Abstract

A MTF is derived that includes isoplanatic effects of tilt correction or short-term imaging systems. The MTF is used to predict degradation in Strehl ratio or resolution due to tilt decorrelation on offset paths for long horizontal paths through constant turbulence and for space-to-earth paths through a path-dependent structure constant Cn2.

© 1980 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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1979 (4)

1978 (3)

1977 (1)

1976 (3)

1975 (2)

1973 (1)

1972 (1)

1970 (1)

Barletti, R.

Buchheim, R. K.

Buffington, A.

Bufton, J. L.

Ceppatelli, G.

Clark, W. L.

T. E. VanZandt, J. L. Green, K. S. Gage, W. L. Clark, Radio Sci. 13, 819 (1978).
[CrossRef]

Clifford, S. F.

Crawford, F. S.

Fitzmaurice, M. W.

Fried, D. L.

D. L. Fried, Proc. Soc. Photo Opt. Instrum. Eng. 75, 79 (1976).

D. L. Fried, Radio Sci. 10, 71 (1975).
[CrossRef]

D. L. Fried, “Isoplanatism Dependence of a Ground-to-Space Laser Transmitter with Adaptive Optics,” Optical Sciences Co. Report TR-249 (March1977).

Gage, K. S.

T. E. VanZandt, J. L. Green, K. S. Gage, W. L. Clark, Radio Sci. 13, 819 (1978).
[CrossRef]

Green, J. L.

T. E. VanZandt, J. L. Green, K. S. Gage, W. L. Clark, Radio Sci. 13, 819 (1978).
[CrossRef]

Greenwood, D. P.

Hufnagel, R. E.

R. E. Hufnagel, in Digest of Topical Meeting on Optical Propagation Through Turbulence (Optical Society of America, Washington, D.C., 1974).

Karo, D. P.

Lawrence, R. S.

Markey, J. K.

Miller, M. G.

M. G. Miller, P. L. Zieske, “Turbulence Environment Characterization,” Rome Air Development Center Technical Report RADC-TR-79-131 (June1979).

Minott, P. O.

Ochs, G. R.

Patero, L.

Pollaine, S.

Pringle, R.

Righini, A.

Schaefgen, H. W.

Schneiderman, A. M.

Shapiro, J. H.

Speroni, N.

Tavis, M. T.

Titterton, P. J.

Valley, G. C.

VanZandt, T. E.

T. E. VanZandt, J. L. Green, K. S. Gage, W. L. Clark, Radio Sci. 13, 819 (1978).
[CrossRef]

Wandzura, S. M.

Wang, J. Y.

Yura, H. T.

Zieske, P. L.

M. G. Miller, P. L. Zieske, “Turbulence Environment Characterization,” Rome Air Development Center Technical Report RADC-TR-79-131 (June1979).

Appl. Opt. (4)

J. Opt. Soc. Am. (9)

Proc. Soc. Photo Opt. Instrum. Eng. (1)

D. L. Fried, Proc. Soc. Photo Opt. Instrum. Eng. 75, 79 (1976).

Radio Sci. (2)

D. L. Fried, Radio Sci. 10, 71 (1975).
[CrossRef]

T. E. VanZandt, J. L. Green, K. S. Gage, W. L. Clark, Radio Sci. 13, 819 (1978).
[CrossRef]

Other (3)

M. G. Miller, P. L. Zieske, “Turbulence Environment Characterization,” Rome Air Development Center Technical Report RADC-TR-79-131 (June1979).

R. E. Hufnagel, in Digest of Topical Meeting on Optical Propagation Through Turbulence (Optical Society of America, Washington, D.C., 1974).

D. L. Fried, “Isoplanatism Dependence of a Ground-to-Space Laser Transmitter with Adaptive Optics,” Optical Sciences Co. Report TR-249 (March1977).

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Figures (5)

Fig. 1
Fig. 1

Isoplanatic relative intensity as a function of path length times angular offset divided by beam diameter for a collimated beam propagating through homogeneous turbulence.

Fig. 2
Fig. 2

Hufnagel 1974 C n 2 model scaled to seeing of 0.5, 1.0, and 1.5 sec of arc at λ = 0.55 μm.

Fig. 3
Fig. 3

Isoplanatic relative intensity as a function of offset angle θ for a space-to-earth geometry with a receiver diameter of 0.5 m and wavelength of 0.55 μm and for the Hufnagel 1974 C n 2 model scaled to 0.5, 1.0, and 1.5 sec of arc.

Fig. 4
Fig. 4

Hufnagel 1974 C n 2 model scaled to 1.0 sec of arc for varying levels of upper atmospheric wind.

Fig. 5
Fig. 5

Isoplanatic relative intensity as a function of offset angle θ for a space-to-earth geometry with a receiver diameter of 0.5 m and wavelength of 0.55 μm and for the Hufnagel 1974 C n 2 model with varying levels of upper atmospheric turbulence and 1-sec of arc seeing.

Equations (21)

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M J ( x , y ) = exp ( - ½ k 2 σ x 2 x 2 - ½ k 2 σ y 2 y 2 ) ,
σ x 2 = 2 [ 1 - C α x ( θ ) ] α x 2 ,
σ y 2 = 2 [ 1 - C α y ( θ ) ] α y 2 ,
α x 2 = α y 2 = 2.086 ( k 2 D 1 / 3 ρ 0 5 / 3 ) - 1 ,
ρ 0 = ( / 8 3 · 1.457 k 2 C n 2 L ) - 3 / 5
ρ 0 = [ 1.457 k 2 0 C n 2 ( z ) d z ] - 3 / 5
M iso t . c . = exp ( - 2.086 ( D / ρ 0 ) 5 / 3 { [ 1 - C α x ( θ ) ] x 2 D 2 + [ 1 - C α y ( θ ) ] y 2 D 2 } ) .
M iso t . c . ( ξ ) = exp { - 1.043 ( D / ρ 0 ) 5 / 3 ξ 2 [ 2 - C α x ( θ ) - C α y ( θ ) ] } × I 0 { 1.043 ( D / ρ 0 ) 5 / 3 ξ 2 [ C α x ( θ ) - C α y ( θ ) ] } ,
C α x ( θ ) = A 0 ( z θ / d ) - A 2 ( z θ / d ) ,
C α y ( θ ) = A 0 ( z θ / d ) + A 2 ( z θ / d ) ,
A 0 , 2 ( Δ ) = 0 d u u - 14 / 3 [ J 2 ( u ) ] 2 J 0 , 2 ( 2 Δ u ) ,
A 0 ( Δ ) = exp ( - 0.5866 Δ 1.759 ) ,             0 Δ 0.55
= 0.6656 Δ - 1 / 3 [ 1 + 1 / ( 6 3 Δ 2 ) ] ,             0.55 < Δ ,
A 2 ( Δ ) = exp ( - 1.941 Δ - 0.4602 ) ,             0 Δ 0.625
= 0.1331 Δ - 1 / 3 [ 1 - 1 / ( 6 Δ 2 ) ] ,             0.625 Δ .
C α y α x ( θ ) = 0 L θ / D d Δ [ A 0 ( Δ ) A 2 ( Δ ) ] / ( L θ / D ) .
M a p ( ξ ) = 2 π [ arccos ξ - ξ ( 1 - ξ 2 ) 1 / 2 ] 0 ξ 1 = 0 1 < ξ .
M atm t . c . ( ξ ) = exp [ - ( D / ρ 0 ) 5 / 3 ξ 5 / 3 ( 1 - 1.043 ξ 1 / 3 ) ] .
I rel = 0 1 d ξ ξ M ap ( ξ ) M atm t . c . ( ξ ) M iso t . c . ( ξ ) 0 1 d ξ ξ M ap ( ξ ) M atm t . c . ( ξ ) .
C α y α x ( θ ) = 0 d z [ A 0 ( z θ / D ) A 2 ( z θ / D ) ] C n 2 ( z ) / 0 d z C n 2 ( z ) .
C n 2 ( z ) = A [ 2.2 × 10 - 23 z 10 exp ( - z ) ( V w V ¯ w ) 2 + 10 - 16 exp ( - z / 1.5 ) ] m - 2 / 3 ,

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