Abstract

We develop a method for transmission of stochastic fields through turbulent media (atmosphere, ocean, biotissues) containing randomly distributed particles. The method is based on the angular spectrum representation of stochastic, statistically stationary, scalar fields, the Rytov perturbation series for propagation in weakly fluctuating media, and the first Born approximation for weak scattering from particulate media. The results for transmission of the deterministic (laser) field may be obtained from our general results as a limiting case.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover and McGraw-Hill, 1967).
  2. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).
  3. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  4. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).
  5. A. Isimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice Hall, 1991).
  6. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  7. S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  8. A. G. Vinogradov and Y. A. Kravtsov, Radiophys. Quantum Electron. 16, 1055 (1973).
  9. G. Gbur and O. Korotkova, J. Opt. Soc. Am. A 24745 (2007).
    [CrossRef]
  10. O. Korotkova and E. Wolf, Phys. Rev. E 75, 056609 (2007).
    [CrossRef]
  11. S. Sahin and O. Korotkova, Opt. Lett. 34, 1762 (2009).
    [CrossRef] [PubMed]
  12. T. Wang and D. Zhao, Opt. Lett. 35, 318 (2010).
    [CrossRef] [PubMed]
  13. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  14. M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).
  15. Z. Tong and O. Korotkova, Phys. Rev. A 82, 033836 (2010).
    [CrossRef]
  16. T. Wang and D. Zhao, Opt. Lett. 35, 2412 (2010).
    [CrossRef] [PubMed]
  17. V. V. Nikishov and V. I. Nikishov, Int. J. Fluid Mech. Res. 27, 82 (2000).
  18. W. Gao, Opt. Commun. 260, 749 (2006).
    [CrossRef]

2010 (3)

2009 (1)

2007 (3)

G. Gbur and O. Korotkova, J. Opt. Soc. Am. A 24745 (2007).
[CrossRef]

O. Korotkova and E. Wolf, Phys. Rev. E 75, 056609 (2007).
[CrossRef]

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

2006 (1)

W. Gao, Opt. Commun. 260, 749 (2006).
[CrossRef]

2002 (1)

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

2000 (1)

V. V. Nikishov and V. I. Nikishov, Int. J. Fluid Mech. Res. 27, 82 (2000).

1999 (1)

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).

1998 (1)

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

1995 (1)

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

1991 (1)

A. Isimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice Hall, 1991).

1983 (1)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

1973 (1)

A. G. Vinogradov and Y. A. Kravtsov, Radiophys. Quantum Electron. 16, 1055 (1973).

1967 (1)

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover and McGraw-Hill, 1967).

1960 (1)

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

Gao, W.

W. Gao, Opt. Commun. 260, 749 (2006).
[CrossRef]

Gbur, G.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Isimaru, A.

A. Isimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice Hall, 1991).

Korotkova, O.

Z. Tong and O. Korotkova, Phys. Rev. A 82, 033836 (2010).
[CrossRef]

S. Sahin and O. Korotkova, Opt. Lett. 34, 1762 (2009).
[CrossRef] [PubMed]

O. Korotkova and E. Wolf, Phys. Rev. E 75, 056609 (2007).
[CrossRef]

G. Gbur and O. Korotkova, J. Opt. Soc. Am. A 24745 (2007).
[CrossRef]

Kravtsov, Y. A.

A. G. Vinogradov and Y. A. Kravtsov, Radiophys. Quantum Electron. 16, 1055 (1973).

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Mandel, L.

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

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Nikishov, V. I.

V. V. Nikishov and V. I. Nikishov, Int. J. Fluid Mech. Res. 27, 82 (2000).

Nikishov, V. V.

V. V. Nikishov and V. I. Nikishov, Int. J. Fluid Mech. Res. 27, 82 (2000).

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

Sahin, S.

Tatarskii, V. I.

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover and McGraw-Hill, 1967).

Tong, Z.

Z. Tong and O. Korotkova, Phys. Rev. A 82, 033836 (2010).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Vinogradov, A. G.

A. G. Vinogradov and Y. A. Kravtsov, Radiophys. Quantum Electron. 16, 1055 (1973).

Wang, T.

Wolf, E.

O. Korotkova and E. Wolf, Phys. Rev. E 75, 056609 (2007).
[CrossRef]

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

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).

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

Zhao, D.

Int. J. Fluid Mech. Res. (1)

V. V. Nikishov and V. I. Nikishov, Int. J. Fluid Mech. Res. 27, 82 (2000).

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

W. Gao, Opt. Commun. 260, 749 (2006).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

Z. Tong and O. Korotkova, Phys. Rev. A 82, 033836 (2010).
[CrossRef]

Phys. Rev. E (1)

O. Korotkova and E. Wolf, Phys. Rev. E 75, 056609 (2007).
[CrossRef]

Radiophys. Quantum Electron. (1)

A. G. Vinogradov and Y. A. Kravtsov, Radiophys. Quantum Electron. 16, 1055 (1973).

Other (9)

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

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover and McGraw-Hill, 1967).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

A. Isimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice Hall, 1991).

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

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

The intensity of a plane wave scattered by particles and normalized by its value on the axis versus radial distance from the optical axis: with turbulence (solid curve); without turbulence (dotted curve).

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

U ( i ) ( r ; ω ) = a ( i ) ( u ; ω ) e i k u · r d 2 u ,
U ( s ) ( r ; ω ) = a ( s ) ( u ; ω ) e i k u · r d 2 u ,
U ( s ) ( r ; ω ) = D F ( r ; ω ) U ( i ) ( r ; ω ) G ( | r r | ; ω ) d 3 r ,
G ( | r r | ; ω ) = e i k | r r | | r r | = i k 2 π 1 u z e i k u · ( r r ) d 2 u .
a ( s ) ( u ; ω ) = i k 2 π u z S ( u , u ; ω ) a ( i ) ( u ; ω ) d 2 u ,
S ( u , u ; ω ) = F [ k ( u u ) ; ω ] ,
U ( i ) ( r , ω ) = a ( i ) ( u , ω ) P u T ( r , ω ) d 2 u ,
a ( i ) ( u ; ω ) = 1 ( 2 π ) 2 U 0 ( ρ , ω ) e - i k u · ρ d 2 ρ ,
W ( r 1 , r 2 ; ω ) = U * ( r 1 ; ω ) U ( r 2 ; ω ) ,
W ( i ) ( r 1 , r 2 ; ω ) = a ( i ) * ( u 1 ; ω ) a ( i ) ( u 2 ; ω ) × P u 1 T * ( r 1 ; ω ) P u 2 T ( r 2 ; ω ) d 2 u 1 d 2 u 2 ,
a ( i ) * ( u 1 ; ω ) a ( i ) ( u 2 ; ω ) = A ( i ) ( u 1 , u 2 ; ω ) = 1 ( 2 π ) 4 U 0 * ( ρ 1 ; ω ) U 0 ( ρ 2 ; ω ) e i k ( u 1 · ρ 1 - u 2 ' · ρ 2 ) d 2 ρ 1 d 2 ρ 2 .
P u T ( r ; ω ) = e i k u · r exp [ ψ u ( 1 ) ( r , ω ) + ψ u ( 2 ) ( r , ω ) + ... ] .
P u 1 T * ( r 1 ; ω ) P u 2 T ( r 2 ; ω ) = e i k ( u 2 · r 2 - u 1 · r 1 ) × exp [ 2 E u 1 , u 2 ( 1 ) ( r 1 , r 2 ; ω ) + E u 1 , u 2 ( 2 ) ( r 1 , r 2 ; ω ) ] .
E u 1 , u 2 ( 1 ) ( r 2 r 1 ; ω ) = 2 π 2 k 2 0 L d z 0 κ d κ Φ n ( z , κ )
E u 1 , u 2 ( 2 ) ( r 2 r 1 ; ω ) = 4 π 2 k 2 0 L d z 0 κ d κ Φ n ( z , κ ) × J 0 [ κ | ( r 2 r 1 ) ( L z ) ( u 2 u 1 ) | ] ,
U ( s ) ( r ; ω ) = a ( s ) ( u ; ω ) P u T ( r ; ω ) d 2 u .
W ( s ) ( r 1 , r 2 ; ω ) = U ( s ) * ( r 1 ; ω ) U ( s ) ( r 2 ; ω ) = a ( s ) * ( u 1 ; ω ) a ( s ) ( u 2 ; ω ) P u 1 T * ( r 1 ; ω ) P u 2 T ( r 2 ; ω ) d 2 u 1 d 2 u 2 .
a ( s ) * ( u 1 ; ω ) a ( s ) ( u 2 ; ω ) = ( k 2 π ) 2 1 u 1 z u 2 z S * ( u 1 , u 1 ; ω ) S ( u 2 , u 2 ; ω ) × a ( i ) * ( u 1 ; ω ) a ( i ) ( u 2 ; ω ) d 2 u 1 d 2 u 2 .
S * ( u 1 , u 1 ; ω ) S ( u 2 , u 2 ; ω ) = C F [ - k ( u 1 u 1 ) , k ( u 2 u 2 ) ; ω ] ,
C F [ K 1 , K 2 ; ω ] = D D F * ( r 1 ; ω ) F ( r 2 ; ω ) × e i ( K 1 · r 1 + K 2 · r 2 ) d 3 r 1 d 3 r 2 .
W ( s ) ( r 1 , r 2 ; ω ) = ( k 2 π ) 2 1 u 1 z u 2 z A ( i ) ( u 1 , u 2 ; ω ) × C F [ K 1 , K 2 ; ω ] d 2 u 1 d 2 u 2 e i k ( u 2 · r 2 u 1 · r 1 ) × exp [ 2 E u 1 , u 2 ( 1 ) ( r 1 , r 2 ; ω ) + E u 1 , u 2 ( 2 ) ( r 1 , r 2 ; ω ) ] d 2 u 1 d 2 u 2 .

Metrics