 ) = 1 . (a2), (a3) Measured amplitude χ e 2 and the phase cosine. (b2), (b3), Same measurements for the case T ( 0 ) = 0 , corresponding to the analytic Fourier transform plotted in (b1).

Equations (6)

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G ( 1 ) ( 0 , 0 ) = G 0 ( 1 ) ( r , r ) T ( r ) h 1 * ( 0 , r ) h 2 ( 0 , r ) d 2 r d 2 r ,
I s ( ξ ) = 1 2 Q ( ξ R ) [ 1 + m cos ( k f ξ Δ r 0 ϕ ) ] ,
G 0 ( 1 ) ( r , r ) = g ( Δ r ) + m 2 exp ( i ϕ ) g ( Δ r Δ r 0 ) + m 2 exp ( i ϕ ) g ( Δ r + Δ r 0 ) ,
Δ G ( 2 ) ( 0 , 0 ) = χ e ( 0 ) + m exp ( i ψ ) [ χ e ( Δ r 0 ) cos ( ϕ ) χ 0 ( Δ r 0 ) sin ( ϕ ) ] 2 ,
χ ( Δ r 0 ) = g ( Δ r ) T ̃ [ k d ( Δ r Δ r 0 ) ] exp ( i k d Δ r Δ r 0 ) d 2 Δ r .
U T ( 0 ) = U ( 0 ) + m 2 exp ( i ϕ ) U ( 0 , Δ r 0 ) + m 2 exp ( i ϕ ) U ( 0 , Δ r 0 ) .

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