Abstract

The problem of spot dancing of the laser beam has attracted theoretical and experimental attention in recent years as one of the important problems in an optical communication system through the atmosphere. An analysis of this problem is made by using the Kolmogorov structure function of the refractive index and geometrical optics. Laser propagation experiments are carried out over 480-m and 1380-m paths. The standard deviations of spot dancing are measured by two methods, and the magnitudes of the structure constant Cn2 are measured at the same time. The theoretical value of the spot dancing shows a satisfactory agreement with the experimental value. In addition, measurements of the fluctuations of spot dancing reveal that the power spectra show an inverse frequency characteristic over the frequency range of about 0.03–10 Hz.

© 1971 Optical Society of America

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References

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  1. L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill, New York, 1960).
  2. P. Beckmann, Radio Science J. Res. NBS/USNC-URSI 69D, 629 (1965).
  3. H. Hodara, Proc. IEEE 54, 368 (1966).
    [CrossRef]
  4. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  5. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 48, Eq. (3.26).
  6. J. I. Davis, Appl. Opt. 5, 139 (1966).
    [CrossRef] [PubMed]
  7. A. van der Ziel, Noise (Prentice-Hall, New York, 1954).
  8. A. van der Ziel, Proc. IEEE 58, 1178 (1970).
    [CrossRef]
  9. L. A. Chernov, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), relation between p. 22, Eq. (51), and p. 26, Ed. (67).

1970 (1)

A. van der Ziel, Proc. IEEE 58, 1178 (1970).
[CrossRef]

1966 (2)

1965 (1)

P. Beckmann, Radio Science J. Res. NBS/USNC-URSI 69D, 629 (1965).

Beckmann, P.

P. Beckmann, Radio Science J. Res. NBS/USNC-URSI 69D, 629 (1965).

Chernov, L. A.

L. A. Chernov, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), relation between p. 22, Eq. (51), and p. 26, Ed. (67).

L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill, New York, 1960).

Davis, J. I.

Hodara, H.

H. Hodara, Proc. IEEE 54, 368 (1966).
[CrossRef]

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 48, Eq. (3.26).

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

van der Ziel, A.

A. van der Ziel, Proc. IEEE 58, 1178 (1970).
[CrossRef]

A. van der Ziel, Noise (Prentice-Hall, New York, 1954).

Appl. Opt. (1)

Proc. IEEE (2)

H. Hodara, Proc. IEEE 54, 368 (1966).
[CrossRef]

A. van der Ziel, Proc. IEEE 58, 1178 (1970).
[CrossRef]

Radio Science J. Res. NBS/USNC-URSI (1)

P. Beckmann, Radio Science J. Res. NBS/USNC-URSI 69D, 629 (1965).

Other (5)

L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill, New York, 1960).

L. A. Chernov, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), relation between p. 22, Eq. (51), and p. 26, Ed. (67).

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 48, Eq. (3.26).

A. van der Ziel, Noise (Prentice-Hall, New York, 1954).

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Figures (6)

Fig. 1
Fig. 1

x component of standard deviation of the spot dancing σ x vs path length L for several values of Cn.

Fig. 2
Fig. 2

Measurements made on a fine day in autumn of the spot dancing of a laser beam propagated on a 480-m path about 20 m above the ground.

Fig. 3
Fig. 3

The spot dancing measurements made simultaneously on 480-m and 1380-m paths about 20 m above the ground.

Fig. 4
Fig. 4

Measurements made simultaneously of the spot dancing and the refractive index structure constant on a fine day on a 1380-m path about 20 m above the ground.

Fig. 5
Fig. 5

Measurements made simultaneously of the spot dancing and the refractive index structure constant on a cloudy and occasionally clear day on a 1380-m path about 20 m above the ground.

Fig. 6
Fig. 6

The power spectra of the fluctuations of the spot dancing on 30 October shown in Fig. 4. The vertical axis is 10 dB/div.

Equations (24)

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[ d ( n s ) / d l ] - grad n = 0 ,
n s = n s = 0 Δ l n d l .
s - s = 0 Δ l n d l .
Δ θ 2 ¯ = 0 Δ l 0 Δ l 1 2 B n ( x 1 - x 2 , y 1 - y 2 , z 1 - z 2 ) d r 1 d r 2 .
Δ θ 2 ¯ = - 2 0 Δ l ( Δ l - r ) 2 B n ( r ) d r .
Δ θ 2 ¯ - 2 Δ l 0 Δ l 2 B n ( r ) d r .
D n ( r ) = 2 [ B n ( o ) - B n ( r ) ] ;
D n ( r ) = 8 π 0 ( 1 - sin κ r κ r ) Φ ( κ ) κ 2 d κ ,
Φ ( κ ) = [ Γ ( 8 3 ) sin ( π / 3 ) / 4 π 2 ] C n 2 κ - 1 .
B n ( r ) = κ 0 κ m Γ ( 8 3 ) sin ( π / 3 ) π C n 2 sin κ r r κ - / 3 8 d κ .
Δ θ 2 ¯ = - 2 Δ l 0 Δ l 2 [ Γ ( 8 3 ) sin ( π / 3 ) π × π / L 0 π / w 0 C n 2 sin κ r r κ - / 3 8 d κ ] d r ,
Δ θ 2 ¯ = 3 Γ ( 8 3 ) sin ( π / 3 ) C n 2 π 1 3 Δ l ( w 0 - 1 3 - L 0 - 1 3 ) = 5.7 C n 2 Δ l ( w 0 - 1 3 - L 0 - 1 3 ) .
σ θ 2 = Δ θ 2 ¯ ( L / Δ l ) = 5.7 C n 2 L ( w 0 - 1 3 - L 0 - 1 3 ) .
σ θ 2 = 5.7 C n 2 L w 0 - 1 3 ( 1 1 6 θ L ω 0 ) ,
σ ρ 2 = 0 L ( L - z ) 2 ( d σ θ 2 / d z ) d z .
σ θ 2 = 1 3 σ θ 2 L 2 ,
σ ρ 2 = 1.90 C n 2 L 3 w 0 - 1 3 .
σ ρ 2 = 1.90 C n 2 w 0 - 1 3 L 3 ( 1 1 3 θ L w 0 ) .
w 0 2 = 4 λ L / π ,
σ ρ 2 = 1.83 C n 2 λ - 1 6 L / 6 17 ,
σ ρ 2 = σ x 2 + σ y 2 = 2 σ x 2 .
σ x = 3.14 C n L / 12 17 [ meter ] .
C T = [ ( T 1 - T 2 ) 2 ¯ ] 1 2 r - 1 3 ,
C n = ( 79 P / T 2 ) 10 - 6 C T ,

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