Abstract

A new fringe tracker based on photon-counting detectors and real-time image processing has been implemented on the Grand Interféromètre à 2 Télescopes at the Observatoire de la Côte d’Azur. Fringe visibilities have been recorded on P Cygni and other stars across the Hα emission line with optical path differences stabilized to between 4 and 7 μm rms (1% of the coherence length). We present our initial results and describe the principle, implementation, and performance of the fringe tracker.

© 1996 Optical Society of America

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  1. A. Labeyrie, G. Schumacher, M. Dugué, C. Thom, F. Foy, D. Bonneau, R. Foy, “Fringes obtained with the large boule interferometer at CERGA,” Astron. Astrophys. 162, 359–364 (1986).
  2. D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).
  3. C. Aime, “Measurement of averaged squared modulus of atmospheric-lens modulation transfer function,” J. Opt. Soc. Am. 64, 1129–1132 (1974).
    [Crossref]
  4. F. Roddier, “Atmospheric limitations to high angular resolution imaging,” in European Southern Observatory Conference Proceedings on Scientific Importance of High Angular Resolution at Infrared and Optical Wavelengths (European Southern Observatory, Garching, Germany, 1981), pp. 5–23.
  5. D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1427–1434 (1965).
    [Crossref]
  6. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [Crossref]
  7. R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence (Springer-Verlag, Berlin, 1994), pp. 63–65.
  8. P. R. Lawson, “Group-delay tracking in optical stellar interferometry with the fast Fourier transform,” J. Opt. Soc. Am. A 12, 366–374 (1995).
    [Crossref]
  9. J. M. Beckers, “Cophasing telescope arrays,” in Diffraction-Limited Imaging with Very Large Telescopes, D. M. Alloin, J. M. Mariotti, eds. (Kluwer, Dordrecht, 1989), pp. 355–364.
    [Crossref]
  10. L. Koechlin, “The I2T interferometer,” in High Resolution Imaging by Interferometry, J. M. Beckers, ed. (European Southern Observatory, Garching bei München, Germany, 1988), pp. 695–704.
  11. L. Koechlin, “Active fringe tracing,” in High Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching bei München, Germany, 1992), pp. 1239–1246.
  12. A. Blazit, “A 40 mm photon counting camera,” in Image Detection and Quality, L. F. Guyot, ed., Proc. SPIE 702, 259–263 (1986).
  13. M. Clampin, J. Crocker, F. Paresce, M. Rafal, “Optical Ranicon detectors for photon counting imaging. I.” Rev. Sci. Instrum. 59, 1269–1285 (1988).
    [Crossref]
  14. A. Labeyrie, “Stellar interferometry methods,” Ann. Rev. Astron. Astrophys. 16, 77–102 (1978).
    [Crossref]
  15. F. Roddier, P. Léna, “Long baseline Michelson interferometry with large ground-based telescopes operating at optical wavelengths,” J. Opt. (Paris) 15, 171–182 (1984).
    [Crossref]
  16. R. Foy, D. Bonneau, A. Blazit, “The multiple QSO PG1115 +08: a fifth component,” Astron. Astrophys. 149, L13–L16 (1985).
  17. W. J. Tango, R. Q. Twiss, “Michelson stellar interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1980), Vol. 17, pp. 239–277.
    [Crossref]
  18. D. Buscher, “Optimizing a ground-based optical interferometer for sensitivity at low light levels,” Mon. Not. R. Astron. Soc. 235, 1203–1226 (1988).
  19. D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

1995 (1)

1994 (2)

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

1988 (2)

D. Buscher, “Optimizing a ground-based optical interferometer for sensitivity at low light levels,” Mon. Not. R. Astron. Soc. 235, 1203–1226 (1988).

M. Clampin, J. Crocker, F. Paresce, M. Rafal, “Optical Ranicon detectors for photon counting imaging. I.” Rev. Sci. Instrum. 59, 1269–1285 (1988).
[Crossref]

1986 (1)

A. Labeyrie, G. Schumacher, M. Dugué, C. Thom, F. Foy, D. Bonneau, R. Foy, “Fringes obtained with the large boule interferometer at CERGA,” Astron. Astrophys. 162, 359–364 (1986).

1985 (1)

R. Foy, D. Bonneau, A. Blazit, “The multiple QSO PG1115 +08: a fifth component,” Astron. Astrophys. 149, L13–L16 (1985).

1984 (1)

F. Roddier, P. Léna, “Long baseline Michelson interferometry with large ground-based telescopes operating at optical wavelengths,” J. Opt. (Paris) 15, 171–182 (1984).
[Crossref]

1978 (1)

A. Labeyrie, “Stellar interferometry methods,” Ann. Rev. Astron. Astrophys. 16, 77–102 (1978).
[Crossref]

1976 (1)

1974 (1)

1965 (1)

Aime, C.

Beckers, J. M.

J. M. Beckers, “Cophasing telescope arrays,” in Diffraction-Limited Imaging with Very Large Telescopes, D. M. Alloin, J. M. Mariotti, eds. (Kluwer, Dordrecht, 1989), pp. 355–364.
[Crossref]

Blazit, A.

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

R. Foy, D. Bonneau, A. Blazit, “The multiple QSO PG1115 +08: a fifth component,” Astron. Astrophys. 149, L13–L16 (1985).

A. Blazit, “A 40 mm photon counting camera,” in Image Detection and Quality, L. F. Guyot, ed., Proc. SPIE 702, 259–263 (1986).

Bonneau, D.

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

A. Labeyrie, G. Schumacher, M. Dugué, C. Thom, F. Foy, D. Bonneau, R. Foy, “Fringes obtained with the large boule interferometer at CERGA,” Astron. Astrophys. 162, 359–364 (1986).

R. Foy, D. Bonneau, A. Blazit, “The multiple QSO PG1115 +08: a fifth component,” Astron. Astrophys. 149, L13–L16 (1985).

Buscher, D.

D. Buscher, “Optimizing a ground-based optical interferometer for sensitivity at low light levels,” Mon. Not. R. Astron. Soc. 235, 1203–1226 (1988).

Clampin, M.

M. Clampin, J. Crocker, F. Paresce, M. Rafal, “Optical Ranicon detectors for photon counting imaging. I.” Rev. Sci. Instrum. 59, 1269–1285 (1988).
[Crossref]

Crocker, J.

M. Clampin, J. Crocker, F. Paresce, M. Rafal, “Optical Ranicon detectors for photon counting imaging. I.” Rev. Sci. Instrum. 59, 1269–1285 (1988).
[Crossref]

Dugué, M.

A. Labeyrie, G. Schumacher, M. Dugué, C. Thom, F. Foy, D. Bonneau, R. Foy, “Fringes obtained with the large boule interferometer at CERGA,” Astron. Astrophys. 162, 359–364 (1986).

Foy, F.

A. Labeyrie, G. Schumacher, M. Dugué, C. Thom, F. Foy, D. Bonneau, R. Foy, “Fringes obtained with the large boule interferometer at CERGA,” Astron. Astrophys. 162, 359–364 (1986).

Foy, R.

A. Labeyrie, G. Schumacher, M. Dugué, C. Thom, F. Foy, D. Bonneau, R. Foy, “Fringes obtained with the large boule interferometer at CERGA,” Astron. Astrophys. 162, 359–364 (1986).

R. Foy, D. Bonneau, A. Blazit, “The multiple QSO PG1115 +08: a fifth component,” Astron. Astrophys. 149, L13–L16 (1985).

Fried, D. L.

Koechlin, L.

L. Koechlin, “The I2T interferometer,” in High Resolution Imaging by Interferometry, J. M. Beckers, ed. (European Southern Observatory, Garching bei München, Germany, 1988), pp. 695–704.

L. Koechlin, “Active fringe tracing,” in High Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching bei München, Germany, 1992), pp. 1239–1246.

Labeyrie, A.

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

A. Labeyrie, G. Schumacher, M. Dugué, C. Thom, F. Foy, D. Bonneau, R. Foy, “Fringes obtained with the large boule interferometer at CERGA,” Astron. Astrophys. 162, 359–364 (1986).

A. Labeyrie, “Stellar interferometry methods,” Ann. Rev. Astron. Astrophys. 16, 77–102 (1978).
[Crossref]

Lawson, P. R.

Léna, P.

F. Roddier, P. Léna, “Long baseline Michelson interferometry with large ground-based telescopes operating at optical wavelengths,” J. Opt. (Paris) 15, 171–182 (1984).
[Crossref]

Merlin, G.

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

Morand, F.

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

Mourard, D.

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

Noll, R. J.

Paresce, F.

M. Clampin, J. Crocker, F. Paresce, M. Rafal, “Optical Ranicon detectors for photon counting imaging. I.” Rev. Sci. Instrum. 59, 1269–1285 (1988).
[Crossref]

Rafal, M.

M. Clampin, J. Crocker, F. Paresce, M. Rafal, “Optical Ranicon detectors for photon counting imaging. I.” Rev. Sci. Instrum. 59, 1269–1285 (1988).
[Crossref]

Rigal, F.

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

Roddier, F.

F. Roddier, P. Léna, “Long baseline Michelson interferometry with large ground-based telescopes operating at optical wavelengths,” J. Opt. (Paris) 15, 171–182 (1984).
[Crossref]

F. Roddier, “Atmospheric limitations to high angular resolution imaging,” in European Southern Observatory Conference Proceedings on Scientific Importance of High Angular Resolution at Infrared and Optical Wavelengths (European Southern Observatory, Garching, Germany, 1981), pp. 5–23.

Sasiela, R. J.

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence (Springer-Verlag, Berlin, 1994), pp. 63–65.

Schumacher, G.

A. Labeyrie, G. Schumacher, M. Dugué, C. Thom, F. Foy, D. Bonneau, R. Foy, “Fringes obtained with the large boule interferometer at CERGA,” Astron. Astrophys. 162, 359–364 (1986).

Stee, Ph.

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

Tallon-Bosc, I.

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

Tango, W. J.

W. J. Tango, R. Q. Twiss, “Michelson stellar interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1980), Vol. 17, pp. 239–277.
[Crossref]

Thom, C.

A. Labeyrie, G. Schumacher, M. Dugué, C. Thom, F. Foy, D. Bonneau, R. Foy, “Fringes obtained with the large boule interferometer at CERGA,” Astron. Astrophys. 162, 359–364 (1986).

Twiss, R. Q.

W. J. Tango, R. Q. Twiss, “Michelson stellar interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1980), Vol. 17, pp. 239–277.
[Crossref]

Vakili, F.

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

Ann. Rev. Astron. Astrophys. (1)

A. Labeyrie, “Stellar interferometry methods,” Ann. Rev. Astron. Astrophys. 16, 77–102 (1978).
[Crossref]

Astron. Astrophys. (4)

R. Foy, D. Bonneau, A. Blazit, “The multiple QSO PG1115 +08: a fifth component,” Astron. Astrophys. 149, L13–L16 (1985).

A. Labeyrie, G. Schumacher, M. Dugué, C. Thom, F. Foy, D. Bonneau, R. Foy, “Fringes obtained with the large boule interferometer at CERGA,” Astron. Astrophys. 162, 359–364 (1986).

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

J. Opt. (Paris) (1)

F. Roddier, P. Léna, “Long baseline Michelson interferometry with large ground-based telescopes operating at optical wavelengths,” J. Opt. (Paris) 15, 171–182 (1984).
[Crossref]

J. Opt. Soc. Am. (3)

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

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

D. Buscher, “Optimizing a ground-based optical interferometer for sensitivity at low light levels,” Mon. Not. R. Astron. Soc. 235, 1203–1226 (1988).

Rev. Sci. Instrum. (1)

M. Clampin, J. Crocker, F. Paresce, M. Rafal, “Optical Ranicon detectors for photon counting imaging. I.” Rev. Sci. Instrum. 59, 1269–1285 (1988).
[Crossref]

Other (7)

W. J. Tango, R. Q. Twiss, “Michelson stellar interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1980), Vol. 17, pp. 239–277.
[Crossref]

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence (Springer-Verlag, Berlin, 1994), pp. 63–65.

J. M. Beckers, “Cophasing telescope arrays,” in Diffraction-Limited Imaging with Very Large Telescopes, D. M. Alloin, J. M. Mariotti, eds. (Kluwer, Dordrecht, 1989), pp. 355–364.
[Crossref]

L. Koechlin, “The I2T interferometer,” in High Resolution Imaging by Interferometry, J. M. Beckers, ed. (European Southern Observatory, Garching bei München, Germany, 1988), pp. 695–704.

L. Koechlin, “Active fringe tracing,” in High Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching bei München, Germany, 1992), pp. 1239–1246.

A. Blazit, “A 40 mm photon counting camera,” in Image Detection and Quality, L. F. Guyot, ed., Proc. SPIE 702, 259–263 (1986).

F. Roddier, “Atmospheric limitations to high angular resolution imaging,” in European Southern Observatory Conference Proceedings on Scientific Importance of High Angular Resolution at Infrared and Optical Wavelengths (European Southern Observatory, Garching, Germany, 1981), pp. 5–23.

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Figures (6)

Fig. 1
Fig. 1

Dispersed fringes follow the equation of a set of diverging lines. The rectangular shaded area corresponds to the dispersed image field.

Fig. 2
Fig. 2

Photograph of a dispersed image of a fringe pattern across a star.

Fig. 3
Fig. 3

Fringes in a dispersed speckle in the image plane.

Fig. 4
Fig. 4

Peaks in the Fourier transform of the dispersed fringe image. The spatial frequency U p is related to the optical delay by the expression U p = χ o (Δλ/λ2), where χ o is the optical path length at the center of the image.

Fig. 5
Fig. 5

Fringe tracker control loop; single baseline setup for the GI2T.

Fig. 6
Fig. 6

Path-difference variations observed on four stars: (a) α Cephei (with a 29-m baseline), (b) δ Cephei (29 m), (c) P Cygni (18 m), and (d) β Lyrae (51 m). The most noticeable feature in the path changes are the steps caused by the change in supports at the telescopes.

Equations (27)

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I ( χ , σ ) = I s ( σ ) [ 1 + γ cos ( 2 π σ χ + ϕ ) ] ,
2 π σ χ + ϕ = 2 k π ,
λ = a x ,
χ = χ o - b y ,
2 π χ 0 - b y a x + ϕ = 2 k π ,
( k - ϕ / 2 π ) a x + b y - χ 0 = 0.
N s = 1 0.44 ( D r 0 ) 2 ,
D ϕ ( r ) = ϕ ( ρ + r ) - ϕ ( ρ ) 2 = 6.88 ( r r 0 ) 5 / 3 ,
ϕ rms 2 = 1.03 ( D r 0 ) 5 / 3 .
Δ χ rms = 0.228 λ ( D r 0 ) 5 / 6 .
k λ 1 + b y 1 = χ 0 ,
( k + 1 ) λ 1 + b ( y 1 + δ y ) = χ 0 .
δ y = - λ 1 / b .
k λ 1 + b y 1 = χ 0 ,
( k + 1 ) ( λ 1 - δ λ ) + b y 1 = χ 0 ,
δ λ = λ 1 / ( k + 1 ) .
δ λ λ 1 2 / ( χ 0 - b y 1 ) ,
U p = Δ x / δ x = Δ λ / δ λ .
U p = ( χ 0 - b y 1 ) Δ λ / λ 2 .
Δ χ max < λ 2 / Δ λ ,
χ 0 U p λ 2 / Δ λ .
V p = Δ y / δ y = - b Δ y / λ 1 ,
I ^ ( x . v p ) = I ( x , y ) exp ( - 2 i π y v p ) d y .
I ^ ( x . v p ) = I ( x , y ) exp ( - 2 i π y v p x ) d y ,
I ( x , y ) = i = 1 n δ ( x - x i , y - y i ) ,
I ^ ( x , v p ) = i = 1 n δ ( x - x i ) exp ( - 2 i π y i v p x ) .
I ^ ( u , v p ) = I ^ ( x , v p ) exp ( - 2 i π u x ) d x .

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