Abstract

Current optical interferometers are affected by unknown turbulent phases on each telescope. We account for this lack of phase information by introducing system aberration parameters, and we solve the image reconstruction problem by minimizing an original joint criterion in the aberrations and in the object. We validate this method by means of simulations. Tests on experimental data are under way.

© 2005 Optical Society of America

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References

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  1. T. J. Cornwell and P. N. Wilkinson, Mon. Not. R. Astron. Soc. 196, 1067 (1981).
    [CrossRef]
  2. S. Meimon, L. M. Mugnier, and G. Le Besnerais, “A convex approximation of the likelihood in optical interferometry,” J. Opt. Soc. Am. A (to be published).
  3. L. M. Mugnier, T. Fusco, and J.-M. Conan, J. Opt. Soc. Am. A 21, 1841 (2004).
    [CrossRef]
  4. F. Roddier, Opt. Commun. 60, 145 (1986).
    [CrossRef]
  5. S. Meimon, L. Mugnier, and G. Le Besnerais, in 19ième Colloque sur le Traitement du Signal et des Images, J.-M. Chassery and C. Jutten, eds. (GRETSI, 2003).
  6. W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes in C (Cambridge U. Press, 1988).
  7. A. Lannes, J. Opt. Soc. Am. A 15, 811 (1998).
    [CrossRef]
  8. E. Thiebaut, Proc. SPIE 4847, 174 (2002).
    [CrossRef]
  9. D. M. Titterington, Astron. Astrophys. 144, 381 (1985).
  10. G. Demoment, IEEE Trans. Acoust., Speech, Signal Process. 37, 2024 (1989).
    [CrossRef]
  11. C. Bouman and K. Sauer, IEEE Trans. Image Process. 2, 296 (1993).
    [CrossRef]
  12. P. J. Green, IEEE Trans. Med. Imaging 9, 84 (1990).
    [CrossRef]
  13. P. R. Lawson, W. D. Cotton, C. A. Hummel, J. D. Monnier, M. Zhao, J. S. Young, H. Thorsteinsson, S. Meimon, L. Mugnier, G. Le Besnerais, E. Thiébaut, and P. G. Tuthill, Proc. SPIE 5491, 886 (2004).
    [CrossRef]
  14. http://www.sc.eso.org/~chummel/oyster/oyster.html.

2004 (2)

L. M. Mugnier, T. Fusco, and J.-M. Conan, J. Opt. Soc. Am. A 21, 1841 (2004).
[CrossRef]

P. R. Lawson, W. D. Cotton, C. A. Hummel, J. D. Monnier, M. Zhao, J. S. Young, H. Thorsteinsson, S. Meimon, L. Mugnier, G. Le Besnerais, E. Thiébaut, and P. G. Tuthill, Proc. SPIE 5491, 886 (2004).
[CrossRef]

2002 (1)

E. Thiebaut, Proc. SPIE 4847, 174 (2002).
[CrossRef]

1998 (1)

1993 (1)

C. Bouman and K. Sauer, IEEE Trans. Image Process. 2, 296 (1993).
[CrossRef]

1990 (1)

P. J. Green, IEEE Trans. Med. Imaging 9, 84 (1990).
[CrossRef]

1989 (1)

G. Demoment, IEEE Trans. Acoust., Speech, Signal Process. 37, 2024 (1989).
[CrossRef]

1986 (1)

F. Roddier, Opt. Commun. 60, 145 (1986).
[CrossRef]

1985 (1)

D. M. Titterington, Astron. Astrophys. 144, 381 (1985).

1981 (1)

T. J. Cornwell and P. N. Wilkinson, Mon. Not. R. Astron. Soc. 196, 1067 (1981).
[CrossRef]

Bouman, C.

C. Bouman and K. Sauer, IEEE Trans. Image Process. 2, 296 (1993).
[CrossRef]

Conan, J.-M.

Cornwell, T. J.

T. J. Cornwell and P. N. Wilkinson, Mon. Not. R. Astron. Soc. 196, 1067 (1981).
[CrossRef]

Cotton, W. D.

P. R. Lawson, W. D. Cotton, C. A. Hummel, J. D. Monnier, M. Zhao, J. S. Young, H. Thorsteinsson, S. Meimon, L. Mugnier, G. Le Besnerais, E. Thiébaut, and P. G. Tuthill, Proc. SPIE 5491, 886 (2004).
[CrossRef]

Demoment, G.

G. Demoment, IEEE Trans. Acoust., Speech, Signal Process. 37, 2024 (1989).
[CrossRef]

Flannery, B.

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes in C (Cambridge U. Press, 1988).

Fusco, T.

Green, P. J.

P. J. Green, IEEE Trans. Med. Imaging 9, 84 (1990).
[CrossRef]

Hummel, C. A.

P. R. Lawson, W. D. Cotton, C. A. Hummel, J. D. Monnier, M. Zhao, J. S. Young, H. Thorsteinsson, S. Meimon, L. Mugnier, G. Le Besnerais, E. Thiébaut, and P. G. Tuthill, Proc. SPIE 5491, 886 (2004).
[CrossRef]

Lannes, A.

Lawson, P. R.

P. R. Lawson, W. D. Cotton, C. A. Hummel, J. D. Monnier, M. Zhao, J. S. Young, H. Thorsteinsson, S. Meimon, L. Mugnier, G. Le Besnerais, E. Thiébaut, and P. G. Tuthill, Proc. SPIE 5491, 886 (2004).
[CrossRef]

Le Besnerais, G.

P. R. Lawson, W. D. Cotton, C. A. Hummel, J. D. Monnier, M. Zhao, J. S. Young, H. Thorsteinsson, S. Meimon, L. Mugnier, G. Le Besnerais, E. Thiébaut, and P. G. Tuthill, Proc. SPIE 5491, 886 (2004).
[CrossRef]

S. Meimon, L. Mugnier, and G. Le Besnerais, in 19ième Colloque sur le Traitement du Signal et des Images, J.-M. Chassery and C. Jutten, eds. (GRETSI, 2003).

S. Meimon, L. M. Mugnier, and G. Le Besnerais, “A convex approximation of the likelihood in optical interferometry,” J. Opt. Soc. Am. A (to be published).

Meimon, S.

P. R. Lawson, W. D. Cotton, C. A. Hummel, J. D. Monnier, M. Zhao, J. S. Young, H. Thorsteinsson, S. Meimon, L. Mugnier, G. Le Besnerais, E. Thiébaut, and P. G. Tuthill, Proc. SPIE 5491, 886 (2004).
[CrossRef]

S. Meimon, L. M. Mugnier, and G. Le Besnerais, “A convex approximation of the likelihood in optical interferometry,” J. Opt. Soc. Am. A (to be published).

S. Meimon, L. Mugnier, and G. Le Besnerais, in 19ième Colloque sur le Traitement du Signal et des Images, J.-M. Chassery and C. Jutten, eds. (GRETSI, 2003).

Monnier, J. D.

P. R. Lawson, W. D. Cotton, C. A. Hummel, J. D. Monnier, M. Zhao, J. S. Young, H. Thorsteinsson, S. Meimon, L. Mugnier, G. Le Besnerais, E. Thiébaut, and P. G. Tuthill, Proc. SPIE 5491, 886 (2004).
[CrossRef]

Mugnier, L.

P. R. Lawson, W. D. Cotton, C. A. Hummel, J. D. Monnier, M. Zhao, J. S. Young, H. Thorsteinsson, S. Meimon, L. Mugnier, G. Le Besnerais, E. Thiébaut, and P. G. Tuthill, Proc. SPIE 5491, 886 (2004).
[CrossRef]

S. Meimon, L. Mugnier, and G. Le Besnerais, in 19ième Colloque sur le Traitement du Signal et des Images, J.-M. Chassery and C. Jutten, eds. (GRETSI, 2003).

Mugnier, L. M.

L. M. Mugnier, T. Fusco, and J.-M. Conan, J. Opt. Soc. Am. A 21, 1841 (2004).
[CrossRef]

S. Meimon, L. M. Mugnier, and G. Le Besnerais, “A convex approximation of the likelihood in optical interferometry,” J. Opt. Soc. Am. A (to be published).

Press, W.

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes in C (Cambridge U. Press, 1988).

Roddier, F.

F. Roddier, Opt. Commun. 60, 145 (1986).
[CrossRef]

Sauer, K.

C. Bouman and K. Sauer, IEEE Trans. Image Process. 2, 296 (1993).
[CrossRef]

Teukolsky, S.

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes in C (Cambridge U. Press, 1988).

Thiebaut, E.

E. Thiebaut, Proc. SPIE 4847, 174 (2002).
[CrossRef]

Thiébaut, E.

P. R. Lawson, W. D. Cotton, C. A. Hummel, J. D. Monnier, M. Zhao, J. S. Young, H. Thorsteinsson, S. Meimon, L. Mugnier, G. Le Besnerais, E. Thiébaut, and P. G. Tuthill, Proc. SPIE 5491, 886 (2004).
[CrossRef]

Thorsteinsson, H.

P. R. Lawson, W. D. Cotton, C. A. Hummel, J. D. Monnier, M. Zhao, J. S. Young, H. Thorsteinsson, S. Meimon, L. Mugnier, G. Le Besnerais, E. Thiébaut, and P. G. Tuthill, Proc. SPIE 5491, 886 (2004).
[CrossRef]

Titterington, D. M.

D. M. Titterington, Astron. Astrophys. 144, 381 (1985).

Tuthill, P. G.

P. R. Lawson, W. D. Cotton, C. A. Hummel, J. D. Monnier, M. Zhao, J. S. Young, H. Thorsteinsson, S. Meimon, L. Mugnier, G. Le Besnerais, E. Thiébaut, and P. G. Tuthill, Proc. SPIE 5491, 886 (2004).
[CrossRef]

Vetterling, W.

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes in C (Cambridge U. Press, 1988).

Wilkinson, P. N.

T. J. Cornwell and P. N. Wilkinson, Mon. Not. R. Astron. Soc. 196, 1067 (1981).
[CrossRef]

Young, J. S.

P. R. Lawson, W. D. Cotton, C. A. Hummel, J. D. Monnier, M. Zhao, J. S. Young, H. Thorsteinsson, S. Meimon, L. Mugnier, G. Le Besnerais, E. Thiébaut, and P. G. Tuthill, Proc. SPIE 5491, 886 (2004).
[CrossRef]

Zhao, M.

P. R. Lawson, W. D. Cotton, C. A. Hummel, J. D. Monnier, M. Zhao, J. S. Young, H. Thorsteinsson, S. Meimon, L. Mugnier, G. Le Besnerais, E. Thiébaut, and P. G. Tuthill, Proc. SPIE 5491, 886 (2004).
[CrossRef]

Astron. Astrophys. (1)

D. M. Titterington, Astron. Astrophys. 144, 381 (1985).

IEEE Trans. Acoust., Speech, Signal Process. (1)

G. Demoment, IEEE Trans. Acoust., Speech, Signal Process. 37, 2024 (1989).
[CrossRef]

IEEE Trans. Image Process. (1)

C. Bouman and K. Sauer, IEEE Trans. Image Process. 2, 296 (1993).
[CrossRef]

IEEE Trans. Med. Imaging (1)

P. J. Green, IEEE Trans. Med. Imaging 9, 84 (1990).
[CrossRef]

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

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

T. J. Cornwell and P. N. Wilkinson, Mon. Not. R. Astron. Soc. 196, 1067 (1981).
[CrossRef]

Opt. Commun. (1)

F. Roddier, Opt. Commun. 60, 145 (1986).
[CrossRef]

Proc. SPIE (2)

E. Thiebaut, Proc. SPIE 4847, 174 (2002).
[CrossRef]

P. R. Lawson, W. D. Cotton, C. A. Hummel, J. D. Monnier, M. Zhao, J. S. Young, H. Thorsteinsson, S. Meimon, L. Mugnier, G. Le Besnerais, E. Thiébaut, and P. G. Tuthill, Proc. SPIE 5491, 886 (2004).
[CrossRef]

Other (4)

http://www.sc.eso.org/~chummel/oyster/oyster.html.

S. Meimon, L. M. Mugnier, and G. Le Besnerais, “A convex approximation of the likelihood in optical interferometry,” J. Opt. Soc. Am. A (to be published).

S. Meimon, L. Mugnier, and G. Le Besnerais, in 19ième Colloque sur le Traitement du Signal et des Images, J.-M. Chassery and C. Jutten, eds. (GRETSI, 2003).

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes in C (Cambridge U. Press, 1988).

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Figures (2)

Fig. 1
Fig. 1

WISARD algorithm loop.

Fig. 2
Fig. 2

Original object and reconstruction maps.

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

ν i ( 12 ) = T 1 T 2 λ , ν i ( 23 ) = T 2 T 3 λ , ν i ( 31 ) = T 3 T 1 λ .
V 0 ( X ) = H X .
V i ( 12 ) = V 0 i ( 12 ) exp i [ α i ( 2 ) α i ( 1 ) ] ,
V i ( 23 ) = V 0 i ( 23 ) exp { i [ α i ( 3 ) α i ( 2 ) ] } ,
V i ( 31 ) = V 0 i ( 31 ) exp { i [ α i ( 1 ) α i ( 3 ) ] } .
φ i ( 12 ) = φ 0 i ( 12 ) + α i ( 2 ) α i ( 1 ) ,
φ i ( 23 ) = φ 0 i ( 23 ) + α i ( 3 ) α i ( 2 ) ,
φ i ( 31 ) = φ 0 i ( 31 ) + α i ( 1 ) α i ( 3 ) .
C i = arg V i ( 12 ) + arg V i ( 23 ) + arg V i ( 31 ) ,
= φ i ( 12 ) + φ i ( 23 ) + φ i ( 31 ) ,
= φ 0 i ( 12 ) + φ 0 i ( 23 ) + φ 0 i ( 31 ) ,
C mes = Ω ( H X ) + Gaussian noise ,
A mes = H X + Gaussian noise .
φ mes i ( 12 ) = φ 0 i ( 12 ) + β 1 i + Gaussian noise ,
φ mes i ( 23 ) = φ 0 i ( 23 ) + β 2 i + Gaussian noise ,
φ mes i ( 31 ) = φ 0 i ( 31 ) β 1 i β 2 i + Gaussian noise ,
φ mes = arg H X + β + Gaussian noise .
C mes i = φ 0 i ( 12 ) + φ 0 i ( 23 ) + φ 0 i ( 31 ) + Gaussian noise ,
V mes = A mes e i φ mes ,
V ( X , β ) = H X exp [ i ( arg H X + β ) ] ,
J ell ( X , β ) = V mes V ( X , β ) C b 2 .
J ell ( X , β ) = i = 1 n a J ell i ( X , β 1 i , β 2 i ) .

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