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References

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  1. D. Greenwood, J. Opt. Soc. Am. 67, 282 (1977).
    [CrossRef]
  2. C. B. Hogge, R. Butts, IEEE Trans. Antennas Propag. AP-24, 144 (1976).
    [CrossRef]
  3. R. Butts, “Laser Digest,” AFWL-TR-80-107, Air Force Weapons Laboratory, Kirtland Air Force Base, N.M. (1980) p. 17.
  4. J. Winocur, Appl. Opt. 21, 433 (1982).
    [CrossRef] [PubMed]
  5. S. F. Clifford, J. Opt. Soc. Am. 61, 1285 (1971).
    [CrossRef]
  6. D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
    [CrossRef]
  7. R. J. Noll, J. Opt. Soc. Am. 66, 207 (1976).
    [CrossRef]
  8. G. I. Taylor, Proc. R. Soc. London Ser. A 132, 476 (1938).

1982 (1)

1977 (1)

1976 (2)

C. B. Hogge, R. Butts, IEEE Trans. Antennas Propag. AP-24, 144 (1976).
[CrossRef]

R. J. Noll, J. Opt. Soc. Am. 66, 207 (1976).
[CrossRef]

1971 (1)

1966 (1)

1938 (1)

G. I. Taylor, Proc. R. Soc. London Ser. A 132, 476 (1938).

Butts, R.

C. B. Hogge, R. Butts, IEEE Trans. Antennas Propag. AP-24, 144 (1976).
[CrossRef]

R. Butts, “Laser Digest,” AFWL-TR-80-107, Air Force Weapons Laboratory, Kirtland Air Force Base, N.M. (1980) p. 17.

Clifford, S. F.

Fried, D. L.

Greenwood, D.

Hogge, C. B.

C. B. Hogge, R. Butts, IEEE Trans. Antennas Propag. AP-24, 144 (1976).
[CrossRef]

Noll, R. J.

Taylor, G. I.

G. I. Taylor, Proc. R. Soc. London Ser. A 132, 476 (1938).

Winocur, J.

Appl. Opt. (1)

IEEE Trans. Antennas Propag. (1)

C. B. Hogge, R. Butts, IEEE Trans. Antennas Propag. AP-24, 144 (1976).
[CrossRef]

J. Opt. Soc. Am. (4)

Proc. R. Soc. London Ser. A (1)

G. I. Taylor, Proc. R. Soc. London Ser. A 132, 476 (1938).

Other (1)

R. Butts, “Laser Digest,” AFWL-TR-80-107, Air Force Weapons Laboratory, Kirtland Air Force Base, N.M. (1980) p. 17.

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Figures (2)

Fig. 1
Fig. 1

Comparison of the exact and parallel approximation tilt power spectra for plane waves.

Fig. 2
Fig. 2

Parallel approximation integral I (πfD/υ).

Equations (12)

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α i ( t ) = 64 π D 4 d 2 r ¯ r i ϕ ( r ¯ , t ) W ( r ¯ ) i = x , y ,
k 2 σ i 2 ( τ ) = α i ( t + τ ) α i ( t ) = ( 64 π D 4 ) 2 d 2 r ¯ d 2 r ¯ r i r i W ( r ¯ ) W ( r ¯ ) · W ϕ ( r ¯ , r ¯ , τ ) ,
W ϕ ( r ¯ , r ¯ , τ ) = ϕ ( r ¯ , t ) ϕ ( r ¯ , t + τ ) ,
σ ¯ i 2 ( f ) = d τ exp ( 2 π i f τ ) σ i 2 ( τ ) .
W ϕ ( r ¯ , r ¯ , τ ) = 2 π 2 k 2 0 L d z 0 d K K Φ n ( K , z ) · J 0 ( K z L | r ¯ r ¯ + υ ¯ τ L z | ) { 1 + cos [ K 2 z k L ( L z ) ] } ,
W δ ϕ ( r ¯ , r ¯ , τ ) = [ ϕ ( r ¯ , t ) ϕ ( r ¯ , t ) ] · [ ϕ ( r ¯ , t , + τ ) ϕ ( r ¯ , t + τ ) ] ,
d 2 r ¯ r ¯ i W ( r ¯ ) = 0.
W δ ϕ ( r ¯ , r ¯ , f ) = 16 π 2 k 2 0 L d z sin 2 ( π | r ¯ r ¯ | f z υ ) × 2 π f / υ d K K Φ n ( K , z ) · [ ( K υ ) 2 ( 2 π f ) 2 ] 1 / 2 { 1 + cos [ K 2 z k L ( L z ) ] } ,
Φ n ( K , z ) = 0.033 C n 2 ( z ) K 11 / 3 .
σ ¯ x , exact 2 ( f ) = 0.033 · 2 25 / 3 π 8 / 3 · 1 D 4 1 f 14 / 3 0 L d z C n 2 ( υ ) z 11 / 13 ( z ) · 0 π / 2 d θ 1 sec 17 / 3 θ · J 2 2 [ π f D υ ( z ) sec θ ] ,
σ ¯ x , approx 2 ( f ) = 0.033 · 2 28 / 3 π 5 / 3 · Γ ( 1 / 2 ) Γ ( 11 / 3 ) Γ ( 11 / 6 ) · 1 D 2 · 1 f 8 / 3 · ( 1 ) . 0 L d z C n 2 ( υ ) z 5 / 3 ( z ) 0 1 d ξ ξ [ cos 1 ξ · ξ ( 1 ξ 2 ) 1 / 2 2 ξ ( 1 ξ 2 ) 3 / 2 ] · sin 2 [ π f D υ ( z ) ξ ] .
I ( π f D υ ) = ( 1 ) · 0 1 d ξ ξ [ cos 1 ξ ξ ( 1 ξ 2 ) 1 / 2 2 ξ ( 1 ξ 2 ) 3 / 2 ] · sin 2 ( π f D υ ξ )

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