Abstract

Adaptive optics systems provide a real-time compensation for atmospheric turbulence. However, the correction is often only partial, and a deconvolution is required for reaching the diffraction limit. The need for a regularized deconvolution is discussed, and such a deconvolution technique is presented. This technique incorporates a positivity constraint and some a priori knowledge of the object (an estimate of its local mean and a model for its power spectral density). This method is then extended to the case of an unknown point-spread function, still taking advantage of similar a priori information on the point-spread function. Deconvolution results are presented for both simulated and experimental data.

© 1998 Optical Society of America

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    [CrossRef]
  43. Y.-L. You, M. Kaveh, “A regularization approach to joint blur identification and image restoration,” IEEE Trans. Image Process. 5, 416–428 (1996).
    [CrossRef] [PubMed]
  44. J. C. Dainty, A. H. Greenaway, “Estimation of spatial power spectra in speckle interferometry,” J. Opt. Soc. Am. A 69, 786–790 (1979).
    [CrossRef]
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  48. C. Dumas, O. R. Hainaut, “Mapping Vesta with adaptive optics: the 1996 opposition,” Bull. Am. Astron. Soc. 28, 1101 (1996).

1997 (2)

P. Y. Madec, D. Rabaud, B. Fleury, J. M. Conan, L. Rousset-Rouvière, F. Mendez, J. Montri, V. Michau, G. Rousset, M. Séchaud, “Essais du banc d’optique adaptative ONERA à l’OHP,” Lett. Observatoire de Haute Provence 16, 2–3 (1997).

J.-P. Véran, F. Rigaut, H. Maı̂tre, D. Rouan, “Estimation of the adaptive optics long-exposure point-spread function using control loop data,” J. Opt. Soc. Am. A 14, 3057–3069 (1997).
[CrossRef]

1996 (3)

C. Dumas, O. R. Hainaut, “Mapping Vesta with adaptive optics: the 1996 opposition,” Bull. Am. Astron. Soc. 28, 1101 (1996).

Y.-L. You, M. Kaveh, “A regularization approach to joint blur identification and image restoration,” IEEE Trans. Image Process. 5, 416–428 (1996).
[CrossRef] [PubMed]

R. G. Lane, “Methods for maximum-likelihood deconvolution,” J. Opt. Soc. Am. A 13, 1992–1998 (1996).
[CrossRef]

1995 (1)

1993 (3)

T. J. Schultz, “Multiframe blind deconvolution of astronomical images,” J. Opt. Soc. Am. A 10, 1064–1073 (1993).
[CrossRef]

S. M. Jefferies, J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astrophys. J. 415, 862–874 (1993).
[CrossRef]

J. Nunez, J. Llacer, “A general Bayesian image reconstruction algorithm with entropy prior: preliminary application to HST data,” Publ. Astron. Soc. Pac. 105, 1192–1208 (1993).
[CrossRef]

1992 (3)

1991 (2)

F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration for fidelity and visual quality,” Comput. Vision Graphics Image Process. 53, 71–84 (1991).

F. Rigaut, G. Rousset, P. Kern, J.-C. Fontanella, J.-P. Gaffard, F. Merkle, P. Léna, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

1990 (2)

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

J. Primot, G. Rousset, J.-C. Fontanella, “Deconvolution from wavefront sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1598–1608 (1990).
[CrossRef]

1989 (1)

G. Demoment, “Image reconstruction and restoration: overview of common estimation structures and problems,” IEEE Trans. Acoust. Speech Signal Process. 37, 2024–2036 (1989).
[CrossRef]

1988 (1)

1987 (1)

1985 (1)

D. M. Titterington, “General structure of regularization procedures in image reconstruction,” Astron. Astrophys. 144, 381–387 (1985).

1981 (1)

M. Z. Nashed, “Operator-theoretic and computational approaches to ill-posed problems with applications to antenna theory,” IEEE Trans. Antennas Propag. AP-29, 220–231 (1981).
[CrossRef]

1979 (1)

J. C. Dainty, A. H. Greenaway, “Estimation of spatial power spectra in speckle interferometry,” J. Opt. Soc. Am. A 69, 786–790 (1979).
[CrossRef]

1977 (3)

J. W. Hardy, J. E. Lefevbre, C. L. Koliopoulos, “Real time atmospheric compensation,” J. Opt. Soc. Am. 67, 360–369 (1977).
[CrossRef]

B. R. Hunt, “Bayesian methods in nonlinear digital image restoration,” IEEE Trans. Comput. C-26, 219–229 (1977).
[CrossRef]

G. Weigelt, “Modified astronomical speckle interferometry speckle masking,” Opt. Commun. 21, 55–59 (1977).
[CrossRef]

1975 (1)

A. Papoulis, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Syst. CS-22, 735 (1975).
[CrossRef]

1974 (3)

K. T. Knox, B. J. Thompson, “Recovery of images from atmospherically degraded short exposure photographs,” Astrophys. J. Lett. 193, L45–L48 (1974).
[CrossRef]

R. W. Gerchberg, “Super-resolution through error energy reduction,” Opt. Acta 21, 709–720 (1974).
[CrossRef]

L. B. Lucy, “An iterative technique for rectification of observed distributions,” Astrophys. J. 79, 745–754 (1974).

1973 (1)

B. R. Hunt, “The application of constrained least squares estimation to image restoration by digital computer,” IEEE Trans. Comput. C-22, 805–812 (1973).
[CrossRef]

1972 (2)

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

W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62, 55–59 (1972).
[CrossRef]

1970 (1)

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

1965 (1)

1962 (1)

D. L. Phillips, “A technique for the numerical solution of certain integral equations of the first kind,” J. Assoc. Comput. Mach. 9, 84–97 (1962).
[CrossRef]

Ageorges, N.

J. C. Christou, D. Bonaccini, N. Ageorges, “Deconvolution of adaptive optics near-infrared system (ADONIS) images,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 68–80 (1997).
[CrossRef]

Alter-Gartenberg, R.

F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration for fidelity and visual quality,” Comput. Vision Graphics Image Process. 53, 71–84 (1991).

Arsenin, V.

A. Tikhonov, V. Arsenin, Solutions of Ill-Posed Problems (Winston, Washington, D.C., 1977).

Ayers, G. R.

Bonaccini, D.

J. C. Christou, D. Bonaccini, N. Ageorges, “Deconvolution of adaptive optics near-infrared system (ADONIS) images,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 68–80 (1997).
[CrossRef]

Boyer, C.

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

Christou, J. C.

S. M. Jefferies, J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astrophys. J. 415, 862–874 (1993).
[CrossRef]

J. C. Christou, D. Bonaccini, N. Ageorges, “Deconvolution of adaptive optics near-infrared system (ADONIS) images,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 68–80 (1997).
[CrossRef]

Conan, J. M.

P. Y. Madec, D. Rabaud, B. Fleury, J. M. Conan, L. Rousset-Rouvière, F. Mendez, J. Montri, V. Michau, G. Rousset, M. Séchaud, “Essais du banc d’optique adaptative ONERA à l’OHP,” Lett. Observatoire de Haute Provence 16, 2–3 (1997).

Conan, J.-M.

E. Thiébaut, J.-M. Conan, “Strict a priori constraints for maximum-likelihood blind deconvolution,” J. Opt. Soc. Am. A 12, 485–492 (1995).
[CrossRef]

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

J.-M. Conan, P.-Y. Madec, G. Rousset, “Image formation in adaptive optics partial correction,” in Active and Adaptive Optics, F. Merkle, ed., Vol. 48 of ESO Conference and Workshop Proceedings (European Southern Observatory, Garching, Germany, 1993), pp. 181–186.

Dainty, J. C.

G. R. Ayers, J. C. Dainty, “Iterative blind deconvolution and its applications,” Opt. Lett. 13, 547–549 (1988).
[CrossRef] [PubMed]

J. C. Dainty, A. H. Greenaway, “Estimation of spatial power spectra in speckle interferometry,” J. Opt. Soc. Am. A 69, 786–790 (1979).
[CrossRef]

Demoment, G.

G. Demoment, “Image reconstruction and restoration: overview of common estimation structures and problems,” IEEE Trans. Acoust. Speech Signal Process. 37, 2024–2036 (1989).
[CrossRef]

Dumas, C.

C. Dumas, O. R. Hainaut, “Mapping Vesta with adaptive optics: the 1996 opposition,” Bull. Am. Astron. Soc. 28, 1101 (1996).

C. Dumas, O. R. Hainaut, “Mapping Vesta in the visible and near-infrared: the 1994 and 1996 oppositions as viewed from the ground,” in Evolution of Igneous Asteroids: Focus on Vesta and the HED Meteorites, D. W. Mittlefehldt, J. J. Papike, eds., Lunar and Planetary Institute Tech. Rep. 96-02(1) (Lunar and Planetary Institute, Houston, Tex., 1996), pp. 7–8.

Fleury, B.

P. Y. Madec, D. Rabaud, B. Fleury, J. M. Conan, L. Rousset-Rouvière, F. Mendez, J. Montri, V. Michau, G. Rousset, M. Séchaud, “Essais du banc d’optique adaptative ONERA à l’OHP,” Lett. Observatoire de Haute Provence 16, 2–3 (1997).

Fontanella, J.-C.

F. Rigaut, G. Rousset, P. Kern, J.-C. Fontanella, J.-P. Gaffard, F. Merkle, P. Léna, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

J. Primot, G. Rousset, J.-C. Fontanella, “Deconvolution from wavefront sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1598–1608 (1990).
[CrossRef]

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

Fried, D. L.

Gaffard, J.-P.

F. Rigaut, G. Rousset, P. Kern, J.-C. Fontanella, J.-P. Gaffard, F. Merkle, P. Léna, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

Gerchberg, R. W.

R. W. Gerchberg, “Super-resolution through error energy reduction,” Opt. Acta 21, 709–720 (1974).
[CrossRef]

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

Gigan, P.

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley-Interscience, New York, 1985), Chap. 8.

Greenaway, A. H.

J. C. Dainty, A. H. Greenaway, “Estimation of spatial power spectra in speckle interferometry,” J. Opt. Soc. Am. A 69, 786–790 (1979).
[CrossRef]

Hainaut, O. R.

C. Dumas, O. R. Hainaut, “Mapping Vesta with adaptive optics: the 1996 opposition,” Bull. Am. Astron. Soc. 28, 1101 (1996).

C. Dumas, O. R. Hainaut, “Mapping Vesta in the visible and near-infrared: the 1994 and 1996 oppositions as viewed from the ground,” in Evolution of Igneous Asteroids: Focus on Vesta and the HED Meteorites, D. W. Mittlefehldt, J. J. Papike, eds., Lunar and Planetary Institute Tech. Rep. 96-02(1) (Lunar and Planetary Institute, Houston, Tex., 1996), pp. 7–8.

Hardy, J. W.

Holmes, T. J.

Huck, F. O.

F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration for fidelity and visual quality,” Comput. Vision Graphics Image Process. 53, 71–84 (1991).

Hunt, B. R.

B. R. Hunt, “Bayesian methods in nonlinear digital image restoration,” IEEE Trans. Comput. C-26, 219–229 (1977).
[CrossRef]

B. R. Hunt, “The application of constrained least squares estimation to image restoration by digital computer,” IEEE Trans. Comput. C-22, 805–812 (1973).
[CrossRef]

Jagourel, P.

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, New Jersey, 1989), Chap. 2.

Jefferies, S. M.

S. M. Jefferies, J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astrophys. J. 415, 862–874 (1993).
[CrossRef]

Kattnig, A. P.

A. P. Kattnig, J. Primot, “Model of the second-order statistic of the radiance field of natural scenes, adapted to system conceiving,” in Visual Information Processing VI, S. K. Park, R. D. Juday, eds., Proc. SPIE3074, 132–141 (1997).
[CrossRef]

Kaveh, M.

Y.-L. You, M. Kaveh, “A regularization approach to joint blur identification and image restoration,” IEEE Trans. Image Process. 5, 416–428 (1996).
[CrossRef] [PubMed]

Kern, P.

F. Rigaut, G. Rousset, P. Kern, J.-C. Fontanella, J.-P. Gaffard, F. Merkle, P. Léna, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

Knox, K. T.

K. T. Knox, B. J. Thompson, “Recovery of images from atmospherically degraded short exposure photographs,” Astrophys. J. Lett. 193, L45–L48 (1974).
[CrossRef]

Koliopoulos, C. L.

Labeyrie, A.

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

Lane, R. G.

Lefevbre, J. E.

Léna, P.

F. Rigaut, G. Rousset, P. Kern, J.-C. Fontanella, J.-P. Gaffard, F. Merkle, P. Léna, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

Levi, A.

A. Levi, H. Stark, “Restoration from phase and magnitude by generalized projections,” in Image Recovery: Theory and Application, H. Stark, ed. (Academic, New York, 1987), Chap. 8, pp. 277–320.

Llacer, J.

J. Nunez, J. Llacer, “A general Bayesian image reconstruction algorithm with entropy prior: preliminary application to HST data,” Publ. Astron. Soc. Pac. 105, 1192–1208 (1993).
[CrossRef]

Lucy, L. B.

L. B. Lucy, “An iterative technique for rectification of observed distributions,” Astrophys. J. 79, 745–754 (1974).

Madec, P. Y.

P. Y. Madec, D. Rabaud, B. Fleury, J. M. Conan, L. Rousset-Rouvière, F. Mendez, J. Montri, V. Michau, G. Rousset, M. Séchaud, “Essais du banc d’optique adaptative ONERA à l’OHP,” Lett. Observatoire de Haute Provence 16, 2–3 (1997).

Madec, P.-Y.

J.-M. Conan, P.-Y. Madec, G. Rousset, “Image formation in adaptive optics partial correction,” in Active and Adaptive Optics, F. Merkle, ed., Vol. 48 of ESO Conference and Workshop Proceedings (European Southern Observatory, Garching, Germany, 1993), pp. 181–186.

Mai^tre, H.

J.-P. Véran, F. Rigaut, H. Maı̂tre, D. Rouan, “Estimation of the adaptive optics long-exposure point-spread function using control loop data,” J. Opt. Soc. Am. A 14, 3057–3069 (1997).
[CrossRef]

J.-P. Véran, F. Rigaut, H. Maı̂tre, “Adaptive optics long exposure point spread function retrieval from wavefront sensor measurements,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference and Workshop Proceedings (European Southern Observatory, Garching, Germany, 1995), pp. 497–502.

Matson, C. L.

Mendez, F.

P. Y. Madec, D. Rabaud, B. Fleury, J. M. Conan, L. Rousset-Rouvière, F. Mendez, J. Montri, V. Michau, G. Rousset, M. Séchaud, “Essais du banc d’optique adaptative ONERA à l’OHP,” Lett. Observatoire de Haute Provence 16, 2–3 (1997).

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F. Rigaut, G. Rousset, P. Kern, J.-C. Fontanella, J.-P. Gaffard, F. Merkle, P. Léna, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

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P. Y. Madec, D. Rabaud, B. Fleury, J. M. Conan, L. Rousset-Rouvière, F. Mendez, J. Montri, V. Michau, G. Rousset, M. Séchaud, “Essais du banc d’optique adaptative ONERA à l’OHP,” Lett. Observatoire de Haute Provence 16, 2–3 (1997).

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A. Papoulis, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Syst. CS-22, 735 (1975).
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J. Primot, G. Rousset, J.-C. Fontanella, “Deconvolution from wavefront sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1598–1608 (1990).
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A. P. Kattnig, J. Primot, “Model of the second-order statistic of the radiance field of natural scenes, adapted to system conceiving,” in Visual Information Processing VI, S. K. Park, R. D. Juday, eds., Proc. SPIE3074, 132–141 (1997).
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Rabaud, D.

P. Y. Madec, D. Rabaud, B. Fleury, J. M. Conan, L. Rousset-Rouvière, F. Mendez, J. Montri, V. Michau, G. Rousset, M. Séchaud, “Essais du banc d’optique adaptative ONERA à l’OHP,” Lett. Observatoire de Haute Provence 16, 2–3 (1997).

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F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration for fidelity and visual quality,” Comput. Vision Graphics Image Process. 53, 71–84 (1991).

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J.-P. Véran, F. Rigaut, H. Maı̂tre, D. Rouan, “Estimation of the adaptive optics long-exposure point-spread function using control loop data,” J. Opt. Soc. Am. A 14, 3057–3069 (1997).
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G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

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Root, W. L.

Rouan, D.

Rousset, G.

P. Y. Madec, D. Rabaud, B. Fleury, J. M. Conan, L. Rousset-Rouvière, F. Mendez, J. Montri, V. Michau, G. Rousset, M. Séchaud, “Essais du banc d’optique adaptative ONERA à l’OHP,” Lett. Observatoire de Haute Provence 16, 2–3 (1997).

F. Rigaut, G. Rousset, P. Kern, J.-C. Fontanella, J.-P. Gaffard, F. Merkle, P. Léna, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

J. Primot, G. Rousset, J.-C. Fontanella, “Deconvolution from wavefront sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1598–1608 (1990).
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J.-M. Conan, P.-Y. Madec, G. Rousset, “Image formation in adaptive optics partial correction,” in Active and Adaptive Optics, F. Merkle, ed., Vol. 48 of ESO Conference and Workshop Proceedings (European Southern Observatory, Garching, Germany, 1993), pp. 181–186.

Rousset-Rouvière, L.

P. Y. Madec, D. Rabaud, B. Fleury, J. M. Conan, L. Rousset-Rouvière, F. Mendez, J. Montri, V. Michau, G. Rousset, M. Séchaud, “Essais du banc d’optique adaptative ONERA à l’OHP,” Lett. Observatoire de Haute Provence 16, 2–3 (1997).

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

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P. Y. Madec, D. Rabaud, B. Fleury, J. M. Conan, L. Rousset-Rouvière, F. Mendez, J. Montri, V. Michau, G. Rousset, M. Séchaud, “Essais du banc d’optique adaptative ONERA à l’OHP,” Lett. Observatoire de Haute Provence 16, 2–3 (1997).

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A. Levi, H. Stark, “Restoration from phase and magnitude by generalized projections,” in Image Recovery: Theory and Application, H. Stark, ed. (Academic, New York, 1987), Chap. 8, pp. 277–320.

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J.-P. Véran, F. Rigaut, H. Maı̂tre, D. Rouan, “Estimation of the adaptive optics long-exposure point-spread function using control loop data,” J. Opt. Soc. Am. A 14, 3057–3069 (1997).
[CrossRef]

J.-P. Véran, F. Rigaut, H. Maı̂tre, “Adaptive optics long exposure point spread function retrieval from wavefront sensor measurements,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference and Workshop Proceedings (European Southern Observatory, Garching, Germany, 1995), pp. 497–502.

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G. Weigelt, “Modified astronomical speckle interferometry speckle masking,” Opt. Commun. 21, 55–59 (1977).
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F. Rigaut, G. Rousset, P. Kern, J.-C. Fontanella, J.-P. Gaffard, F. Merkle, P. Léna, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

D. M. Titterington, “General structure of regularization procedures in image reconstruction,” Astron. Astrophys. 144, 381–387 (1985).

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C. Dumas, O. R. Hainaut, “Mapping Vesta with adaptive optics: the 1996 opposition,” Bull. Am. Astron. Soc. 28, 1101 (1996).

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F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration for fidelity and visual quality,” Comput. Vision Graphics Image Process. 53, 71–84 (1991).

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IEEE Trans. Circuits Syst. (1)

A. Papoulis, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Syst. CS-22, 735 (1975).
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Y.-L. You, M. Kaveh, “A regularization approach to joint blur identification and image restoration,” IEEE Trans. Image Process. 5, 416–428 (1996).
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D. L. Phillips, “A technique for the numerical solution of certain integral equations of the first kind,” J. Assoc. Comput. Mach. 9, 84–97 (1962).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (10)

J. Primot, G. Rousset, J.-C. Fontanella, “Deconvolution from wavefront sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1598–1608 (1990).
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M. C. Roggemann, C. L. Matson, “Power spectrum and Fourier phase spectrum estimation by using fully and partially compensating adaptive optics and bispectrum postprocessing,” J. Opt. Soc. Am. A 9, 1525–1535 (1992).
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J.-P. Véran, F. Rigaut, H. Maı̂tre, D. Rouan, “Estimation of the adaptive optics long-exposure point-spread function using control loop data,” J. Opt. Soc. Am. A 14, 3057–3069 (1997).
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Lett. Observatoire de Haute Provence (1)

P. Y. Madec, D. Rabaud, B. Fleury, J. M. Conan, L. Rousset-Rouvière, F. Mendez, J. Montri, V. Michau, G. Rousset, M. Séchaud, “Essais du banc d’optique adaptative ONERA à l’OHP,” Lett. Observatoire de Haute Provence 16, 2–3 (1997).

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Optik (1)

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

Publ. Astron. Soc. Pac. (1)

J. Nunez, J. Llacer, “A general Bayesian image reconstruction algorithm with entropy prior: preliminary application to HST data,” Publ. Astron. Soc. Pac. 105, 1192–1208 (1993).
[CrossRef]

Other (13)

A. P. Kattnig, J. Primot, “Model of the second-order statistic of the radiance field of natural scenes, adapted to system conceiving,” in Visual Information Processing VI, S. K. Park, R. D. Juday, eds., Proc. SPIE3074, 132–141 (1997).
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A. K. Katsaggelos, ed., Digital Image Restoration, Springer Series in Information Sciences, (Springer-Verlag, Berlin, 1991), Chap. 1.
[CrossRef]

H. L. Van Trees, Detection, Estimation, and Modulation Theory Part I (Wiley, New York, 1968).

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, New York, 1991).

J.-M. Conan, P.-Y. Madec, G. Rousset, “Image formation in adaptive optics partial correction,” in Active and Adaptive Optics, F. Merkle, ed., Vol. 48 of ESO Conference and Workshop Proceedings (European Southern Observatory, Garching, Germany, 1993), pp. 181–186.

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

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, New Jersey, 1989), Chap. 2.

A. Tikhonov, V. Arsenin, Solutions of Ill-Posed Problems (Winston, Washington, D.C., 1977).

A. Levi, H. Stark, “Restoration from phase and magnitude by generalized projections,” in Image Recovery: Theory and Application, H. Stark, ed. (Academic, New York, 1987), Chap. 8, pp. 277–320.

J.-P. Véran, F. Rigaut, H. Maı̂tre, “Adaptive optics long exposure point spread function retrieval from wavefront sensor measurements,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference and Workshop Proceedings (European Southern Observatory, Garching, Germany, 1995), pp. 497–502.

J. W. Goodman, Statistical Optics (Wiley-Interscience, New York, 1985), Chap. 8.

J. C. Christou, D. Bonaccini, N. Ageorges, “Deconvolution of adaptive optics near-infrared system (ADONIS) images,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 68–80 (1997).
[CrossRef]

C. Dumas, O. R. Hainaut, “Mapping Vesta in the visible and near-infrared: the 1994 and 1996 oppositions as viewed from the ground,” in Evolution of Igneous Asteroids: Focus on Vesta and the HED Meteorites, D. W. Mittlefehldt, J. J. Papike, eds., Lunar and Planetary Institute Tech. Rep. 96-02(1) (Lunar and Planetary Institute, Houston, Tex., 1996), pp. 7–8.

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Figures (7)

Fig. 1
Fig. 1

Normalized OTF versus spatial frequency: AO-corrected OTF (solid curve). The aberration-free OTF (dotted curve) and the uncorrected OTF (dashed line) are shown for comparison. The spatial frequency is normalized to the telescope cutoff.

Fig. 2
Fig. 2

(a) True object on 128 × 128 pixels, (b) AO-corrected image: simulation with Strehl ratio equal to 0.10, field of view 4.2 arc sec, wavelength 0.5 μm.

Fig. 3
Fig. 3

Normalized PSD models versus spatial frequency: adequate model corresponding to the true object (solid curve), and -4th power-law model corresponding to the Laplacian-type regularization (dashed curve). The square modulus of the true-object Fourier transform (circular average) is shown for comparison (dotted curve). The spatial frequency is normalized to the telescope cutoff frequency. The mean object is assumed here to be constant.

Fig. 4
Fig. 4

Objects restored by classical deconvolution by the RLS estimator with the true PSF, without a positivity constraint: (a) Laplacian-type (f -4) regularization, (b) regularization derived from the good (f -3) object PSD model. The distance to the true object is d(ô, o) = 63 for (a) and 56 for (b).

Fig. 5
Fig. 5

Object restored by classical deconvolution by the RLS estimator with the true PSF and a positivity constraint. The regularization is derived from the f -3 PSD model. The distance to the true object is d(ô, o) = 53.

Fig. 6
Fig. 6

Comparison of (a) classical, (b) myopic deconvolutions. In both cases the image hr of a reference star is available, but r 0 is 5 cm for hr (it was 10 cm for the image i). In (a) the PSF is taken as hr; in (b) the mean PSF is taken as the circular average of hr and PSD h is taken as the circular average of | r |2 [see Eq. (23)]. Positivity constraints are applied on the object and the PSF, and the object regularization is derived from the f -3 PSD model. The distance to the true object is d(ô, o) = 442 in the classical case and 127 in the myopic one.

Fig. 7
Fig. 7

Observation of the asteroid Vesta with the Office National d’Études et de Recherches AO bench (7 June 1996, 20:58UT): (a) corrected image (estimated Strehl ratio 0.09), (b) object restored by myopic deconvolution with positivity constraint and regularization on both the object and the PSF. The imaging wavelength is 0.7 μm (40-nm spectral bandwidth) with a 5-min exposure time. The estimated number of detected photons is 3.46 × 107. The field of view for the figure is 1.65 arc sec (the image presented here is the processed image truncated to half its size).

Equations (23)

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

i r = h r   *   o r + n r ,
i = H o + n ,
p o | i     p i | o p o .
o ˆ map = arg   max o   p o | i .
o ˆ mmse = arg   min o ˆ   E o ˆ - o 2 ,
o ˆ mmse = E o | i =     o p o | i d o .
p o | i     p i | o p o   exp - 1 / 2 i - H o t R n - 1 i - H o × exp - 1 / 2 o - o m t R o - l o - o m ,
J o = i - H o t R n - 1 i - H o + o - o m t R o - 1 o - o m ,
R o = F - 1   diag PSD o F ,
R n = F - 1   diag PSD n F ,
H = F - 1   diag DFT h F ,
PSD o = DFT ( E o r - o m r o r + r - o m r + r ) = E | õ f - õ m f | 2 = E | õ f | 2 - | õ m f | 2 .
J o = f | h ˜ f õ f - i ˜ f | 2 PSD n f + | õ f - õ m f | 2 PSD o f ,
o ˆ ˜ w f = h ˜ * f i ˜ f | h ˜ f | 2 + PSD n f PSD o f + PSD n f PSD o f | h ˜ f | 2 + PSD n f PSD o f õ m f .
J o = r H o r - i r ln H o ) r + o - o m t R o - 1 o - o m .
PSD o f = E | õ f | 2 - | õ m f | 2 = N ph 2 / 1 + f / f 0 p - | õ m f | 2 ,
d o ˆ ,   o = 1 N pix pixels | o ˆ r - o r | 2 1 / 2 photons / pixel ,
o ˆ ,   h ˆ =   arg   max o ,   h   p o ,   h | i = arg   max o ,   h   p i | o ,   h | p o p h =   arg   min o ,   h   J o ,   h
J o ,   h = f | h ˜ f õ f - i ˜ f | 2 PSD n f + | õ f - õ m f | 2 PSD o f + | h ˜ f - h ˜ m f | 2 PSD h f ,
PSD h f = E | h ˜ f - h ˜ m f | 2 = E | h ˜ f | 2 - | h ˜ m f | 2 .
PSD h f = τ / T STF m f - | h ˜ m f | 2 ,
PSD ͡ h f = | h ˜ r | 2 f - | h ˜ r f | 2 ,
PSD ͡ h f = | h ˜ r | 2 f

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