Abstract

We present a method to extract from a single image both object and point spread function using low contrast features of an extended field of view. Invoking the principal ergodic on stochastic turbulent phenomena, we show that the aberration parameters, characteristics of the earth’s turbulence, can be recovered from multiple features within an isoplanatic patch. The ensemble statistics is replacing the spatial statistics of a single realization to derive an equivalent modulation transfer function and to apply usual deconvolution techniques such as Richardson–Lucy algorithms. The reliability of this postprocessing treatment has been tested on synthetic data, on solar granulation observations performed at La Lunette Jean Rosch du Pic du Midi, and during the event of the Venus transit at La Tour Solaire de Meudon.

© 2010 Optical Society of America

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References

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  1. A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).
  2. O. Von Der Luhe, “Wavefront error measurement technique using extended, incoherent light sources,” Opt. Eng. (Bellingham) 27, 1078–1087 (1988).
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    [CrossRef]
  4. E. Thiébaut and J. M. Conan, “Strict a priori constraints for maximum-likelihood blind deconvolution,” J. Opt. Soc. Am. A 12, 485–492 (1995).
    [CrossRef]
  5. M. G. Lofdahl and G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).
  6. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]
  7. R. Gerchberg and W. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  8. R. Gonsalves, “Phase retrieval from modulus data,” J. Opt. Soc. Am. 66, 961–964 (1976).
    [CrossRef]
  9. R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. (Bellingham) 21, 829–832 (1982).
  10. R. A. Gonsalves, “Phase retrieval by differential intensity measurements,” J. Opt. Soc. Am. A 4, 166–170 (1987).
    [CrossRef]
  11. R. Kupke, F. Roddier, and D. L. Mickey, “Wavefront curvature sensing on extended arbitrary scenes: simulation results,” Proc. SPIE 3353, 918–929 (1998).
    [CrossRef]
  12. O. Von Der Luhe, “Speckle imaging of solar small scale structure I—Methods,” Astron. Astrophys. 268, 374–390 (1993).
  13. H. M. Adorf and M. J. Oldfield, “Paralellism for HST image restoration,” in Astronomical Data Analysis Software and Systems I, ASP Conference Series, D.M.Worrall, C.Biemesderfer, and J.Barnes, eds. (1992), Vol. 25, pp. 215–225.
  14. R. White, “Improvements to the Richardson–Lucy-method,” in Newsletter of STScI’s Image Restoration Project (1993), Vol. 1, pp. 11–23.
  15. G. Molodij, F. Roddier, R. Kupke, and D. L. Mickey, “Curvature wavefront sensor for solar adaptive optics,” Sol. Phys. 206, 189–207 (2002).
    [CrossRef]
  16. F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Astron. Soc. Pac. 103, 131–149 (1991).
    [CrossRef]
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    [CrossRef]
  18. F. Roddier, “Error propagation in a close-loop adaptive optics system: a comparison between Shack–Hartmann and curvature wave-front sensor,” Opt. Commun. 113, 357–359 (1995).
    [CrossRef]
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  20. M. Rieutord, T. Roudier, H. G. Ludwig, A. Nordlund, and R. Stein, “Are granules good tracers of solar surface velocity fields?” Astron. Astrophys. 377, L14–L17 (2001).
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    [CrossRef]
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    [CrossRef]
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  24. R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, Site Testing at Tenerife by Balloon Borne Radiosonder and Optical Quality of the Atlantic Air Mass over the Canary Island, Rep. 102 (JOSO, 1973).
  25. T. Roudier, F. Ligniéres, M. Rieutord, P. N. Brandt, and J. M. Malherbe, “Families of fragmenting granules and their relation to meso- and supergranular flow fields,” Astron. Astrophys. 409, 299–308 (2003).
    [CrossRef]
  26. L. J. November, “Measurement of geometric distortion in a turbulent atmosphere,” Appl. Opt. 25, 392–397 (1986).
    [CrossRef] [PubMed]
  27. A. M. Title, T. D. Tarbell, K. P. Topka, S. H. Ferguson, R. A. Shine, and SOUP Team, “Statistical properties of solar granulation derived from the SOUP instrument on Spacelab 2,” Astrophys. J. 336, 475–494 (1989).
    [CrossRef]
  28. N. Meunier, S. Rondi, M. Rieutord, and F. Beigbeder, “CALAS a camera for the large-scale of the solar surface” in ASP Conference Series, K.Sankarasubramanian, M.Pen, and A.Pevtsov, eds. (2005), Vol. 346, p. 53.

2005 (1)

N. Meunier, S. Rondi, M. Rieutord, and F. Beigbeder, “CALAS a camera for the large-scale of the solar surface” in ASP Conference Series, K.Sankarasubramanian, M.Pen, and A.Pevtsov, eds. (2005), Vol. 346, p. 53.

2003 (1)

T. Roudier, F. Ligniéres, M. Rieutord, P. N. Brandt, and J. M. Malherbe, “Families of fragmenting granules and their relation to meso- and supergranular flow fields,” Astron. Astrophys. 409, 299–308 (2003).
[CrossRef]

2002 (1)

G. Molodij, F. Roddier, R. Kupke, and D. L. Mickey, “Curvature wavefront sensor for solar adaptive optics,” Sol. Phys. 206, 189–207 (2002).
[CrossRef]

2001 (1)

M. Rieutord, T. Roudier, H. G. Ludwig, A. Nordlund, and R. Stein, “Are granules good tracers of solar surface velocity fields?” Astron. Astrophys. 377, L14–L17 (2001).
[CrossRef]

1998 (1)

R. Kupke, F. Roddier, and D. L. Mickey, “Wavefront curvature sensing on extended arbitrary scenes: simulation results,” Proc. SPIE 3353, 918–929 (1998).
[CrossRef]

1996 (1)

G. Molodij and J. Rayrole, “Performance analysis for T.H.E.M.I.S (*) image stabilizer optical system. II. Anisoplanatism limitations (*) Telescope héliographique pour l’étude du magnetisme et des instabilites de l’atmosphere solaire,” Astron. Astrophys. Suppl. Ser. 28, 229–244 (1996).

1995 (3)

1994 (1)

M. G. Lofdahl and G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).

1993 (2)

O. Von Der Luhe, “Speckle imaging of solar small scale structure I—Methods,” Astron. Astrophys. 268, 374–390 (1993).

R. White, “Improvements to the Richardson–Lucy-method,” in Newsletter of STScI’s Image Restoration Project (1993), Vol. 1, pp. 11–23.

1992 (1)

H. M. Adorf and M. J. Oldfield, “Paralellism for HST image restoration,” in Astronomical Data Analysis Software and Systems I, ASP Conference Series, D.M.Worrall, C.Biemesderfer, and J.Barnes, eds. (1992), Vol. 25, pp. 215–225.

1991 (1)

F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

1989 (2)

L. Schwartz, Théorie des distributions, (Academic, 1989).

A. M. Title, T. D. Tarbell, K. P. Topka, S. H. Ferguson, R. A. Shine, and SOUP Team, “Statistical properties of solar granulation derived from the SOUP instrument on Spacelab 2,” Astrophys. J. 336, 475–494 (1989).
[CrossRef]

1988 (1)

O. Von Der Luhe, “Wavefront error measurement technique using extended, incoherent light sources,” Opt. Eng. (Bellingham) 27, 1078–1087 (1988).

1987 (1)

1986 (1)

1982 (3)

1978 (1)

1976 (2)

1973 (1)

R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, Site Testing at Tenerife by Balloon Borne Radiosonder and Optical Quality of the Atlantic Air Mass over the Canary Island, Rep. 102 (JOSO, 1973).

1972 (1)

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

1970 (1)

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Adorf, H. M.

H. M. Adorf and M. J. Oldfield, “Paralellism for HST image restoration,” in Astronomical Data Analysis Software and Systems I, ASP Conference Series, D.M.Worrall, C.Biemesderfer, and J.Barnes, eds. (1992), Vol. 25, pp. 215–225.

Baba, N.

Barletti, R.

R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, Site Testing at Tenerife by Balloon Borne Radiosonder and Optical Quality of the Atlantic Air Mass over the Canary Island, Rep. 102 (JOSO, 1973).

Beigbeder, F.

N. Meunier, S. Rondi, M. Rieutord, and F. Beigbeder, “CALAS a camera for the large-scale of the solar surface” in ASP Conference Series, K.Sankarasubramanian, M.Pen, and A.Pevtsov, eds. (2005), Vol. 346, p. 53.

Brandt, P. N.

T. Roudier, F. Ligniéres, M. Rieutord, P. N. Brandt, and J. M. Malherbe, “Families of fragmenting granules and their relation to meso- and supergranular flow fields,” Astron. Astrophys. 409, 299–308 (2003).
[CrossRef]

Ceppatelli, G.

R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, Site Testing at Tenerife by Balloon Borne Radiosonder and Optical Quality of the Atlantic Air Mass over the Canary Island, Rep. 102 (JOSO, 1973).

Conan, J. M.

Ferguson, S. H.

A. M. Title, T. D. Tarbell, K. P. Topka, S. H. Ferguson, R. A. Shine, and SOUP Team, “Statistical properties of solar granulation derived from the SOUP instrument on Spacelab 2,” Astrophys. J. 336, 475–494 (1989).
[CrossRef]

Fienup, J. R.

Gerchberg, R.

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Gonsalves, R.

Gonsalves, R. A.

R. A. Gonsalves, “Phase retrieval by differential intensity measurements,” J. Opt. Soc. Am. A 4, 166–170 (1987).
[CrossRef]

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. (Bellingham) 21, 829–832 (1982).

Graves, J. E.

F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Kupke, R.

G. Molodij, F. Roddier, R. Kupke, and D. L. Mickey, “Curvature wavefront sensor for solar adaptive optics,” Sol. Phys. 206, 189–207 (2002).
[CrossRef]

R. Kupke, F. Roddier, and D. L. Mickey, “Wavefront curvature sensing on extended arbitrary scenes: simulation results,” Proc. SPIE 3353, 918–929 (1998).
[CrossRef]

Labeyrie, A.

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Ligniéres, F.

T. Roudier, F. Ligniéres, M. Rieutord, P. N. Brandt, and J. M. Malherbe, “Families of fragmenting granules and their relation to meso- and supergranular flow fields,” Astron. Astrophys. 409, 299–308 (2003).
[CrossRef]

Lofdahl, M. G.

M. G. Lofdahl and G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).

Ludwig, H. G.

M. Rieutord, T. Roudier, H. G. Ludwig, A. Nordlund, and R. Stein, “Are granules good tracers of solar surface velocity fields?” Astron. Astrophys. 377, L14–L17 (2001).
[CrossRef]

Malherbe, J. M.

T. Roudier, F. Ligniéres, M. Rieutord, P. N. Brandt, and J. M. Malherbe, “Families of fragmenting granules and their relation to meso- and supergranular flow fields,” Astron. Astrophys. 409, 299–308 (2003).
[CrossRef]

Markey, J. K.

Meunier, N.

N. Meunier, S. Rondi, M. Rieutord, and F. Beigbeder, “CALAS a camera for the large-scale of the solar surface” in ASP Conference Series, K.Sankarasubramanian, M.Pen, and A.Pevtsov, eds. (2005), Vol. 346, p. 53.

Mickey, D. L.

G. Molodij, F. Roddier, R. Kupke, and D. L. Mickey, “Curvature wavefront sensor for solar adaptive optics,” Sol. Phys. 206, 189–207 (2002).
[CrossRef]

R. Kupke, F. Roddier, and D. L. Mickey, “Wavefront curvature sensing on extended arbitrary scenes: simulation results,” Proc. SPIE 3353, 918–929 (1998).
[CrossRef]

Miura, N.

Molodij, G.

G. Molodij, F. Roddier, R. Kupke, and D. L. Mickey, “Curvature wavefront sensor for solar adaptive optics,” Sol. Phys. 206, 189–207 (2002).
[CrossRef]

G. Molodij and J. Rayrole, “Performance analysis for T.H.E.M.I.S (*) image stabilizer optical system. II. Anisoplanatism limitations (*) Telescope héliographique pour l’étude du magnetisme et des instabilites de l’atmosphere solaire,” Astron. Astrophys. Suppl. Ser. 28, 229–244 (1996).

Moroder, E.

R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, Site Testing at Tenerife by Balloon Borne Radiosonder and Optical Quality of the Atlantic Air Mass over the Canary Island, Rep. 102 (JOSO, 1973).

Noll, R. J.

Nordlund, A.

M. Rieutord, T. Roudier, H. G. Ludwig, A. Nordlund, and R. Stein, “Are granules good tracers of solar surface velocity fields?” Astron. Astrophys. 377, L14–L17 (2001).
[CrossRef]

Northcott, M.

F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

November, L. J.

Oldfield, M. J.

H. M. Adorf and M. J. Oldfield, “Paralellism for HST image restoration,” in Astronomical Data Analysis Software and Systems I, ASP Conference Series, D.M.Worrall, C.Biemesderfer, and J.Barnes, eds. (1992), Vol. 25, pp. 215–225.

Paterno, L.

R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, Site Testing at Tenerife by Balloon Borne Radiosonder and Optical Quality of the Atlantic Air Mass over the Canary Island, Rep. 102 (JOSO, 1973).

Rayrole, J.

G. Molodij and J. Rayrole, “Performance analysis for T.H.E.M.I.S (*) image stabilizer optical system. II. Anisoplanatism limitations (*) Telescope héliographique pour l’étude du magnetisme et des instabilites de l’atmosphere solaire,” Astron. Astrophys. Suppl. Ser. 28, 229–244 (1996).

Rieutord, M.

N. Meunier, S. Rondi, M. Rieutord, and F. Beigbeder, “CALAS a camera for the large-scale of the solar surface” in ASP Conference Series, K.Sankarasubramanian, M.Pen, and A.Pevtsov, eds. (2005), Vol. 346, p. 53.

T. Roudier, F. Ligniéres, M. Rieutord, P. N. Brandt, and J. M. Malherbe, “Families of fragmenting granules and their relation to meso- and supergranular flow fields,” Astron. Astrophys. 409, 299–308 (2003).
[CrossRef]

M. Rieutord, T. Roudier, H. G. Ludwig, A. Nordlund, and R. Stein, “Are granules good tracers of solar surface velocity fields?” Astron. Astrophys. 377, L14–L17 (2001).
[CrossRef]

Righini, A.

R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, Site Testing at Tenerife by Balloon Borne Radiosonder and Optical Quality of the Atlantic Air Mass over the Canary Island, Rep. 102 (JOSO, 1973).

Roddier, F.

G. Molodij, F. Roddier, R. Kupke, and D. L. Mickey, “Curvature wavefront sensor for solar adaptive optics,” Sol. Phys. 206, 189–207 (2002).
[CrossRef]

R. Kupke, F. Roddier, and D. L. Mickey, “Wavefront curvature sensing on extended arbitrary scenes: simulation results,” Proc. SPIE 3353, 918–929 (1998).
[CrossRef]

F. Roddier, “Error propagation in a close-loop adaptive optics system: a comparison between Shack–Hartmann and curvature wave-front sensor,” Opt. Commun. 113, 357–359 (1995).
[CrossRef]

F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Rondi, S.

N. Meunier, S. Rondi, M. Rieutord, and F. Beigbeder, “CALAS a camera for the large-scale of the solar surface” in ASP Conference Series, K.Sankarasubramanian, M.Pen, and A.Pevtsov, eds. (2005), Vol. 346, p. 53.

Roudier, T.

T. Roudier, F. Ligniéres, M. Rieutord, P. N. Brandt, and J. M. Malherbe, “Families of fragmenting granules and their relation to meso- and supergranular flow fields,” Astron. Astrophys. 409, 299–308 (2003).
[CrossRef]

M. Rieutord, T. Roudier, H. G. Ludwig, A. Nordlund, and R. Stein, “Are granules good tracers of solar surface velocity fields?” Astron. Astrophys. 377, L14–L17 (2001).
[CrossRef]

Saxton, W.

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Scharmer, G. B.

M. G. Lofdahl and G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).

Schwartz, L.

L. Schwartz, Théorie des distributions, (Academic, 1989).

Shine, R. A.

A. M. Title, T. D. Tarbell, K. P. Topka, S. H. Ferguson, R. A. Shine, and SOUP Team, “Statistical properties of solar granulation derived from the SOUP instrument on Spacelab 2,” Astrophys. J. 336, 475–494 (1989).
[CrossRef]

Stein, R.

M. Rieutord, T. Roudier, H. G. Ludwig, A. Nordlund, and R. Stein, “Are granules good tracers of solar surface velocity fields?” Astron. Astrophys. 377, L14–L17 (2001).
[CrossRef]

Tarbell, T. D.

A. M. Title, T. D. Tarbell, K. P. Topka, S. H. Ferguson, R. A. Shine, and SOUP Team, “Statistical properties of solar granulation derived from the SOUP instrument on Spacelab 2,” Astrophys. J. 336, 475–494 (1989).
[CrossRef]

Teague, M.

Thiébaut, E.

Title, A. M.

A. M. Title, T. D. Tarbell, K. P. Topka, S. H. Ferguson, R. A. Shine, and SOUP Team, “Statistical properties of solar granulation derived from the SOUP instrument on Spacelab 2,” Astrophys. J. 336, 475–494 (1989).
[CrossRef]

Topka, K. P.

A. M. Title, T. D. Tarbell, K. P. Topka, S. H. Ferguson, R. A. Shine, and SOUP Team, “Statistical properties of solar granulation derived from the SOUP instrument on Spacelab 2,” Astrophys. J. 336, 475–494 (1989).
[CrossRef]

Von Der Luhe, O.

O. Von Der Luhe, “Speckle imaging of solar small scale structure I—Methods,” Astron. Astrophys. 268, 374–390 (1993).

O. Von Der Luhe, “Wavefront error measurement technique using extended, incoherent light sources,” Opt. Eng. (Bellingham) 27, 1078–1087 (1988).

Wang, J. Y.

White, R.

R. White, “Improvements to the Richardson–Lucy-method,” in Newsletter of STScI’s Image Restoration Project (1993), Vol. 1, pp. 11–23.

Appl. Opt. (2)

Astron. Astrophys. (4)

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

O. Von Der Luhe, “Speckle imaging of solar small scale structure I—Methods,” Astron. Astrophys. 268, 374–390 (1993).

M. Rieutord, T. Roudier, H. G. Ludwig, A. Nordlund, and R. Stein, “Are granules good tracers of solar surface velocity fields?” Astron. Astrophys. 377, L14–L17 (2001).
[CrossRef]

T. Roudier, F. Ligniéres, M. Rieutord, P. N. Brandt, and J. M. Malherbe, “Families of fragmenting granules and their relation to meso- and supergranular flow fields,” Astron. Astrophys. 409, 299–308 (2003).
[CrossRef]

Astron. Astrophys. Suppl. Ser. (2)

G. Molodij and J. Rayrole, “Performance analysis for T.H.E.M.I.S (*) image stabilizer optical system. II. Anisoplanatism limitations (*) Telescope héliographique pour l’étude du magnetisme et des instabilites de l’atmosphere solaire,” Astron. Astrophys. Suppl. Ser. 28, 229–244 (1996).

M. G. Lofdahl and G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).

Astron. Soc. Pac. (1)

F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Astrophys. J. (1)

A. M. Title, T. D. Tarbell, K. P. Topka, S. H. Ferguson, R. A. Shine, and SOUP Team, “Statistical properties of solar granulation derived from the SOUP instrument on Spacelab 2,” Astrophys. J. 336, 475–494 (1989).
[CrossRef]

J. Opt. Soc. Am. (4)

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

Opt. Commun. (1)

F. Roddier, “Error propagation in a close-loop adaptive optics system: a comparison between Shack–Hartmann and curvature wave-front sensor,” Opt. Commun. 113, 357–359 (1995).
[CrossRef]

Opt. Eng. (Bellingham) (2)

O. Von Der Luhe, “Wavefront error measurement technique using extended, incoherent light sources,” Opt. Eng. (Bellingham) 27, 1078–1087 (1988).

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. (Bellingham) 21, 829–832 (1982).

Optik (1)

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Proc. SPIE (1)

R. Kupke, F. Roddier, and D. L. Mickey, “Wavefront curvature sensing on extended arbitrary scenes: simulation results,” Proc. SPIE 3353, 918–929 (1998).
[CrossRef]

Sol. Phys. (1)

G. Molodij, F. Roddier, R. Kupke, and D. L. Mickey, “Curvature wavefront sensor for solar adaptive optics,” Sol. Phys. 206, 189–207 (2002).
[CrossRef]

Other (5)

N. Meunier, S. Rondi, M. Rieutord, and F. Beigbeder, “CALAS a camera for the large-scale of the solar surface” in ASP Conference Series, K.Sankarasubramanian, M.Pen, and A.Pevtsov, eds. (2005), Vol. 346, p. 53.

L. Schwartz, Théorie des distributions, (Academic, 1989).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, Site Testing at Tenerife by Balloon Borne Radiosonder and Optical Quality of the Atlantic Air Mass over the Canary Island, Rep. 102 (JOSO, 1973).

H. M. Adorf and M. J. Oldfield, “Paralellism for HST image restoration,” in Astronomical Data Analysis Software and Systems I, ASP Conference Series, D.M.Worrall, C.Biemesderfer, and J.Barnes, eds. (1992), Vol. 25, pp. 215–225.

R. White, “Improvements to the Richardson–Lucy-method,” in Newsletter of STScI’s Image Restoration Project (1993), Vol. 1, pp. 11–23.

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Figures (14)

Fig. 1
Fig. 1

(A) Reference synthesized image granulation patterns using Rieutord’s algorithms. (B) Simulation of an aberrated granulation image with known OTF (equivalent Fried parameter of 13 cm at 0.5 μ m ). (C) Deconvolution using the ergodic method and Richardson–Lucy (100 iterations). (D) Deconvolution with the known simulated OTF (5000 iterations). Bottom: Intensity profiles along the selected dotted lines (color correspondence with upper images).

Fig. 2
Fig. 2

Extraction of the isotropic reference in a single image composed of different structures where the Laplacian irradiance is high. The segmentation method yields the quasi-point artifact on axis that is an estimation of the modulation transfer function. (A) Single synthesized granulation image through the atmospheric turbulence ( r 0 : 13 cm). (B) Mean spatial isotropic reference composed of 10 targets. (C) 100 targets. (D) 1000 targets. Bottom: Intensity profiles along the selected dotted line from Image (A) in black. Superimposed, closely identical intensity profiles after deconvolution using the ergodic method with 10 (red solid line) and 1000 (green solid line) targets.

Fig. 3
Fig. 3

Examples of deconvolution using Richardson–Lucy (100 iterations) with the retrieved OTF when using the ergodic method. (A) Reference synthesized image granulation patterns using Rieutord’s algorithms. (B) Deconvolution for terrestrial turbulent condition ( r 0 = 10   cm at 0.5 μ m ). (C) Deconvolution for r 0 = 13   cm . (D) Deconvolution for r 0 = 22   cm . Bottom: Intensity profiles along the selected dotted lines (color correspondence with upper images).

Fig. 4
Fig. 4

Comparison of intensity profiles along the same selected lines across the granulation image for different atmospheric turbulence conditions (from top to bottom: r 0 = 10 , 13, 18, and 22 cm at 0.5 μ m ). Black dotted lines are for the reference intensity without turbulence. Blue dotted lines are for intensity through the simulated turbulences. Red solid lines correspond to the intensity profiles using the retrieved OTF from the ergodic deconvolution method, while green solid lines correspond to the deconvolution with known OTFs.

Fig. 5
Fig. 5

Top: Solar granulation images (field of view of 16 arc sec) after and before restoration (top left and right, respectively). Bottom: Corresponding normalized intensity profiles across the horizontal direction (80 pixels) at the center of the image (continuous line for the left image and dotted line corresponding to the right). Richardson–Lucy algorithm and retrieved MTF are applied on the original granulation image shown on the right panel (recorded at moderate rate cadency at La Lunette Jean Rosch on July 21, 2005 at 8:39 UT). The rms contrast is 4.3% before restoration (right) and 8.3% afterward (left).

Fig. 6
Fig. 6

Best (left panels) and worst (right panels) images of the sequence at 8:39 UT before restoration (top) and after restoration (bottom). In both cases, the contrast gain is about a factor of 2. High resolution details (center of the black zone) appear only on best quality images of the sequence after restoration. (a) Best image, contrast: 4.3%. (b) Worst image, contrast: 3.5%. (c) Deconvolution of the best image, contrast: 8.3%. (d) Deconvolution of the worst image, contrast: 8.1%.

Fig. 7
Fig. 7

Rms contrast versus the image’s number in the sequence before and after deconvolution. Blue crosses [the contrast is ( 4.3 ± 0.8 ) % ] and black stars [the contrast is ( 8.3 ± 0.08 ) % ] are for a set of 50 images of a 30 s sequence. The red line corresponds to the restoration of the mean image after the removal of seeing distortions and intensity fluctuations (the contrast is 8.1%).

Fig. 8
Fig. 8

Comparison between the best restored image (top right) and the restored mean image (top left). High resolution details appear on the center dark part of the image after the postprocessing and the analysis of the entire sequence. The rms contrast value is 8.3% for the best restored image, while the value is 8.1% for the restored mean image.

Fig. 9
Fig. 9

Rms contrast gain after restoration of the mean image (on the set of 50 frames) versus the rms contrast of the images before deconvolution for 19 different sequences (different fields of view) performed at La Lunette Jean Rosch between 6:24 and 8:39 UT.

Fig. 10
Fig. 10

Deconvolution of static and turbulence aberrations on Venus during its transit across the Sun disk using Richardson–Lucy algorithm (100 iterations) and the retrieved MTF from the granulation surrounding the planet. Observations were performed on June 8, 2004 at La Tour Solaire de l’Observatoire de Paris-Meudon in the G band. The diameter of Venus is 21 arc sec. The deconvolved rms granulation contrast becomes 5.9% (instead of 2.9% before).

Fig. 11
Fig. 11

Intensity profiles across the diameter of the Venus disk before (solid black line) and after (dotted red line) deconvolution. One can remark the static aberrations on the peculiar shape of the Venus disk before deconvolution. The scatter light is compensated during the deconvolution process as indicated by the intensity level on the disk. The large-scale intensity variation is due to the center to limb variation of the Sun.

Fig. 12
Fig. 12

Detection of the refraction of the Sun light by Venus atmosphere (Venus arc) after deconvolution (between the third and the fourth contacts at 11 h 07 TU, Observatoire de Paris-Meudon). The arc intensity close to the detector noise limit is artificially enhanced to be clearly visible on the image.

Fig. 13
Fig. 13

Intensity profiles across the Venus disk after (solid black line) and before (dotted red line) deconvolution. The correction of static aberrations and scatter light with the determination of the MTF from the Sun granulation allows the detection of the Venus atmosphere arc on the background.

Fig. 14
Fig. 14

Postprocessing on extended and complex field of view using the proposed method. This active region was observed at La Lunette Jean Rosch, 21st of September 2000, 11 h 21 TU. 10° north, 37° east; λ = 5780   Å . The field of view on the solar surface is 102 , 000 × 57 , 000   km . The resolution is 0.23 arc sec corresponding to 170 km on the Sun. The detector is a pixelink CMOS ( 1240 × 1024   pixels ) .

Tables (2)

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Table 1 Estimation of the Image Quality with the rms Contrast Criteria a

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Table 2 Estimation of the Standard Deviation a

Equations (4)

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I ( r ) = O ( r ) P ( r ) = O ( r ) P ( r r ) d r ,
i I i ( r ) = i O i ( r ) P ( r r ) d r = P ( r r ) O ( r ) ¯ d r .
i I i ( r ) = P ̂ ( ν ν ) O ̂ ( ν ) ¯ d ν .
P ̂ ( ν ) , δ ( ν ν o ) = P ̂ ( ν ) ν = ν o ,

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