Abstract

No abstract available.

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. E. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation, NTIS-IT No. 68-50464, edited by J. W. Strobehn (National Technical Information Service, Springfield, Va., 1971), Ch. IV.
  2. S. F. Clifford, J. Opt. Soc. Am. 61, 1285 (1971).
    [CrossRef]
  3. S. F. Clifford, G. M. B. Bouricius, G. R. Ochs, and Margot H. Ackley, J. Opt. Soc. Am. 61, 1279 (1971).
    [CrossRef]
  4. V. I. Tatarski, Wave Propagation in a Turbulent Medium, translated by R. S. Silverman (McGraw–Hill, New York, 1961), Eqs. (2.13) and (1.55).

1971 (2)

Ackley, Margot H.

Bouricius, G. M. B.

Clifford, S. F.

Ochs, G. R.

Tatarski, V. E.

V. E. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation, NTIS-IT No. 68-50464, edited by J. W. Strobehn (National Technical Information Service, Springfield, Va., 1971), Ch. IV.

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium, translated by R. S. Silverman (McGraw–Hill, New York, 1961), Eqs. (2.13) and (1.55).

J. Opt. Soc. Am. (2)

Other (2)

V. E. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation, NTIS-IT No. 68-50464, edited by J. W. Strobehn (National Technical Information Service, Springfield, Va., 1971), Ch. IV.

V. I. Tatarski, Wave Propagation in a Turbulent Medium, translated by R. S. Silverman (McGraw–Hill, New York, 1961), Eqs. (2.13) and (1.55).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

F. 1
F. 1

Normalized phase-difference spectrum, W δ s ( f ) ( υ ρ ) / 4.38 { 1 2 } k 2 L C n 2 ρ 5 / 3 ,vs normalized frequency, 2πf/f(ρ/υ), for the particular case when the normalized separation, 1.071ρ/L0 = 0.1.

Tables (2)

Tables Icon

Table I Limiting case results for plane-wave and spherical-wave time spectra with outer scale as a parameter. Ω ≡ f/f0, f0 ≡ (υ(2πλL)−1/2, β2 ≡1 + (1.071υ/2π/L0)2.

Tables Icon

Table II Low-frequency asymptotic results for plane- and spherical-wave time spectra with outer scale as a parameter. f ≪ 1.071υ/2πL0.

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

R χ , s ( τ ) = 0 L d d z B χ , s ( υ τ L z ) d z
R χ , s ( τ ) = B χ , s ( υ τ )
R δ , s ( τ ) = [ s ( r , t ) s ( r + ρ , t ) ] [ s ( r υ τ , t ) s ( r + ρ υ τ , t ) ] .
R δ s ( τ ) = 2 B s ( υ τ ) B s ( υ ( τ ρ / υ ) ) B s ( υ ( τ + ρ / υ ) )
R δ s ( τ ) = 0 L d d z { 2 B s ( υ τ L z ) B s ( υ L z ( τ ρ z υ L ) ) B s ( υ L z ( τ + ρ z υ L ) ) } d z .
W χ , s ( f ) = 4 0 d τ cos ( 2 π f τ ) R χ , s ( τ ) .
B χ , s ( ρ ) = 2 π 2 k 2 0 L d z 0 d κ κ Φ n ( κ ) J 0 ( κ ρ z L ) × { 1 cos [ κ 2 z ( L z ) k L ] } ,
Φ ( κ ) = 0.033 C n 2 { ( 1.071 L 0 ) 2 + κ 2 } 11 / 6 ,
D n ( ρ ) = { C n 2 ρ 2 / 3 , ρ L 0 C n 2 L 0 2 / 3 , ρ L 0
z / L = ( u + 1 ) / 2
σ = { ( κ υ / 2 π f ) 2 1 } β 2 ,
β 2 = { 1 + ( 1.071 υ / 2 π f L 0 ) 2 }
Ω = 2 π f ( L / κ ) 1 / 2 / υ ,
W χ , s = 0.132 π 5 / 2 k 2 / 3 C n 2 L 7 / 3 υ 1 Ω 8 / 3 β 8 / 3 Γ ( 4 / 3 ) / Γ ( 11 / 6 ) × Re 0 1 d u ( 1 exp [ i Ω 2 ( u 1 ) / 4 ] × 1 F 1 ( 1 / 2 ; 1 / 3 ; i β 2 Ω 2 ( u 2 1 ) / 4 ) + Γ ( 4 / 3 ) Γ ( 11 / 6 ) / ( π 1 / 2 Γ ( 4 / 3 ) ) ( i β 2 Ω 2 ( u 2 1 ) / 4 ) 4 / 3 × 1 F 1 ( 11 / 6 ; 7 / 3 ; i β 2 Ω 2 ( u 2 1 ) / 4 ) ,
F 1 ( a ; b ; x ) = Γ ( b ) Γ ( a ) n = 0 Γ ( a + n ) Γ ( b + n ) x n n !
= Γ ( b ) { e + i π a x a Γ ( b a ) n = 0 Γ ( a + n ) Γ ( 1 + a b + n ) Γ ( a ) Γ ( 1 + a b + ) n ! ( x ) n + e z x a b Γ ( a ) n = 0 Γ ( b a + n ) Γ ( b a ) Γ ( 1 a + n ) Γ ( 1 a ) x n n ! } , π 2 < arg ( x ) < 3 π 2 .
W δ s ( f ) = 0.264 π 2 k 2 / 3 L 7 / 3 C n 2 υ 1 Ω 8 / 3 β 8 / 3 × 0 1 d u [ 1 cos ( π ρ f u υ ) cos ( π ρ f υ ) ] × 0 d σ σ 1 / 2 ( σ + 1 ) 11 / 6 { 1 + cos [ Ω 2 ( σ β 2 + 1 ) ( 1 u 2 ) 4 ] } ,
B χ , s ( ρ ) = 2 π 2 k 2 L 0 d κ κ J 0 ( κ ρ ) { 1 k κ 2 L sin κ 2 L k } Φ n ( κ ) .
z = Ω 2 ( ( κ υ / 2 π f ) 2 1 )
W χ , s ( f ) = 0.033 π 2 k 2 / 3 L 7 / 3 C n 2 υ 1 × 0 d z z 1 / 2 [ 1 sin ( z + Ω 2 ) ( z + Ω 2 ) ] ( z + β 2 Ω 2 ) 11 / 6 .
sin ( x + a ) ( x + a ) = 0 1 d b cos ( b ( x + a ) )
W χ , s ( f ) = 0.033 π 5 / 2 k 2 / 3 L 7 / 3 C n 2 Γ ( 4 / 3 ) Γ 1 ( 11 / 6 ) Ω 8 / 3 β 8 / 3 × [ 1 Re 0 1 d b e i b Ω 2 { F 1 ( 1 / 2 ; 1 / 3 ; i b β 2 Ω 2 ) + Γ ( 4 / 3 ) Γ ( 11 / 6 ) Γ 1 ( 4 / 3 ) π 1 / 2 ( i b Ω 2 β 2 ) 4 / 3 × 1 F 1 ( 11 / 6 ; 7 / 3 ; i b β 2 Ω 2 ) } ] .
W δ s ( f ) = 2 [ 1 cos ( 2 π ρ f υ ) ] W s ( f ) .
( 2 π f ρ υ ) , ( 1.071 ρ L 0 ) , and W δ s ( f ) ( υ / ρ ) k 2 L C n 2 ρ 5 / 3
W δ s ( f ) ( υ / ρ ) k 2 L C n 2 ρ 5 / 3 = 4.38 { 1 2 } [ 1 sin ( 2 π f ρ / υ ) ( 2 π f ρ / υ ) ] × ( 1 + ( 1.071 ρ / L 0 ) 2 ( 2 π f ρ / υ ) 2 ) 4 / 3 ( 2 π f ρ υ ) 8 / 3 ,
W δ s ( f ) ( υ ρ ) / 4.38 { 1 2 } k 2 L C n 2 ρ 5 / 3 ,