Abstract

The lidar equation in a double-scattering approximation, applicable for the case of an inhomogeneous atmosphere, has been derived. It is shown that a doubly scattered flux contains information on the microstructure of the medium investigated. Calculations of the intensity of doubly scattered radiation reflected from clouds are given as an illustrative example. It follows from these calculations that double scattering depends essentially on the distance from the lidar to the cloud sounded.

© 1979 Optical Society of America

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References

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  1. V. E. Zuev, N. V. Kozlov, E. V. Makienko, I. E. Naats, I. V. Samokhvalov, Izv. Akad. Nauk SSSR, Ser. Fiz. Atmos. Okeana 13, 648 (1977).
  2. B. V. Kaul, I. V. Samokhvalov, Fizika 8, 109 (1975).
  3. B. V. Kaul, I. V. Samokhvalov, Fizika 1, 80 (1976).
  4. A. Cohen, M. Graber, Opt. Quantum Electron. 7, 221(1975).
    [CrossRef]
  5. K. N. Liou, R. M. Schotland. J. Atmos. Sci. 28, 772 (1971).
    [CrossRef]
  6. A. Cohen, in Proceedings of VIIIth International Laser Radar Conference, (Drexel U.P., Philadelphia, Pennsylvania, 1977), invited paper.
  7. E. W. Eloranta, Fourth Conference on Laser Radar Studies of the Atmosphere, Tucson, Arizona, 1972, abstracts 25–27.
  8. E. W. Barret, O. Ben-Dov, J. Appl. Meteorol. 6, 500 (1967).
    [CrossRef]
  9. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier, New York, 1969).
  10. V. M. Zakharov, O. K. Kostko, Meteorologicheskaya Lazernaya Lokatsiya (Gidrometeoizdat, Leningrad, 1977).
  11. S. R. Pal, A. J. Carswall, Appl. Opt. 12, 1530 (1973).
    [CrossRef] [PubMed]
  12. V. E. Zuev, G. M. Krekov, G. G. Matvienko, A. I. Popkov, in Lazernoe Zondirovanie Atmosfery (Izdat. Nauka, Moscow, 1976), p. 29.

1977 (1)

V. E. Zuev, N. V. Kozlov, E. V. Makienko, I. E. Naats, I. V. Samokhvalov, Izv. Akad. Nauk SSSR, Ser. Fiz. Atmos. Okeana 13, 648 (1977).

1976 (1)

B. V. Kaul, I. V. Samokhvalov, Fizika 1, 80 (1976).

1975 (2)

A. Cohen, M. Graber, Opt. Quantum Electron. 7, 221(1975).
[CrossRef]

B. V. Kaul, I. V. Samokhvalov, Fizika 8, 109 (1975).

1973 (1)

1971 (1)

K. N. Liou, R. M. Schotland. J. Atmos. Sci. 28, 772 (1971).
[CrossRef]

1967 (1)

E. W. Barret, O. Ben-Dov, J. Appl. Meteorol. 6, 500 (1967).
[CrossRef]

Barret, E. W.

E. W. Barret, O. Ben-Dov, J. Appl. Meteorol. 6, 500 (1967).
[CrossRef]

Ben-Dov, O.

E. W. Barret, O. Ben-Dov, J. Appl. Meteorol. 6, 500 (1967).
[CrossRef]

Carswall, A. J.

Cohen, A.

A. Cohen, M. Graber, Opt. Quantum Electron. 7, 221(1975).
[CrossRef]

A. Cohen, in Proceedings of VIIIth International Laser Radar Conference, (Drexel U.P., Philadelphia, Pennsylvania, 1977), invited paper.

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier, New York, 1969).

Eloranta, E. W.

E. W. Eloranta, Fourth Conference on Laser Radar Studies of the Atmosphere, Tucson, Arizona, 1972, abstracts 25–27.

Graber, M.

A. Cohen, M. Graber, Opt. Quantum Electron. 7, 221(1975).
[CrossRef]

Kaul, B. V.

B. V. Kaul, I. V. Samokhvalov, Fizika 1, 80 (1976).

B. V. Kaul, I. V. Samokhvalov, Fizika 8, 109 (1975).

Kostko, O. K.

V. M. Zakharov, O. K. Kostko, Meteorologicheskaya Lazernaya Lokatsiya (Gidrometeoizdat, Leningrad, 1977).

Kozlov, N. V.

V. E. Zuev, N. V. Kozlov, E. V. Makienko, I. E. Naats, I. V. Samokhvalov, Izv. Akad. Nauk SSSR, Ser. Fiz. Atmos. Okeana 13, 648 (1977).

Krekov, G. M.

V. E. Zuev, G. M. Krekov, G. G. Matvienko, A. I. Popkov, in Lazernoe Zondirovanie Atmosfery (Izdat. Nauka, Moscow, 1976), p. 29.

Liou, K. N.

K. N. Liou, R. M. Schotland. J. Atmos. Sci. 28, 772 (1971).
[CrossRef]

Makienko, E. V.

V. E. Zuev, N. V. Kozlov, E. V. Makienko, I. E. Naats, I. V. Samokhvalov, Izv. Akad. Nauk SSSR, Ser. Fiz. Atmos. Okeana 13, 648 (1977).

Matvienko, G. G.

V. E. Zuev, G. M. Krekov, G. G. Matvienko, A. I. Popkov, in Lazernoe Zondirovanie Atmosfery (Izdat. Nauka, Moscow, 1976), p. 29.

Naats, I. E.

V. E. Zuev, N. V. Kozlov, E. V. Makienko, I. E. Naats, I. V. Samokhvalov, Izv. Akad. Nauk SSSR, Ser. Fiz. Atmos. Okeana 13, 648 (1977).

Pal, S. R.

Popkov, A. I.

V. E. Zuev, G. M. Krekov, G. G. Matvienko, A. I. Popkov, in Lazernoe Zondirovanie Atmosfery (Izdat. Nauka, Moscow, 1976), p. 29.

Samokhvalov, I. V.

V. E. Zuev, N. V. Kozlov, E. V. Makienko, I. E. Naats, I. V. Samokhvalov, Izv. Akad. Nauk SSSR, Ser. Fiz. Atmos. Okeana 13, 648 (1977).

B. V. Kaul, I. V. Samokhvalov, Fizika 1, 80 (1976).

B. V. Kaul, I. V. Samokhvalov, Fizika 8, 109 (1975).

Schotland, R. M.

K. N. Liou, R. M. Schotland. J. Atmos. Sci. 28, 772 (1971).
[CrossRef]

Zakharov, V. M.

V. M. Zakharov, O. K. Kostko, Meteorologicheskaya Lazernaya Lokatsiya (Gidrometeoizdat, Leningrad, 1977).

Zuev, V. E.

V. E. Zuev, N. V. Kozlov, E. V. Makienko, I. E. Naats, I. V. Samokhvalov, Izv. Akad. Nauk SSSR, Ser. Fiz. Atmos. Okeana 13, 648 (1977).

V. E. Zuev, G. M. Krekov, G. G. Matvienko, A. I. Popkov, in Lazernoe Zondirovanie Atmosfery (Izdat. Nauka, Moscow, 1976), p. 29.

Appl. Opt. (1)

Fizika (2)

B. V. Kaul, I. V. Samokhvalov, Fizika 8, 109 (1975).

B. V. Kaul, I. V. Samokhvalov, Fizika 1, 80 (1976).

Izv. Akad. Nauk SSSR, Ser. Fiz. Atmos. Okeana (1)

V. E. Zuev, N. V. Kozlov, E. V. Makienko, I. E. Naats, I. V. Samokhvalov, Izv. Akad. Nauk SSSR, Ser. Fiz. Atmos. Okeana 13, 648 (1977).

J. Appl. Meteorol. (1)

E. W. Barret, O. Ben-Dov, J. Appl. Meteorol. 6, 500 (1967).
[CrossRef]

J. Atmos. Sci. (1)

K. N. Liou, R. M. Schotland. J. Atmos. Sci. 28, 772 (1971).
[CrossRef]

Opt. Quantum Electron. (1)

A. Cohen, M. Graber, Opt. Quantum Electron. 7, 221(1975).
[CrossRef]

Other (5)

A. Cohen, in Proceedings of VIIIth International Laser Radar Conference, (Drexel U.P., Philadelphia, Pennsylvania, 1977), invited paper.

E. W. Eloranta, Fourth Conference on Laser Radar Studies of the Atmosphere, Tucson, Arizona, 1972, abstracts 25–27.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier, New York, 1969).

V. M. Zakharov, O. K. Kostko, Meteorologicheskaya Lazernaya Lokatsiya (Gidrometeoizdat, Leningrad, 1977).

V. E. Zuev, G. M. Krekov, G. G. Matvienko, A. I. Popkov, in Lazernoe Zondirovanie Atmosfery (Izdat. Nauka, Moscow, 1976), p. 29.

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Figures (2)

Fig. 1
Fig. 1

Scheme of formation of double-scattered radiation beams.

Fig. 2
Fig. 2

Dependence of δ(r) on the sounding depth of a homogeneous cloud of C2 type.9 φ0 = 0.005, σ0 = 16.8 km−1, 1 − H = 1.0 km, 2 − H = 0.5 km, 3 − H = 0.2 km. The points represent the results of calculation using the Eloranta data.7

Equations (21)

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r 1 + ρ + x = 2 r ,
ρ = [ r ( r - x ) / r - x sin 2 φ / 2 ] ,
d F 1 2 ( x , r ) = k A F 0 σ ( x , φ ) T ( α , x , ρ ) ( 1 / ρ 2 ) ( 1 / r 2 ) σ ( ρ , φ ) d x d v ,
T ( α , x , ρ ) = exp { - [ 0 x α ( ξ ) d ξ + 0 ρ α ( ξ ) d ξ + 0 r 1 α ( ξ ) d ξ ] }
ρ + r 1 = 2 r - x
ρ + r 1 = 2 ( r - Δ r ) - x .
ρ = ρ - r 1 2 r 2 - 2 r x sin 2 φ / 2 + x 2 sin 2 φ / 2 Δ r ,
F 1 2 ( r ) = 2 π k F 0 e - 2 τ Δ r 0 φ 2 x ( φ ) r - Δ r ) × σ ( x , φ ) σ ( x , φ ) sin φ r 2 - ( 2 r - x ) x sin 2 φ / 2 d x d φ ,
x ( φ ) = r ( 1 - tan φ 0 / 2 cotan φ / 2 ) ,
φ 2 = 2 arctan ( φ 0 r / 2 Δ r ) ,
x = x + ρ cos φ = x + [ r ( r - x ) / r - x sin 2 φ / 2 ] cos φ .
ρ ( φ ) = ( Δ r / cos 2 φ / 2 ) .
F 2 2 ( r ) = 2 π A F 0 k e - 2 τ Δ r σ ( r ) [ 0 φ 2 0 ρ ( φ ) γ ( r , φ ) σ ( ρ , φ ) sin φ ( r - ρ ) 2 d ρ d φ + φ 2 π 0 ρ ( φ ) γ ( r , φ ) σ ( ρ , φ ) sin φ ( r - ρ ) 2 d ρ d φ ] ,
ρ ( φ ) = r [ sin φ 0 / sin ( φ - φ 0 ) ] .
F 2 ( r ) = F 1 ( r ) 2 π r 2 γ π ( r ) [ 0 π / 2 x ( φ ) r × σ ( x ) γ ( x , φ ) γ ( r , π - φ ) sin φ r 2 - ( 2 r - x ) sin 2 φ / 2 d x d φ + 0 π / 2 x ( φ ) r σ ( x ) γ ( r , φ ) γ ( x , π - φ ) sin φ x 2 d x d φ + 2 σ ( r ) Δ r r 2 0 φ 2 γ ( r , φ ) γ ( r , π - φ ) tan φ / 2 d φ ] ,
x ( φ ) = r { 1 - [ sin φ 0 / sin ( φ + φ 0 ) ] } .
δ ( r ) = F ( 2 ) ( r ) F ( 1 ) ( r ) = 4 π r σ 0 φ 0 γ π 0 π / 2 γ ( φ ) γ ( π - φ ) d φ + 4 π Δ r σ 0 γ π 0 φ 2 γ ( φ ) γ ( π - φ ) tan φ 2 d φ .
δ ( r ) = 2 π ( r 2 - H 2 ) σ 0 H γ π 0 φ 1 γ ( φ ) γ ( π - φ ) φ d φ + 4 π r φ 0 σ 0 γ π φ 1 π / 2 γ ( φ ) γ ( π - φ ) d φ + 4 π Δ r σ 0 γ π 0 φ 2 γ ( φ ) γ ( π - φ ) tan φ / 2 d τ ,
φ 1 arctan ( r φ 0 / r - H ) .
F ( r ) = F 1 ( r ) + F 2 ( r ) = F 1 ( r ) [ 1 + δ ( r ) ] .
F ( r ) = ( k A F 0 Δ r / r 2 ) σ π ( r ) exp [ - ( 1 - ξ ) 2 τ ( r ) ] ,

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