Abstract

We investigate the pyramid wave-front sensor’s capability to reconstruct in a closed loop, with only one sensor, the wave fronts on both apertures of a stellar interferometer, including the differential piston: The method consists of placing the principal element of this sensor, namely, a refractive-square-based pyramid, in a combined focal plane of the interferometer instead of using two sensors, one for each individual telescope. We show that the sensor signals allow one to measure the wave-front aberrations on both apertures and the differential piston at the same time. The performance of an adaptive-optics loop is computed numerically for the Large Binocular Telescope in terms of differential-piston rejection under several conditions. The results show that atmospheric correction including differential-piston compensation is possible as long as the corrected Strehl ratio at the wave-front sensing wavelength is greater than 20%.

© 2002 Optical Society of America

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References

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    [CrossRef]
  2. C. Verinaud and F. Cassaing, Astron. Astrophys. 365, 314 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. C. Verinaud and S. Esposito, 2001, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.
  11. A. Riccardi, G. Brusa, C. del Vecchio, P. Salinari, R. Biasi, M. Andrighettoni, D. Gallieni, F. Zocchi, M. Lloyd-Hart, F. Wildi, and H. M. Martin, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.
  12. M. Carbillet, L. Fini, B. Femenia, S. Esposito, A. Riccardi, E. Viard, and N. Hubin, Astron. Soc. Pac. Conf. Ser. 238, 249 (2001).

2001 (3)

C. Verinaud and F. Cassaing, Astron. Astrophys. 365, 314 (2001).
[CrossRef]

S. Esposito and A. Riccardi, Astron. Astrophys. 369, L9 (2001).
[CrossRef]

M. Carbillet, L. Fini, B. Femenia, S. Esposito, A. Riccardi, E. Viard, and N. Hubin, Astron. Soc. Pac. Conf. Ser. 238, 249 (2001).

2000 (1)

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, and S. Lévêque, Proc. SPIE 4006, 152 (2000).
[CrossRef]

1998 (2)

J. Hill and P. Salinari, Proc. SPIE 3352, 23 (1998).
[CrossRef]

A. Riccardi, N. Bindi, R. Ragazzoni, S. Esposito, and P. Stefanini, Proc. SPIE 3353, 941 (1998).
[CrossRef]

1996 (2)

1975 (1)

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

Andrighettoni, M.

A. Riccardi, G. Brusa, C. del Vecchio, P. Salinari, R. Biasi, M. Andrighettoni, D. Gallieni, F. Zocchi, M. Lloyd-Hart, F. Wildi, and H. M. Martin, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.

Biasi, R.

A. Riccardi, G. Brusa, C. del Vecchio, P. Salinari, R. Biasi, M. Andrighettoni, D. Gallieni, F. Zocchi, M. Lloyd-Hart, F. Wildi, and H. M. Martin, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.

Bindi, N.

A. Riccardi, N. Bindi, R. Ragazzoni, S. Esposito, and P. Stefanini, Proc. SPIE 3353, 941 (1998).
[CrossRef]

Blazit, A.

Bonneau, D.

Brusa, G.

A. Riccardi, G. Brusa, C. del Vecchio, P. Salinari, R. Biasi, M. Andrighettoni, D. Gallieni, F. Zocchi, M. Lloyd-Hart, F. Wildi, and H. M. Martin, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.

Carbillet, M.

M. Carbillet, L. Fini, B. Femenia, S. Esposito, A. Riccardi, E. Viard, and N. Hubin, Astron. Soc. Pac. Conf. Ser. 238, 249 (2001).

Cassaing, F.

C. Verinaud and F. Cassaing, Astron. Astrophys. 365, 314 (2001).
[CrossRef]

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, and S. Lévêque, Proc. SPIE 4006, 152 (2000).
[CrossRef]

Coudrain, C.

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, and S. Lévêque, Proc. SPIE 4006, 152 (2000).
[CrossRef]

del Vecchio, C.

A. Riccardi, G. Brusa, C. del Vecchio, P. Salinari, R. Biasi, M. Andrighettoni, D. Gallieni, F. Zocchi, M. Lloyd-Hart, F. Wildi, and H. M. Martin, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.

Di Folco, E.

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, and S. Lévêque, Proc. SPIE 4006, 152 (2000).
[CrossRef]

Esposito, S.

S. Esposito and A. Riccardi, Astron. Astrophys. 369, L9 (2001).
[CrossRef]

M. Carbillet, L. Fini, B. Femenia, S. Esposito, A. Riccardi, E. Viard, and N. Hubin, Astron. Soc. Pac. Conf. Ser. 238, 249 (2001).

A. Riccardi, N. Bindi, R. Ragazzoni, S. Esposito, and P. Stefanini, Proc. SPIE 3353, 941 (1998).
[CrossRef]

C. Verinaud and S. Esposito, 2001, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.

Femenia, B.

M. Carbillet, L. Fini, B. Femenia, S. Esposito, A. Riccardi, E. Viard, and N. Hubin, Astron. Soc. Pac. Conf. Ser. 238, 249 (2001).

Fini, L.

M. Carbillet, L. Fini, B. Femenia, S. Esposito, A. Riccardi, E. Viard, and N. Hubin, Astron. Soc. Pac. Conf. Ser. 238, 249 (2001).

Fleury, B.

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, and S. Lévêque, Proc. SPIE 4006, 152 (2000).
[CrossRef]

Gallieni, D.

A. Riccardi, G. Brusa, C. del Vecchio, P. Salinari, R. Biasi, M. Andrighettoni, D. Gallieni, F. Zocchi, M. Lloyd-Hart, F. Wildi, and H. M. Martin, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.

Glindemann, A.

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, and S. Lévêque, Proc. SPIE 4006, 152 (2000).
[CrossRef]

Hill, J.

J. Hill and P. Salinari, Proc. SPIE 3352, 23 (1998).
[CrossRef]

Hubin, N.

M. Carbillet, L. Fini, B. Femenia, S. Esposito, A. Riccardi, E. Viard, and N. Hubin, Astron. Soc. Pac. Conf. Ser. 238, 249 (2001).

Koechlin, L.

Labeyrie, A.

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

Lawson, P. R.

Lévêque, S.

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, and S. Lévêque, Proc. SPIE 4006, 152 (2000).
[CrossRef]

Lloyd-Hart, M.

A. Riccardi, G. Brusa, C. del Vecchio, P. Salinari, R. Biasi, M. Andrighettoni, D. Gallieni, F. Zocchi, M. Lloyd-Hart, F. Wildi, and H. M. Martin, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.

Madec, P.-Y.

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, and S. Lévêque, Proc. SPIE 4006, 152 (2000).
[CrossRef]

Martin, H. M.

A. Riccardi, G. Brusa, C. del Vecchio, P. Salinari, R. Biasi, M. Andrighettoni, D. Gallieni, F. Zocchi, M. Lloyd-Hart, F. Wildi, and H. M. Martin, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.

Morand, F.

Mourard, D.

Ragazzoni, R.

A. Riccardi, N. Bindi, R. Ragazzoni, S. Esposito, and P. Stefanini, Proc. SPIE 3353, 941 (1998).
[CrossRef]

R. Ragazzoni, J. Mod. Opt. 43, 289 (1996).
[CrossRef]

Riccardi, A.

S. Esposito and A. Riccardi, Astron. Astrophys. 369, L9 (2001).
[CrossRef]

M. Carbillet, L. Fini, B. Femenia, S. Esposito, A. Riccardi, E. Viard, and N. Hubin, Astron. Soc. Pac. Conf. Ser. 238, 249 (2001).

A. Riccardi, N. Bindi, R. Ragazzoni, S. Esposito, and P. Stefanini, Proc. SPIE 3353, 941 (1998).
[CrossRef]

A. Riccardi, G. Brusa, C. del Vecchio, P. Salinari, R. Biasi, M. Andrighettoni, D. Gallieni, F. Zocchi, M. Lloyd-Hart, F. Wildi, and H. M. Martin, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.

Roddier, F.

F. Roddier, 1999, ASP conf., “Working on the fringes” (Danapoint), vol. 194.

Salinari, P.

J. Hill and P. Salinari, Proc. SPIE 3352, 23 (1998).
[CrossRef]

A. Riccardi, G. Brusa, C. del Vecchio, P. Salinari, R. Biasi, M. Andrighettoni, D. Gallieni, F. Zocchi, M. Lloyd-Hart, F. Wildi, and H. M. Martin, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.

Stee, Ph.

Stefanini, P.

A. Riccardi, N. Bindi, R. Ragazzoni, S. Esposito, and P. Stefanini, Proc. SPIE 3353, 941 (1998).
[CrossRef]

Tallon-Bosc, I.

Vakili, F.

Verinaud, C.

C. Verinaud and F. Cassaing, Astron. Astrophys. 365, 314 (2001).
[CrossRef]

C. Verinaud and S. Esposito, 2001, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.

Viard, E.

M. Carbillet, L. Fini, B. Femenia, S. Esposito, A. Riccardi, E. Viard, and N. Hubin, Astron. Soc. Pac. Conf. Ser. 238, 249 (2001).

Wildi, F.

A. Riccardi, G. Brusa, C. del Vecchio, P. Salinari, R. Biasi, M. Andrighettoni, D. Gallieni, F. Zocchi, M. Lloyd-Hart, F. Wildi, and H. M. Martin, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.

Zocchi, F.

A. Riccardi, G. Brusa, C. del Vecchio, P. Salinari, R. Biasi, M. Andrighettoni, D. Gallieni, F. Zocchi, M. Lloyd-Hart, F. Wildi, and H. M. Martin, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.

Appl. Opt. (1)

Astron. Astrophys. (2)

C. Verinaud and F. Cassaing, Astron. Astrophys. 365, 314 (2001).
[CrossRef]

S. Esposito and A. Riccardi, Astron. Astrophys. 369, L9 (2001).
[CrossRef]

Astron. Soc. Pac. Conf. Ser. (1)

M. Carbillet, L. Fini, B. Femenia, S. Esposito, A. Riccardi, E. Viard, and N. Hubin, Astron. Soc. Pac. Conf. Ser. 238, 249 (2001).

Astrophys. J. (1)

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

J. Mod. Opt. (1)

R. Ragazzoni, J. Mod. Opt. 43, 289 (1996).
[CrossRef]

Proc. SPIE (3)

J. Hill and P. Salinari, Proc. SPIE 3352, 23 (1998).
[CrossRef]

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, and S. Lévêque, Proc. SPIE 4006, 152 (2000).
[CrossRef]

A. Riccardi, N. Bindi, R. Ragazzoni, S. Esposito, and P. Stefanini, Proc. SPIE 3353, 941 (1998).
[CrossRef]

Other (3)

C. Verinaud and S. Esposito, 2001, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.

A. Riccardi, G. Brusa, C. del Vecchio, P. Salinari, R. Biasi, M. Andrighettoni, D. Gallieni, F. Zocchi, M. Lloyd-Hart, F. Wildi, and H. M. Martin, presented at the European Space Observatory conference, “Beyond Conventional Adaptive Optics,” Venice, May 7–10, 2001.

F. Roddier, 1999, ASP conf., “Working on the fringes” (Danapoint), vol. 194.

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Figures (4)

Fig. 1
Fig. 1

General concept for using a pyramid wave-front sensor (WFS) in an interferometer.

Fig. 2
Fig. 2

Wave-front sensor geometrical scheme and diffraction effects.

Fig. 3
Fig. 3

Signal response of the pyramid wave-front sensor to piston, tip–tilt, and defocus applied on one aperture.

Fig. 4
Fig. 4

Results of simulations. Dashed curve: Atmo-spheric differential piston. Solid curves: residual differential piston after correction. These curves have been shifted along the y axis for better readability.

Equations (2)

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Iix,y=FT-1Hixf,yfFTPx,yexpiϕx,y2,
Sxx,y=I1x,y+I2x,y-I3x,y+I4x,y/I0, Syx,y=I1x,y+I4x,y-I2x,y+I3x,y/I0,

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