Abstract

The coupling between a turbulence-distorted optical beam and a single-mode waveguide is addressed. The coupling efficiency and the coupled phase are derived, both without aberrations and with small aberrations. These analytical expressions are validated by numerical simulations. Correction with adaptive optics is investigated. In the general case, the Strehl ratio is a pessimistic estimator, and the coupled phase is different and has a smaller variance than the classical phase averaged over the pupil. Application fields are heterodyne detection and stellar interferometry, for which spatial and modal filtering are distinguished.

© 2001 Optical Society of America

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References

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  1. F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” Progress in Optics, E. Wolf, ed. (North Holland, Amsterdam, 1981), Vol. XIX, pp. 281–376.
  2. E. G. Neumann, Single-Mode Fibers (Springer-Verlag, Berlin, 1988).
  3. P. Connes, C. Froehly, P. Facq, “A fiber-linked version of project TRIO,” in Colloquium on Kilometric Optical Arrays in Space, SP 226 (European Space Agency, Paris, 1984), pp. 49–61.
  4. V. Coudé du Foresto, G. Perrin, C. Ruilier, B. Mennesson, W. Traub, M. Lacasse, “FLUOR fibered instrument at the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part I, 856–863 (1998).
    [CrossRef]
  5. G. Perrin, “Une unité de recombinaison à fibres pour l’interféromètre IOTA. Application à l’étude des étoiles de type tardif,” Ph.D. thesis (Université de Paris VII, 1996).
  6. V. Coudé du Foresto, G. Perrin, C. Ruilier, B. Mennesson, W. Traub, M. Lacasse, “FLUOR fibered instrument at the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, parts I and II (1998).
  7. J.-M. Conan, “Étude de la correction partielle en optique adaptative,” Ph.D. thesis (Université de Paris XI, Orsay, 1994).
  8. M. Ollivier, J. M. Mariotti, “Improvement of the rejection rate of a nulling interferometer by spatial filtering,” Appl. Opt. 36, 5340–5346 (1997).
    [CrossRef] [PubMed]
  9. E. Serabyn, J. K. Walace, G. J. Hardy, E. G. H. Schmidtlin, H. T. Nguyen, “Deep nulling of visible laser light,” Appl. Opt. 38, 7128–7132 (1999).
    [CrossRef]
  10. F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry. I. Concept and astronomical applications,” Astron. Astrophys., Suppl. Ser. 138, 1–10 (1999).
    [CrossRef]
  11. W. R. Leeb, P. J. Winzer, K. H. Kudielka, “Aperture dependence of the mixing efficiency, the signal-to-noise ratio, and the speckle number in coherent lidar receivers,” Appl. Opt. 37, 3143–3148 (1998).
    [CrossRef]
  12. S. Shaklan, F. Roddier, “Coupling starlight into single-mode fiber optics,” Appl. Opt. 27, 2234–2338 (1988).
    [CrossRef]
  13. C. Ruilier, “A study of degraded light coupling into single-mode fibers,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part I, 319–329 (1998).
    [CrossRef]
  14. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  15. S. Prasad, G. Loos, “Spatial filtering of atmospheric decorrelation from wavefronts for interferometry,” Opt. Commun. 99, 380–392 (1993).
    [CrossRef]
  16. V. N. Mahajan, “Strehl ratio for primary aberrations in terms of their aberration variance,” J. Opt. Soc. Am. A 6, 860–861 (1983).
    [CrossRef]
  17. G. Rousset, “Wave-front sensors,” in Adaptive Optics in Astronomy, F. Roddier, ed. (Cambridge U. Press, Cambridge, UK, 1999), Chap. 5, pp. 91–130.
  18. F. Roddier, “Maximum gain and efficiency of adaptive optics systems,” Publ. Astron. Soc. Pac. 109, 815–820 (1997).
    [CrossRef]
  19. N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. (Bellingham) 29, 1174–1180 (1990).
    [CrossRef]
  20. S. Prasad, “Coupling and sensitivity enhancement with multiple-core fibers in ground-based interferometry,” in Fiber Optics in Astronomical Applications, S. Barden, ed., Proc. SPIE2476, 96–107 (1995).
    [CrossRef]
  21. J.-M. Conan, G. Rousset, P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995).
    [CrossRef]
  22. C. Ruilier, “Filtrage modal et recombinaison de grands télescopes. Contributions à l’instrument FLUOR,” Ph.D. thesis (Université de Paris VII, 1999).
  23. M. Ollivier, “Contribution à la recherche d’exoplanètes. Coronographie interférentielle pour la mission DARWIN,” Ph.D. thesis (Université de Paris XI, Orsay, 1999).
  24. J. M. Mariotti, V. Coudé du Foresto, G. Perrin, P. Léna, “Interferometric connection of large telescopes at Mauna Kea,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part II, 785–792 (1998).
    [CrossRef]
  25. F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, S. Lévêque, “An optimized fringe tracker for the VLTI/PRIMA instrument,” in Interferometry in Optical Astronomy,” P. L. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 152–163 (2000).
    [CrossRef]

1999 (2)

E. Serabyn, J. K. Walace, G. J. Hardy, E. G. H. Schmidtlin, H. T. Nguyen, “Deep nulling of visible laser light,” Appl. Opt. 38, 7128–7132 (1999).
[CrossRef]

F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry. I. Concept and astronomical applications,” Astron. Astrophys., Suppl. Ser. 138, 1–10 (1999).
[CrossRef]

1998 (1)

1997 (2)

F. Roddier, “Maximum gain and efficiency of adaptive optics systems,” Publ. Astron. Soc. Pac. 109, 815–820 (1997).
[CrossRef]

M. Ollivier, J. M. Mariotti, “Improvement of the rejection rate of a nulling interferometer by spatial filtering,” Appl. Opt. 36, 5340–5346 (1997).
[CrossRef] [PubMed]

1995 (1)

1993 (1)

S. Prasad, G. Loos, “Spatial filtering of atmospheric decorrelation from wavefronts for interferometry,” Opt. Commun. 99, 380–392 (1993).
[CrossRef]

1990 (1)

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. (Bellingham) 29, 1174–1180 (1990).
[CrossRef]

1988 (1)

S. Shaklan, F. Roddier, “Coupling starlight into single-mode fiber optics,” Appl. Opt. 27, 2234–2338 (1988).
[CrossRef]

1983 (1)

V. N. Mahajan, “Strehl ratio for primary aberrations in terms of their aberration variance,” J. Opt. Soc. Am. A 6, 860–861 (1983).
[CrossRef]

1976 (1)

Benech, P.

F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry. I. Concept and astronomical applications,” Astron. Astrophys., Suppl. Ser. 138, 1–10 (1999).
[CrossRef]

Berger, J.-P.

F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry. I. Concept and astronomical applications,” Astron. Astrophys., Suppl. Ser. 138, 1–10 (1999).
[CrossRef]

Cassaing, F.

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, S. Lévêque, “An optimized fringe tracker for the VLTI/PRIMA instrument,” in Interferometry in Optical Astronomy,” P. L. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 152–163 (2000).
[CrossRef]

Conan, J.-M.

J.-M. Conan, G. Rousset, P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995).
[CrossRef]

J.-M. Conan, “Étude de la correction partielle en optique adaptative,” Ph.D. thesis (Université de Paris XI, Orsay, 1994).

Connes, P.

P. Connes, C. Froehly, P. Facq, “A fiber-linked version of project TRIO,” in Colloquium on Kilometric Optical Arrays in Space, SP 226 (European Space Agency, Paris, 1984), pp. 49–61.

Coudé du Foresto, V.

V. Coudé du Foresto, G. Perrin, C. Ruilier, B. Mennesson, W. Traub, M. Lacasse, “FLUOR fibered instrument at the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part I, 856–863 (1998).
[CrossRef]

V. Coudé du Foresto, G. Perrin, C. Ruilier, B. Mennesson, W. Traub, M. Lacasse, “FLUOR fibered instrument at the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, parts I and II (1998).

J. M. Mariotti, V. Coudé du Foresto, G. Perrin, P. Léna, “Interferometric connection of large telescopes at Mauna Kea,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part II, 785–792 (1998).
[CrossRef]

Coudrain, C.

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, S. Lévêque, “An optimized fringe tracker for the VLTI/PRIMA instrument,” in Interferometry in Optical Astronomy,” P. L. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 152–163 (2000).
[CrossRef]

Di Folco, E.

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, S. Lévêque, “An optimized fringe tracker for the VLTI/PRIMA instrument,” in Interferometry in Optical Astronomy,” P. L. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 152–163 (2000).
[CrossRef]

Facq, P.

P. Connes, C. Froehly, P. Facq, “A fiber-linked version of project TRIO,” in Colloquium on Kilometric Optical Arrays in Space, SP 226 (European Space Agency, Paris, 1984), pp. 49–61.

Fleury, B.

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, S. Lévêque, “An optimized fringe tracker for the VLTI/PRIMA instrument,” in Interferometry in Optical Astronomy,” P. L. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 152–163 (2000).
[CrossRef]

Froehly, C.

P. Connes, C. Froehly, P. Facq, “A fiber-linked version of project TRIO,” in Colloquium on Kilometric Optical Arrays in Space, SP 226 (European Space Agency, Paris, 1984), pp. 49–61.

Glindemann, A.

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, S. Lévêque, “An optimized fringe tracker for the VLTI/PRIMA instrument,” in Interferometry in Optical Astronomy,” P. L. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 152–163 (2000).
[CrossRef]

Hardy, G. J.

Kern, P.

F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry. I. Concept and astronomical applications,” Astron. Astrophys., Suppl. Ser. 138, 1–10 (1999).
[CrossRef]

Kudielka, K. H.

Lacasse, M.

V. Coudé du Foresto, G. Perrin, C. Ruilier, B. Mennesson, W. Traub, M. Lacasse, “FLUOR fibered instrument at the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, parts I and II (1998).

V. Coudé du Foresto, G. Perrin, C. Ruilier, B. Mennesson, W. Traub, M. Lacasse, “FLUOR fibered instrument at the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part I, 856–863 (1998).
[CrossRef]

Leeb, W. R.

Léna, P.

J. M. Mariotti, V. Coudé du Foresto, G. Perrin, P. Léna, “Interferometric connection of large telescopes at Mauna Kea,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part II, 785–792 (1998).
[CrossRef]

Lévêque, S.

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, S. Lévêque, “An optimized fringe tracker for the VLTI/PRIMA instrument,” in Interferometry in Optical Astronomy,” P. L. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 152–163 (2000).
[CrossRef]

Loos, G.

S. Prasad, G. Loos, “Spatial filtering of atmospheric decorrelation from wavefronts for interferometry,” Opt. Commun. 99, 380–392 (1993).
[CrossRef]

Madec, P.-Y.

J.-M. Conan, G. Rousset, P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995).
[CrossRef]

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, S. Lévêque, “An optimized fringe tracker for the VLTI/PRIMA instrument,” in Interferometry in Optical Astronomy,” P. L. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 152–163 (2000).
[CrossRef]

Mahajan, V. N.

V. N. Mahajan, “Strehl ratio for primary aberrations in terms of their aberration variance,” J. Opt. Soc. Am. A 6, 860–861 (1983).
[CrossRef]

Malbet, F.

F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry. I. Concept and astronomical applications,” Astron. Astrophys., Suppl. Ser. 138, 1–10 (1999).
[CrossRef]

Mariotti, J. M.

M. Ollivier, J. M. Mariotti, “Improvement of the rejection rate of a nulling interferometer by spatial filtering,” Appl. Opt. 36, 5340–5346 (1997).
[CrossRef] [PubMed]

J. M. Mariotti, V. Coudé du Foresto, G. Perrin, P. Léna, “Interferometric connection of large telescopes at Mauna Kea,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part II, 785–792 (1998).
[CrossRef]

Mennesson, B.

V. Coudé du Foresto, G. Perrin, C. Ruilier, B. Mennesson, W. Traub, M. Lacasse, “FLUOR fibered instrument at the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, parts I and II (1998).

V. Coudé du Foresto, G. Perrin, C. Ruilier, B. Mennesson, W. Traub, M. Lacasse, “FLUOR fibered instrument at the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part I, 856–863 (1998).
[CrossRef]

Neumann, E. G.

E. G. Neumann, Single-Mode Fibers (Springer-Verlag, Berlin, 1988).

Nguyen, H. T.

Noll, R. J.

Ollivier, M.

M. Ollivier, J. M. Mariotti, “Improvement of the rejection rate of a nulling interferometer by spatial filtering,” Appl. Opt. 36, 5340–5346 (1997).
[CrossRef] [PubMed]

M. Ollivier, “Contribution à la recherche d’exoplanètes. Coronographie interférentielle pour la mission DARWIN,” Ph.D. thesis (Université de Paris XI, Orsay, 1999).

Perrin, G.

J. M. Mariotti, V. Coudé du Foresto, G. Perrin, P. Léna, “Interferometric connection of large telescopes at Mauna Kea,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part II, 785–792 (1998).
[CrossRef]

V. Coudé du Foresto, G. Perrin, C. Ruilier, B. Mennesson, W. Traub, M. Lacasse, “FLUOR fibered instrument at the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part I, 856–863 (1998).
[CrossRef]

G. Perrin, “Une unité de recombinaison à fibres pour l’interféromètre IOTA. Application à l’étude des étoiles de type tardif,” Ph.D. thesis (Université de Paris VII, 1996).

V. Coudé du Foresto, G. Perrin, C. Ruilier, B. Mennesson, W. Traub, M. Lacasse, “FLUOR fibered instrument at the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, parts I and II (1998).

Prasad, S.

S. Prasad, G. Loos, “Spatial filtering of atmospheric decorrelation from wavefronts for interferometry,” Opt. Commun. 99, 380–392 (1993).
[CrossRef]

S. Prasad, “Coupling and sensitivity enhancement with multiple-core fibers in ground-based interferometry,” in Fiber Optics in Astronomical Applications, S. Barden, ed., Proc. SPIE2476, 96–107 (1995).
[CrossRef]

Roddier, F.

F. Roddier, “Maximum gain and efficiency of adaptive optics systems,” Publ. Astron. Soc. Pac. 109, 815–820 (1997).
[CrossRef]

S. Shaklan, F. Roddier, “Coupling starlight into single-mode fiber optics,” Appl. Opt. 27, 2234–2338 (1988).
[CrossRef]

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” Progress in Optics, E. Wolf, ed. (North Holland, Amsterdam, 1981), Vol. XIX, pp. 281–376.

Roddier, N.

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. (Bellingham) 29, 1174–1180 (1990).
[CrossRef]

Rousselet-Perraut, K.

F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry. I. Concept and astronomical applications,” Astron. Astrophys., Suppl. Ser. 138, 1–10 (1999).
[CrossRef]

Rousset, G.

J.-M. Conan, G. Rousset, P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995).
[CrossRef]

G. Rousset, “Wave-front sensors,” in Adaptive Optics in Astronomy, F. Roddier, ed. (Cambridge U. Press, Cambridge, UK, 1999), Chap. 5, pp. 91–130.

Ruilier, C.

C. Ruilier, “A study of degraded light coupling into single-mode fibers,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part I, 319–329 (1998).
[CrossRef]

C. Ruilier, “Filtrage modal et recombinaison de grands télescopes. Contributions à l’instrument FLUOR,” Ph.D. thesis (Université de Paris VII, 1999).

V. Coudé du Foresto, G. Perrin, C. Ruilier, B. Mennesson, W. Traub, M. Lacasse, “FLUOR fibered instrument at the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part I, 856–863 (1998).
[CrossRef]

V. Coudé du Foresto, G. Perrin, C. Ruilier, B. Mennesson, W. Traub, M. Lacasse, “FLUOR fibered instrument at the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, parts I and II (1998).

Schanen-Duport, I.

F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry. I. Concept and astronomical applications,” Astron. Astrophys., Suppl. Ser. 138, 1–10 (1999).
[CrossRef]

Schmidtlin, E. G. H.

Serabyn, E.

Shaklan, S.

S. Shaklan, F. Roddier, “Coupling starlight into single-mode fiber optics,” Appl. Opt. 27, 2234–2338 (1988).
[CrossRef]

Traub, W.

V. Coudé du Foresto, G. Perrin, C. Ruilier, B. Mennesson, W. Traub, M. Lacasse, “FLUOR fibered instrument at the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, parts I and II (1998).

V. Coudé du Foresto, G. Perrin, C. Ruilier, B. Mennesson, W. Traub, M. Lacasse, “FLUOR fibered instrument at the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part I, 856–863 (1998).
[CrossRef]

Walace, J. K.

Winzer, P. J.

Appl. Opt. (4)

Astron. Astrophys., Suppl. Ser. (1)

F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry. I. Concept and astronomical applications,” Astron. Astrophys., Suppl. Ser. 138, 1–10 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

V. N. Mahajan, “Strehl ratio for primary aberrations in terms of their aberration variance,” J. Opt. Soc. Am. A 6, 860–861 (1983).
[CrossRef]

J.-M. Conan, G. Rousset, P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995).
[CrossRef]

Opt. Commun. (1)

S. Prasad, G. Loos, “Spatial filtering of atmospheric decorrelation from wavefronts for interferometry,” Opt. Commun. 99, 380–392 (1993).
[CrossRef]

Opt. Eng. (Bellingham) (1)

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. (Bellingham) 29, 1174–1180 (1990).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

F. Roddier, “Maximum gain and efficiency of adaptive optics systems,” Publ. Astron. Soc. Pac. 109, 815–820 (1997).
[CrossRef]

Other (14)

S. Prasad, “Coupling and sensitivity enhancement with multiple-core fibers in ground-based interferometry,” in Fiber Optics in Astronomical Applications, S. Barden, ed., Proc. SPIE2476, 96–107 (1995).
[CrossRef]

G. Rousset, “Wave-front sensors,” in Adaptive Optics in Astronomy, F. Roddier, ed. (Cambridge U. Press, Cambridge, UK, 1999), Chap. 5, pp. 91–130.

C. Ruilier, “Filtrage modal et recombinaison de grands télescopes. Contributions à l’instrument FLUOR,” Ph.D. thesis (Université de Paris VII, 1999).

M. Ollivier, “Contribution à la recherche d’exoplanètes. Coronographie interférentielle pour la mission DARWIN,” Ph.D. thesis (Université de Paris XI, Orsay, 1999).

J. M. Mariotti, V. Coudé du Foresto, G. Perrin, P. Léna, “Interferometric connection of large telescopes at Mauna Kea,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part II, 785–792 (1998).
[CrossRef]

F. Cassaing, B. Fleury, C. Coudrain, P.-Y. Madec, E. Di Folco, A. Glindemann, S. Lévêque, “An optimized fringe tracker for the VLTI/PRIMA instrument,” in Interferometry in Optical Astronomy,” P. L. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 152–163 (2000).
[CrossRef]

C. Ruilier, “A study of degraded light coupling into single-mode fibers,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part I, 319–329 (1998).
[CrossRef]

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” Progress in Optics, E. Wolf, ed. (North Holland, Amsterdam, 1981), Vol. XIX, pp. 281–376.

E. G. Neumann, Single-Mode Fibers (Springer-Verlag, Berlin, 1988).

P. Connes, C. Froehly, P. Facq, “A fiber-linked version of project TRIO,” in Colloquium on Kilometric Optical Arrays in Space, SP 226 (European Space Agency, Paris, 1984), pp. 49–61.

V. Coudé du Foresto, G. Perrin, C. Ruilier, B. Mennesson, W. Traub, M. Lacasse, “FLUOR fibered instrument at the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, part I, 856–863 (1998).
[CrossRef]

G. Perrin, “Une unité de recombinaison à fibres pour l’interféromètre IOTA. Application à l’étude des étoiles de type tardif,” Ph.D. thesis (Université de Paris VII, 1996).

V. Coudé du Foresto, G. Perrin, C. Ruilier, B. Mennesson, W. Traub, M. Lacasse, “FLUOR fibered instrument at the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, parts I and II (1998).

J.-M. Conan, “Étude de la correction partielle en optique adaptative,” Ph.D. thesis (Université de Paris XI, Orsay, 1994).

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Figures (5)

Fig. 1
Fig. 1

Weighted scalar product matrix of the first 91 Zernike polynomials.

Fig. 2
Fig. 2

Covariance γi,i (left scale, solid symbols) and mean cross-coupled energy Σij|γij|2/Npol (right scale, open symbols) for the first 91 Zernike polynomials.

Fig. 3
Fig. 3

Coupling loss ρϕ/ρ0 for the first Zernike modes, computed by simulation (symbols) and approximation (17) (dotted curves). Solid curve, Strehl ratio approximation given by approximation (19) and Eq. (8).

Fig. 4
Fig. 4

Relative coupling fluctuations σt(ρϕ)/ρϕt given by approximation (28) (dotted curve) and by simulation (symbols).

Fig. 5
Fig. 5

Coupled energy E in arbitrary units given by Eq. (29) (dotted curve) and by simulation (symbols).

Tables (2)

Tables Icon

Table 1 γi,i Terms for the First Zernike Polynomials

Tables Icon

Table 2 Coordinates of the Maxima of Fig. 5 Given by Approximations (30 ) and (31 ) (top) and Simulation (bottom)

Equations (34)

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ϕ(r)=i=1aiZi2rD.
Pϕ=P0exp(iϕ)=i=0pi(ϕ)Mi,
P0(r)=1ifα2|r|D10otherwise.
X|YW=R2W(r)X(r)Y*(r)d2r.
XW=X|1W1|1W,
σW2(X)=X2W-XW2.
Zi|ZjP0=δij,
σP02(ϕ)=i=2ai2.
I=|Pϕ+R|2P0=2 Rei=0pi(ϕ)ri*+incoh.terms.
Ωϕ=Pϕ|M0P0(Pϕ|PϕP0×M0|M0P0)1/2,
Wϕ=PϕM0*,
ρϕ=|Ωϕ|2,
Ψϕ=arg Ωϕ.
ρ0(α, β)=2exp(-β2)-exp(-β2α2)β(1-α2)1/22,
β=π2DλωF.
ΩϕΩ0=Pϕ|M0P0P0|M0P0=exp(iϕ)W0.
ρϕ/ρ0exp[-σW02(ϕ)],
ΨϕϕW0.
M0=1  ρϕρ0exp[-σP02(ϕ)].
γij=Zi|ZjW0δij.
γi,j0.8δi,j.
ϕres=ϕ-a2Z2.
a2opt=ϕ|Z2W0Z2|Z2W0=i=1aiγ2,iγ2,2.
ϕP02(ϕ)t=i=i0+1ai20.46(n+1)-5/3Dτ05/3.
ρϕt/ρ01-σW02(ϕ)t.
σW02(ϕ)ti=i0+1γijai2t0.8σP02(ϕres).
σt(ρϕ)ρ0σt[σW02(ϕ)].
σt(ρϕ)ρϕt0.816 σP02(ϕres)n+1.
E=(D/r0)2ρϕt.
(D/r0)opt2.037(n+1)
Eopt1.251ρ0(n+1)2.
exp(iϕ)=exp(iϕ)×exp[i(ϕ-ϕ)].
exp(iϕ)=exp(iϕ)1-12 σ2(ϕ)+
exp(iϕ)×exp[-σ2(ϕ)/2].

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