Abstract

A general condition is derived for the distance beyond which the far-zone approximation can be used in studying propagation of light from a partially coherent source. The distance steadily increases as a function of the coherence radius across the source, reaching the usual value in the coherent limit.

© 2005 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
    [CrossRef]
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
    [CrossRef]
  3. G. S. Agarwal, G. Gbur, and E. Wolf, Opt. Lett. 29, 459 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
  5. A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” arXiv.org print/archive, quant-ph/0504082, April 11, 2005.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2005 (1)

B. E.A. Saleh, M. C. Teich, and A. V. Sergienko, Phys. Rev. Lett. 94, 223601 (2005).
[CrossRef]

2004 (1)

2003 (1)

1978 (1)

1977 (1)

Agarwal, G. S.

Borghi, R.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
[CrossRef]

Carter, W. H.

Gbur, G.

Goodman, J. W.

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

Leader, J. C.

Mandel, L.

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

Saleh, B. E.A.

B. E.A. Saleh, M. C. Teich, and A. V. Sergienko, Phys. Rev. Lett. 94, 223601 (2005).
[CrossRef]

Santarsiero, M.

Sergienko, A. V.

B. E.A. Saleh, M. C. Teich, and A. V. Sergienko, Phys. Rev. Lett. 94, 223601 (2005).
[CrossRef]

Teich, M. C.

B. E.A. Saleh, M. C. Teich, and A. V. Sergienko, Phys. Rev. Lett. 94, 223601 (2005).
[CrossRef]

Wolf, E.

G. S. Agarwal, G. Gbur, and E. Wolf, Opt. Lett. 29, 459 (2004).
[CrossRef] [PubMed]

W. H. Carter and E. Wolf, J. Opt. Soc. Am. 67, 785 (1977).
[CrossRef]

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

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

B. E.A. Saleh, M. C. Teich, and A. V. Sergienko, Phys. Rev. Lett. 94, 223601 (2005).
[CrossRef]

Other (4)

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” arXiv.org print/archive, quant-ph/0504082, April 11, 2005.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
[CrossRef]

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

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

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Equations (13)

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z R s 2 λ .
W ( r 1 , r 2 , 0 ) = S 0 ( r 1 + r 2 2 ) μ 0 ( r 1 r 2 ) ,
W ( r 1 , r 2 , z ) = 1 λ 2 z 2 W ( v 1 , v 2 , 0 ) exp { i k 2 z [ ( r 2 v 2 ) 2 ( r 1 v 1 ) 2 ] } d 2 v 1 d 2 v 2 ,
W ( r 1 , r 2 , z ) = exp [ i k ( r 2 2 r 1 2 ) ( 2 z ) ] λ 2 z 2 W ( v 1 , v 2 , 0 ) exp [ i k 2 z ( v 2 2 v 1 2 r 2 v 2 + r 1 v 1 ) ] d 2 v 1 d 2 v 2 ,
W ( r 1 , r 2 , z ) = exp [ i k ( r 2 2 r 1 2 ) ( 2 z ) ] λ 2 z 2 W ( v 1 , v 2 , 0 ) exp [ i k 2 z ( r 1 v 1 r 2 v 2 ) ] d 2 v 1 d 2 v 2 ,
k 2 z ( v 2 2 v 1 2 )
k 2 z v 2 2 v 1 2 M π ,
W ( v 1 , v 2 , 0 ) = [ S 0 ( v 1 ) S 0 ( v 2 ) ] 1 2 μ 0 ( v 1 , v 2 ) .
v 2 2 v 1 2 M = 1 4 v 2 v 1 M v 2 + v 1 M .
v 2 v 1 M = min [ R c , 2 R s ] ,
v 2 2 v 1 2 M = 1 2 R s min [ R c , 2 R s ] .
z R s min [ R c , 2 R s ] 2 λ .
z R s R c λ .

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