Abstract

Measurements and analysis of a blue-green pulsed propagation through fog have identified three distinct regions for energy transport. Region I small number of attenuation lengths τ in the path (0 < τ < 13): here, the direct unscattered beam dominates with an exponential pathloss decay of 4.34 dB/τ. Region II medium number of scattering lengths (13 < τ < 32): multiple scattering is strongly peaked in the forward direction. This energy exhibits small spatial, angular, and temporal spreading and is the main contributor to the received signal. This component also decays exponentially but at at much slower rate of ~2 dB/τ. Region III very large number of scattering lengths (τ > 32): the direct beam and the forwardscattered beam have decayed to the point where the diffusion type multiple-scattered radiation is the dominant energy received. This component does not decay exponentially but results in large spatial, angular, and temporal spreading. This paper presents quantitative data on Region II.

© 1979 Optical Society of America

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References

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  1. E. A. Bucher, Appl. Opt. 12, 2391 (1973).
    [CrossRef] [PubMed]
  2. E. A. Bucher, Proceedings of National Electronics Conference Vol. 29 (1974), p. 180.
  3. R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976).
  4. R. S. Kennedy, Fading Dispersive Communication Channels (Wiley, New York, 1969).
  5. R. Price, P. E. Green, Proc. IRE 46, 555 (1958).
    [CrossRef]
  6. R. A. Dell-Imagine, “A Study of Multiple Scattering of Optical Radiation with Application to Laser Communications,” in Advances in Communication Systems, V. A. Balakrishnar, Ed. (Academic, New York, 1966), p. 1.
  7. H. M. Heggestad, “Optical Communication Through Multiple-Scattering Media,” Research Laboratory for Electronics, MIT, Cambridge, Technical Report 472 (1968).
  8. D. Arnush, J. Opt. Soc. Am. 62, 1109 (1972).
    [CrossRef]
  9. S. T. Hong, A. Ishimara, Radio Sci. 11, 551 (1976).
    [CrossRef]
  10. A. Ishimara, Proc. IEEE 65, 1030 (1976).
    [CrossRef]
  11. R. L. Fante, IEEE Trans. Antennas Propag. AP-21, 750 (1973).
    [CrossRef]
  12. H. T. Yura, Radiance Section, URSI Proceedings, Commission F of the Conference on Propagation in Nonionized Media, La Bouk, France (1977).
  13. L. B. Stotts, J. Opt. Soc. Am. 67, 815 (1976).
    [CrossRef]
  14. C. H. Liu, K. C. Yeh, J. Opt. Soc. Am. 67, 1261 (1977).
    [CrossRef]
  15. D. L. Fried, Opt. Lett. 1, 104 (1977).
    [CrossRef] [PubMed]
  16. G. N. Plass, G. W. Kattawar, Appl. Opt. 7, 415 (1968).
    [CrossRef] [PubMed]
  17. E. A. Bucher, R. M. Lerner, C. W. Niessen, Proc. IEEE 58, 1564 (1970).
    [CrossRef]
  18. E. A. Bucher, R. M. Lerner, Appl. Opt. 12, 2401 (1973).
    [CrossRef] [PubMed]
  19. W. H. Paik, M. Tebyani, D. J. Epstein, R. S. Kennedy, J. H. Shapiro, Appl. Opt. 17, 899 (1978).
    [CrossRef] [PubMed]
  20. G. C. Mooradian, V. J. Adrian, P. H. Levine, W. R. Stone, “Extended Line-of-Sight Optical Communications Study,” NELC Technical Report 1988, 30June1976.
  21. A. Gordon, Proc. Soc. Photo Opt. Instrum. Eng. 64, 85 (1975).
  22. W. H. Wells, “Theory of Small Angle Scattering,” in Optics of the Sea, AGARD-LS-61, August1973.
  23. E. Fermi, Nuclear Physics (U. Chicago Press, Chicago, 1950).
  24. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 643–647.
  25. G. C. Mooradian, M. Geller, L. B. Stotts, H. G. Hughes, “Experimental Test Plan to Investigate the Propagation of Blue/Green Radiation Through Clouds,” NELC Technical Note 3233, 1October1977. NELC technical notes are informal documents intended chiefly for internal use.
  26. J. R. Clark, J. R. Baird, IEEE National Telecommunications Conference Record 1, 6.1 (1975).
  27. H. G. Hughes, “Aerosol Extinction of Photopic and IR Wavelengths,” NOSC Technical Report 143, 23August1977.
  28. L. B. Stotts, Appl. Opt. 17, 504 (1978).
    [CrossRef] [PubMed]

1978 (2)

1977 (3)

G. C. Mooradian, M. Geller, L. B. Stotts, H. G. Hughes, “Experimental Test Plan to Investigate the Propagation of Blue/Green Radiation Through Clouds,” NELC Technical Note 3233, 1October1977. NELC technical notes are informal documents intended chiefly for internal use.

C. H. Liu, K. C. Yeh, J. Opt. Soc. Am. 67, 1261 (1977).
[CrossRef]

D. L. Fried, Opt. Lett. 1, 104 (1977).
[CrossRef] [PubMed]

1976 (3)

S. T. Hong, A. Ishimara, Radio Sci. 11, 551 (1976).
[CrossRef]

A. Ishimara, Proc. IEEE 65, 1030 (1976).
[CrossRef]

L. B. Stotts, J. Opt. Soc. Am. 67, 815 (1976).
[CrossRef]

1975 (2)

A. Gordon, Proc. Soc. Photo Opt. Instrum. Eng. 64, 85 (1975).

J. R. Clark, J. R. Baird, IEEE National Telecommunications Conference Record 1, 6.1 (1975).

1974 (1)

E. A. Bucher, Proceedings of National Electronics Conference Vol. 29 (1974), p. 180.

1973 (4)

E. A. Bucher, Appl. Opt. 12, 2391 (1973).
[CrossRef] [PubMed]

R. L. Fante, IEEE Trans. Antennas Propag. AP-21, 750 (1973).
[CrossRef]

E. A. Bucher, R. M. Lerner, Appl. Opt. 12, 2401 (1973).
[CrossRef] [PubMed]

W. H. Wells, “Theory of Small Angle Scattering,” in Optics of the Sea, AGARD-LS-61, August1973.

1972 (1)

1970 (1)

E. A. Bucher, R. M. Lerner, C. W. Niessen, Proc. IEEE 58, 1564 (1970).
[CrossRef]

1968 (1)

1958 (1)

R. Price, P. E. Green, Proc. IRE 46, 555 (1958).
[CrossRef]

Adrian, V. J.

G. C. Mooradian, V. J. Adrian, P. H. Levine, W. R. Stone, “Extended Line-of-Sight Optical Communications Study,” NELC Technical Report 1988, 30June1976.

Arnush, D.

Baird, J. R.

J. R. Clark, J. R. Baird, IEEE National Telecommunications Conference Record 1, 6.1 (1975).

Bucher, E. A.

E. A. Bucher, Proceedings of National Electronics Conference Vol. 29 (1974), p. 180.

E. A. Bucher, Appl. Opt. 12, 2391 (1973).
[CrossRef] [PubMed]

E. A. Bucher, R. M. Lerner, Appl. Opt. 12, 2401 (1973).
[CrossRef] [PubMed]

E. A. Bucher, R. M. Lerner, C. W. Niessen, Proc. IEEE 58, 1564 (1970).
[CrossRef]

Clark, J. R.

J. R. Clark, J. R. Baird, IEEE National Telecommunications Conference Record 1, 6.1 (1975).

Dell-Imagine, R. A.

R. A. Dell-Imagine, “A Study of Multiple Scattering of Optical Radiation with Application to Laser Communications,” in Advances in Communication Systems, V. A. Balakrishnar, Ed. (Academic, New York, 1966), p. 1.

Epstein, D. J.

Fante, R. L.

R. L. Fante, IEEE Trans. Antennas Propag. AP-21, 750 (1973).
[CrossRef]

Fermi, E.

E. Fermi, Nuclear Physics (U. Chicago Press, Chicago, 1950).

Fried, D. L.

Gagliardi, R. M.

R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976).

Geller, M.

G. C. Mooradian, M. Geller, L. B. Stotts, H. G. Hughes, “Experimental Test Plan to Investigate the Propagation of Blue/Green Radiation Through Clouds,” NELC Technical Note 3233, 1October1977. NELC technical notes are informal documents intended chiefly for internal use.

Gordon, A.

A. Gordon, Proc. Soc. Photo Opt. Instrum. Eng. 64, 85 (1975).

Green, P. E.

R. Price, P. E. Green, Proc. IRE 46, 555 (1958).
[CrossRef]

Heggestad, H. M.

H. M. Heggestad, “Optical Communication Through Multiple-Scattering Media,” Research Laboratory for Electronics, MIT, Cambridge, Technical Report 472 (1968).

Hong, S. T.

S. T. Hong, A. Ishimara, Radio Sci. 11, 551 (1976).
[CrossRef]

Hughes, H. G.

G. C. Mooradian, M. Geller, L. B. Stotts, H. G. Hughes, “Experimental Test Plan to Investigate the Propagation of Blue/Green Radiation Through Clouds,” NELC Technical Note 3233, 1October1977. NELC technical notes are informal documents intended chiefly for internal use.

H. G. Hughes, “Aerosol Extinction of Photopic and IR Wavelengths,” NOSC Technical Report 143, 23August1977.

Ishimara, A.

S. T. Hong, A. Ishimara, Radio Sci. 11, 551 (1976).
[CrossRef]

A. Ishimara, Proc. IEEE 65, 1030 (1976).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 643–647.

Karp, S.

R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976).

Kattawar, G. W.

Kennedy, R. S.

W. H. Paik, M. Tebyani, D. J. Epstein, R. S. Kennedy, J. H. Shapiro, Appl. Opt. 17, 899 (1978).
[CrossRef] [PubMed]

R. S. Kennedy, Fading Dispersive Communication Channels (Wiley, New York, 1969).

Lerner, R. M.

E. A. Bucher, R. M. Lerner, Appl. Opt. 12, 2401 (1973).
[CrossRef] [PubMed]

E. A. Bucher, R. M. Lerner, C. W. Niessen, Proc. IEEE 58, 1564 (1970).
[CrossRef]

Levine, P. H.

G. C. Mooradian, V. J. Adrian, P. H. Levine, W. R. Stone, “Extended Line-of-Sight Optical Communications Study,” NELC Technical Report 1988, 30June1976.

Liu, C. H.

Mooradian, G. C.

G. C. Mooradian, M. Geller, L. B. Stotts, H. G. Hughes, “Experimental Test Plan to Investigate the Propagation of Blue/Green Radiation Through Clouds,” NELC Technical Note 3233, 1October1977. NELC technical notes are informal documents intended chiefly for internal use.

G. C. Mooradian, V. J. Adrian, P. H. Levine, W. R. Stone, “Extended Line-of-Sight Optical Communications Study,” NELC Technical Report 1988, 30June1976.

Niessen, C. W.

E. A. Bucher, R. M. Lerner, C. W. Niessen, Proc. IEEE 58, 1564 (1970).
[CrossRef]

Paik, W. H.

Plass, G. N.

Price, R.

R. Price, P. E. Green, Proc. IRE 46, 555 (1958).
[CrossRef]

Shapiro, J. H.

Stone, W. R.

G. C. Mooradian, V. J. Adrian, P. H. Levine, W. R. Stone, “Extended Line-of-Sight Optical Communications Study,” NELC Technical Report 1988, 30June1976.

Stotts, L. B.

L. B. Stotts, Appl. Opt. 17, 504 (1978).
[CrossRef] [PubMed]

G. C. Mooradian, M. Geller, L. B. Stotts, H. G. Hughes, “Experimental Test Plan to Investigate the Propagation of Blue/Green Radiation Through Clouds,” NELC Technical Note 3233, 1October1977. NELC technical notes are informal documents intended chiefly for internal use.

L. B. Stotts, J. Opt. Soc. Am. 67, 815 (1976).
[CrossRef]

Tebyani, M.

Wells, W. H.

W. H. Wells, “Theory of Small Angle Scattering,” in Optics of the Sea, AGARD-LS-61, August1973.

Yeh, K. C.

Yura, H. T.

H. T. Yura, Radiance Section, URSI Proceedings, Commission F of the Conference on Propagation in Nonionized Media, La Bouk, France (1977).

Appl. Opt. (5)

IEEE National Telecommunications Conference Record (1)

J. R. Clark, J. R. Baird, IEEE National Telecommunications Conference Record 1, 6.1 (1975).

IEEE Trans. Antennas Propag. (1)

R. L. Fante, IEEE Trans. Antennas Propag. AP-21, 750 (1973).
[CrossRef]

J. Opt. Soc. Am. (3)

NELC Technical Note 3233 (1)

G. C. Mooradian, M. Geller, L. B. Stotts, H. G. Hughes, “Experimental Test Plan to Investigate the Propagation of Blue/Green Radiation Through Clouds,” NELC Technical Note 3233, 1October1977. NELC technical notes are informal documents intended chiefly for internal use.

Opt. Lett. (1)

Optics of the Sea (1)

W. H. Wells, “Theory of Small Angle Scattering,” in Optics of the Sea, AGARD-LS-61, August1973.

Proc. IEEE (2)

A. Ishimara, Proc. IEEE 65, 1030 (1976).
[CrossRef]

E. A. Bucher, R. M. Lerner, C. W. Niessen, Proc. IEEE 58, 1564 (1970).
[CrossRef]

Proc. IRE (1)

R. Price, P. E. Green, Proc. IRE 46, 555 (1958).
[CrossRef]

Proc. Soc. Photo Opt. Instrum. Eng. (1)

A. Gordon, Proc. Soc. Photo Opt. Instrum. Eng. 64, 85 (1975).

Proceedings of National Electronics Conference (1)

E. A. Bucher, Proceedings of National Electronics Conference Vol. 29 (1974), p. 180.

Radio Sci. (1)

S. T. Hong, A. Ishimara, Radio Sci. 11, 551 (1976).
[CrossRef]

Other (9)

R. A. Dell-Imagine, “A Study of Multiple Scattering of Optical Radiation with Application to Laser Communications,” in Advances in Communication Systems, V. A. Balakrishnar, Ed. (Academic, New York, 1966), p. 1.

H. M. Heggestad, “Optical Communication Through Multiple-Scattering Media,” Research Laboratory for Electronics, MIT, Cambridge, Technical Report 472 (1968).

R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976).

R. S. Kennedy, Fading Dispersive Communication Channels (Wiley, New York, 1969).

G. C. Mooradian, V. J. Adrian, P. H. Levine, W. R. Stone, “Extended Line-of-Sight Optical Communications Study,” NELC Technical Report 1988, 30June1976.

H. T. Yura, Radiance Section, URSI Proceedings, Commission F of the Conference on Propagation in Nonionized Media, La Bouk, France (1977).

E. Fermi, Nuclear Physics (U. Chicago Press, Chicago, 1950).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 643–647.

H. G. Hughes, “Aerosol Extinction of Photopic and IR Wavelengths,” NOSC Technical Report 143, 23August1977.

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Figures (27)

Fig. 1
Fig. 1

Schematic representation of laser angular brightness distribution after traversing a cloud.

Fig. 2
Fig. 2

Aerial photograph of Point Loma showing the two propagation paths.

Fig. 3
Fig. 3

Profile of propagation paths utilized.

Fig. 4
Fig. 4

Dual wavelength transmitter.

Fig. 5
Fig. 5

Dual wavelength narrow FOV receiver.

Fig. 6
Fig. 6

Wide FOV receiver.

Fig. 7
Fig. 7

Interior of trailer showing the narrow and wide FOV receivers.

Fig. 8
Fig. 8

PMT gate circuit.

Fig. 9
Fig. 9

Experimental fog path loss as a function of receiver FOV for 26 October 1977. The transmitter was not immersed in fog.

Fig. 10
Fig. 10

Experimental fog path loss as a function of receiver FOV for 26 October 1977. The transmitter was not immersed in fog.

Fig. 11
Fig. 11

Experimental fog path loss as a function of receiver FOV for 26 October 1977. The transmitter was not immersed in fog.

Fig. 12
Fig. 12

Time history of pulses after propagating through fog.

Fig. 13
Fig. 13

Time history of pulses after propagating through fog.

Fig. 14
Fig. 14

Time history of pulses after propagating through fog.

Fig. 15
Fig. 15

Time history of pulses after propagating through fog.

Fig. 16
Fig. 16

Time history of pulse after propagating through fog.

Fig. 17
Fig. 17

Time history of pulse after propagating through fog.

Fig. 18
Fig. 18

Time history of pulse after propagating through fog.

Fig. 19
Fig. 19

Time history of pulse after propagating through fog.

Fig. 20
Fig. 20

Fog path loss as a function of optical thickness for 12 October 1977.

Fig. 21
Fig. 21

Example of measured aerosol size distributions at Point Loma.

Fig. 22
Fig. 22

The scalar phase function p(|γ|) associated with the particle density given in Fig. 21.

Fig. 23
Fig. 23

Comparison of the forwardscatter model and field data for 26 October 1977.

Fig. 24
Fig. 24

Comparison of the forwardscatter model and field data for 26 October 1977.

Fig. 25
Fig. 25

Comparison of the forwardscatter model and field data for 26 October 1977.

Fig. 26
Fig. 26

Comparison of the 12 October 1977 fog path loss data with the forwardscatter model and Bucher’s multiple-scatter model.

Fig. 27
Fig. 27

Three regions of energy transport.

Tables (4)

Tables Icon

Table I Power Budget for Clear Air Laser Irradiance Propagation

Tables Icon

Table II Attenuation Coefficient and Optical Thickness for Fog on 7 February 1977 (Derived from Visiometer Data) a

Tables Icon

Table III Path Loss of the 0.96-km Link in Fog of 12 October 1977

Tables Icon

Table IV Comparison of Experimental and Theoretical Multipath Time Spreading

Equations (23)

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[ d d τ + 1 ] I ( z , r , γ ) I 0 ( z , r , γ ) + ω 0 - + p ( γ - γ ) I ( z , r , γ ) d 2 γ ,
I 0 ( z , r , γ ) ω 0 P t π r 0 2 exp ( - r 2 / r 0 2 ) p ( γ ) ,
0 γ θ = r 1 / z 0
0 γ θ FOV
[ d d τ + 1 ] I ( z , r , γ ) I 0 ( z , r , γ ) + ω 0 p ( γ - γ ) I ( z , r , γ ) d 2 γ . γ - γ θ FOV .
{ d d τ + [ 1 - ω 0 ϕ ( θ FOV ) ] } I ( z , r , γ ) ~ I 0 ( z , r , γ ) ,
ϕ ( θ FOV ) = 0 2 π 0 θ FOV p ( θ ) sin θ d θ d ρ .
[ d d τ + ( 1 - ω 0 ϕ ) ] F ( z ) ~ ω 0 ϕ P t exp ( - τ )
F ( z ) ~ P t exp [ - ( 1 - ω 0 ϕ ) τ ] [ 1 - exp ( - ω 0 ϕ τ ) ] .
l fs ¯ ~ 1 ω 0 ϕ k ext .
r fs ~ x 3 / 2 ( ω 0 ϕ k ext θ 0 2 ) 1 / 2 ,
P R P t r 1 2 exp [ - ( 1 - ω 0 ϕ ) τ ] [ 1 - exp ( - ω 0 ϕ τ ) ] ω 0 τ ϕ θ 0 2 z 2 .
θ scat ~ ( ω 0 τ ϕ θ 0 ) 1 / 2
p 0 ( γ ) = exp ( - γ 2 / θ 0 2 ) π θ 0 2
P R P t r 1 2 exp [ - ( 1 - ω 0 ϕ ) τ ] [ 1 - exp ( - ω 0 ϕ τ ) ] ω 0 τ ϕ θ 0 2 z 2 ,
ϕ = ϕ ( θ FOV ) = 0 2 π 0 θ FOV p ( θ ) sin θ d θ d ρ , θ 0 = 1 ( π p ( γ ) 1 / 2 | γ = 0 .
P R P t A π ( θ z 0 ) 2 exp ( - k ext z 0 ) ,
L f ( τ ) r 1 2 exp [ - ( 1 - ω 0 ϕ ) τ ] [ 1 - exp ( - ω 0 ϕ τ ) ] ω 0 τ ϕ θ 0 2 z 2 .
L d ( τ ) = 4 r 1 2 exp ( - τ ) ( θ D z 0 ) 2 ,
10 log ( power received in fog power received in clear air ) ,
θ 0 = 1 [ π p ( 0 ) ] 1 / 2 ,
ϕ = 0 2 π 0 θ FOV p ( θ ) sin θ d θ
T ¯ ( θ ) z 0 c { 0.30 ω 0 τ θ 2 [ ( 1 + 2.25 ω 0 τ θ 2 ) 1.5 - 1 ] - 1 } ,

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