Abstract

There is no unique definition of the fringe contrast in a random structure such as the image given by a Michelson stellar interferometer. A new definition is given here which leads to a contrast value independent of the seeing conditions provided the wave-front perturbations on the two apertures are uncorrelated. Moreover, if simultaneous observations through a single aperture are available, the seeing effects can be completely removed.

© 1976 Optical Society of America

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References

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  1. C. Roddier and F. Roddier, J. Opt. Soc. Am. 66, 580–584 (1976).
    [Crossref]
  2. D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
    [Crossref]
  3. R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).
    [Crossref]
  4. D. Korff, J. Opt. Soc. Am. 63, 971 (1973).
    [Crossref]
  5. A. Labeyrie, Astrophys. J. Lett. 196, L71 (1975).
    [Crossref]

1976 (1)

1975 (1)

A. Labeyrie, Astrophys. J. Lett. 196, L71 (1975).
[Crossref]

1973 (1)

1966 (1)

1964 (1)

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Figures (1)

FIG. 1
FIG. 1

Fringe contrast C 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.

Equations (30)

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T ( f ) = B ( f ) · S - 1 R 2 P ( u ) P ( u - f ) d 2 u ,
B ( f ) = ψ ( u ) ψ * ( u - f )
P ( u ) = P 0 ( u ) + P 0 ( u - f 0 ) ,
P 0 ( u ) = { 1 if u < D / λ , 0 if u > D / λ .
T ( f ) = B ( f ) · S - 1 R 2 [ P 0 ( u ) + P 0 ( u - f 0 ) ] × [ P 0 ( u - f ) + P 0 ( u - f 0 - f ) ] d 2 u = B ( f ) · S - 1 [ 2 Λ ( f ) + Λ ( f + f 0 ) + Λ ( f - f 0 ) ] ,
Λ ( f ) = R 2 P 0 ( u ) P 0 ( u - f ) d 2 u
T ( f ) = 2 B ( f ) S - 1 Λ ( f ) = B ( f ) S 0 - 1 Λ ( f ) ,
W 4 ( f ) = T ( f ) 2 = B 2 ( f ) S 0 - 2 Λ 2 ( f )
E 4 = S 0 - 2 R 2 B 2 ( f ) Λ 2 ( f ) d 2 f .
E 3 = 1 2 S 0 - 2 R 2 B 2 ( f ) Λ 2 ( f ) d 2 f .
C = E 3 / E 4 = 1 2 ,
I = Z 1 + Z 2 2 = Z 1 2 + Z 2 2 + 2 Re Z 1 Z 2 * ,
( Δ I ) 2 = 4 ( Re Z 1 Z 2 * ) 2 = 2 Z 1 Z 2 * 2 = 2 I 1 I 2 .
I 1 + I 2 2 = 4 I 1 2 .
C = ( Δ I 2 ) / I 1 + I 2 2 = I 1 I 2 / 2 I 1 2 .
I 1 I 2 = I 1 · I 2 = I 1 2 ,
M ( f , f ) = ψ * ( u ) ψ ( u - f ) ψ ( u - f ) ψ * ( u - f - f )
M ( f , f ) = B 2 ( f ) + B 2 ( f ) .
E 3 = 1 2 S 0 - 2 R 4 M ( f , f ) A 0 ( f - f 0 , f ) d 2 f d 2 f ,
A 0 ( f , f ) = R 2 P 0 ( u ) P 0 ( u - f ) P 0 ( u - f ) P 0 ( u - f - f ) d 2 u
E 3 = 1 2 S 0 - 2 R 2 B 2 ( f ) R 2 A 0 ( f - f 0 , f ) d 2 f d 2 f + 1 2 S 0 - 2 R 2 B 2 ( f ) R 2 A 0 ( f - f 0 , f ) d 2 f d 2 f .
E 3 = 1 2 S 0 - 2 R 2 B 2 ( f ) Λ 2 ( f ) d 2 f + 1 2 S 0 - 2 R 2 B 2 ( f ) Λ 2 ( f - f 0 ) d 2 f
C = E 3 E 4 = 1 2 ( 1 + R 2 B 2 ( f ) Λ 2 ( f - f 0 ) d 2 f / R 2 B 2 ( f ) Λ 2 ( f ) d 2 f ) .
ψ ( u ) = exp i ϕ ( u ) ,
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 ) ] .
( I 1 + I 2 ) 2 - 2 I 1 2 = 2 I 1 I 2 ,
V = ( Δ I ) 2 ( I 1 + I 2 ) 2 - 2 I 1 2 = ( Δ I ) 2 2 I 1 I 2 .
V = E 3 / [ ( E 1 + E 2 ) - 2 E 0 ] .