Abstract

Optical wireless communication has been the subject of much research in recent years because of the increasing interest in laser satellite–ground links and urban optical wireless communication. The major sources of performance degradation have been identified as the spatial, angular, and temporal spread of the propagating beam when the propagation channel is multiscattering, resulting in reduced power reception and intersignal interference, as well as turbulence-induced scintillations and noise due to receiver circuitry and background illumination. However, coherence effects due to multipath interference caused by a scattering propagation channel do not appear to have been treated in detail in the scientific literature. We attempt a theoretical analysis of coherence interference in optical wireless communication through scattering channels and try to quantify the resultant performance degradation for different media. We conclude that coherence interference is discernible in optical wireless communication through scattering channels and is highly dependent on the microscopic nature of the propagation medium.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Jaruwatanadilok, A. Ishimaru, and Y. Kuga, "Optical imaging through clouds and fog," IEEE Trans. Geosci. Remote Sens. 41, 1834-1843 (2003).
    [CrossRef]
  2. S. Jaruwatandilok, U. Ketprom, Y. Kuga, and A. Ishimaru, "Modeling the point-to-point wireless communication channel under the adverse weather conditions," IEICE Trans. Fundamentals , Special Issue on Wave Technologies for Wireless and Optical Communications E87-C, 1455-1462 (2004).
  3. R. Elaloufi, R. Carminati, and J. Greffet, "Time-dependent transport through scattering media: from radiative transfer to diffusion," J. Opt. 4, S103-S108 (2002).
    [CrossRef]
  4. G. N. Plass and G. W. Kattawar, "Monte Carlo calculations of light scattering from clouds," Appl. Opt. 7, 415-419 (1968).
    [CrossRef] [PubMed]
  5. D. Kedar and S. Arnon, "Optical wireless communication through fog in the presence of pointing errors," Appl. Opt. 42, 4946-4954 (2003).
    [CrossRef] [PubMed]
  6. S. Arnon, D. Sadot, and N. S. Kopeika, "Simple mathematical models for temporal, spatial, angular and attenuation characteristics of light propagating through the atmosphere for space optical communication: Monte Carlo simulations," J. Mod. Opt. 41, 1955-1972 (1994).
    [CrossRef]
  7. K. Furutsu, "Multiple scattering of waves in a medium of randomly distributed particles and derivation of the transport equation," Radio Sci. 10, 29-44 (1975).
    [CrossRef]
  8. Y. Shen, K. Lu, and W. Gu, "Coherent and incoherent crosstalk in WDM optical networks," J. Lightwave Technol. 17, 759-764 (1999).
    [CrossRef]
  9. K. Ho and J. M. Kahn, "Methods for crosstalk measurement and reduction in dense WDM systems," J. Lightwave Technol. 14, 1127-1135 (1996).
    [CrossRef]
  10. C. Yu, W. Wang, and S. D. Brorson, "System degradation due to multipath coherent crosstalk in WDM network nodes," J. Lightwave Technol. 16, 1380-1386 (1998).
    [CrossRef]
  11. P. Saengudomlert and M. Médard, "Guaranteeing the BER in transparent optical networks using OOK signaling," IEEE J. Sel. Areas Eng. 20, 786-799 (2002).
    [CrossRef]
  12. D. Kedar and S. Arnon, "Coherence interference in optical wireless communication through scattering channels," in Free-Space Laser Communication and Laser Imaging V (SPIE Press, 2005).
  13. N. S. Kopeika, A System Engineering Approach to Imaging (SPIE Press, 1998).
  14. A. Yariv, Optical Electronics in Modern Communication (Oxford U. Press, 1997).
  15. C. H. Henry, "Phase noise in semiconductor lasers," J. Lightwave Technol. 4, 298-311 (1986).
    [CrossRef]
  16. M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, 1968).
  17. L. L. Foldy, "The multiple scattering of waves," Phys. Rev. 67, 107-119 (1945).
    [CrossRef]
  18. A. Ishimaru, "Correlation functions of a wave in a random distribution of stationary and moving scatterers," Radio Sci. 10, 45-52 (1975).
    [CrossRef]
  19. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Press, 1998).
  20. E. P. Shettle, "Models of aerosols, clouds and precipitation for atmospheric propagation studies" (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).
  21. T. S. Chu and D. C. Hogg, "Effects of precipitation on propagation at 0.63, 3.5, and 10.6 microns," Bell Syst. Tech. J. 47, 723-759 (1968).
  22. R. W. Fenn, S. A. Clough, W. O. Gallery, R. E. Good, F. X. Kreizys, J. D. Mill, L. S. Rothman, E. P. Shettle, and F. E. Volz, "Optical and infrared properties of the atmosphere," in Handbook of Geophysics and Space Environment, A. S. Jeursa, ed. (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1985), Chap. 18.
  23. A. Kokhanovsky, Optics of Light Scattering Media: Problems and Solutions (Wiley, 1999).
  24. M. Tur, "Numerical solutions for the fourth moment of a finite beam propagating in a random medium," J. Opt. Soc. Am. A 2, 2161-2170 (1985).
    [CrossRef]
  25. X. Zhu and J. M. Kahn, "Free-space optical communication through atmospheric turbulence channels," IEEE Trans. Commun. 50, 1293-1300 (2002).
    [CrossRef]

2004 (1)

S. Jaruwatandilok, U. Ketprom, Y. Kuga, and A. Ishimaru, "Modeling the point-to-point wireless communication channel under the adverse weather conditions," IEICE Trans. Fundamentals , Special Issue on Wave Technologies for Wireless and Optical Communications E87-C, 1455-1462 (2004).

2003 (2)

S. Jaruwatanadilok, A. Ishimaru, and Y. Kuga, "Optical imaging through clouds and fog," IEEE Trans. Geosci. Remote Sens. 41, 1834-1843 (2003).
[CrossRef]

D. Kedar and S. Arnon, "Optical wireless communication through fog in the presence of pointing errors," Appl. Opt. 42, 4946-4954 (2003).
[CrossRef] [PubMed]

2002 (3)

X. Zhu and J. M. Kahn, "Free-space optical communication through atmospheric turbulence channels," IEEE Trans. Commun. 50, 1293-1300 (2002).
[CrossRef]

P. Saengudomlert and M. Médard, "Guaranteeing the BER in transparent optical networks using OOK signaling," IEEE J. Sel. Areas Eng. 20, 786-799 (2002).
[CrossRef]

R. Elaloufi, R. Carminati, and J. Greffet, "Time-dependent transport through scattering media: from radiative transfer to diffusion," J. Opt. 4, S103-S108 (2002).
[CrossRef]

1999 (1)

1998 (1)

1996 (1)

K. Ho and J. M. Kahn, "Methods for crosstalk measurement and reduction in dense WDM systems," J. Lightwave Technol. 14, 1127-1135 (1996).
[CrossRef]

1994 (1)

S. Arnon, D. Sadot, and N. S. Kopeika, "Simple mathematical models for temporal, spatial, angular and attenuation characteristics of light propagating through the atmosphere for space optical communication: Monte Carlo simulations," J. Mod. Opt. 41, 1955-1972 (1994).
[CrossRef]

1986 (1)

C. H. Henry, "Phase noise in semiconductor lasers," J. Lightwave Technol. 4, 298-311 (1986).
[CrossRef]

1985 (1)

1975 (2)

A. Ishimaru, "Correlation functions of a wave in a random distribution of stationary and moving scatterers," Radio Sci. 10, 45-52 (1975).
[CrossRef]

K. Furutsu, "Multiple scattering of waves in a medium of randomly distributed particles and derivation of the transport equation," Radio Sci. 10, 29-44 (1975).
[CrossRef]

1968 (2)

T. S. Chu and D. C. Hogg, "Effects of precipitation on propagation at 0.63, 3.5, and 10.6 microns," Bell Syst. Tech. J. 47, 723-759 (1968).

G. N. Plass and G. W. Kattawar, "Monte Carlo calculations of light scattering from clouds," Appl. Opt. 7, 415-419 (1968).
[CrossRef] [PubMed]

1945 (1)

L. L. Foldy, "The multiple scattering of waves," Phys. Rev. 67, 107-119 (1945).
[CrossRef]

Andrews, L. C.

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

Arnon, S.

D. Kedar and S. Arnon, "Optical wireless communication through fog in the presence of pointing errors," Appl. Opt. 42, 4946-4954 (2003).
[CrossRef] [PubMed]

S. Arnon, D. Sadot, and N. S. Kopeika, "Simple mathematical models for temporal, spatial, angular and attenuation characteristics of light propagating through the atmosphere for space optical communication: Monte Carlo simulations," J. Mod. Opt. 41, 1955-1972 (1994).
[CrossRef]

D. Kedar and S. Arnon, "Coherence interference in optical wireless communication through scattering channels," in Free-Space Laser Communication and Laser Imaging V (SPIE Press, 2005).

Beran, M. J.

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, 1968).

Brorson, S. D.

Carminati, R.

R. Elaloufi, R. Carminati, and J. Greffet, "Time-dependent transport through scattering media: from radiative transfer to diffusion," J. Opt. 4, S103-S108 (2002).
[CrossRef]

Chu, T. S.

T. S. Chu and D. C. Hogg, "Effects of precipitation on propagation at 0.63, 3.5, and 10.6 microns," Bell Syst. Tech. J. 47, 723-759 (1968).

Clough, S. A.

R. W. Fenn, S. A. Clough, W. O. Gallery, R. E. Good, F. X. Kreizys, J. D. Mill, L. S. Rothman, E. P. Shettle, and F. E. Volz, "Optical and infrared properties of the atmosphere," in Handbook of Geophysics and Space Environment, A. S. Jeursa, ed. (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1985), Chap. 18.

Elaloufi, R.

R. Elaloufi, R. Carminati, and J. Greffet, "Time-dependent transport through scattering media: from radiative transfer to diffusion," J. Opt. 4, S103-S108 (2002).
[CrossRef]

Fenn, R. W.

R. W. Fenn, S. A. Clough, W. O. Gallery, R. E. Good, F. X. Kreizys, J. D. Mill, L. S. Rothman, E. P. Shettle, and F. E. Volz, "Optical and infrared properties of the atmosphere," in Handbook of Geophysics and Space Environment, A. S. Jeursa, ed. (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1985), Chap. 18.

Foldy, L. L.

L. L. Foldy, "The multiple scattering of waves," Phys. Rev. 67, 107-119 (1945).
[CrossRef]

Furutsu, K.

K. Furutsu, "Multiple scattering of waves in a medium of randomly distributed particles and derivation of the transport equation," Radio Sci. 10, 29-44 (1975).
[CrossRef]

Gallery, W. O.

R. W. Fenn, S. A. Clough, W. O. Gallery, R. E. Good, F. X. Kreizys, J. D. Mill, L. S. Rothman, E. P. Shettle, and F. E. Volz, "Optical and infrared properties of the atmosphere," in Handbook of Geophysics and Space Environment, A. S. Jeursa, ed. (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1985), Chap. 18.

Good, R. E.

R. W. Fenn, S. A. Clough, W. O. Gallery, R. E. Good, F. X. Kreizys, J. D. Mill, L. S. Rothman, E. P. Shettle, and F. E. Volz, "Optical and infrared properties of the atmosphere," in Handbook of Geophysics and Space Environment, A. S. Jeursa, ed. (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1985), Chap. 18.

Greffet, J.

R. Elaloufi, R. Carminati, and J. Greffet, "Time-dependent transport through scattering media: from radiative transfer to diffusion," J. Opt. 4, S103-S108 (2002).
[CrossRef]

Gu, W.

Henry, C. H.

C. H. Henry, "Phase noise in semiconductor lasers," J. Lightwave Technol. 4, 298-311 (1986).
[CrossRef]

Ho, K.

K. Ho and J. M. Kahn, "Methods for crosstalk measurement and reduction in dense WDM systems," J. Lightwave Technol. 14, 1127-1135 (1996).
[CrossRef]

Hogg, D. C.

T. S. Chu and D. C. Hogg, "Effects of precipitation on propagation at 0.63, 3.5, and 10.6 microns," Bell Syst. Tech. J. 47, 723-759 (1968).

Ishimaru, A.

S. Jaruwatandilok, U. Ketprom, Y. Kuga, and A. Ishimaru, "Modeling the point-to-point wireless communication channel under the adverse weather conditions," IEICE Trans. Fundamentals , Special Issue on Wave Technologies for Wireless and Optical Communications E87-C, 1455-1462 (2004).

S. Jaruwatanadilok, A. Ishimaru, and Y. Kuga, "Optical imaging through clouds and fog," IEEE Trans. Geosci. Remote Sens. 41, 1834-1843 (2003).
[CrossRef]

A. Ishimaru, "Correlation functions of a wave in a random distribution of stationary and moving scatterers," Radio Sci. 10, 45-52 (1975).
[CrossRef]

Jaruwatanadilok, S.

S. Jaruwatanadilok, A. Ishimaru, and Y. Kuga, "Optical imaging through clouds and fog," IEEE Trans. Geosci. Remote Sens. 41, 1834-1843 (2003).
[CrossRef]

Jaruwatandilok, S.

S. Jaruwatandilok, U. Ketprom, Y. Kuga, and A. Ishimaru, "Modeling the point-to-point wireless communication channel under the adverse weather conditions," IEICE Trans. Fundamentals , Special Issue on Wave Technologies for Wireless and Optical Communications E87-C, 1455-1462 (2004).

Kahn, J. M.

X. Zhu and J. M. Kahn, "Free-space optical communication through atmospheric turbulence channels," IEEE Trans. Commun. 50, 1293-1300 (2002).
[CrossRef]

K. Ho and J. M. Kahn, "Methods for crosstalk measurement and reduction in dense WDM systems," J. Lightwave Technol. 14, 1127-1135 (1996).
[CrossRef]

Kattawar, G. W.

Kedar, D.

D. Kedar and S. Arnon, "Optical wireless communication through fog in the presence of pointing errors," Appl. Opt. 42, 4946-4954 (2003).
[CrossRef] [PubMed]

D. Kedar and S. Arnon, "Coherence interference in optical wireless communication through scattering channels," in Free-Space Laser Communication and Laser Imaging V (SPIE Press, 2005).

Ketprom, U.

S. Jaruwatandilok, U. Ketprom, Y. Kuga, and A. Ishimaru, "Modeling the point-to-point wireless communication channel under the adverse weather conditions," IEICE Trans. Fundamentals , Special Issue on Wave Technologies for Wireless and Optical Communications E87-C, 1455-1462 (2004).

Kokhanovsky, A.

A. Kokhanovsky, Optics of Light Scattering Media: Problems and Solutions (Wiley, 1999).

Kopeika, N. S.

S. Arnon, D. Sadot, and N. S. Kopeika, "Simple mathematical models for temporal, spatial, angular and attenuation characteristics of light propagating through the atmosphere for space optical communication: Monte Carlo simulations," J. Mod. Opt. 41, 1955-1972 (1994).
[CrossRef]

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE Press, 1998).

Kreizys, F. X.

R. W. Fenn, S. A. Clough, W. O. Gallery, R. E. Good, F. X. Kreizys, J. D. Mill, L. S. Rothman, E. P. Shettle, and F. E. Volz, "Optical and infrared properties of the atmosphere," in Handbook of Geophysics and Space Environment, A. S. Jeursa, ed. (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1985), Chap. 18.

Kuga, Y.

S. Jaruwatandilok, U. Ketprom, Y. Kuga, and A. Ishimaru, "Modeling the point-to-point wireless communication channel under the adverse weather conditions," IEICE Trans. Fundamentals , Special Issue on Wave Technologies for Wireless and Optical Communications E87-C, 1455-1462 (2004).

S. Jaruwatanadilok, A. Ishimaru, and Y. Kuga, "Optical imaging through clouds and fog," IEEE Trans. Geosci. Remote Sens. 41, 1834-1843 (2003).
[CrossRef]

Lu, K.

Médard, M.

P. Saengudomlert and M. Médard, "Guaranteeing the BER in transparent optical networks using OOK signaling," IEEE J. Sel. Areas Eng. 20, 786-799 (2002).
[CrossRef]

Mill, J. D.

R. W. Fenn, S. A. Clough, W. O. Gallery, R. E. Good, F. X. Kreizys, J. D. Mill, L. S. Rothman, E. P. Shettle, and F. E. Volz, "Optical and infrared properties of the atmosphere," in Handbook of Geophysics and Space Environment, A. S. Jeursa, ed. (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1985), Chap. 18.

Parrent, G. B.

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, 1968).

Phillips, R. L.

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

Plass, G. N.

Rothman, L. S.

R. W. Fenn, S. A. Clough, W. O. Gallery, R. E. Good, F. X. Kreizys, J. D. Mill, L. S. Rothman, E. P. Shettle, and F. E. Volz, "Optical and infrared properties of the atmosphere," in Handbook of Geophysics and Space Environment, A. S. Jeursa, ed. (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1985), Chap. 18.

Sadot, D.

S. Arnon, D. Sadot, and N. S. Kopeika, "Simple mathematical models for temporal, spatial, angular and attenuation characteristics of light propagating through the atmosphere for space optical communication: Monte Carlo simulations," J. Mod. Opt. 41, 1955-1972 (1994).
[CrossRef]

Saengudomlert, P.

P. Saengudomlert and M. Médard, "Guaranteeing the BER in transparent optical networks using OOK signaling," IEEE J. Sel. Areas Eng. 20, 786-799 (2002).
[CrossRef]

Shen, Y.

Shettle, E. P.

R. W. Fenn, S. A. Clough, W. O. Gallery, R. E. Good, F. X. Kreizys, J. D. Mill, L. S. Rothman, E. P. Shettle, and F. E. Volz, "Optical and infrared properties of the atmosphere," in Handbook of Geophysics and Space Environment, A. S. Jeursa, ed. (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1985), Chap. 18.

E. P. Shettle, "Models of aerosols, clouds and precipitation for atmospheric propagation studies" (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

Tur, M.

Volz, F. E.

R. W. Fenn, S. A. Clough, W. O. Gallery, R. E. Good, F. X. Kreizys, J. D. Mill, L. S. Rothman, E. P. Shettle, and F. E. Volz, "Optical and infrared properties of the atmosphere," in Handbook of Geophysics and Space Environment, A. S. Jeursa, ed. (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1985), Chap. 18.

Wang, W.

Yariv, A.

A. Yariv, Optical Electronics in Modern Communication (Oxford U. Press, 1997).

Yu, C.

Zhu, X.

X. Zhu and J. M. Kahn, "Free-space optical communication through atmospheric turbulence channels," IEEE Trans. Commun. 50, 1293-1300 (2002).
[CrossRef]

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

T. S. Chu and D. C. Hogg, "Effects of precipitation on propagation at 0.63, 3.5, and 10.6 microns," Bell Syst. Tech. J. 47, 723-759 (1968).

IEEE J. Sel. Areas Eng. (1)

P. Saengudomlert and M. Médard, "Guaranteeing the BER in transparent optical networks using OOK signaling," IEEE J. Sel. Areas Eng. 20, 786-799 (2002).
[CrossRef]

IEEE Trans. Commun. (1)

X. Zhu and J. M. Kahn, "Free-space optical communication through atmospheric turbulence channels," IEEE Trans. Commun. 50, 1293-1300 (2002).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

S. Jaruwatanadilok, A. Ishimaru, and Y. Kuga, "Optical imaging through clouds and fog," IEEE Trans. Geosci. Remote Sens. 41, 1834-1843 (2003).
[CrossRef]

IEICE Trans. Fundamentals (1)

S. Jaruwatandilok, U. Ketprom, Y. Kuga, and A. Ishimaru, "Modeling the point-to-point wireless communication channel under the adverse weather conditions," IEICE Trans. Fundamentals , Special Issue on Wave Technologies for Wireless and Optical Communications E87-C, 1455-1462 (2004).

J. Lightwave Technol. (4)

C. H. Henry, "Phase noise in semiconductor lasers," J. Lightwave Technol. 4, 298-311 (1986).
[CrossRef]

Y. Shen, K. Lu, and W. Gu, "Coherent and incoherent crosstalk in WDM optical networks," J. Lightwave Technol. 17, 759-764 (1999).
[CrossRef]

C. Yu, W. Wang, and S. D. Brorson, "System degradation due to multipath coherent crosstalk in WDM network nodes," J. Lightwave Technol. 16, 1380-1386 (1998).
[CrossRef]

K. Ho and J. M. Kahn, "Methods for crosstalk measurement and reduction in dense WDM systems," J. Lightwave Technol. 14, 1127-1135 (1996).
[CrossRef]

J. Mod. Opt. (1)

S. Arnon, D. Sadot, and N. S. Kopeika, "Simple mathematical models for temporal, spatial, angular and attenuation characteristics of light propagating through the atmosphere for space optical communication: Monte Carlo simulations," J. Mod. Opt. 41, 1955-1972 (1994).
[CrossRef]

J. Opt. (1)

R. Elaloufi, R. Carminati, and J. Greffet, "Time-dependent transport through scattering media: from radiative transfer to diffusion," J. Opt. 4, S103-S108 (2002).
[CrossRef]

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

Phys. Rev. (1)

L. L. Foldy, "The multiple scattering of waves," Phys. Rev. 67, 107-119 (1945).
[CrossRef]

Radio Sci. (2)

A. Ishimaru, "Correlation functions of a wave in a random distribution of stationary and moving scatterers," Radio Sci. 10, 45-52 (1975).
[CrossRef]

K. Furutsu, "Multiple scattering of waves in a medium of randomly distributed particles and derivation of the transport equation," Radio Sci. 10, 29-44 (1975).
[CrossRef]

Other (8)

D. Kedar and S. Arnon, "Coherence interference in optical wireless communication through scattering channels," in Free-Space Laser Communication and Laser Imaging V (SPIE Press, 2005).

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE Press, 1998).

A. Yariv, Optical Electronics in Modern Communication (Oxford U. Press, 1997).

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

E. P. Shettle, "Models of aerosols, clouds and precipitation for atmospheric propagation studies" (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, 1968).

R. W. Fenn, S. A. Clough, W. O. Gallery, R. E. Good, F. X. Kreizys, J. D. Mill, L. S. Rothman, E. P. Shettle, and F. E. Volz, "Optical and infrared properties of the atmosphere," in Handbook of Geophysics and Space Environment, A. S. Jeursa, ed. (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1985), Chap. 18.

A. Kokhanovsky, Optics of Light Scattering Media: Problems and Solutions (Wiley, 1999).

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 (2)

Fig. 1
Fig. 1

Probability distribution functions of scatter angle for (a) moderate fog and (b) heavy fog derived using Mie theory; radiation wavelength is 670 nm.

Fig. 2
Fig. 2

Scatter-induced scintillation index versus OD for heavy and moderate fogs; radiation wavelength is 670 nm.

Equations (16)

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

Γ m 12 ( r 1 , r 2 , τ ) = lim T 1 2 T - T T U 1 ( r 1 , t ) × U 2 * ( r 2 , t + τ ) d t ,
lim | r 1 r 2 | l c Γ m 12 ( r 1 , r 2 , τ ) 0 .
lim τ τ c Γ m 12 ( r 1 , r 2 , τ )        0 .
U ( r 1 ) = U ( r 1 ) + U f ( r 1 ) ,
| U ( r 1 ) | 2 = | U ( r 1 ) | 2 + | U f ( r 1 ) | 2 .
σ scat 2 = | U ( r 1 ) | 2 | U ( r 1 ) | 2 | U ( r 1 ) | 2 .
E tot = E cos ω t + i = 1 N ε i cos ( ω t + φ i ) .
P = 1 2 [ E tot ] [ E tot * ] .
P = E 2 2 + i = 1 N ε i     2 2 + E i = 1 N ε i cos ( φ i ) + 1 2 i = 1 N j = 1 , j i N ε i ε j × cos ( φ i φ j )
P = U tot U tot * .
U sc = i = 1 N ε i cos ( ω t + φ i ) ,
U tot = U T + U sc .
U sc = i = 1 N s ε i cos ( ω t + φ i ) + j = 1 N d ε j cos ( ω t + φ j ) ,
P ¯ av = 1 2 π 0 2 π P ( φ ) f ( φ ) d φ .
σ co   int 2 = 1 2 π 0 2 π [ P ( φ ) P ¯ av ] 2 f ( φ ) d φ .
σ I     2 = exp ( 4 σ χ 2 ) 1 ,

Metrics