Abstract

Statistical estimates of selected scintillation parameters for an infrared laser ground-to-space communication system are presented for a point-receiving aperture. The quantities estimated here are the fraction of time that the signal power is both above and below a given value, the mean number of times per second the signal power crosses a given signal level, and the mean duration of both surges and fades for a given log-irradiance variance.

© 1983 Optical Society of America

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References

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  1. R. E. Hufnagel, “Variations of Atmospheric Turbulence,” in Digest of Topical Meeting on Optical Propagation Through Turbulence, (Optical Society of America, Washington, D.C., 1974), paper WA1.
  2. R. L. Fante, Proc. IEEE 68, 1424 (1980).
    [CrossRef]
  3. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  4. R. Barletti, G. Ceppatelli, L. Paterna, A. Righini, N. Speroni, J. Opt. Soc. Am. 66, 1380 (1976).
    [CrossRef]
  5. J. Vernin et al., Appl. Opt. 18, 243 (1979).
    [CrossRef] [PubMed]
  6. P. Beckman, Probability in Communication and Engineering (Harcourt, Brace, Jovanovich, New York, 1967), Chap. 6.

1980

R. L. Fante, Proc. IEEE 68, 1424 (1980).
[CrossRef]

1979

1976

Barletti, R.

Beckman, P.

P. Beckman, Probability in Communication and Engineering (Harcourt, Brace, Jovanovich, New York, 1967), Chap. 6.

Ceppatelli, G.

Fante, R. L.

R. L. Fante, Proc. IEEE 68, 1424 (1980).
[CrossRef]

Hufnagel, R. E.

R. E. Hufnagel, “Variations of Atmospheric Turbulence,” in Digest of Topical Meeting on Optical Propagation Through Turbulence, (Optical Society of America, Washington, D.C., 1974), paper WA1.

Paterna, L.

Righini, A.

Speroni, N.

Tatarskii, V. I.

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

Vernin, J.

Appl. Opt.

J. Opt. Soc. Am.

Proc. IEEE

R. L. Fante, Proc. IEEE 68, 1424 (1980).
[CrossRef]

Other

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

P. Beckman, Probability in Communication and Engineering (Harcourt, Brace, Jovanovich, New York, 1967), Chap. 6.

R. E. Hufnagel, “Variations of Atmospheric Turbulence,” in Digest of Topical Meeting on Optical Propagation Through Turbulence, (Optical Society of America, Washington, D.C., 1974), paper WA1.

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Figures (9)

Fig. 1
Fig. 1

Normalized log-irradiance variance as a function of root-mean-square wind speed V.

Fig. 2
Fig. 2

Normalized irradiance temporal frequency spectrum for various values of V at λ = 2.91 μm.

Fig. 3
Fig. 3

Fraction of time that irradiance is <3, 6, and 10 dB below the mean irradiance.

Fig. 4
Fig. 4

Fraction of time that irradiance is >3 and 6 dB above the mean irradiance level.

Fig. 5
Fig. 5

Mean level crossing frequency as a function of normalized log-irradiance variance for various fade levels, λ = 2.91 μm.

Fig. 6
Fig. 6

Mean level crossing frequency as a function of fade level for various wavelengths; V = 36 m/sec, θ = 0°.

Fig. 7
Fig. 7

Mean level crossing frequency as a function of fade level for various wavelengths; V = 36 m/sec, θ = 60°.

Fig. 8
Fig. 8

Mean level crossing frequency at λ = 1.32 μm for various root-mean-square wind speeds and zenith angles.

Fig. 9
Fig. 9

Mean duration of 3- and 6-dB fades as a function of normalized log-irradiance variance.

Tables (1)

Tables Icon

Table I Log-irradiance Variance at Several Wavelengths for Various Values of the Root-Mean-Square Wind Speed and Zenith Armies

Equations (33)

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V = [ 1 15 5 20 υ 2 ( h ) d h ) ] 1 / 2 .
i ( r , t ) = I ( r , t ) I m exp ( l ) ,
P l ( l ) = 1 ( 2 π σ l 2 ) 1 / 2 exp [ ( l l m ) 2 2 σ l 2 ] ,
σ l 2 = ( l l m ) 2 = [ ln ( I / I m ) ] 2 .
P l ( l ) = 1 ( 2 π σ l 2 ) 1 / 2 exp { ( l + ( 1 / 2 ) σ l 2 ) 2 2 σ l 2 } .
P i ( i ) = 1 ( 2 π σ l 2 ) 1 / 2 1 i exp { 1 2 σ l 2 [ ln i + 1 2 σ l 2 ] 2 } .
σ l 2 ( I I m ) 2 I m 2 = exp [ σ l 2 ] 1 σ l 2 , for σ l 2 1 .
σ l 2 2.24 k 7 / 6 ( sec θ ) 11 / 6 0 H C n 2 ( h ) h 5 / 6 d h ,
C n 2 ( h ) = 2.72 × 10 16 [ 3 V 2 ( h 10 ) 10 exp ( h ) + exp ( h / 1.5 ) ] ( m 2 / 3 ) ,
σ l 2 [ 7.41 × 10 2 ( V 27 ) 2 + 4.45 × 10 3 ] λ 7 / 6 ( sec θ ) 11 / 6 ,
C i ( r 1 , r 2 ) = [ i ( r 1 , t ) i m ] [ i ( r 2 , t ) i m ] .
C i ( r ) = exp [ C l ( r ) ] 1 C l ( r ) , for σ l 2 1 ,
C l ( r ) = [ l ( r 1 ) l m ] [ l ( r 2 ) l m ] .
b l ( r ) = 0 H C n 2 ( h ) d h 0 J 0 [ K r ( h / H ) ] sin 2 [ K 2 h / 2 k ] K 8 / 3 d K 0 H C n 2 ( h ) d h 0 sin 2 [ K 2 h / 2 k ] K 8 / 3 d K ,
r l ~ ( H h 0 ) ( λ Δ h ) 1 / 2 ,
P ( f ) 8.27 ( sec θ ) 7 / 3 k 2 / 3 0 H C n 2 ( h ) h 4 / 3 υ n ( h ) d h × 0 [ x 2 + f 2 f 2 0 ( h ) ] 11 / 6 sin 2 [ x 2 + f 2 / f 0 2 ( h ) ] d x ,
f 0 ( h ) = [ 2 k h sec θ ] 1 / 2 υ n ( h ) .
S = 10 log ( I / I m ) ,
F = 10 | log ( I / I m ) | .
l S = [ ln ( 10 ) / 10 ] S 0.23 S ( surges ) ,
l F = [ ln ( 10 ) / 10 ] F 0.23 | F | ( fades ) .
frac ( i i 0 ) = P i ( i i 0 ) = P l ( l l 0 ) ,
frac ( i i 0 ) = P i ( i i 0 ) = P l ( l l 0 ) ,
frac ( i i 0 ) = 1 ( 2 π σ l ) 1 / 2 F l 0 exp [ ( l + ( 1 / 2 ) σ l 2 ) 2 2 σ l 2 ] d l = 1 2 { 1 + erf [ F l 0 + ( 1 / 2 ) σ l 2 2 σ l ] } ,
F l 0 0.23 F 0 ,
frac ( i i 0 ) = 1 2 { 1 erf [ S l 0 + ( 1 / 2 ) σ l 2 2 σ l ] } ,
S l 0 0.23 S 0 ,
ν ( l 0 ) = ν 0 exp { [ l + ( 1 / 2 ) σ l 2 ] 2 2 σ l 2 } ,
ν 0 = [ 0 f 2 P ( f ) d f / 0 P ( f ) d f ] 1 / 2 ,
ν ( F 0 ) ν 0 exp { [ 0.23 F 0 + ( 1 / 2 ) σ l 2 ] 2 2 σ l 2 } .
ν + ( S 0 ) ν 0 exp { [ 0.23 S 0 + ( 1 / 2 ) σ l 2 ] 2 2 σ l 2 } .
T ( l 0 ) = P l ( l < l 0 ) ν ( l 0 ) 1 2 ν 0 exp { [ 0.23 F 0 + ( 1 / 2 ) σ l 2 ] 2 2 σ l 2 } × ( 1 + erf { [ 0.23 F 0 + ( 1 / 2 ) σ l 2 ] 2 2 σ l 2 } )
T + ( l 0 ) = P l ( l > l 0 ) ν + ( l 0 ) 1 2 ν 0 exp { [ 0.23 S 0 + ( 1 / 2 ) σ l 2 ] 2 2 σ l 2 } × ( 1 erf { [ 0.23 S 0 + ( 1 / 2 ) σ l 2 ] 2 2 σ l } ) .

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