Abstract

The effects of multiple scattering on the interpretation of the time dependence of elastic backscattering of laser pulses from the ocean (lidar) are investigated through solving the radiative transfer equation by Monte Carlo techniques. In particular, after removal of the geometric loss factors, it is found that the backscattered power is a decaying exponential function of time, over the time interval required for photons to travel four attenuation lengths through the water. The effective attenuation coefficient of this exponential decay is found to be strongly dependent on the parameters of the lidar system and on the optical properties of the water. The significant parameter is the ratio of the radius of the spot on the sea surface viewed by the lidar receiver optics to the mean free path of photons in the water. For values of this parameter near zero, the decay is determined by the beam attenuation coefficient, while for values greater than ~5–6, the decay is given by the attenuation coefficient for downwelling irradiance, often referred to as the diffuse attenuation coefficient. Between these two extremes the interpretation of the effective attenuation coefficient requires, essentially, complete knowledge of the inherent optical properties of the water: the beam attenuation coefficient and the volume scattering function.

© 1982 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  6. W. A. Hovis et al., Science 210, 60 (1980).
    [CrossRef] [PubMed]
  7. H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, Science 210, 63 (1980).
    [CrossRef] [PubMed]
  8. P. B. Mumola, O. Jarrett, C. A. Brown, “Multiwavelength Laser-Induced Fluorescence of Algae in-vivo: A New Remote Sensing Technique,” in Proceedings, Second Joint Conference on Sensing of Environmental Pollutants, Washington, D.C., 10–12 Dec. 1973 (Instrument Society of America, Pittsburgh, 1974), p. 53.
  9. M. Bristow, D. Nielsen, R. Furtek, “A Laser-Fluorosensor Technique for Water Quality Assessment,” in Proceedings, Thirteenth International Symposium on Remote Sensing of the Environment, 23–27 Apr. 1979 (Environmental Research Institute of Michigan, Ann Arbor, 1979), p. 397.
  10. F. H. Farmer, C. A. Brown, O. Jarrett, J. W. Campbell, W. Staton, “Remote Sensing of Phytoplankton Density and Diversity in Narraganset Bay Using an Airborne Fluorosensor,” in Proceedings, Thirteenth International Symposium on Remote Sensing of the Environment, 23–27 Apr. 1979 (Environmental Research Institute of Michigan, Ann Arbor, 1979), p. 1783.
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    [CrossRef]

1981

1980

H. R. Gordon, Appl. Opt. 19, 2092 (1980).
[CrossRef]

W. A. Hovis et al., Science 210, 60 (1980).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, Science 210, 63 (1980).
[CrossRef] [PubMed]

F. E. Hoge, R. N. Swift, E. B. Frederick, Appl. Opt. 19, 871 (1980).
[CrossRef] [PubMed]

1979

D. A. Leonard, B. Caputo, F. E. Hoge, Appl. Opt. 18, 1732 (1979).
[CrossRef] [PubMed]

K. S. Baker, R. C. Smith, Proc. Soc. Photo-Opt. Instrum. Eng. 208, 60 (1979).

1977

W. A. Hovis, K. C. Leung, Opt. Eng. 16, 153 (1977).
[CrossRef]

H. H. Kim, Appl. Opt. 16, 46 (1977).
[CrossRef] [PubMed]

1975

1972

1969

G. D. Hickman, J. E. Hogg, Remote Sensing Environ. 1, 47 (1969).
[CrossRef]

1968

G. Kullenberg, Deep Sea Res. 15, 423 (1968).

Baker, K. S.

K. S. Baker, R. C. Smith, Proc. Soc. Photo-Opt. Instrum. Eng. 208, 60 (1979).

Bristow, M.

M. Bristow, D. Nielsen, D. Bundy, R. Furtek, Appl. Opt. 20, 2889 (1981).
[CrossRef] [PubMed]

M. Bristow, D. Nielsen, R. Furtek, “A Laser-Fluorosensor Technique for Water Quality Assessment,” in Proceedings, Thirteenth International Symposium on Remote Sensing of the Environment, 23–27 Apr. 1979 (Environmental Research Institute of Michigan, Ann Arbor, 1979), p. 397.

Brown, C. A.

P. B. Mumola, O. Jarrett, C. A. Brown, “Multiwavelength Laser-Induced Fluorescence of Algae in-vivo: A New Remote Sensing Technique,” in Proceedings, Second Joint Conference on Sensing of Environmental Pollutants, Washington, D.C., 10–12 Dec. 1973 (Instrument Society of America, Pittsburgh, 1974), p. 53.

F. H. Farmer, C. A. Brown, O. Jarrett, J. W. Campbell, W. Staton, “Remote Sensing of Phytoplankton Density and Diversity in Narraganset Bay Using an Airborne Fluorosensor,” in Proceedings, Thirteenth International Symposium on Remote Sensing of the Environment, 23–27 Apr. 1979 (Environmental Research Institute of Michigan, Ann Arbor, 1979), p. 1783.

Brown, O. B.

Bundy, D.

Byrne, J. D.

J. G. Hirschberg, A. W. Wouters, J. D. Byrne, “Ocean Parameters Using the Brillouin Effect,” in Ocean Remote Sensing Using Lasers, H. R. Gordon, Ed. NOAA Tech. Memo. ERL PMEL-18 (1980), p. 29.

Campbell, J. W.

L. R. Poole, D. D. Venable, J. W. Campbell, Appl. Opt. 20, 3653 (1981).
[CrossRef] [PubMed]

F. H. Farmer, C. A. Brown, O. Jarrett, J. W. Campbell, W. Staton, “Remote Sensing of Phytoplankton Density and Diversity in Narraganset Bay Using an Airborne Fluorosensor,” in Proceedings, Thirteenth International Symposium on Remote Sensing of the Environment, 23–27 Apr. 1979 (Environmental Research Institute of Michigan, Ann Arbor, 1979), p. 1783.

Caputo, B.

Clark, D. K.

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, Science 210, 63 (1980).
[CrossRef] [PubMed]

Farmer, F. H.

F. H. Farmer, C. A. Brown, O. Jarrett, J. W. Campbell, W. Staton, “Remote Sensing of Phytoplankton Density and Diversity in Narraganset Bay Using an Airborne Fluorosensor,” in Proceedings, Thirteenth International Symposium on Remote Sensing of the Environment, 23–27 Apr. 1979 (Environmental Research Institute of Michigan, Ann Arbor, 1979), p. 1783.

Frederick, E. B.

Furtek, R.

M. Bristow, D. Nielsen, D. Bundy, R. Furtek, Appl. Opt. 20, 2889 (1981).
[CrossRef] [PubMed]

M. Bristow, D. Nielsen, R. Furtek, “A Laser-Fluorosensor Technique for Water Quality Assessment,” in Proceedings, Thirteenth International Symposium on Remote Sensing of the Environment, 23–27 Apr. 1979 (Environmental Research Institute of Michigan, Ann Arbor, 1979), p. 397.

Gordon, H. R.

Hickman, G. D.

G. D. Hickman, J. E. Hogg, Remote Sensing Environ. 1, 47 (1969).
[CrossRef]

Hirschberg, J. G.

J. G. Hirschberg, A. W. Wouters, J. D. Byrne, “Ocean Parameters Using the Brillouin Effect,” in Ocean Remote Sensing Using Lasers, H. R. Gordon, Ed. NOAA Tech. Memo. ERL PMEL-18 (1980), p. 29.

Hoge, F. E.

Hogg, J. E.

G. D. Hickman, J. E. Hogg, Remote Sensing Environ. 1, 47 (1969).
[CrossRef]

Hovis, W. A.

W. A. Hovis et al., Science 210, 60 (1980).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, Science 210, 63 (1980).
[CrossRef] [PubMed]

W. A. Hovis, K. C. Leung, Opt. Eng. 16, 153 (1977).
[CrossRef]

Jacobs, M. M.

Jarrett, O.

F. H. Farmer, C. A. Brown, O. Jarrett, J. W. Campbell, W. Staton, “Remote Sensing of Phytoplankton Density and Diversity in Narraganset Bay Using an Airborne Fluorosensor,” in Proceedings, Thirteenth International Symposium on Remote Sensing of the Environment, 23–27 Apr. 1979 (Environmental Research Institute of Michigan, Ann Arbor, 1979), p. 1783.

P. B. Mumola, O. Jarrett, C. A. Brown, “Multiwavelength Laser-Induced Fluorescence of Algae in-vivo: A New Remote Sensing Technique,” in Proceedings, Second Joint Conference on Sensing of Environmental Pollutants, Washington, D.C., 10–12 Dec. 1973 (Instrument Society of America, Pittsburgh, 1974), p. 53.

Kattawar, G. W.

Kim, H. H.

Kullenberg, G.

G. Kullenberg, Deep Sea Res. 15, 423 (1968).

Leonard, D. A.

Leung, K. C.

W. A. Hovis, K. C. Leung, Opt. Eng. 16, 153 (1977).
[CrossRef]

Mueller, J. L.

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, Science 210, 63 (1980).
[CrossRef] [PubMed]

Mumola, P. B.

P. B. Mumola, O. Jarrett, C. A. Brown, “Multiwavelength Laser-Induced Fluorescence of Algae in-vivo: A New Remote Sensing Technique,” in Proceedings, Second Joint Conference on Sensing of Environmental Pollutants, Washington, D.C., 10–12 Dec. 1973 (Instrument Society of America, Pittsburgh, 1974), p. 53.

Nielsen, D.

M. Bristow, D. Nielsen, D. Bundy, R. Furtek, Appl. Opt. 20, 2889 (1981).
[CrossRef] [PubMed]

M. Bristow, D. Nielsen, R. Furtek, “A Laser-Fluorosensor Technique for Water Quality Assessment,” in Proceedings, Thirteenth International Symposium on Remote Sensing of the Environment, 23–27 Apr. 1979 (Environmental Research Institute of Michigan, Ann Arbor, 1979), p. 397.

Plass, G. N.

Poole, L. R.

Preisendorfer, R. W.

R. W. Preisendorfer, IUGG Monograph 10 (International Union of Geodesy and Geophysics, Paris, 1961), p. 11.

Schwiesow, R. L.

R. L. Schwiesow, “Lidar High-Resolution Spectroscopy for Oceanographic Measurements,” in Ocean Remote Sensing Using Lasers, H. R. Gordon, Ed., NOAA Tech. Memo. ERL PMEL-18 (1980), p. 11.

Smith, R. C.

K. S. Baker, R. C. Smith, Proc. Soc. Photo-Opt. Instrum. Eng. 208, 60 (1979).

Staton, W.

F. H. Farmer, C. A. Brown, O. Jarrett, J. W. Campbell, W. Staton, “Remote Sensing of Phytoplankton Density and Diversity in Narraganset Bay Using an Airborne Fluorosensor,” in Proceedings, Thirteenth International Symposium on Remote Sensing of the Environment, 23–27 Apr. 1979 (Environmental Research Institute of Michigan, Ann Arbor, 1979), p. 1783.

Swift, R. N.

Venable, D. D.

Wouters, A. W.

J. G. Hirschberg, A. W. Wouters, J. D. Byrne, “Ocean Parameters Using the Brillouin Effect,” in Ocean Remote Sensing Using Lasers, H. R. Gordon, Ed. NOAA Tech. Memo. ERL PMEL-18 (1980), p. 29.

Appl. Opt.

Deep Sea Res.

G. Kullenberg, Deep Sea Res. 15, 423 (1968).

J. Opt. Soc. Am.

F. E. Hoge, J. Opt. Soc. Am. 71, 1643 (1981).

Opt. Eng.

W. A. Hovis, K. C. Leung, Opt. Eng. 16, 153 (1977).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

K. S. Baker, R. C. Smith, Proc. Soc. Photo-Opt. Instrum. Eng. 208, 60 (1979).

Remote Sensing Environ.

G. D. Hickman, J. E. Hogg, Remote Sensing Environ. 1, 47 (1969).
[CrossRef]

Science

W. A. Hovis et al., Science 210, 60 (1980).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, Science 210, 63 (1980).
[CrossRef] [PubMed]

Other

P. B. Mumola, O. Jarrett, C. A. Brown, “Multiwavelength Laser-Induced Fluorescence of Algae in-vivo: A New Remote Sensing Technique,” in Proceedings, Second Joint Conference on Sensing of Environmental Pollutants, Washington, D.C., 10–12 Dec. 1973 (Instrument Society of America, Pittsburgh, 1974), p. 53.

M. Bristow, D. Nielsen, R. Furtek, “A Laser-Fluorosensor Technique for Water Quality Assessment,” in Proceedings, Thirteenth International Symposium on Remote Sensing of the Environment, 23–27 Apr. 1979 (Environmental Research Institute of Michigan, Ann Arbor, 1979), p. 397.

F. H. Farmer, C. A. Brown, O. Jarrett, J. W. Campbell, W. Staton, “Remote Sensing of Phytoplankton Density and Diversity in Narraganset Bay Using an Airborne Fluorosensor,” in Proceedings, Thirteenth International Symposium on Remote Sensing of the Environment, 23–27 Apr. 1979 (Environmental Research Institute of Michigan, Ann Arbor, 1979), p. 1783.

J. F. R. Gower, Ed., Passive Radiometry of the Ocean (Reidel, Dordrecht, Holland, 1980).

J. F. R. Gower, Ed., Oceanography from Space (Plenum, New York, 1981).
[CrossRef]

H. R. Gordon, Ed., Ocean Remote Sensing Using Lasers, NOAA Tech. Memo. ERL PMEL-18 (1980).

K. L. Carder, Ed., “Oceanic Lidar,” NASA Conf. Publ. 2194 (1980).

R. L. Schwiesow, “Lidar High-Resolution Spectroscopy for Oceanographic Measurements,” in Ocean Remote Sensing Using Lasers, H. R. Gordon, Ed., NOAA Tech. Memo. ERL PMEL-18 (1980), p. 11.

R. W. Preisendorfer, IUGG Monograph 10 (International Union of Geodesy and Geophysics, Paris, 1961), p. 11.

J. G. Hirschberg, A. W. Wouters, J. D. Byrne, “Ocean Parameters Using the Brillouin Effect,” in Ocean Remote Sensing Using Lasers, H. R. Gordon, Ed. NOAA Tech. Memo. ERL PMEL-18 (1980), p. 29.

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Figures (6)

Fig. 1
Fig. 1

Scattering phase functions KA and KC used in the present study.

Fig. 2
Fig. 2

Sample of the simulated normalized returned power (dt[dP/dt]norm) as a function of time for c = 0.5 m−1, ω0 = 0.7, γ = 20.4 mrad, and phase function KA.

Fig. 3
Fig. 3

k/c as a function of cR for ω0 = 0.5 and phase function KA.

Fig. 4
Fig. 4

k/c as a function of cR for ω0 = 0.3(0.2)0.9 and phase functions KA and KC.

Fig. 5
Fig. 5

k/K as a function of cR for ω0 = 0.3(0.2)0.9 and phase functions KA and KC.

Fig. 6
Fig. 6

Locus of points in(ω0cR) space for which k = 1.1K. Above the line, k is within 10 % of K.

Tables (1)

Tables Icon

Table I k/K and β′(180)/β(180) for cR ≥ 20.4

Equations (7)

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d P ( t ) = T 2 P 2 A β ( 180 ) exp [ - c v ( t - t 0 ) / m ] v d t / 2 m [ m H + v ( t - t 0 ) / 2 m ] 2 ,
β ( 180 ) exp [ - c v ( t - t 0 ) / m ] = × ( 2 m / P 0 A v T 2 ) [ m H + v ( t - t 0 ) / 2 m ] 2 d P ( t ) / d t [ d P ( t ) / d t ] norm ,
β ( 180 ) exp [ - k v ( t - t 0 ) / m ] = [ d P ( t ) / d t ] norm ,
Δ t = 0.2 ( m / c v ) ,
Δ t = 0.2 ( m / k v ) ;
k ~ c ( 1 - ω 0 ) ,
P = [ P 0 A T 2 / 2 m 2 H 2 ] [ β ( 180 ) / k ] .

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