Abstract

Atmospheric turbulence in the internal light path of a telescope produces noncommon path phase differences that degrade the image quality of adaptive-optics systems employing laser guide stars. The spatial covariance and rms wavefront errors produced by this effect are derived. It is found that the tilt-removed wavefront error ranges from about 12nm for a representative 30m telescope to 59nm for a 100m telescope of similar optical design. For adaptive-optics systems that aim to derive tip-tilt information from the laser guide stars the error is considerably larger, ranging from 22nm for the 30m telescope to 256nm for the 100m telescope. This effect can be a significant impediment to the performance of such systems.

© 2006 Optical Society of America

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References

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    [Crossref]
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2006 (1)

A. Tokovinin and T. Travouillon, Mon. Not. R. Astron. Soc. 365, 1235 (2006).
[Crossref]

1995 (1)

R. Foy, A. Migus, F. Biraben, P. R. McCullough, and M. Tallon, Astron. Astrophys. Suppl. Ser. 111, 569 (1995).

1994 (1)

1991 (1)

1976 (1)

Beckers, J.

J. Beckers, in Proceedings of European Southern Observatory Conference and Workshop on Very Large Telescope and Their Instrumentation, M.-H.Ulrich, ed., Vol. 30 of ESO Conference and Workshop Proceedings (European Southern Observatory, 1988), pp. 693-703.

Biraben, F.

R. Foy, A. Migus, F. Biraben, P. R. McCullough, and M. Tallon, Astron. Astrophys. Suppl. Ser. 111, 569 (1995).

Ellerbroek, B. L.

Foy, R.

R. Foy, A. Migus, F. Biraben, P. R. McCullough, and M. Tallon, Astron. Astrophys. Suppl. Ser. 111, 569 (1995).

McCullough, P. R.

R. Foy, A. Migus, F. Biraben, P. R. McCullough, and M. Tallon, Astron. Astrophys. Suppl. Ser. 111, 569 (1995).

Migus, A.

R. Foy, A. Migus, F. Biraben, P. R. McCullough, and M. Tallon, Astron. Astrophys. Suppl. Ser. 111, 569 (1995).

Noll, R. J.

Tallon, M.

R. Foy, A. Migus, F. Biraben, P. R. McCullough, and M. Tallon, Astron. Astrophys. Suppl. Ser. 111, 569 (1995).

Tokovinin, A.

A. Tokovinin and T. Travouillon, Mon. Not. R. Astron. Soc. 365, 1235 (2006).
[Crossref]

Travouillon, T.

A. Tokovinin and T. Travouillon, Mon. Not. R. Astron. Soc. 365, 1235 (2006).
[Crossref]

Welsh, B. M.

Appl. Opt. (1)

Astron. Astrophys. Suppl. Ser. (1)

R. Foy, A. Migus, F. Biraben, P. R. McCullough, and M. Tallon, Astron. Astrophys. Suppl. Ser. 111, 569 (1995).

J. Opt. Soc. Am. (1)

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

Mon. Not. R. Astron. Soc. (1)

A. Tokovinin and T. Travouillon, Mon. Not. R. Astron. Soc. 365, 1235 (2006).
[Crossref]

Other (1)

J. Beckers, in Proceedings of European Southern Observatory Conference and Workshop on Very Large Telescope and Their Instrumentation, M.-H.Ulrich, ed., Vol. 30 of ESO Conference and Workshop Proceedings (European Southern Observatory, 1988), pp. 693-703.

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Figures (3)

Fig. 1
Fig. 1

The propagation of object and laser rays from a point P in the telescope exit pupil to the object focus F and laser focus G.

Fig. 2
Fig. 2

The coefficient Q ( η , μ ) of the tilt-removed NCP variance averaged over the pupil [Eq. (9)].

Fig. 3
Fig. 3

Variation of the rms NCP error with outer scale L 0 . Values of σ ζ ( η , μ ) obtained by using the modified von Kármán spectrum with specified L 0 and inner scale l 0 = 1 cm , normalized by the Kolmogorov value ( L 0 = , l 0 = 0 ). Here η = 0.0333 , μ = 0.95 , and f = 45 m , appropriate for the 30 m telescope example described in the text.

Equations (11)

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ζ ( r ) = 0 f [ ξ ( r f ) n ( ( 1 z f ) r , z ) ξ ( r g ) n ( ( 1 z g ) r , z ) ] d z ,
B ζ ( r 1 ; r 2 ) ζ ( r 1 ) ζ ( r 2 ) = 0 f d z 1 0 f d z 2 [ ξ ( r 1 f ) n ( ( 1 z 1 f ) r 1 , z 1 ) ξ ( r 1 g ) n ( ( 1 z 1 g ) r 1 , z 1 ) ] [ ξ ( r 2 f ) n ( ( 1 z 2 f ) r 2 , z 2 ) ξ ( r 2 g ) n ( ( 1 z 2 g ) r 2 , z 2 ) ] = 0 f d z 1 0 f d z 2 [ ξ ( r 1 f ) ξ ( r 2 f ) B n ( ( 1 z 1 f ) r 1 ( 1 z 2 f ) r 2 , z 1 z 2 ) ξ ( r 1 f ) ξ ( r 2 g ) B n ( ( 1 z 1 f ) r 1 ( 1 z 2 g ) r 2 , z 1 z 2 ) ξ ( r 1 g ) ξ ( r 2 f ) B n ( ( 1 z 1 g ) r 1 ( 1 z 2 f ) r 2 , z 1 z 2 ) + ξ ( r 1 g ) ξ ( r 2 g ) B n ( ( 1 z 1 g ) r 1 ( 1 z 2 g ) r 2 , z 1 z 2 ) ] ,
B n ( s ) = 4 π s 0 Φ n ( κ ) sin ( κ s ) κ d κ .
σ ζ 2 = 2 0 1 B ζ ( R ρ , 0 ; R ρ , 0 ) ρ d ρ ,
ζ ( R ρ , ϕ ) = j = 1 a j Z j ( ρ , ϕ ) .
a j a k = 1 π 2 B ζ ( R ρ , ϕ ; R ρ , ϕ ) Z j ( ρ , ϕ ) Z k ( ρ , ϕ ) ρ ρ d ρ d ρ d ϕ d ϕ .
a 1 2 = 2 π 0 1 ρ d ρ 0 1 ρ d ρ 0 2 π d ϕ B ζ ( R ρ , 0 ; R ρ , ϕ ) ,
a 2 2 = a 3 2 = 8 π 0 1 ρ 2 d ρ 0 1 ρ 2 d ρ 0 2 π cos ϕ d ϕ B ζ ( R ρ , 0 ; R ρ , ϕ ) ,
Φ n ( κ ) = 0.033 C n 2 κ 11 3 .
σ ptt 2 = Q ( η , μ ) ( 1 μ ) η 2 C n 2 f 8 3 ,
Φ n ( κ ) = 0.033 C n 2 [ κ 2 + ( 2 π L 0 ) 2 ] 11 6 exp [ ( κ l 0 5.92 ) 2 ] .

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