Abstract

The intensity fluctuations in the focal plane of a receiving telescope of radiation reflected in a turbulent atmosphere have been analyzed. It was found that, when fluctuations of an incident wave are saturated, the focusing can significantly modify the variance of the reflected radiation intensity in comparison with the corresponding value in the aperture plane of the receiving telescope.

© 1984 Optical Society of America

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References

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  1. A. B. Krupnik, A. I. Saichev, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 24, 1234–1238 (1981).
  2. V. I. Gel’fgat, Akust. Zh. 22, 123–124 (1976).
  3. K. S. Gochelashvili, V. I. Shishov, Zh. Eksp. Teor. Fiz. 74, 1974–1978 (1978).
  4. V. I. Tatarskii, Wave Propagation in the Turbulent Atmosphere (Nauka, Moscow, 1967).
  5. V. L. Mironov, Laser Beam Propagation in the Turbulent Atmosphere (Nauka, Novosibirsk, 1981).
  6. V. P. Aksenov, V. A. Banakh, V. L. Mironov, in Paper Abstracts, All-Union Meeting on Atmospheric Optics, Tomsk, 1980, Part II, p. 128.
  7. V. P. Aksenov, V. A. Banakh, V. L. Mironov, J. Opt. Soc. Am. A 1, 263–274 (1984).
    [CrossRef]
  8. V. P. Aksenov, V. A. Banakh, V. L. Mironov, in Paper Abstracts, All-Union Meeting on Atmospheric Optics, Tomsk, 1980, Part II, p. 124.
  9. Yu. A. Kravtsov, A. I. Saichev, Zh. Eksp. Teor. Fiz. 83, 532 (1982).

1984 (1)

1982 (1)

Yu. A. Kravtsov, A. I. Saichev, Zh. Eksp. Teor. Fiz. 83, 532 (1982).

1981 (1)

A. B. Krupnik, A. I. Saichev, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 24, 1234–1238 (1981).

1978 (1)

K. S. Gochelashvili, V. I. Shishov, Zh. Eksp. Teor. Fiz. 74, 1974–1978 (1978).

1976 (1)

V. I. Gel’fgat, Akust. Zh. 22, 123–124 (1976).

Aksenov, V. P.

V. P. Aksenov, V. A. Banakh, V. L. Mironov, J. Opt. Soc. Am. A 1, 263–274 (1984).
[CrossRef]

V. P. Aksenov, V. A. Banakh, V. L. Mironov, in Paper Abstracts, All-Union Meeting on Atmospheric Optics, Tomsk, 1980, Part II, p. 124.

V. P. Aksenov, V. A. Banakh, V. L. Mironov, in Paper Abstracts, All-Union Meeting on Atmospheric Optics, Tomsk, 1980, Part II, p. 128.

Banakh, V. A.

V. P. Aksenov, V. A. Banakh, V. L. Mironov, J. Opt. Soc. Am. A 1, 263–274 (1984).
[CrossRef]

V. P. Aksenov, V. A. Banakh, V. L. Mironov, in Paper Abstracts, All-Union Meeting on Atmospheric Optics, Tomsk, 1980, Part II, p. 124.

V. P. Aksenov, V. A. Banakh, V. L. Mironov, in Paper Abstracts, All-Union Meeting on Atmospheric Optics, Tomsk, 1980, Part II, p. 128.

Gel’fgat, V. I.

V. I. Gel’fgat, Akust. Zh. 22, 123–124 (1976).

Gochelashvili, K. S.

K. S. Gochelashvili, V. I. Shishov, Zh. Eksp. Teor. Fiz. 74, 1974–1978 (1978).

Kravtsov, Yu. A.

Yu. A. Kravtsov, A. I. Saichev, Zh. Eksp. Teor. Fiz. 83, 532 (1982).

Krupnik, A. B.

A. B. Krupnik, A. I. Saichev, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 24, 1234–1238 (1981).

Mironov, V. L.

V. P. Aksenov, V. A. Banakh, V. L. Mironov, J. Opt. Soc. Am. A 1, 263–274 (1984).
[CrossRef]

V. P. Aksenov, V. A. Banakh, V. L. Mironov, in Paper Abstracts, All-Union Meeting on Atmospheric Optics, Tomsk, 1980, Part II, p. 124.

V. L. Mironov, Laser Beam Propagation in the Turbulent Atmosphere (Nauka, Novosibirsk, 1981).

V. P. Aksenov, V. A. Banakh, V. L. Mironov, in Paper Abstracts, All-Union Meeting on Atmospheric Optics, Tomsk, 1980, Part II, p. 128.

Saichev, A. I.

Yu. A. Kravtsov, A. I. Saichev, Zh. Eksp. Teor. Fiz. 83, 532 (1982).

A. B. Krupnik, A. I. Saichev, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 24, 1234–1238 (1981).

Shishov, V. I.

K. S. Gochelashvili, V. I. Shishov, Zh. Eksp. Teor. Fiz. 74, 1974–1978 (1978).

Tatarskii, V. I.

V. I. Tatarskii, Wave Propagation in the Turbulent Atmosphere (Nauka, Moscow, 1967).

Akust. Zh. (1)

V. I. Gel’fgat, Akust. Zh. 22, 123–124 (1976).

Izv. Vyssh. Uchebn. Zaved. Radiofiz. (1)

A. B. Krupnik, A. I. Saichev, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 24, 1234–1238 (1981).

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

Zh. Eksp. Teor. Fiz. (2)

Yu. A. Kravtsov, A. I. Saichev, Zh. Eksp. Teor. Fiz. 83, 532 (1982).

K. S. Gochelashvili, V. I. Shishov, Zh. Eksp. Teor. Fiz. 74, 1974–1978 (1978).

Other (4)

V. I. Tatarskii, Wave Propagation in the Turbulent Atmosphere (Nauka, Moscow, 1967).

V. L. Mironov, Laser Beam Propagation in the Turbulent Atmosphere (Nauka, Novosibirsk, 1981).

V. P. Aksenov, V. A. Banakh, V. L. Mironov, in Paper Abstracts, All-Union Meeting on Atmospheric Optics, Tomsk, 1980, Part II, p. 128.

V. P. Aksenov, V. A. Banakh, V. L. Mironov, in Paper Abstracts, All-Union Meeting on Atmospheric Optics, Tomsk, 1980, Part II, p. 124.

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Equations (29)

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U R ( x 0 , ρ ) = d 2 r K ( r ) U ( x , r ) G ( x , x 0 ; r , ρ ) ,
U ( x , r ) = d 2 t U 0 ( t ) G ( x , x 0 ; r , t )
2 i k x G + Δ ρ G + k 2 1 ( x , ρ ) G = 0 , G ( x , x ; r , ρ ) = δ ( r ρ ) ,
U F ( 0 ) = i k 2 π F t exp ( i k F t ) d 2 ρ T ( ρ ) U R ( x 0 , ρ ) ,
U F ( 0 ) = i k 2 π F t | U ( x 0 , 0 ) | e i k F t d 2 r K ( r ) U 2 ( x , r ) .
I F ( 0 ) = [ k 2 π F t | U ( x 0 , 0 ) | ] 2 d 2 r 1 , 2 × K ( r 1 ) K * ( r 2 ) ¯ U 2 ( x , r 1 ) U 2 * ( x , r 2 ) ,
I F 2 ( 0 ) = [ k 2 π F t | U ( x 0 , 0 ) | ] 4 d 2 r 1 , 2 , 3 , 4 × K ( r 1 ) K * ( r 2 ) K ( r 3 ) K * ( r 4 ) ¯ U 2 ( x , r 1 ) × U 2 * ( x , r 2 ) U 2 ( x , r 3 ) U 2 * ( x , r 4 ) .
K ( r ) = 2 π k 2 δ ( r ) ,
U F ( 0 ) = [ i k F t | U ( x 0 , 0 ) | ] e i k F t U 2 ( x , 0 ) ,
I F ( 0 ) = [ 1 k F t | U ( x 0 , 0 ) | ] 2 I 2 ( 0 ) ,
I F 2 ( 0 ) = [ 1 k F t | U ( x 0 , 0 ) | ] 2 I 4 ( 0 ) ,
K ( r ) = 0
K ( r 1 ) K * ( r 2 ) ¯ = 4 π k 2 | K ( r 1 ) | 2 δ ( r 1 r 2 ) .
K ( r 1 ) K * ( r 2 ) K ( r 3 ) K * ( r 4 ) ¯ = K ( r 1 ) K * ( r 2 ) ¯ K ( r 3 ) K * ( r 4 ) ¯ + K ( r 1 ) K * ( r 4 ) K ( r 2 ) K * ( r 3 ) ¯ = ( 4 π k 2 ) 2 | K ( r 1 ) | 2 | K ( r 3 ) | 2 × [ δ ( r 1 r 2 ) δ ( r 3 r 4 ) + δ ( r 1 r 4 ) δ ( r 2 r 3 ) ] .
I F ( 0 ) = 1 π ( F t | U ( x 0 , 0 ) | ) 2 d 2 r | K ( r ) | 2 I 2 ( r ) ,
I F 2 ( 0 ) = 1 π 2 ( F t | U ( x 0 , 0 ) | ) 4 d 2 r 1 d 2 r 2 | K ( r 1 ) | 2 × | K ( r 2 ) | 2 I 2 ( r 1 ) I 2 ( r 2 ) .
I F ( 0 ) = [ | U ( x 0 , 0 ) | k F t ] 2 [ 2 + 0 . 86 β 0 4 / 5 + O ( β 0 8 ) ] , β 0 1 , Ω β 0 12 / 5 ,
I F ( 0 ) = [ | U ( x 0 , 0 ) | k F t ] 2 [ 1 + β 0 2 + O ( β 0 4 ) ] , β 0 < 1 , Ω 1 = 0 ,
σ I , F 2 = 5 + 14 . 6 β 0 4 / 5 1 + 0 . 86 β 0 4 / 5 + O ( β 0 8 / 5 ) , β 0 1 , Ω β 0 12 / 5 ,
σ I , F 2 = 4 β 0 2 + O ( β 0 4 ) , β 0 2 1 , Ω 1 = 0 ,
σ I , F 2 = 11 + 70 . 1 β 0 4 / 5 1 + 0 . 86 β 0 4 / 5 + O ( β 0 8 / 5 ) , β 0 1 , Ω β 0 12 / 5
σ I , F 2 = 1 + 10 β 0 2 + O ( β 0 4 ) , β 0 < 1 , Ω 1 = 0 .
I F ( 0 ) = k π [ d 2 r | K ( r ) | 2 ] I F ( 0 ) ,
U F ( 0 ) = ( i k F t ) e i k F t U R ( x 0 , 0 ) ,
β 0 1 , Ω t β 0 12 / 5 , σ I , F 2 = 1 + 5 . 22 β 0 4 / 5 + O ( β 0 8 / 5 ) if β 0 12 / 5 Ω R β 0 12 / 5
σ I , F 2 = 7 + 26 . 4 β 0 4 / 5 1 + 0 . 8 β 0 4 / 5 + O ( β 0 8 / 5 ) if Ω R β 0 12 / 5 ;
β 0 < 1 , Ω t 1 = 0 , σ I , F 2 = 1 + 1 . 37 β 0 2 + O ( β 0 4 ) if Ω R = 1 ; and σ I , F 2 = 1 + 4 . 18 β 0 2 + O ( β 0 4 ) if Ω R 1 .
σ I , F 2 = 3 + 13 . 1 β 0 4 / 5 + O ( β 0 8 / 5 ) , β 0 1 , Ω t β 0 12 / 5 ,
σ I , F 2 = 2 . 1 β 0 2 + O ( β 0 4 ) , β 0 < 1 , Ω t 1 .

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