Abstract

In long-baseline optical stellar interferometry, it is necessary to maintain optical path equality between the two arms of an interferometer in order to measure the fringe visibility. There will be errors in matching the optical paths because of a number of factors, and it is desirable to use an automatic system to monitor and correct such path errors. One type of system is a delay tracker, based on imaging of the channeled spectrum. The tracking algorithm is designed to maintain a fixed number of fringes, ideally linearly spaced, across the observed spectral band. This results in a constant optical path difference, which may be incompatible with the requirement of path equality for the measurement of fringe visibility. In a practical interferometer that uses an optical path-length compensator operating in air, there is a complication since air paths introduce differential dispersion. This dispersion can be compensated for by including dispersion correction. By modifying the operation of an appropriately designed dispersion corrector, we show that it is possible to make the optical path difference zero at the measurement wavelength and, at the same time, to produce linearly spaced channel fringes across the tracking band.

© 1998 Optical Society of America

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References

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  1. S. Lévêque, B. Koehler, O. von der Lühe, “Longitudinal dispersion compensation for the Very Large Telescope Interferometer,” Astrophys. Space Sci. 239, 305–314 (1996).
    [CrossRef]
  2. J. Davis, “The Sydney University Stellar Interferometer (SUSI),” in Proceedings of International Astronomical Union Symposium No. 158, Very High Angular Resolution Imaging, J. G. Robertson, W. J. Tango, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1994), pp. 135–142.
    [CrossRef]
  3. M. G. Lacasse, W. A. Traub, “Glass compensation for an air filled delay line,” in High-Resolution Imaging by Interferometry, F. Merkle, ed. (European Southern Observatory, Garching bei München, Germany, 1988), pp. 959–970.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. P. R. Lawson, J. Davis, “Dispersion compensation in stellar interferometry,” Appl. Opt. 35, 612–620 (1996).
    [CrossRef] [PubMed]
  7. S. D. Dyer, D. A. Christensen, “Dispersion effects in fiber-optic interferometry,” Opt. Eng. 36, 2440–2447 (1997).
    [CrossRef]
  8. P. R. Lawson, “Group-delay tracking in stellar interferometry with the fast Fourier transform,” J. Opt. Soc. Am. A 12, 366–374 (1995).
    [CrossRef]
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    [CrossRef] [PubMed]

1997 (1)

S. D. Dyer, D. A. Christensen, “Dispersion effects in fiber-optic interferometry,” Opt. Eng. 36, 2440–2447 (1997).
[CrossRef]

1996 (2)

S. Lévêque, B. Koehler, O. von der Lühe, “Longitudinal dispersion compensation for the Very Large Telescope Interferometer,” Astrophys. Space Sci. 239, 305–314 (1996).
[CrossRef]

P. R. Lawson, J. Davis, “Dispersion compensation in stellar interferometry,” Appl. Opt. 35, 612–620 (1996).
[CrossRef] [PubMed]

1995 (2)

1990 (1)

1967 (1)

Christensen, D. A.

S. D. Dyer, D. A. Christensen, “Dispersion effects in fiber-optic interferometry,” Opt. Eng. 36, 2440–2447 (1997).
[CrossRef]

Davis, J.

P. R. Lawson, J. Davis, “Dispersion compensation in stellar interferometry,” Appl. Opt. 35, 612–620 (1996).
[CrossRef] [PubMed]

J. Davis, “The Sydney University Stellar Interferometer (SUSI),” in Proceedings of International Astronomical Union Symposium No. 158, Very High Angular Resolution Imaging, J. G. Robertson, W. J. Tango, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1994), pp. 135–142.
[CrossRef]

Dyer, S. D.

S. D. Dyer, D. A. Christensen, “Dispersion effects in fiber-optic interferometry,” Opt. Eng. 36, 2440–2447 (1997).
[CrossRef]

Koehler, B.

S. Lévêque, B. Koehler, O. von der Lühe, “Longitudinal dispersion compensation for the Very Large Telescope Interferometer,” Astrophys. Space Sci. 239, 305–314 (1996).
[CrossRef]

Lacasse, M. G.

M. G. Lacasse, W. A. Traub, “Glass compensation for an air filled delay line,” in High-Resolution Imaging by Interferometry, F. Merkle, ed. (European Southern Observatory, Garching bei München, Germany, 1988), pp. 959–970.

Lawson, P. R.

Lévêque, S.

S. Lévêque, B. Koehler, O. von der Lühe, “Longitudinal dispersion compensation for the Very Large Telescope Interferometer,” Astrophys. Space Sci. 239, 305–314 (1996).
[CrossRef]

Owens, J. C.

Tango, W. J.

ten Brummelaar, T. A.

Traub, W. A.

M. G. Lacasse, W. A. Traub, “Glass compensation for an air filled delay line,” in High-Resolution Imaging by Interferometry, F. Merkle, ed. (European Southern Observatory, Garching bei München, Germany, 1988), pp. 959–970.

von der Lühe, O.

S. Lévêque, B. Koehler, O. von der Lühe, “Longitudinal dispersion compensation for the Very Large Telescope Interferometer,” Astrophys. Space Sci. 239, 305–314 (1996).
[CrossRef]

Appl. Opt. (4)

Astrophys. Space Sci. (1)

S. Lévêque, B. Koehler, O. von der Lühe, “Longitudinal dispersion compensation for the Very Large Telescope Interferometer,” Astrophys. Space Sci. 239, 305–314 (1996).
[CrossRef]

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

Opt. Eng. (1)

S. D. Dyer, D. A. Christensen, “Dispersion effects in fiber-optic interferometry,” Opt. Eng. 36, 2440–2447 (1997).
[CrossRef]

Other (2)

J. Davis, “The Sydney University Stellar Interferometer (SUSI),” in Proceedings of International Astronomical Union Symposium No. 158, Very High Angular Resolution Imaging, J. G. Robertson, W. J. Tango, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1994), pp. 135–142.
[CrossRef]

M. G. Lacasse, W. A. Traub, “Glass compensation for an air filled delay line,” in High-Resolution Imaging by Interferometry, F. Merkle, ed. (European Southern Observatory, Garching bei München, Germany, 1988), pp. 959–970.

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Figures (6)

Fig. 1
Fig. 1

Representation of the channeled spectrum for a vacuum path difference of 200 m, λ m = 442 nm, and a tracking bandwidth of 234 nm centered on λ t = 609 nm. The left-hand dashed line indicates the measurement wavelength; the tracking band lies between the right-hand dashed line and the end of the plot. Note that the scale of the abscissa is linear in detector coordinates but nonlinear in wavelength.

Fig. 2
Fig. 2

Relative phase variation near the measurement wavelength. Curves a, b, and c correspond to vacuum OPD’s x 0 = 0 m, 200 m, and 400 m, respectively.

Fig. 3
Fig. 3

Deviation from linearity across the tracking bandwidth. The best-fitting straight line has been subtracted from the actual phase variation across the band. Curves a, b, and c correspond to vacuum OPD’s x 0 = 0 m, 200 m, and 400 m, respectively.

Fig. 4
Fig. 4

Similar to Fig. 1, except the measurement wavelength has been shifted to λ m = 480 nm.

Fig. 5
Fig. 5

Similar to Fig. 2, except that λ m = 480 nm.

Fig. 6
Fig. 6

Similar to Fig. 3, except that λ m = 480 nm.

Tables (2)

Tables Icon

Table 1 Coefficients b for Air, BK-7, and F7

Tables Icon

Table 2 Coefficients a for a 60° SF52 Prism Calculated for 609 nm

Equations (24)

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X σ = x 0 + i = 1 N   n i σ x i ,
Φ σ = 2 π σ X σ .
Φ σ = Φ m + 2 π x 0 + b 1   ·   x σ - σ m + b 2 · x σ - σ m 2 + b 3 · x σ - σ m 3 + ,
b k · x = i = 1 N   b k i σ m x i ,
x 0 + i = 1 3   b 1 i σ m x i = 0 ,
i = 1 3   b 2 i σ m x i = 0 ,
i = 1 3   b 3 i σ m x i = 0 .
x 0 + i = 1 3   b 1 i σ t x i = a 1 ω ,
i = 1 3   b 2 i σ t x i = a 2 ω ,
i = 1 3   b 3 i σ t x i = a 3 ω ,
a 1 = d y d σ ,
a 2 = - 1 2 d 2 σ d y 2 d y d σ 3 ,
a 3 = 1 6 3   d y d σ d 2 σ d y 2 - d 3 σ d y 3 d y d σ 4 .
ω = N y σ t - Δ σ / 2 - y σ t + Δ σ / 2 .
x 0 + i = 1 3   b 1 i σ m x i = 0 ,
x 0 + i = 1 3   b 1 i σ t x i = a 1 ω ,
i = 1 3   b 2 i σ t x i = a 2 ω .
x air = - 0.00891737 - 1.000511660 x 0 ,
x BK - 7 = + 0.0101687 + 0.000585478 x 0 ,
x F - 7 = - 0.00401839 - 0.0000622974 x 0 .
x air = - 0.0187940 - 1.000549601 x 0 ,
x BK - 7 = + 0.0216843 + 0.000629714 x 0 ,
x F - 7 = - 0.00871109 - 0.0000803241 x 0 .
S y = 1 / 2 1 + cos   Φ y

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