Abstract

As important analysis tools, microscopes with high spatial resolution are indispensable for scientific research and clinical diagnosis. We report a proof-of-principle experimental demonstration of a two-arm microscope scheme and show that, by measuring the second-order correlation of light fields, more details of an object can be obtained through recording more information about the initial illumination field. The effects arising from the transverse coherence length and the axial correlation depth of the illumination field are also discussed.

© 2009 Optical Society of America

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  1. C. J. R. Sheppard and A. Choudhury, Opt. Acta 24, 1051 (1977).
    [CrossRef]
  2. S. W. Hell and J. Wichmann, Opt. Lett. 19, 780 (1994).
    [CrossRef] [PubMed]
  3. E. Abbe, Arch. Mikrosc. Anat. Entwicklungmech 9, 413 (1873).
    [CrossRef]
  4. R. M. Satava, W. Poe, and G. Joyce, Am. Surg. 54, 73 (1988).
    [PubMed]
  5. T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
    [CrossRef] [PubMed]
  6. R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
    [CrossRef] [PubMed]
  7. F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 94, 183602 (2005).
    [CrossRef] [PubMed]
  8. A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mol. Spectrosc. 53, 739 (2006).
  9. J. Cheng and S. Han, Phys. Rev. Lett. 92, 093903 (2004).
    [CrossRef] [PubMed]
  10. M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, Y. Bai, and S. Han, Phys. Lett. A 366, 569 (2007).
    [CrossRef]
  11. L. Rayleigh, Philos. Mag. 8, 261 (1879).
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  13. J. W. Goodman, in Speckle Phenomena in Optics: Theory and Applications (Version 6.1) (Roberts and Company, 2006), pp. 67-76.

2007 (1)

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, Y. Bai, and S. Han, Phys. Lett. A 366, 569 (2007).
[CrossRef]

2006 (1)

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mol. Spectrosc. 53, 739 (2006).

2005 (1)

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

2004 (1)

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

2002 (1)

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

1995 (1)

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

1994 (1)

1988 (1)

R. M. Satava, W. Poe, and G. Joyce, Am. Surg. 54, 73 (1988).
[PubMed]

1977 (1)

C. J. R. Sheppard and A. Choudhury, Opt. Acta 24, 1051 (1977).
[CrossRef]

1879 (1)

L. Rayleigh, Philos. Mag. 8, 261 (1879).

1873 (1)

E. Abbe, Arch. Mikrosc. Anat. Entwicklungmech 9, 413 (1873).
[CrossRef]

Abbe, E.

E. Abbe, Arch. Mikrosc. Anat. Entwicklungmech 9, 413 (1873).
[CrossRef]

Bache, M.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mol. Spectrosc. 53, 739 (2006).

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

Bai, Y.

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, Y. Bai, and S. Han, Phys. Lett. A 366, 569 (2007).
[CrossRef]

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.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mol. Spectrosc. 53, 739 (2006).

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

Cheng, J.

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

Choudhury, A.

C. J. R. Sheppard and A. Choudhury, Opt. Acta 24, 1051 (1977).
[CrossRef]

Ferri, F.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mol. Spectrosc. 53, 739 (2006).

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

Gatti, A.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mol. Spectrosc. 53, 739 (2006).

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

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

J. W. Goodman, in Speckle Phenomena in Optics: Theory and Applications (Version 6.1) (Roberts and Company, 2006), pp. 67-76.

Han, S.

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, Y. Bai, and S. Han, Phys. Lett. A 366, 569 (2007).
[CrossRef]

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

Hell, S. W.

Joyce, G.

R. M. Satava, W. Poe, and G. Joyce, Am. Surg. 54, 73 (1988).
[PubMed]

Liu, H.

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, Y. Bai, and S. Han, Phys. Lett. A 366, 569 (2007).
[CrossRef]

Liu, Y.

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, Y. Bai, and S. Han, Phys. Lett. A 366, 569 (2007).
[CrossRef]

Lugiato, L. A.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mol. Spectrosc. 53, 739 (2006).

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

Magatti, D.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mol. Spectrosc. 53, 739 (2006).

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

Pittman, T. B.

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

Poe, W.

R. M. Satava, W. Poe, and G. Joyce, Am. Surg. 54, 73 (1988).
[PubMed]

Rayleigh, L.

L. Rayleigh, Philos. Mag. 8, 261 (1879).

Satava, R. M.

R. M. Satava, W. Poe, and G. Joyce, Am. Surg. 54, 73 (1988).
[PubMed]

Sergienko, A. V.

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

Shen, X.

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, Y. Bai, and S. Han, Phys. Lett. A 366, 569 (2007).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard and A. Choudhury, Opt. Acta 24, 1051 (1977).
[CrossRef]

Shih, Y. H.

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

Wei, Q.

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, Y. Bai, and S. Han, Phys. Lett. A 366, 569 (2007).
[CrossRef]

Wichmann, J.

Zhang, M.

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, Y. Bai, and S. Han, Phys. Lett. A 366, 569 (2007).
[CrossRef]

Am. Surg. (1)

R. M. Satava, W. Poe, and G. Joyce, Am. Surg. 54, 73 (1988).
[PubMed]

Arch. Mikrosc. Anat. Entwicklungmech (1)

E. Abbe, Arch. Mikrosc. Anat. Entwicklungmech 9, 413 (1873).
[CrossRef]

J. Mol. Spectrosc. (1)

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mol. Spectrosc. 53, 739 (2006).

Opt. Acta (1)

C. J. R. Sheppard and A. Choudhury, Opt. Acta 24, 1051 (1977).
[CrossRef]

Opt. Lett. (1)

Philos. Mag. (1)

L. Rayleigh, Philos. Mag. 8, 261 (1879).

Phys. Lett. A (1)

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, Y. Bai, and S. Han, Phys. Lett. A 366, 569 (2007).
[CrossRef]

Phys. Rev. A (1)

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

Phys. Rev. Lett. (3)

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

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

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

Other (2)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

J. W. Goodman, in Speckle Phenomena in Optics: Theory and Applications (Version 6.1) (Roberts and Company, 2006), pp. 67-76.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup of a two-arm imaging system.

Fig. 2
Fig. 2

The acquired images of the double slit from the two-arm imaging system. (a) was obtained directly by the test arm with L t = 6 mm , averaged over 2500 CCD frames. Ghost images were retrieved through the correlation between the same test arm L t = 6 mm and different reference arms: (b) L r = 6 mm , (c) L r = 10 mm , and (d) L r =15 mm (statistics over 5000 CCD frames). Solid curves in (e) display the normalized horizontal sections of the images, and dashed curves show theoretical predictions from Eq. (6).

Fig. 3
Fig. 3

The reconstructed images of the double slit under the different transverse coherence lengths: (a) l c = 40.7 μ m , (b) l c = 23.7 μ m , and (c) l c = 10.3 μ m (5000 CCD frames were used). The normalized horizontal sections of the images are plotted in (d) with solid curves, and dashed curves correspond to the analytical results of Eq. (8).

Fig. 4
Fig. 4

The reconstructed images of the double slit in different positions: (a) Δ z = 0 , (b) Δ z = 1 mm , (c) Δ z = 2 mm , (d) Δ z = 3 mm , (e) Δ z = 4 mm , and (f) Δ z = 5 mm , with 5000 averages. In (g), solid curves are the normalized horizontal sections of the images, and dashed curves are analytical calculations from Eq. (9).

Equations (9)

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δ x = 0.61 λ NA 1.22 λ d 1 L t ,
G ( x t , x r ) = source d x I ( x ) h t ( x t , x ) h r * ( x r , x ) 2 ,
h t ( x t , x ) = d x 0 e j k d 0 j λ d 0 exp [ j π λ d 0 ( x x 0 ) 2 ] t ( x 0 ) × sinc [ L t λ d 1 ( x 0 + x t M t ) ] ,
h r ( x r , x ) = d x 0 e j k d 0 j λ d 0 exp [ j π λ d 0 ( x x 0 ) 2 ] × sinc [ L r λ d 3 ( x 0 + x r M r ) ] ,
G ( x t , x r ) = d x 0 t ( x 0 ) sinc [ L t λ d 1 ( x 0 + x t M t ) ] × sinc [ L r λ d 3 ( x 0 + x r M r ) ] 2 ,
G ( M t M r x r , x r ) = d x 0 t ( x 0 ) sinc [ L t λ d 1 ( x 0 + x r M r ) ] × sinc [ L r λ d 3 ( x 0 + x r M r ) ] 2 ,
h g ( x r M t M r , x r ) = sinc [ L t λ d 1 ( x 0 + x r M r ) ] × sinc [ L r λ d 3 ( x 0 + x r M r ) ]
G ( x t , x r ) = d x 0 d x 0 t ( x 0 ) sinc [ D λ d 0 ( x 0 x 0 ) ] × sinc [ L t λ d 1 ( x 0 + x t M t ) ] sinc [ L r λ d 3 ( x 0 + x r M r ) ] 2 ,
G ( x t , x r ) 1 ( d 0 + Δ z ) 2 d x d x 0 d x 0 t ( x 0 ) exp [ j π ( x x 0 ) 2 λ ( d 0 + Δ z ) ] sinc [ L t λ ( x 0 d 1 Δ z + x t d 2 ) ] exp [ j π λ d 0 ( x x 0 ) 2 ] sinc [ L r λ ( x 0 d 3 + x r d 4 ) ] 2 .

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