Abstract

The effects of uncompensated dispersion on the fringe visibility in a two beam interferometer are examined for a long baseline stellar interferometer with a path compensator in air rather than in vacuo. We derive a criterion based on the central fringe visibility for evaluating the effects of dispersion and develop a method for selecting suitable compensating media. By limiting the optical bandwidth to ~100 nm and using a compensating system with two glasses it is possible to achieve high fringe visibility in a stellar interferometer with excess air paths of the order of 500 m. The results are generally applicable to other two beam interferometers.

© 1990 Optical Society of America

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References

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  1. W. H. Steel, Interferometry (Cambridge, U.P., London, 1983), p. 78.
  2. W. J. Tango, R. Q. Twiss, “Michelson Stellar Interferometry,” Prog. Opt. 17, 240–277, (1980).
  3. C. A. Murray, Vectorial Astrometry (A. Hilger, Bristol, U.K., 1983).
  4. J. Davis, “The Sydney University Stellar Interferometry Programme: A Progress Report,” in Proceedings, Joint Workshop on High-Resolution Imaging, J. W. Goad, Ed. (National Optical Astronomy Observatories, 1987) pp. 121–124.
  5. D. A. Palmer, “White Light Fringes and Dispersion in Two-Beam Interferometry,” Opt. Acta 32, 811–814 (1985).
    [CrossRef]
  6. L. Mertz, Transformations in Optics (Wiley, New York, 1965).
  7. J. R. Birch, T. J. Parker, “Dispersive Fourier Transform Spectroscopy,” in Infrared & Millimeter Waves, Vol. 2, K. J. Button, Ed. (Academic, New York, 1979), pp. 138–271.
  8. R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1978).
  9. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U.P., London, 1986), Chap. 5.
  10. J. C. Owens, “Optical Refractive Index of Air: Dependence on Temperature, Pressure, and Composition,” Appl. Opt. 6, 51–59 (1967).
    [CrossRef] [PubMed]
  11. W. L. Wolf, “Properties of Optical Materials,” in Handbook of Optics, W. G. Driscoll, W. Vaughn, Eds. (McGraw-Hill, New York, 1978).

1985 (1)

D. A. Palmer, “White Light Fringes and Dispersion in Two-Beam Interferometry,” Opt. Acta 32, 811–814 (1985).
[CrossRef]

1980 (1)

W. J. Tango, R. Q. Twiss, “Michelson Stellar Interferometry,” Prog. Opt. 17, 240–277, (1980).

1967 (1)

Birch, J. R.

J. R. Birch, T. J. Parker, “Dispersive Fourier Transform Spectroscopy,” in Infrared & Millimeter Waves, Vol. 2, K. J. Button, Ed. (Academic, New York, 1979), pp. 138–271.

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1978).

Davis, J.

J. Davis, “The Sydney University Stellar Interferometry Programme: A Progress Report,” in Proceedings, Joint Workshop on High-Resolution Imaging, J. W. Goad, Ed. (National Optical Astronomy Observatories, 1987) pp. 121–124.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U.P., London, 1986), Chap. 5.

Mertz, L.

L. Mertz, Transformations in Optics (Wiley, New York, 1965).

Murray, C. A.

C. A. Murray, Vectorial Astrometry (A. Hilger, Bristol, U.K., 1983).

Owens, J. C.

Palmer, D. A.

D. A. Palmer, “White Light Fringes and Dispersion in Two-Beam Interferometry,” Opt. Acta 32, 811–814 (1985).
[CrossRef]

Parker, T. J.

J. R. Birch, T. J. Parker, “Dispersive Fourier Transform Spectroscopy,” in Infrared & Millimeter Waves, Vol. 2, K. J. Button, Ed. (Academic, New York, 1979), pp. 138–271.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U.P., London, 1986), Chap. 5.

Steel, W. H.

W. H. Steel, Interferometry (Cambridge, U.P., London, 1983), p. 78.

Tango, W. J.

W. J. Tango, R. Q. Twiss, “Michelson Stellar Interferometry,” Prog. Opt. 17, 240–277, (1980).

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U.P., London, 1986), Chap. 5.

Twiss, R. Q.

W. J. Tango, R. Q. Twiss, “Michelson Stellar Interferometry,” Prog. Opt. 17, 240–277, (1980).

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U.P., London, 1986), Chap. 5.

Wolf, W. L.

W. L. Wolf, “Properties of Optical Materials,” in Handbook of Optics, W. G. Driscoll, W. Vaughn, Eds. (McGraw-Hill, New York, 1978).

Appl. Opt. (1)

Opt. Acta (1)

D. A. Palmer, “White Light Fringes and Dispersion in Two-Beam Interferometry,” Opt. Acta 32, 811–814 (1985).
[CrossRef]

Prog. Opt. (1)

W. J. Tango, R. Q. Twiss, “Michelson Stellar Interferometry,” Prog. Opt. 17, 240–277, (1980).

Other (8)

C. A. Murray, Vectorial Astrometry (A. Hilger, Bristol, U.K., 1983).

J. Davis, “The Sydney University Stellar Interferometry Programme: A Progress Report,” in Proceedings, Joint Workshop on High-Resolution Imaging, J. W. Goad, Ed. (National Optical Astronomy Observatories, 1987) pp. 121–124.

W. H. Steel, Interferometry (Cambridge, U.P., London, 1983), p. 78.

L. Mertz, Transformations in Optics (Wiley, New York, 1965).

J. R. Birch, T. J. Parker, “Dispersive Fourier Transform Spectroscopy,” in Infrared & Millimeter Waves, Vol. 2, K. J. Button, Ed. (Academic, New York, 1979), pp. 138–271.

R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1978).

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U.P., London, 1986), Chap. 5.

W. L. Wolf, “Properties of Optical Materials,” in Handbook of Optics, W. G. Driscoll, W. Vaughn, Eds. (McGraw-Hill, New York, 1978).

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Figures (5)

Fig. 1
Fig. 1

Mach-Zehnder model for a stellar interferometer with dispersive media. The extra vacuum path C0 is approximately matched by the air path C1. Additional blocks of glass of thickness x2, x3, …, and indices n2, n3, …, are used to compensate for the residual dispersion.

Fig. 2
Fig. 2

Central fringe visibility as a function of the excess air path. No dispersion compensation is used, and the bandwidth is flat from 1.35 to 2.40 μm−1.

Fig. 3
Fig. 3

Central fringe visibility obtained using silica and BK7 compensators. The bandwidth is the same as for Fig. 2.

Fig. 4
Fig. 4

Central fringe visibility obtained with a two glass compensator (BK7 and F7). The bandwidth is the same as for Fig. 2.

Fig. 5
Fig. 5

Dispersed channeled spectrum obtained using a BK7-F7 compensator for (a) 10 m, (b) 50 m, (c) 100 m, and (d) 500 m of excess air path.

Tables (1)

Tables Icon

Table I Dispersion Coefficients for Selected Media (σ = 1.875 μm−1)

Equations (21)

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X ( t ) = - B · s ^ ( t ) + 0 + atm ( t ) .
X ( σ ) = x o + i = 1 N n i ( σ ) x i ,
C ( X ) = 0 I ( σ ) exp { - 2 π i X ( σ ) σ } d σ 0 I ( σ ) d σ ,
g ( s ) = I ( σ ¯ + s ) / 0 I ( σ ) d σ .
σ X ( σ ) = σ ¯ X ( σ ¯ ) + ( x o + b 1 · x ) s + ( b 2 · x ) s 2 + ( b 3 · x ) s 3 + ,
b k · x = 1 = 1 N b k ( i ) x i ,
b k ( i ) = 1 k ! ( k d k - 1 n i d σ ¯ k - 1 + σ ¯ d k n i d σ ¯ k ) .
ψ ( s ) = ( b 2 · x ) s 2 + ( b 3 · x ) s 3 + ,
C ( ξ ) = exp [ - 2 π i X ( σ ¯ ) σ ¯ ] - g ( s ) exp [ - 2 π i ψ ( s ) ] exp ( - 2 π i ξ s ) d s .
C ( 0 ) 1 ,
- C ( ξ ) 2 d ξ = - g 2 ( s ) d s = const .
ξ ¯ = - ξ C ( ξ ) 2 d ξ - C ( ξ ) 2 d ξ ,
ξ ¯ = - - g 2 ( s ) ψ ( s ) d s - g 2 ( s ) d s .
ψ ( s ) = 2 s ( b 2 · x ) + ,
σ ¯ = 0 σ I 2 ( σ ) d σ / 0 I 2 ( σ ) d σ ,
- s g 2 ( s ) d s = 0
C ( 0 ) 2 1 - 4 π 2 Δ 2 ψ ,
Δ 2 ψ = k = 2 m l = 2 m f k l ( b k · x ) ( b l · x ) Δ σ k + l ,
b 1 · x = - x 0 b 2 · x = 0 . . . b N · x = 0.
S ( λ ) = I ( λ ) { 1 + cos [ 2 π ψ ( λ - 1 - λ 0 - 1 ) ] } δ λ ,
σ n ( σ ) = σ ¯ n ( σ ¯ ) + b 1 ( σ - σ ¯ ) + b 2 ( σ - σ ¯ ) 2 + ,

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