Abstract

The inverse problem of the interaction of an isotropic Gaussian Schell-model beam with a semirough target in turbulent atmosphere is investigated. It is found that we can determine the target size and the transverse correlation width of the target by measuring the transverse beam widths and the transverse coherence widths of the beams at the source plane and the receiver plane. Our results are useful for remote sensing and bistatic LIDAR system.

© 2011 Optical Society of America

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References

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  5. O. Korotkova, L. C. Andrews, and R. L. Phillips, Opt. Eng. 43, 330 (2004).
    [CrossRef]
  6. Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
    [CrossRef]
  7. G. Gbur and O. Korotkova, J. Opt. Soc. Am. A 24, 745 (2007).
    [CrossRef]
  8. Y. Cai, Q. Lin, H. T. Eyyuboğlu, and Y. Baykal, Opt. Commun. 278, 157 (2007).
    [CrossRef]
  9. Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Yahya Baykal, and O. Korotkova, Opt. Express 17, 17344 (2009).
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    [CrossRef] [PubMed]
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    [CrossRef]
  19. R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 31, 2419 (1985).
    [CrossRef] [PubMed]
  20. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  21. Q. Lin and Y. Cai, Opt. Lett. 27, 216 (2002).
    [CrossRef]
  22. F. Wang and Y. Cai, J. Opt. Soc. Am. A 24, 1937 (2007).
    [CrossRef]
  23. J. W. Goodman, in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer, 1975), Chap. 2.

2010 (2)

2009 (3)

2008 (3)

2007 (3)

2006 (1)

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

2004 (3)

Y. Baykal, Opt. Commun. 231, 129 (2004).
[CrossRef]

O. Korotkova, L. C. Andrews, and R. L. Phillips, Opt. Eng. 43, 330 (2004).
[CrossRef]

O. Korotkova, L. C. Andrews, and R. L. Phillips, Proc. SPIE 5237, 49 (2004).
[CrossRef]

2003 (1)

O. Korotkova, L. C. Andrews, and R. L. Phillips, Proc. SPIE 5086, 173 (2003).
[CrossRef]

2002 (1)

1985 (1)

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

1979 (1)

Andrews, L. C.

O. Korotkova, L. C. Andrews, and R. L. Phillips, Opt. Eng. 43, 330 (2004).
[CrossRef]

O. Korotkova, L. C. Andrews, and R. L. Phillips, Proc. SPIE 5237, 49 (2004).
[CrossRef]

O. Korotkova, L. C. Andrews, and R. L. Phillips, Proc. SPIE 5086, 173 (2003).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
[CrossRef]

Baykal, Y.

Y. Cai, O. Korotkova, H. T. Eyyuboğlu, and Y. Baykal, Opt. Express 16, 15834 (2008).
[CrossRef] [PubMed]

Y. Cai, Q. Lin, H. T. Eyyuboğlu, and Y. Baykal, Opt. Commun. 278, 157 (2007).
[CrossRef]

Y. Baykal, Opt. Commun. 231, 129 (2004).
[CrossRef]

Baykal, Yahya

Cai, Y.

Dan, Y.

Eyyuboglu, H. T.

Gbur, G.

Goodman, J. W.

J. W. Goodman, in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer, 1975), Chap. 2.

He, S.

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

Ji, X.

Korotkova, O.

S. Zhu, Y. Cai, and O. Korotkova, Opt. Express 18, 12587 (2010).
[CrossRef] [PubMed]

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Yahya Baykal, and O. Korotkova, Opt. Express 17, 17344 (2009).
[CrossRef] [PubMed]

O. Korotkova, Y. Cai, and E. Watson, Appl. Phys. B 94, 681 (2009).
[CrossRef]

O. Korotkova, Opt. Commun. 281, 2342 (2008).

Y. Cai, O. Korotkova, H. T. Eyyuboğlu, and Y. Baykal, Opt. Express 16, 15834 (2008).
[CrossRef] [PubMed]

G. Gbur and O. Korotkova, J. Opt. Soc. Am. A 24, 745 (2007).
[CrossRef]

O. Korotkova, L. C. Andrews, and R. L. Phillips, Opt. Eng. 43, 330 (2004).
[CrossRef]

O. Korotkova, L. C. Andrews, and R. L. Phillips, Proc. SPIE 5237, 49 (2004).
[CrossRef]

O. Korotkova, L. C. Andrews, and R. L. Phillips, Proc. SPIE 5086, 173 (2003).
[CrossRef]

Lin, Q.

Y. Cai, Q. Lin, H. T. Eyyuboğlu, and Y. Baykal, Opt. Commun. 278, 157 (2007).
[CrossRef]

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

Lü, B.

Mandel, L.

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

Mukunda, N.

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

Phillips, R. L.

O. Korotkova, L. C. Andrews, and R. L. Phillips, Proc. SPIE 5237, 49 (2004).
[CrossRef]

O. Korotkova, L. C. Andrews, and R. L. Phillips, Opt. Eng. 43, 330 (2004).
[CrossRef]

O. Korotkova, L. C. Andrews, and R. L. Phillips, Proc. SPIE 5086, 173 (2003).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
[CrossRef]

Plonus, M. A.

Qu, J.

Simon, R.

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

Sudarshan, E. C. G.

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

Wang, F.

Wang, S. C. H.

Watson, E.

O. Korotkova, Y. Cai, and E. Watson, Appl. Phys. B 94, 681 (2009).
[CrossRef]

Wolf, E.

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

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).

Yang, A.

Yuan, Y.

Zhang, B.

Zhang, E.

Zhu, S.

Appl. Phys. B (1)

O. Korotkova, Y. Cai, and E. Watson, Appl. Phys. B 94, 681 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

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

J. Opt. Soc. Am. (1)

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

Opt. Commun. (3)

O. Korotkova, Opt. Commun. 281, 2342 (2008).

Y. Cai, Q. Lin, H. T. Eyyuboğlu, and Y. Baykal, Opt. Commun. 278, 157 (2007).
[CrossRef]

Y. Baykal, Opt. Commun. 231, 129 (2004).
[CrossRef]

Opt. Eng. (1)

O. Korotkova, L. C. Andrews, and R. L. Phillips, Opt. Eng. 43, 330 (2004).
[CrossRef]

Opt. Express (5)

Opt. Lett. (2)

Phys. Rev. A (1)

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

Proc. SPIE (2)

O. Korotkova, L. C. Andrews, and R. L. Phillips, Proc. SPIE 5237, 49 (2004).
[CrossRef]

O. Korotkova, L. C. Andrews, and R. L. Phillips, Proc. SPIE 5086, 173 (2003).
[CrossRef]

Other (4)

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

J. W. Goodman, in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer, 1975), Chap. 2.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
[CrossRef]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).

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Figures (1)

Fig. 1
Fig. 1

Schematic diagram for a GSM beam interacting with a semirough target in turbulent atmosphere and its equivalent (unfolded) version.

Equations (22)

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W ( r 1 , r 2 ) = G 0 exp [ r 1 2 + r 2 2 4 σ s 2 ( r 1 r 2 ) 2 2 δ s 2 i k R s 1 2 ( r 1 2 r 2 2 ) ] ,
W ( r ˜ ) = exp ( i k 2 r ˜ T M 0 1 r ˜ ) ,
M 0 1 = ( ( i 2 k σ I 2 i k δ I 2 ) I i k δ I 2 I i k δ I 2 I ( i 2 k σ I 2 i k δ I 2 ) I ) .
W ( t ˜ ) = 1 [ det ( A ˜ + B ˜ M 0 1 + B ˜ P ˜ 0 ) ] 1 / 2 exp [ i k 2 t ˜ T M 1 1 t ˜ ] ,
M 1 1 = ( B ˜ 1 1 2 P ˜ ) T ( M 0 1 + B ˜ 1 A ˜ + P ˜ ) 1 ( B ˜ 1 1 2 P ˜ ) + ( D ˜ B ˜ 1 + P ˜ ) .
A ˜ = ( I 0 I 0 I I ) , B ˜ = ( z I 0 I 0 I z I ) , D ˜ = ( ( 1 z / f ) I 0 I 0 I ( 1 z / f ) I ) , P ˜ = 2 i k ρ 0 2 ( I I I I ) ,
T ( t 1 ) T * ( t 2 ) = 4 π β 2 k 2 exp [ i k 2 t ˜ T T ˜ t ˜ ] ,
T ˜ = ( ( 2 i k ω R 2 2 i k l c 2 ) I 2 i k l c 2 I 2 i k l c 2 I ( 2 i k ω R 2 2 i k l c 2 ) I ) ,
W ( ρ ˜ ) = 4 π β 2 k 2 [ det ( I ˜ + B ˜ M 1 1 + B ˜ T ˜ + B ˜ P ˜ 0 ) ] 1 / 2 [ det ( A ˜ + B ˜ M 0 1 + B ˜ P ˜ 0 ) ] 1 / 2 × exp [ i k 2 ρ ˜ T M 2 1 ρ ˜ ] ,
M 2 1 = P ˜ 0 + B ˜ 1 ( B ˜ 1 0.5 P ˜ 0 ) T ( M 1 1 + T ˜ + B ˜ 1 + P ˜ 0 ) 1 ( B ˜ 1 0.5 P ˜ 0 ) .
M 2 1 = ( m 11 I m 12 I m 21 I m 22 I ) = ( ( R out 1 i 2 k σ out 2 i k δ out 2 ) I i k δ out 2 I i k δ out 2 I ( R out 1 i 2 k σ out 2 i k δ out 2 ) I ) ,
1 δ out 2 = k i m 12 , 1 σ out 2 = k i ( m 11 + m 22 ) + 2 k i m 12 .
ρ 0 2 δ out 2 = e 1 ω R 4 + 4 b 1 ω R 2 + 2 b 1 l c 2 + f 1 l c 2 ω R 2 + g 1 l c 2 ω R 4 a 1 ω R 4 + 2 b 1 ω R 2 + b 1 l c 2 + c 1 l c 2 ω R 2 + d 1 l c 2 ω R 4 ,
1 σ out 2 = e 2 l c 2 ω R 2 + f 2 l c 2 ω R 4 a 1 ω R 4 + 2 b 1 ω R 2 + b 1 l c 2 + c 1 l c 2 ω R 2 + d 1 l c 2 ω R 4 ,
a 1 = 8 R 2 z 2 ρ 0 2 δ 2 σ 2 , b 1 = 16 R 2 z 2 ρ 0 2 δ 2 σ 4 , c 1 = R 2 z 2 σ 2 [ 16 ρ 0 2 σ 2 + δ 2 ( 8 ρ 0 2 + 32 σ 2 ) ] , d 1 = 8 k 2 R z ρ 0 2 δ 2 σ 4 + 4 k 2 z 2 δ 2 ρ 0 2 σ 4 + R 2 [ 4 k 2 ρ 0 2 δ 2 σ 4 + z 2 ( 4 ρ 0 2 σ 2 + δ 2 ( ρ 0 2 + 8 σ 2 ) ) ] , e 1 = ρ 0 2 R 2 δ 2 σ 2 ( 16 z 2 + 8 k 2 ρ 0 2 σ 2 ) , f 1 = R 2 z 2 σ 2 [ 32 ρ 0 2 σ 2 + δ 2 ( 16 ρ 0 2 + 48 σ 2 ) ] , g 1 = 24 k 2 R z ρ 0 2 δ 2 σ 4 + 8 k 2 z 2 ρ 0 2 δ 2 σ 4 + R 2 [ k 2 ρ 0 2 ( 24 δ 2 + 4 ρ 0 2 ) σ 4 + z 2 ( 8 ρ 0 2 σ 2 + δ 2 ( 2 ρ 0 2 + 12 σ 2 ) ) ] , e 2 = 16 k 2 R 2 ρ 0 2 δ 2 σ 4 , f 2 = 4 k 2 R 2 ρ 0 2 δ 2 σ 2 , δ 2 = 4 k 2 ρ 0 4 δ I 2 σ I 4 + z 2 ρ 0 2 ( 4 ρ 0 2 σ I 2 + δ I 2 ( ρ 0 2 + 8 σ I 2 ) ) k 2 ρ 0 2 ( 24 δ I 2 + 4 ρ 0 2 ) σ I 4 + z 2 ( 8 ρ 0 2 σ I 2 + δ I 2 ( 2 ρ 0 2 + 12 σ I 2 ) ) , σ 2 = 4 k 2 ρ 0 2 δ I 2 σ I 4 + z 2 ( 4 ρ 0 2 σ I 2 + δ I 2 ( ρ 0 2 + 8 σ I 2 ) ) 4 k 2 ρ 0 2 δ I 2 σ I 2 , 1 R = 1 f + z ( ρ 0 2 σ I 2 + δ I 2 ( 0.25 ρ 0 2 + 3 σ I 2 ) ) k 2 ρ 0 2 δ I 2 σ I 4 + z 2 ( ρ 0 2 σ I 2 + δ I 2 ( 0.25 ρ 0 2 + 2 σ I 2 ) ) .
δ out 2 e 1 ω R 2 + 4 δ out 2 b 1 ρ 0 2 a 1 ω R 2 2 ρ 0 2 b 1 a 1 ω R 2 + 2 b 1 = ρ 0 2 b 1 + ρ 0 2 c 1 ω R 2 + ρ 0 2 d 1 ω R 4 2 δ out 2 b 1 δ out 2 f 1 ω R 2 δ out 2 g 1 ω R 4 σ out 2 e 2 ω R 2 + σ out 2 f 2 ω R 4 b 1 c 1 ω R 2 d 1 ω R 4 .
A 1 ω R 4 + B 1 ω R 2 + C 1 = 0 ,
A 1 = δ out 2 σ out 2 e 1 f 2 δ out 2 e 1 d 1 ρ 0 2 σ out 2 a 1 f 2 + δ out 2 a 1 g 1 , B 1 = δ out 2 σ out 2 e 1 e 2 δ out 2 e 1 c 1 + 4 δ out 2 σ out 2 b 1 f 2 4 δ out 2 b 1 d 1 ρ 0 2 σ out 2 a 1 e 2 2 ρ 0 2 σ out 2 b 1 f 2 + δ out 2 a 1 f 1 + 2 δ out 2 b 1 g 1 , C 1 = 4 δ out 2 σ out 2 b 1 e 2 4 δ out 2 b 1 c 1 δ out 2 e 1 b 1 2 ρ 0 2 σ out 2 b 1 e 2 + 2 δ out 2 a 1 b 1 + 2 δ out 2 b 1 f 1 .
ω R 1 2 = B 1 + B 1 2 4 A 1 C 1 2 A 1 ,
ω R 2 2 = B 1 B 1 2 4 A 1 C 1 2 A 1 .
l c 1 2 = a 1 ω R 1 4 + 2 b 1 ω R 1 2 σ out 2 e 2 ω R 1 2 + σ out 2 f 2 ω R 1 4 b 1 c 1 ω R 1 2 d 1 ω R 1 4 ,
l c 2 2 = a 1 ω R 2 4 + 2 b 1 ω R 2 2 σ out 2 e 2 ω R 2 2 + σ out 2 f 2 ω R 2 4 b 1 c 1 ω R 2 2 d 1 ω R 2 4 ,

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