Abstract

A technique for measuring atmospheric extinction of light, or visibility, from the backscattered signal of a modulated cw laser is presented. The extinction coefficient is contained in the amplitude and phase of the return signal and can be extracted in several ways from certain amplitude and/or phase measurements. No assumption about a relationship between the extinction coefficient and backscattering coefficient need be made.

© 1971 Optical Society of America

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References

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  1. R. T. H. Collis, Appl. Opt. 9, 1782 (1970).
    [CrossRef] [PubMed]
  2. R. G. Fleagle, J. A. Businger, Atmospheric Physics (Academic, New York, 1963).
  3. W. E. K. Middleton, Vision Through the Atmosphere (University of Toronto Press, Toronto, 1952).
  4. J. A. Curcio, G. L. Knestrick, J. Opt. Soc. Am. 48, 686 (1958).
    [CrossRef]
  5. R. W. Fenn, Appl. Opt. 5, 293 (1965).
    [CrossRef]
  6. H. Vogt, J. Atmos. Sci. 25, 912 (1968).
    [CrossRef]

1970

1968

H. Vogt, J. Atmos. Sci. 25, 912 (1968).
[CrossRef]

1965

1958

Businger, J. A.

R. G. Fleagle, J. A. Businger, Atmospheric Physics (Academic, New York, 1963).

Collis, R. T. H.

Curcio, J. A.

Fenn, R. W.

Fleagle, R. G.

R. G. Fleagle, J. A. Businger, Atmospheric Physics (Academic, New York, 1963).

Knestrick, G. L.

Middleton, W. E. K.

W. E. K. Middleton, Vision Through the Atmosphere (University of Toronto Press, Toronto, 1952).

Vogt, H.

H. Vogt, J. Atmos. Sci. 25, 912 (1968).
[CrossRef]

Appl. Opt.

J. Atmos. Sci.

H. Vogt, J. Atmos. Sci. 25, 912 (1968).
[CrossRef]

J. Opt. Soc. Am.

Other

R. G. Fleagle, J. A. Businger, Atmospheric Physics (Academic, New York, 1963).

W. E. K. Middleton, Vision Through the Atmosphere (University of Toronto Press, Toronto, 1952).

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Figures (3)

Fig. 1
Fig. 1

Typical lidar receiver/transmitter geometry showing overlapping fields of view and common volume element AC(z)dz.

Fig. 2
Fig. 2

Normalized backscattered power (A12 + B12(m−2) as a function of the modulation wavelength (m) for 100-m, 200-m, 500-m, and 1000-m visibility.

Fig. 3
Fig. 3

Relative phase of the backscattered intensity as a function of the visibility (m) for modulation wavelength of 50-m, 75-m, 100-m, and 300-m.

Equations (17)

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I out = I in sin 2 π δ ,
π δ = α + ( π / 2 ) ( V / V 1 2 ) sin ω t ,
I out / I in = 1 2 { 1 - cos 2 α [ J 0 ( π V V 1 2 ) + 2 n = 1 J 2 n ( π V V 1 2 ) cos 2 n ω t ] + sin 2 α [ 2 n = 1 J 2 n + 1 ( π V V 1 2 ) sin ( 2 n + 1 ) ω t ] } ,
I out n = I n { sin n ω t n = odd , cos n ω t n = even ,
I out n = I n { sin n ω [ t - ( z / c ) ] n = odd , cos n ω [ t - ( z / c ) ] n = even ,
V i s = 3.912 / γ 4 / γ ,
γ s = i σ i n i ,
β = i d σ i d Ω | π n i ,
P ( t ) = 0 d z β A C ( z ) A D A B ( z ) z 2 e - 2 γ z P ( t - 2 z c ) .
A C ( z ) A B ( z ) = f ( z ) { 0 , z = 0 , 1 , z .
P n ( t ) = A D 0 d z β f ( z ) e - 2 γ z z 2 P n × { sin n ω ( t - 2 z c ) n = odd , cos n ω ( t - 2 z c ) n = even ,
P n ( t ) = A D P n { A n ( ω ) sin n ω t - B n ( ω ) cos n ω t , A n ( ω ) cos n ω t + B n ( ω ) sin n ω t ,
A n ( ω ) = β 0 d z f ( z ) ( e - 2 γ z / z 2 ) cos 2 n ω z c
and             B n ( ω ) = β 0 d z f ( z ) ( e - 2 γ z / z 2 ) sin 2 n ω z c .
P n ( t ) = A D P n ( A n 2 + B n 2 ) 1 2 { sin ( n ω t - ϕ n ) , cos ( n ω t - ϕ n ) ,
ϕ n = tan - 1 ( B n / A n )
I noise = g ( 2 e Δ f P B η ) 1 2 ,

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