Abstract

Based on the fourth-order correlation of light, lensless imaging with incoherent or partially coherent light is investigated theoretically by use of classical optical coherence theory. A novel lensless optical system for implementing imaging is proposed. The visibility and quality of the image are influenced by the coherence and transverse size of the light source. The results suggest useful imaging applications in x-ray, γ-ray, or other wavelengths where no effective lens is available, and they have potential applications in optical metrology and holography.

© 2007 Optical Society of America

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Corrections

Yangjian Cai and Fei Wang, "Lensless imaging with partially coherent light: erratum," Opt. Lett. 32, 1359-1359 (2007)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-32-11-1359

References

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    [CrossRef]

2006 (1)

Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

2003 (1)

2002 (2)

2000 (1)

J. Pu and S. Nemoto, IEEE J. Quantum Electron. 36, 1407 (2000).
[CrossRef]

1999 (1)

K. D. Mielenz, J. Res. Natl. Inst. Stand. Technol. 104, 479 (1999).

1996 (1)

1994 (1)

1993 (1)

1992 (1)

J. C. Marron and K. S. Schroeder, Appl. Phys. Lett. 31, 255 (1992).

1987 (1)

E. Wolf, Nature 326, 363 (1987).
[CrossRef]

1985 (1)

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 31, 2419 (1985).
[CrossRef] [PubMed]

1966 (1)

F. T. Arecchi, A. Berne, and A. Sona, Phys. Rev. Lett. 17, 260 (1966).
[CrossRef]

Arecchi, F. T.

F. T. Arecchi, A. Berne, and A. Sona, Phys. Rev. Lett. 17, 260 (1966).
[CrossRef]

Arons, E.

Azana, J.

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Berne, A.

F. T. Arecchi, A. Berne, and A. Sona, Phys. Rev. Lett. 17, 260 (1966).
[CrossRef]

Cai, Y.

Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

Q. Lin and Y. Cai, Opt. Lett. 27, 216 (2002).
[CrossRef]

Davidson, F. M.

Dilworth, D.

Friberg, A. T.

He, S.

Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

Lin, Q.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Chaps. 5, 8, and 9.

Marron, J. C.

J. C. Marron and K. S. Schroeder, Appl. Phys. Lett. 31, 255 (1992).

Mielenz, K. D.

K. D. Mielenz, J. Res. Natl. Inst. Stand. Technol. 104, 479 (1999).

Mukunda, N.

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 31, 2419 (1985).
[CrossRef] [PubMed]

Nemoto, S.

J. Pu and S. Nemoto, IEEE J. Quantum Electron. 36, 1407 (2000).
[CrossRef]

Pu, J.

J. Pu and S. Nemoto, IEEE J. Quantum Electron. 36, 1407 (2000).
[CrossRef]

Ricklin, J. C.

Schroeder, K. S.

J. C. Marron and K. S. Schroeder, Appl. Phys. Lett. 31, 255 (1992).

Simon, R.

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 31, 2419 (1985).
[CrossRef] [PubMed]

Sona, A.

F. T. Arecchi, A. Berne, and A. Sona, Phys. Rev. Lett. 17, 260 (1966).
[CrossRef]

Sudarshan, E. C. G.

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 31, 2419 (1985).
[CrossRef] [PubMed]

Sun, P. C.

Tervonen, E.

Turunen, J.

Wolf, E.

E. Wolf, Nature 326, 363 (1987).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Chaps. 5, 8, and 9.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

J. C. Marron and K. S. Schroeder, Appl. Phys. Lett. 31, 255 (1992).

IEEE J. Quantum Electron. (1)

J. Pu and S. Nemoto, IEEE J. Quantum Electron. 36, 1407 (2000).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Res. Natl. Inst. Stand. Technol. (1)

K. D. Mielenz, J. Res. Natl. Inst. Stand. Technol. 104, 479 (1999).

Nature (1)

E. Wolf, Nature 326, 363 (1987).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 31, 2419 (1985).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

F. T. Arecchi, A. Berne, and A. Sona, Phys. Rev. Lett. 17, 260 (1966).
[CrossRef]

Other (3)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Chaps. 5, 8, and 9.

R.A.Fisher, ed., Optical Phase Conjugation (Academic, 1983).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

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Figures (2)

Fig. 1
Fig. 1

Lensless optical system for implementing imaging with incoherent light.

Fig. 2
Fig. 2

Lensless imaging of a double slit formed with a partially coherent GSM source (a) of various transverse sizes with σ g = 0.0001 mm , (b) of various transverse coherence widths with σ 1 = 5 mm .

Equations (10)

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G ( 2 ) ( u 1 , u 2 ) = E ( u 1 ) E ( u 2 ) E * ( u 2 ) E * ( u 1 ) = h 1 ( u 1 , x 1 ) h 2 ( u 2 , x 2 ) h 2 * ( u 2 , x 3 ) h 1 * ( u 1 , x 4 ) E ( x 1 ) E ( x 2 ) E * ( x 3 ) E * ( x 4 ) d x 1 d x 2 d x 3 d x 4 = I ( u 1 ) I ( u 2 ) + g 2 ( u 1 , u 2 ) ,
I ( u i ) = h i ( u i , x 1 ) h i * ( u i , x 2 ) E ( x 1 ) E * ( x 2 ) d x 1 d x 2 , i = 1 , 2 ,
g 2 ( u 1 , u 2 ) = Γ ( u 1 , u 2 ) 2 = E ( x 1 ) E * ( x 2 ) h 1 ( u 1 , x 1 ) h 2 * ( u 2 , x 2 ) d x 1 d x 2 2 .
h 1 ( u 1 , x 1 ) = ( 1 λ 2 z 1 z 2 ) 1 2 exp [ i π λ z 1 ( x 1 ν 1 ) 2 i π λ z 2 ( ν 1 u 1 ) 2 ] H ( ν 1 ) d ν 1 ,
h 2 ( u 2 , x 2 ) = ( i λ z ) 1 2 exp [ i π λ z ( x 2 u 2 ) 2 ] .
Γ ( x 1 , x 2 ) = E ( x 1 ) E * ( x 2 ) = I 0 δ ( x 1 x 2 ) ,
Γ ( u 1 = 0 , u 2 ) 2 = 1 λ 3 z 1 z 2 z H ( ν 1 ) exp [ i π λ ( 1 z 1 1 z ) x 1 2 + 2 i π λ ( ν 1 z 1 u 2 z ) x 1 ] × exp [ i π λ ( 1 z 1 + 1 z 2 ) ν 1 2 ] d x 1 d ν 1 2 .
Γ ( u 1 = 0 , u 2 ) 2 = 1 λ z 2 H ( u 2 ) 2 .
Γ ( u 1 , u 2 ) 2 = 1 λ z δ ( u 1 u 2 ) H ( u 1 ) 2 .
Γ ( u 1 , u 2 ) 2 d u 1 = 1 λ z H ( u 2 ) 2 .

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