Abstract

Because of atmospheric turbulence, the fringes produced by a Michelson stellar interferometer appear as a random modulation of the two superimposed stellar images. The contribution of the related high spatial frequency peaks in the image Wiener spectrum has been computed as a function of the diameter of the apertures and of the seeing conditions. This contribution appears to be independent of the seeing condition for large apertures.

© 1976 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. A. Michelson, Astrophys. J. 51, 257 (1920).
    [Crossref]
  2. A. A. Michelson and F. G. Pease, Astrophys. J. 53, 249 (1921).
    [Crossref]
  3. J. A. Anderson, Astrophys. J. 51, 263 (1920).
    [Crossref]
  4. A. Labeyrie, Astrophys. J. Lett. 196, L 71 (1975).
    [Crossref]
  5. A. Labeyrie, Nouv. Rev. Opt. 5, 141 (1974).
    [Crossref]
  6. D. Korff, G. Dryden, and M. Miller, Opt. Commun. 5, 187 (1972).
    [Crossref]
  7. D. Korff, J. Opt. Soc. Am. 63, 971 (1973).
    [Crossref]
  8. J. C. Dainty, Opt. Commun. 7, 129 (1973).
    [Crossref]
  9. F. Roddier, Opt. Commun. 10, 103 (1974).
    [Crossref]
  10. D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
    [Crossref]

1975 (1)

A. Labeyrie, Astrophys. J. Lett. 196, L 71 (1975).
[Crossref]

1974 (2)

A. Labeyrie, Nouv. Rev. Opt. 5, 141 (1974).
[Crossref]

F. Roddier, Opt. Commun. 10, 103 (1974).
[Crossref]

1973 (2)

D. Korff, J. Opt. Soc. Am. 63, 971 (1973).
[Crossref]

J. C. Dainty, Opt. Commun. 7, 129 (1973).
[Crossref]

1972 (1)

D. Korff, G. Dryden, and M. Miller, Opt. Commun. 5, 187 (1972).
[Crossref]

1966 (1)

1921 (1)

A. A. Michelson and F. G. Pease, Astrophys. J. 53, 249 (1921).
[Crossref]

1920 (2)

J. A. Anderson, Astrophys. J. 51, 263 (1920).
[Crossref]

A. A. Michelson, Astrophys. J. 51, 257 (1920).
[Crossref]

Anderson, J. A.

J. A. Anderson, Astrophys. J. 51, 263 (1920).
[Crossref]

Dainty, J. C.

J. C. Dainty, Opt. Commun. 7, 129 (1973).
[Crossref]

Dryden, G.

D. Korff, G. Dryden, and M. Miller, Opt. Commun. 5, 187 (1972).
[Crossref]

Fried, D. L.

Korff, D.

D. Korff, J. Opt. Soc. Am. 63, 971 (1973).
[Crossref]

D. Korff, G. Dryden, and M. Miller, Opt. Commun. 5, 187 (1972).
[Crossref]

Labeyrie, A.

A. Labeyrie, Astrophys. J. Lett. 196, L 71 (1975).
[Crossref]

A. Labeyrie, Nouv. Rev. Opt. 5, 141 (1974).
[Crossref]

Michelson, A. A.

A. A. Michelson and F. G. Pease, Astrophys. J. 53, 249 (1921).
[Crossref]

A. A. Michelson, Astrophys. J. 51, 257 (1920).
[Crossref]

Miller, M.

D. Korff, G. Dryden, and M. Miller, Opt. Commun. 5, 187 (1972).
[Crossref]

Pease, F. G.

A. A. Michelson and F. G. Pease, Astrophys. J. 53, 249 (1921).
[Crossref]

Roddier, F.

F. Roddier, Opt. Commun. 10, 103 (1974).
[Crossref]

Astrophys. J. (3)

A. A. Michelson, Astrophys. J. 51, 257 (1920).
[Crossref]

A. A. Michelson and F. G. Pease, Astrophys. J. 53, 249 (1921).
[Crossref]

J. A. Anderson, Astrophys. J. 51, 263 (1920).
[Crossref]

Astrophys. J. Lett. (1)

A. Labeyrie, Astrophys. J. Lett. 196, L 71 (1975).
[Crossref]

J. Opt. Soc. Am. (2)

Nouv. Rev. Opt. (1)

A. Labeyrie, Nouv. Rev. Opt. 5, 141 (1974).
[Crossref]

Opt. Commun. (3)

D. Korff, G. Dryden, and M. Miller, Opt. Commun. 5, 187 (1972).
[Crossref]

J. C. Dainty, Opt. Commun. 7, 129 (1973).
[Crossref]

F. Roddier, Opt. Commun. 10, 103 (1974).
[Crossref]

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 (2)

FIG. 1
FIG. 1

Overlap area of four translated pupil images: (a) |f| < D/λ and |f′| < D/λ; (b) |f| < D/λ and |f′ − f0| < D/λ; (c) |f′| < D/λ and |ff0| < D/λ.

FIG. 2
FIG. 2

Contribution R of the interference fringes to the image Wiener spectrum as a function of the aperture diameter D of the telescopes, for several values of the base length L, the seeing parameter r0 being taken as unity. Full lines, Korff’s model. Dotted line, Gaussian model (uncorrelated apertures).

Equations (49)

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

W ( f ) = T ( f ) 2 = S - 2 R 2 M ( f , f ) A ( f , f ) d f ,
M ( f , f ) = Ψ * ( u ) Ψ ( u - f ) Ψ ( u - f ) Ψ * ( u - f - f )
A ( f , f ) = R 2 P ( u ) P ( u - f ) P ( u - f ) P ( u - f - f ) d u
P ( u ) = P 0 ( u ) + P 0 ( u - f 0 ) ,
P 0 ( u ) = { 1 , if u < D / λ 0 , if u > D / λ .
P 0 ( u ) P 0 ( u - f ) P 0 ( u - f ) P 0 ( u - f - f ) + P 0 ( u - f 0 ) P 0 ( u - f - f 0 ) P 0 ( u - f - f 0 ) P 0 ( u - f - f - f 0 )
A 0 ( f , f ) = R 2 P 0 ( u ) P 0 ( u - f ) P 0 ( u - f ) P 0 ( u - f - f ) d u ;
W 1 ( f ) = 1 2 S 0 - 2 R 2 M ( f , f ) A 0 ( f , f ) d f ,
W 1 ( f ) = 1 2 T 0 ( f ) 2 ,
E 1 = W 1 ( f ) d f = 1 2 S 0 - 2 R 4 M ( f , f ) A 0 ( f , f ) d f d f ,
E 1 = 1 2 R 2 T 0 ( f ) 2 d f .
P 0 ( u - f 0 ) P 0 ( u - f - f 0 ) P 0 ( u - f ) P 0 ( u - f - f ) + P 0 ( u ) P 0 ( u - f ) P 0 ( u - f - f 0 ) P 0 ( u - f - f - f 0 )
A 0 ( f , f + f 0 ) + A 0 ( f , f - f 0 )
W 2 ( f ) = 1 4 S 0 - 2 R 2 M ( f , f ) [ A 0 ( f , f + f 0 ) + A 0 ( f , f - f 0 ) ] d f
W 2 ( f ) = 1 2 S 0 - 2 R 2 M ( f , f ) A 0 ( f , f - f 0 ) d f ,
E 2 = W 2 ( f ) d f = 1 2 S 0 - 2 R 4 M ( f , f ) A 0 ( f , f - f 0 ) d f d f .
P 0 ( u - f 0 ) P 0 ( u - f ) P 0 ( u - f - f 0 ) P 0 ( u - f - f ) + P 0 ( u ) P 0 ( u - f - f 0 ) P 0 ( u - f ) P 0 ( u - f - f - f 0 )
A 0 ( f + f 0 , f ) + A 0 ( f - f 0 , f )
W 3 ( f ) = 1 4 S 0 - 2 R 2 M ( f , f ) [ A 0 ( f + f 0 , f ) + A 0 ( f - f 0 , f ) ] d f ,
E 3 = W 3 ( f ) d f = 1 2 S 0 - 2 R 4 M ( f , f ) A 0 ( f - f 0 , f ) d f d f .
E 3 = E 2 .
R = E 3 E 1 + E 2 = E 2 E 1 + E 2 = 1 1 + E 1 / E 2 .
M ( f , f ) = Ψ * ( u ) Ψ ( u - f ) Ψ ( u - f ) Ψ * ( u - f - f ) Ψ * ( u ) Ψ ( u - f ) Ψ ( u - f ) Ψ * ( u - f - f ) = B 2 ( f ) ,
W 2 ( f ) = 1 2 S 0 - 2 B 2 ( f ) R 2 A 0 ( f , f - f 0 ) d f ,
W 2 ( f ) = 1 2 S 0 - 2 B 2 ( f ) Λ 2 ( f ) ,
T 0 ( f ) = B ( f ) S 0 - 1 Λ ( f ) ,
W 2 ( f ) = 1 2 T 0 ( f ) 2 ,
E 1 E 2 = T 0 ( f ) 2 d f T 0 ( f ) 2 d f ,
Ψ * ( u ) Ψ ( u - f ) Ψ ( u - f ) Ψ * ( u - f - f ) = Ψ * ( u ) Ψ ( u - f ) Ψ ( u - f ) Ψ * ( u - f - f ) + Ψ * ( u ) Ψ ( u - f ) Ψ ( u - f ) Ψ * ( u - f - f ) ;
M ( f , f ) = B 2 ( f ) + B 2 ( f ) .
E 1 = 1 2 S 0 - 2 R 4 [ B 2 ( f ) + B 2 ( f ) ] A 0 ( f , f ) d f d f
E 1 = S 0 - 2 R 2 B 2 ( f ) R 2 A 0 ( f , f ) d f d f ;
E 1 = S 0 - 2 R 2 B 2 ( f ) Λ 2 ( f ) d f ;
E 1 = T 0 ( f ) 2 d f ,
E 1 = 2 E 2
R = 1 1 + E 1 / E 2 = 1 3 ,
Z 1 ( α ) = Ψ ( u ) P 0 ( u ) exp ( - 2 i π α · u ) d u , Z 2 ( α ) = Ψ ( u ) P 0 ( u - f 0 ) exp ( - 2 i π α · u ) d u ,
Z 1 + Z 2 2 = Z 1 2 + Z 2 2 + 2 Re Z 1 Z 2 * ,
( I 1 + I 2 ) 2 = I 1 2 + I 2 2 + 2 I 1 I 2 .
I 1 I 2 = I 1 I 2 = I 1 2 .
I 2 2 = I 1 2 = 2 I 1 2 ,
( I 1 + I 2 ) 2 = 6 I 1 2 .
( Δ I ) 2 = 4 ( Re Z 1 Z 2 * ) 2 = 2 Z 1 Z 2 * 2 = 2 I 1 I 2
( Δ I ) 2 = 2 I 1 2 .
R = ( Δ I ) 2 I 1 + I 2 ) 2 = 2 I 1 2 6 I 1 2 = 1 3 ,
Ψ ( u ) = exp i ϕ ( u ) ,
D ( f ) = ϕ ( u + f ) - ϕ ( u ) 2 = 6.88 ( λ f / r 0 ) 5 / 3 ,
B ( f ) = exp - 3.44 ( λ f / r 0 ) 5 / 3 ,
M ( f , f ) = exp - 6.88 ( λ / r 0 ) 5 / 3 × [ f 5 / 3 + f 5 / 3 - 1 2 ( f + f 5 / 3 - f - f 5 / 3 ) ] .