Abstract

The phase structure function has been used as a convenient way to characterize aberrations introduced on optical propagation by the atmosphere. It forms the theoretical basis for the calculation of such things as the long- and short-exposure atmospheric transfer function. The structure function is difficult to measure directly and is usually assumed to follow Kolmogorov statistics. We present here a technique for direct measurement of the structure function through the use of a Shack–Hartmann wave-front sensor. Experiments confirm that the atmosphere behaves according to Kolmogorov theory most of the time. However, some instances of non-Kolmogorov behavior have been noted.

© 1992 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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  11. J. McWilliams, Phys. Fluids A 2, 547 (1990).
    [CrossRef]

1990 (3)

1988 (1)

1985 (1)

J. Fontanella, J. Opt. (Paris) 16, 257 (1985).
[CrossRef]

1982 (1)

E. Wallner, Proc. Soc. Photo-Opt. Instrum. Eng. 351, 42 (1982).

1977 (1)

1967 (1)

G. Heidbreder, IEEE Trans. Antennas Propag. AP-15, 90 (1967).
[CrossRef]

1966 (1)

Bester, M.

M. Bester, W. Danchi, C. Degiacomi, L. Greenhill, C. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. (to be published).

Caccia, J.

Coqueugniot, Y.

Coulman, C.

Danchi, W.

M. Bester, W. Danchi, C. Degiacomi, L. Greenhill, C. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. (to be published).

Dayton, D.

Degiacomi, C.

M. Bester, W. Danchi, C. Degiacomi, L. Greenhill, C. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. (to be published).

Fender, J.

Fontanella, J.

Fried, D.

Gonglewski, J.

Greenhill, L.

M. Bester, W. Danchi, C. Degiacomi, L. Greenhill, C. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. (to be published).

Heidbreder, G.

G. Heidbreder, IEEE Trans. Antennas Propag. AP-15, 90 (1967).
[CrossRef]

McWilliams, J.

J. McWilliams, Phys. Fluids A 2, 547 (1990).
[CrossRef]

Pierson, R.

Primot, J.

Roddier, C.

Rousset, G.

Spielbusch, B.

Townes, C.

M. Bester, W. Danchi, C. Degiacomi, L. Greenhill, C. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. (to be published).

Vernin, J.

Voelz, D.

Wallner, E.

E. Wallner, Proc. Soc. Photo-Opt. Instrum. Eng. 351, 42 (1982).

Winker, D.

D. Winker, in Annual Meeting, Vol. 11 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), paper WL2.

Appl. Opt. (3)

IEEE Trans. Antennas Propag. (1)

G. Heidbreder, IEEE Trans. Antennas Propag. AP-15, 90 (1967).
[CrossRef]

J. Opt. (Paris) (1)

J. Fontanella, J. Opt. (Paris) 16, 257 (1985).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Phys. Fluids A (1)

J. McWilliams, Phys. Fluids A 2, 547 (1990).
[CrossRef]

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

E. Wallner, Proc. Soc. Photo-Opt. Instrum. Eng. 351, 42 (1982).

Other (2)

M. Bester, W. Danchi, C. Degiacomi, L. Greenhill, C. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. (to be published).

D. Winker, in Annual Meeting, Vol. 11 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), paper WL2.

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Figures (4)

Fig. 1
Fig. 1

Optics layout for structure function measurement.

Fig. 2
Fig. 2

Phase structure functions illustrating Kolmogorov and non-Kolmogorov behavior.

Fig. 3
Fig. 3

Theoretical phase difference structure functions.

Fig. 4
Fig. 4

Phase difference structure functions illustrating Kolmogorov and non-Kolmogorov behavior.

Equations (7)

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D ϕ ( r ) = | ϕ ( υ ) ϕ ( υ ) | 2 ,
r = | υ υ | .
D ϕ ( r ) = 6.88 ( r r 0 ) 5 / 3 .
D Δ ø ( r , x ) = [ Δ ø ( x + r ) Δ ø ( x ) ] 2 ¯ = 2 Δ ø ( x ) 2 ¯ 2 Δ ø ( x + r ) Δ ø ( x ) . ¯
Δ ( x + r ) Δ ( x ) ¯ = 1 2 W x + r ( y ) W x ( z ) D ( y , z ) d y d z ,
Δ ( x + r ) Δ ( x ) ¯ = 1 2 diff 2 [ D ( r ) ] .
D Δ ( x + r ) diff 2 [ D ( o ) ] diff 2 [ D ( r ) ] ,

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