Abstract

We study the theoretical noise limitations of a spectrally resolved Michelson interferometer operating in a multispeckle and photon-counting mode. We derive an expression of the signal-to-noise ratio of the fringe modulation in the (cross-) spectral density of short exposures, which allows us to give the signal-to-noise ratio of the various visibility estimators defined in our previous paper [J. Opt. Soc. Am. A 16, 872 (1999)]. These estimators and the corresponding signal-to-noise-ratio expressions are used in the data processing software of the GI2T interferometer in order to estimate the visibility and the accuracy of the measurements.

© 2001 Optical Society of America

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  1. P. Berio, D. Mourard, D. Bonneau, O. Chesneau, P. Stee, N. Thureau, F. Vakili, J. Borgnino, “Spectrally resolved Michelson interferometry. I. Exact formalism in the multispeckle mode,” J. Opt. Soc. Am. A 16, 872–881 (1999).
    [CrossRef]
  2. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 9.
  3. J. C. Dainty, A. H. Greenaway, “Estimation of spatial power spectra in speckle interferometry,” J. Opt. Soc. Am. 69, 786–790 (1979).
    [CrossRef]
  4. F. Roddier, “Pupil plane versus image plane in Michelson stellar interferometry,” J. Opt. Soc. Am. A 3, 2160–2166 (1986).
    [CrossRef]
  5. A. Chelli, “The phase problem in optical interferometry—error analysis in the presence of photon noise,” Astron. Astrophys. 225, 277–290 (1989).
  6. R. Petrov, F. Roddier, C. Aime, “Signal to noise ratio in differential speckle interferometry,” J. Opt. Soc. Am. A 3, 634–644 (1986).
    [CrossRef]
  7. D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
    [CrossRef]
  8. S. Ragland, D. Bonneau, D. Mourard, P. Berio, “Interferometric investigations of highly evolved stars,” in Interferometry in Optical Astronomy, P. J. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 523–530 (2000).
    [CrossRef]
  9. P. Berio, Ph. Stee, D. Mourard, D. Bonneau, O. Chesneau, N. Thureau, D. Le Mignant, R. Hirata, “Interferometic insight into γ Cassiopeiae long-term variability,” Astron. Astrophys. 345, 203–210 (1999).
  10. F. Vakili, D. Mourard, Ph. Stee, D. Bonneau, P. Berio, O. Chesneau, N. Thureau, F. Morand, “Evidence of one-armed oscillations in the equatorial disk of ζ Tau from GI2T spectrally resolved interferometry,” Astron. Astrophys. 335, 261–265 (1998).
  11. F. Vakili, D. Mourard, D. Bonneau, F. Morand, Ph. Stee, “Subtle structures in the wind of P Cygni,” Astron. Astrophys. 323, 183–188 (1997).
  12. 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]
  13. A. Papoulis, Probability Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965).

1999 (2)

P. Berio, Ph. Stee, D. Mourard, D. Bonneau, O. Chesneau, N. Thureau, D. Le Mignant, R. Hirata, “Interferometic insight into γ Cassiopeiae long-term variability,” Astron. Astrophys. 345, 203–210 (1999).

P. Berio, D. Mourard, D. Bonneau, O. Chesneau, P. Stee, N. Thureau, F. Vakili, J. Borgnino, “Spectrally resolved Michelson interferometry. I. Exact formalism in the multispeckle mode,” J. Opt. Soc. Am. A 16, 872–881 (1999).
[CrossRef]

1998 (1)

F. Vakili, D. Mourard, Ph. Stee, D. Bonneau, P. Berio, O. Chesneau, N. Thureau, F. Morand, “Evidence of one-armed oscillations in the equatorial disk of ζ Tau from GI2T spectrally resolved interferometry,” Astron. Astrophys. 335, 261–265 (1998).

1997 (1)

F. Vakili, D. Mourard, D. Bonneau, F. Morand, Ph. Stee, “Subtle structures in the wind of P Cygni,” Astron. Astrophys. 323, 183–188 (1997).

1989 (1)

A. Chelli, “The phase problem in optical interferometry—error analysis in the presence of photon noise,” Astron. Astrophys. 225, 277–290 (1989).

1986 (2)

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]

1979 (1)

Aime, C.

Antonelli, P.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Berio, P.

P. Berio, Ph. Stee, D. Mourard, D. Bonneau, O. Chesneau, N. Thureau, D. Le Mignant, R. Hirata, “Interferometic insight into γ Cassiopeiae long-term variability,” Astron. Astrophys. 345, 203–210 (1999).

P. Berio, D. Mourard, D. Bonneau, O. Chesneau, P. Stee, N. Thureau, F. Vakili, J. Borgnino, “Spectrally resolved Michelson interferometry. I. Exact formalism in the multispeckle mode,” J. Opt. Soc. Am. A 16, 872–881 (1999).
[CrossRef]

F. Vakili, D. Mourard, Ph. Stee, D. Bonneau, P. Berio, O. Chesneau, N. Thureau, F. Morand, “Evidence of one-armed oscillations in the equatorial disk of ζ Tau from GI2T spectrally resolved interferometry,” Astron. Astrophys. 335, 261–265 (1998).

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

S. Ragland, D. Bonneau, D. Mourard, P. Berio, “Interferometric investigations of highly evolved stars,” in Interferometry in Optical Astronomy, P. J. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 523–530 (2000).
[CrossRef]

Blanc, J. C.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Blazit, A.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Boit, J. L.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Bonneau, D.

P. Berio, Ph. Stee, D. Mourard, D. Bonneau, O. Chesneau, N. Thureau, D. Le Mignant, R. Hirata, “Interferometic insight into γ Cassiopeiae long-term variability,” Astron. Astrophys. 345, 203–210 (1999).

P. Berio, D. Mourard, D. Bonneau, O. Chesneau, P. Stee, N. Thureau, F. Vakili, J. Borgnino, “Spectrally resolved Michelson interferometry. I. Exact formalism in the multispeckle mode,” J. Opt. Soc. Am. A 16, 872–881 (1999).
[CrossRef]

F. Vakili, D. Mourard, Ph. Stee, D. Bonneau, P. Berio, O. Chesneau, N. Thureau, F. Morand, “Evidence of one-armed oscillations in the equatorial disk of ζ Tau from GI2T spectrally resolved interferometry,” Astron. Astrophys. 335, 261–265 (1998).

F. Vakili, D. Mourard, D. Bonneau, F. Morand, Ph. Stee, “Subtle structures in the wind of P Cygni,” Astron. Astrophys. 323, 183–188 (1997).

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

S. Ragland, D. Bonneau, D. Mourard, P. Berio, “Interferometric investigations of highly evolved stars,” in Interferometry in Optical Astronomy, P. J. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 523–530 (2000).
[CrossRef]

Borgnino, J.

Chelli, A.

A. Chelli, “The phase problem in optical interferometry—error analysis in the presence of photon noise,” Astron. Astrophys. 225, 277–290 (1989).

Chesneau, O.

P. Berio, D. Mourard, D. Bonneau, O. Chesneau, P. Stee, N. Thureau, F. Vakili, J. Borgnino, “Spectrally resolved Michelson interferometry. I. Exact formalism in the multispeckle mode,” J. Opt. Soc. Am. A 16, 872–881 (1999).
[CrossRef]

P. Berio, Ph. Stee, D. Mourard, D. Bonneau, O. Chesneau, N. Thureau, D. Le Mignant, R. Hirata, “Interferometic insight into γ Cassiopeiae long-term variability,” Astron. Astrophys. 345, 203–210 (1999).

F. Vakili, D. Mourard, Ph. Stee, D. Bonneau, P. Berio, O. Chesneau, N. Thureau, F. Morand, “Evidence of one-armed oscillations in the equatorial disk of ζ Tau from GI2T spectrally resolved interferometry,” Astron. Astrophys. 335, 261–265 (1998).

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Clausse, J. M.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Corneloup, J. M.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Dainty, J. C.

Dalla, R.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Dugue, M.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Glentzlin, A.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 9.

Greenaway, A. H.

Hill, L.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Hirata, R.

P. Berio, Ph. Stee, D. Mourard, D. Bonneau, O. Chesneau, N. Thureau, D. Le Mignant, R. Hirata, “Interferometic insight into γ Cassiopeiae long-term variability,” Astron. Astrophys. 345, 203–210 (1999).

Labeyrie, A.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Le Merrer, J.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Le Mignant, D.

P. Berio, Ph. Stee, D. Mourard, D. Bonneau, O. Chesneau, N. Thureau, D. Le Mignant, R. Hirata, “Interferometic insight into γ Cassiopeiae long-term variability,” Astron. Astrophys. 345, 203–210 (1999).

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]

Menardi, S.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Merlin, G.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Morand, F.

F. Vakili, D. Mourard, Ph. Stee, D. Bonneau, P. Berio, O. Chesneau, N. Thureau, F. Morand, “Evidence of one-armed oscillations in the equatorial disk of ζ Tau from GI2T spectrally resolved interferometry,” Astron. Astrophys. 335, 261–265 (1998).

F. Vakili, D. Mourard, D. Bonneau, F. Morand, Ph. Stee, “Subtle structures in the wind of P Cygni,” Astron. Astrophys. 323, 183–188 (1997).

Moreaux, G.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Mourard, D.

P. Berio, Ph. Stee, D. Mourard, D. Bonneau, O. Chesneau, N. Thureau, D. Le Mignant, R. Hirata, “Interferometic insight into γ Cassiopeiae long-term variability,” Astron. Astrophys. 345, 203–210 (1999).

P. Berio, D. Mourard, D. Bonneau, O. Chesneau, P. Stee, N. Thureau, F. Vakili, J. Borgnino, “Spectrally resolved Michelson interferometry. I. Exact formalism in the multispeckle mode,” J. Opt. Soc. Am. A 16, 872–881 (1999).
[CrossRef]

F. Vakili, D. Mourard, Ph. Stee, D. Bonneau, P. Berio, O. Chesneau, N. Thureau, F. Morand, “Evidence of one-armed oscillations in the equatorial disk of ζ Tau from GI2T spectrally resolved interferometry,” Astron. Astrophys. 335, 261–265 (1998).

F. Vakili, D. Mourard, D. Bonneau, F. Morand, Ph. Stee, “Subtle structures in the wind of P Cygni,” Astron. Astrophys. 323, 183–188 (1997).

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

S. Ragland, D. Bonneau, D. Mourard, P. Berio, “Interferometric investigations of highly evolved stars,” in Interferometry in Optical Astronomy, P. J. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 523–530 (2000).
[CrossRef]

Papoulis, A.

A. Papoulis, Probability Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965).

Petrov, R.

R. Petrov, F. Roddier, C. Aime, “Signal to noise ratio in differential speckle interferometry,” J. Opt. Soc. Am. A 3, 634–644 (1986).
[CrossRef]

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Ragland, S.

S. Ragland, D. Bonneau, D. Mourard, P. Berio, “Interferometric investigations of highly evolved stars,” in Interferometry in Optical Astronomy, P. J. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 523–530 (2000).
[CrossRef]

Rebattu, S.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Roddier, F.

Rousselet-Perraut, K.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Stee, P.

Stee, Ph.

P. Berio, Ph. Stee, D. Mourard, D. Bonneau, O. Chesneau, N. Thureau, D. Le Mignant, R. Hirata, “Interferometic insight into γ Cassiopeiae long-term variability,” Astron. Astrophys. 345, 203–210 (1999).

F. Vakili, D. Mourard, Ph. Stee, D. Bonneau, P. Berio, O. Chesneau, N. Thureau, F. Morand, “Evidence of one-armed oscillations in the equatorial disk of ζ Tau from GI2T spectrally resolved interferometry,” Astron. Astrophys. 335, 261–265 (1998).

F. Vakili, D. Mourard, D. Bonneau, F. Morand, Ph. Stee, “Subtle structures in the wind of P Cygni,” Astron. Astrophys. 323, 183–188 (1997).

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Tallon-Bosc, I.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Thureau, N.

P. Berio, Ph. Stee, D. Mourard, D. Bonneau, O. Chesneau, N. Thureau, D. Le Mignant, R. Hirata, “Interferometic insight into γ Cassiopeiae long-term variability,” Astron. Astrophys. 345, 203–210 (1999).

P. Berio, D. Mourard, D. Bonneau, O. Chesneau, P. Stee, N. Thureau, F. Vakili, J. Borgnino, “Spectrally resolved Michelson interferometry. I. Exact formalism in the multispeckle mode,” J. Opt. Soc. Am. A 16, 872–881 (1999).
[CrossRef]

F. Vakili, D. Mourard, Ph. Stee, D. Bonneau, P. Berio, O. Chesneau, N. Thureau, F. Morand, “Evidence of one-armed oscillations in the equatorial disk of ζ Tau from GI2T spectrally resolved interferometry,” Astron. Astrophys. 335, 261–265 (1998).

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Trastour, J.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Vakili, F.

P. Berio, D. Mourard, D. Bonneau, O. Chesneau, P. Stee, N. Thureau, F. Vakili, J. Borgnino, “Spectrally resolved Michelson interferometry. I. Exact formalism in the multispeckle mode,” J. Opt. Soc. Am. A 16, 872–881 (1999).
[CrossRef]

F. Vakili, D. Mourard, Ph. Stee, D. Bonneau, P. Berio, O. Chesneau, N. Thureau, F. Morand, “Evidence of one-armed oscillations in the equatorial disk of ζ Tau from GI2T spectrally resolved interferometry,” Astron. Astrophys. 335, 261–265 (1998).

F. Vakili, D. Mourard, D. Bonneau, F. Morand, Ph. Stee, “Subtle structures in the wind of P Cygni,” Astron. Astrophys. 323, 183–188 (1997).

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Vaultier, G.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Verinaud, C.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Voet, C.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

Astron. Astrophys. (4)

P. Berio, Ph. Stee, D. Mourard, D. Bonneau, O. Chesneau, N. Thureau, D. Le Mignant, R. Hirata, “Interferometic insight into γ Cassiopeiae long-term variability,” Astron. Astrophys. 345, 203–210 (1999).

F. Vakili, D. Mourard, Ph. Stee, D. Bonneau, P. Berio, O. Chesneau, N. Thureau, F. Morand, “Evidence of one-armed oscillations in the equatorial disk of ζ Tau from GI2T spectrally resolved interferometry,” Astron. Astrophys. 335, 261–265 (1998).

F. Vakili, D. Mourard, D. Bonneau, F. Morand, Ph. Stee, “Subtle structures in the wind of P Cygni,” Astron. Astrophys. 323, 183–188 (1997).

A. Chelli, “The phase problem in optical interferometry—error analysis in the presence of photon noise,” Astron. Astrophys. 225, 277–290 (1989).

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. (1)

J. Opt. Soc. Am. A (3)

Other (4)

A. Papoulis, Probability Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 9.

D. Mourard, N. Thureau, P. Antonelli, P. Berio, J. C. Blanc, A. Blazit, J. L. Boit, D. Bonneau, O. Chesneau, J. M. Clausse, J. M. Corneloup, R. Dalla, M. Dugue, A. Glentzlin, L. Hill, A. Labeyrie, J. Le Merrer, S. Menardi, G. Merlin, G. Moreaux, R. Petrov, S. Rebattu, K. Rousselet-Perraut, Ph. Stee, I. Tallon-Bosc, J. Trastour, F. Vakili, C. Verinaud, C. Voet, G. Vaultier, “The GI2T/REGAIN interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 517–525 (1998).
[CrossRef]

S. Ragland, D. Bonneau, D. Mourard, P. Berio, “Interferometric investigations of highly evolved stars,” in Interferometry in Optical Astronomy, P. J. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 523–530 (2000).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic representation of a (cross-) spectral density comprising two low-frequency components (seeing and speckle distributions) and two high-frequency components (fringe distributions).

Fig. 2
Fig. 2

SNR of the C1 estimator with respect to the star magnitude mR. The observing parameters are r0,500 nm=12 cm, M=9000 (corresponding to 3 min of observation), λ=600 nm, L=30 m, and Δλ=4.5 nm (solid curve) or Δλ=0.05 nm (dashed curve).

Fig. 3
Fig. 3

SNR of the C1 estimator with respect to the star magnitude mR. The observing parameters are r0,500 nm=15 cm, M=9000 (corresponding to 3 min of observation), λ=600 nm, L=30 m, and Δλ=4.5 nm (solid curve) or Δλ=0.05 nm (dashed curve).

Fig. 4
Fig. 4

SNR of the C1 (solid curve) and C2(L/λ) (dashed curve) estimators with respect to the star magnitude mR. The observing parameters are r0,500 nm=12 cm, M=9000 (corresponding to 3 min of observation), λ=600 nm, L=30 m, and Δλ=4.5 nm.

Fig. 5
Fig. 5

SNR of the C1 estimator with respect to the star magnitude mR. Solid curve, SNR|C1| for the cross-spectral density processing with Δλ1=0.05 nm and Δλ2=4.5 nm; dashed curve, SNRC1 for the spectral density processing with Δλ1=0.05 nm. The observing parameters are r0,500 nm=12 cm, M=9000 (corresponding to 3 min of observation), λ=600 nm, and L=30 m.

Fig. 6
Fig. 6

Standard deviation of the relative phase estimate (estimator C1) with respect to the star magnitude mR. The observing parameters are M=9000 (corresponding to 3 min of observation), λ1=600 nm, Δλ1=0.05 nm, λ2=605 nm, Δλ2=4.5 nm, L=30 m, and r0,500 nm=12 cm (solid curve) or r0,500 nm=15 cm (dashed curve).

Equations (45)

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C1=2EfrEsp,
C2(f)=2W(f)Wspeckle(f-L/λ),
Efr=jW(fj),Esp=kWspeckle(fk),
SNRC1=C1σC1,
σC124Esp2 σEfr2+4Efr2Esp4 σEsp2,
σEsp2Esp2Efr2 σEfr2.
SNRC1Efr2σEfr.
SNRC1N¯Mjw(fj)2{N¯2jw2(fj)+2N¯jw(fj)+jl[w(fj-fl)+w(fj+fl)]}1/2,
SNRC2(fi)W(fj)2σfr(fj),
SNRC2(fj)N¯Mw(fj)2[N¯2w2(fj)+2Nw¯(fj)+w(2fj)+1]1/2.
E12fr=jW12(fj),E12sp=kW12speckle(fk),
SNR|C1|=|C1|σ|C1|,
SNR|C1||E12fr|2σ|E12fr|,
SNR|C1|N¯1N¯2M|w12(fj)|2[N¯1N¯2j|w12(fj)|2+N¯1jw1(fj)+N¯2jw2(fj)+jl|w12(fj-fl)|]1/2,
σarg C1[jl|w12(fj-fl)|-jl|w12(fj+fl)|+N¯1jw1(fj)+N¯2jw2(fj)]1/22MN¯1N¯2j|w12(fj)|.
SNR|C2|(fj)|w12fr(fj)|2σ12fr(fj),
SNR|C2|(fj)
N¯1N¯2M|w12(fj)|2[N¯1N¯2|w12(fj)|2+N¯1w1(fj)+N¯2w2(fj)+1]1/2.
σarg (C2)(fj)[1-|w12(2fj)|+N¯1w1(fj)+N¯2w2(fj)]1/22MN¯1N¯2|w12(fj)|.
d(u)=k=1Nδ(u-uk),
Qj=|d˜(fj)|2-N=k=1Nl=1Nexp[2iπfj(uk-ul)]-N,
Efr=jQj,
σEfr2=ij[E(QiQj)-E(Qi)E(Qj)]=ijCov(Qi, Qj),
E(Qj)=|(I˜)(fj)|2=N¯2w(fj),
E(QiQj)2N¯3w(fi)δij+N¯2[w(fi+fj)+w(fi-fj)]+(1+δij)N¯4w(fi)w(fj),
σEfr22N¯3jw(fj)+N¯2ij[w(fi+fj)+w(fi-fj)]+N¯4jw2(fj).
σfr2(fj)N¯4w2(fj)+2N¯3w(fj)+N¯2w(2fj)+N¯2.
|E12fr|=j|W12(fj)|=j|I˜1(fj)I˜2(fj)|,
|E12fr|j|O˜1(fj)O˜2*(fj)||S˜(fj)|2,
|E12fr|jQj,
Qj=d˜1(fj)d˜2*(fj)=k=1N1l=1N2exp[2iπfj(uk-vl)],
σE12fr2=ij[E(QiQj*)-E(Qi)E(Qj*)]=ijCov(Qi, Qj).
E(Qj)=N¯1N¯2w12(fj),
E(QiQj*)=N¯12N¯2w1(fj)δij+N¯1N¯22w2(fj)δij+ N¯1N¯2×|w12(fi-fj)|+(1+δij)×N¯12N¯22w12(fi)w12*(fj),
σE12fr2=N¯12N¯2jw1(fj)+N¯1N¯22jw2(fj)+N¯1N¯2ij|w12(fi-fj)|+N¯12N¯22j|w12(fj)|2.
σ12fr2(fj)=N¯12N¯2w1(fj)+N¯1N¯22w2(fj)+N¯12N¯22|w12(fj)|2.
arg(C1)=arctanYX,
σarg(C1)2
σY2E2(X)+σX2E2(Y)-2 Cov(X,Y)E(X)E(Y)[E2(X)+E2(Y)]2.
σarg(C1)2E(Y2)E2(X).
σarg(C1)2
ij{E[Qi(Qj*-Qj)]+E[Qi*(Qj-Qj*)]}2N¯12N¯22[j|w12(fj)|]2.
E[Qi(Qj*-Qj)]=N¯1N¯2[|w12(fi-fj)|-|w12(fi+fj)|]+ N¯12N¯2w1(fj)δij+N¯1N¯22w2(fj)δij.
σarg(C1)2ij|w12(fi-fj)|-ij|w12(fi+fj)|+N¯1jw1(fj)+N¯2jw2(fj)2N¯1N¯2[j|w12(fj)|]2.
σarg(C2)2(fj)1-|w12(2fj)|+N¯1w1(fj)+N¯2w2(fj)2N¯1N¯2|w12(fj)|2.

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