Abstract

Statistical behavior of the adaptive-optics- (AO-) corrected short-exposure point-spread function (PSF) is derived assuming a perfect correction of the phase’s low spatial frequencies. Analytical expressions of the Strehl ratio (SR) fluctuations of on- and off-axis short-exposure PSFs are obtained. A theoretical expression of the short SR angular correlation is proposed and used to derive a definition of an anisoplanatic angle for AO-corrected images. Several applications of the analytical expressions are proposed: AO performance characterization, postprocessing imaging, light coupling into fiber, and exoplanet detection from a ground-based telescope.

© 2004 Optical Society of America

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    [CrossRef]
  33. F. Roddier, J. M. Gilli, G. Lund, “On the origin of speckle boilding and its effects in stellar speckle interferometry,” J. Opt. (Paris) 13, 263–271 (1982).
    [CrossRef]
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    [CrossRef]

2001 (1)

1999 (2)

V. F. Canales, M. P. Cagigal, “Rician distribution to describe speckle statistics in adaptive optics,” Appl. Opt. 38, 766–771 (1999).
[CrossRef]

T. Fusco, J.-P. Véran, J.-M. Conan, L. Mugnier, “Myopic deconvolution method for adaptive optics images of stellar fields,” 134, 1–10 (1999).

1998 (2)

1997 (2)

1995 (2)

S. Stahl, D. Sandler, “Optimization and performance of adaptive optics for imaging extrasolar planets,” Astrophys. J. Lett. 454, L153–L156 (1995).

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]

1991 (2)

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).

M. C. Roggemann, “Limited degree-of-freedom adaptive optics and image reconstruction,” Appl. Opt. 30, 4227–4233 (1991).
[CrossRef] [PubMed]

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, 29–32 (1990).

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

1989 (1)

F. Chassat, “Calcul du domaine d’isoplanétisme d’un système d’optique adaptative fonctionnant à travers la turbulence atmosphérique,” J. Opt. (Paris) 20, 13–23 (1989).
[CrossRef]

1982 (3)

D. L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. 72, 52–61 (1982).
[CrossRef]

F. Roddier, J. M. Gilli, J. Vernin, “On the isoplanatic patch size in stellar speckle interferometry,” J. Opt. (Paris) 13, 63–70 (1982).
[CrossRef]

F. Roddier, J. M. Gilli, G. Lund, “On the origin of speckle boilding and its effects in stellar speckle interferometry,” J. Opt. (Paris) 13, 263–271 (1982).
[CrossRef]

1977 (1)

D. P. Greenwood, “Bandwidth specification for adaptive optics systems,” J. Opt. Soc. Am. A 67, 390–393 (1977).
[CrossRef]

1976 (1)

1953 (1)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229 (1953).
[CrossRef]

Abé, L.

D. Mouillet, A.-M. Lagrange, J.-L. Beuzit, F. Ménard, C. Moutou, T. Fusco, L. Abé, T. Gillot, R. Soummer, P. Riaud, “VLT-‘Planet Finder’: specifications for a ground-based high contrast imager,” in Scientific Highlights 2002, F. Combes, D. Barret, eds. (EDP Sciences, Les Ulis, France, 2002).

Babcock, H. W.

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229 (1953).
[CrossRef]

Beuzit, J.-L.

D. Mouillet, T. Fusco, A.-M. Lagrange, J.-L. Beuzit, “ ‘Planet Finder’ on the VLT: context, goals and critical specification for adaptive optics,” in Astronomy with High Contrast Imaging: From Planetary Systems to Active Galactic Nuclei, C. Aime, R. Soummer, eds., EAS Publication Series (EDP Sciences, Les Ulis, France, 2002).

D. Mouillet, A.-M. Lagrange, J.-L. Beuzit, F. Ménard, C. Moutou, T. Fusco, L. Abé, T. Gillot, R. Soummer, P. Riaud, “VLT-‘Planet Finder’: specifications for a ground-based high contrast imager,” in Scientific Highlights 2002, F. Combes, D. Barret, eds. (EDP Sciences, Les Ulis, France, 2002).

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, 29–32 (1990).

Cagigal, M. P.

Canales, V. F.

Cassaing, F.

Chassat, F.

F. Chassat, “Calcul du domaine d’isoplanétisme d’un système d’optique adaptative fonctionnant à travers la turbulence atmosphérique,” J. Opt. (Paris) 20, 13–23 (1989).
[CrossRef]

Chauvin, G.

T. Fusco, L. M. Mugnier, J.-M. Conan, F. Marchis, G. Chauvin, G. Rousset, A.-M. Lagrange, D. Mouillet, F. Roddier, “Deconvolution of astronomical images obtained from ground-based telescopes with adaptive optics,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 1065–1075 (2002).
[CrossRef]

Conan, J. M.

J. M. Conan, P. Y. Madec, G. Rousset, “Evaluation of image quality obtained with adaptive optics partial correction,” in Progress in Telescope and Instrumentation Technologies, M.-H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1992), pp. 471–474.

Conan, J.-M.

T. Fusco, J.-P. Véran, J.-M. Conan, L. Mugnier, “Myopic deconvolution method for adaptive optics images of stellar fields,” 134, 1–10 (1999).

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998).
[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]

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

J.-M. Conan, T. Fusco, L. Mugnier, F. Marchis, C. Roddier, F. Roddier, “Deconvolution of adaptive optics images: from theory to practice,” in Adaptive Optical Systems Tech-nology, P. Wizinowich, ed., Proc. SPIE4007, 913–924 (2000).
[CrossRef]

T. Fusco, L. M. Mugnier, J.-M. Conan, F. Marchis, G. Chauvin, G. Rousset, A.-M. Lagrange, D. Mouillet, F. Roddier, “Deconvolution of astronomical images obtained from ground-based telescopes with adaptive optics,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 1065–1075 (2002).
[CrossRef]

Dainty, J. C.

J. C. Dainty, “Stellar speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 255–280.

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).

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, 29–32 (1990).

Fried, D. L.

Fusco, T.

T. Fusco, J.-P. Véran, J.-M. Conan, L. Mugnier, “Myopic deconvolution method for adaptive optics images of stellar fields,” 134, 1–10 (1999).

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998).
[CrossRef]

T. Fusco, L. M. Mugnier, J.-M. Conan, F. Marchis, G. Chauvin, G. Rousset, A.-M. Lagrange, D. Mouillet, F. Roddier, “Deconvolution of astronomical images obtained from ground-based telescopes with adaptive optics,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 1065–1075 (2002).
[CrossRef]

D. Mouillet, T. Fusco, A.-M. Lagrange, J.-L. Beuzit, “ ‘Planet Finder’ on the VLT: context, goals and critical specification for adaptive optics,” in Astronomy with High Contrast Imaging: From Planetary Systems to Active Galactic Nuclei, C. Aime, R. Soummer, eds., EAS Publication Series (EDP Sciences, Les Ulis, France, 2002).

D. Mouillet, A.-M. Lagrange, J.-L. Beuzit, F. Ménard, C. Moutou, T. Fusco, L. Abé, T. Gillot, R. Soummer, P. Riaud, “VLT-‘Planet Finder’: specifications for a ground-based high contrast imager,” in Scientific Highlights 2002, F. Combes, D. Barret, eds. (EDP Sciences, Les Ulis, France, 2002).

J.-M. Conan, T. Fusco, L. Mugnier, F. Marchis, C. Roddier, F. Roddier, “Deconvolution of adaptive optics images: from theory to practice,” in Adaptive Optical Systems Tech-nology, P. Wizinowich, ed., Proc. SPIE4007, 913–924 (2000).
[CrossRef]

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, 29–32 (1990).

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, 29–32 (1990).

Gilli, J. M.

F. Roddier, J. M. Gilli, J. Vernin, “On the isoplanatic patch size in stellar speckle interferometry,” J. Opt. (Paris) 13, 63–70 (1982).
[CrossRef]

F. Roddier, J. M. Gilli, G. Lund, “On the origin of speckle boilding and its effects in stellar speckle interferometry,” J. Opt. (Paris) 13, 263–271 (1982).
[CrossRef]

Gillot, T.

D. Mouillet, A.-M. Lagrange, J.-L. Beuzit, F. Ménard, C. Moutou, T. Fusco, L. Abé, T. Gillot, R. Soummer, P. Riaud, “VLT-‘Planet Finder’: specifications for a ground-based high contrast imager,” in Scientific Highlights 2002, F. Combes, D. Barret, eds. (EDP Sciences, Les Ulis, France, 2002).

Goodman, J.

J. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 255–280.

Goodman, J. W.

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

Greenwood, D. P.

D. P. Greenwood, “Bandwidth specification for adaptive optics systems,” J. Opt. Soc. Am. A 67, 390–393 (1977).
[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, 29–32 (1990).

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, 29–32 (1990).

Lagrange, A.-M.

D. Mouillet, T. Fusco, A.-M. Lagrange, J.-L. Beuzit, “ ‘Planet Finder’ on the VLT: context, goals and critical specification for adaptive optics,” in Astronomy with High Contrast Imaging: From Planetary Systems to Active Galactic Nuclei, C. Aime, R. Soummer, eds., EAS Publication Series (EDP Sciences, Les Ulis, France, 2002).

D. Mouillet, A.-M. Lagrange, J.-L. Beuzit, F. Ménard, C. Moutou, T. Fusco, L. Abé, T. Gillot, R. Soummer, P. Riaud, “VLT-‘Planet Finder’: specifications for a ground-based high contrast imager,” in Scientific Highlights 2002, F. Combes, D. Barret, eds. (EDP Sciences, Les Ulis, France, 2002).

T. Fusco, L. M. Mugnier, J.-M. Conan, F. Marchis, G. Chauvin, G. Rousset, A.-M. Lagrange, D. Mouillet, F. Roddier, “Deconvolution of astronomical images obtained from ground-based telescopes with adaptive optics,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 1065–1075 (2002).
[CrossRef]

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, 29–32 (1990).

Lund, G.

F. Roddier, J. M. Gilli, G. Lund, “On the origin of speckle boilding and its effects in stellar speckle interferometry,” J. Opt. (Paris) 13, 263–271 (1982).
[CrossRef]

Madec, P. Y.

G. Rousset, P. Y. Madec, D. Rabaud, “Adaptive optics partial correction simulation for two telescopes,” in High Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1991), pp. 1095–1104.

J. M. Conan, P. Y. Madec, G. Rousset, “Evaluation of image quality obtained with adaptive optics partial correction,” in Progress in Telescope and Instrumentation Technologies, M.-H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1992), pp. 471–474.

Madec, P.-Y.

Mai^tre, H.

Marchis, F.

J.-M. Conan, T. Fusco, L. Mugnier, F. Marchis, C. Roddier, F. Roddier, “Deconvolution of adaptive optics images: from theory to practice,” in Adaptive Optical Systems Tech-nology, P. Wizinowich, ed., Proc. SPIE4007, 913–924 (2000).
[CrossRef]

T. Fusco, L. M. Mugnier, J.-M. Conan, F. Marchis, G. Chauvin, G. Rousset, A.-M. Lagrange, D. Mouillet, F. Roddier, “Deconvolution of astronomical images obtained from ground-based telescopes with adaptive optics,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 1065–1075 (2002).
[CrossRef]

Ménard, F.

D. Mouillet, A.-M. Lagrange, J.-L. Beuzit, F. Ménard, C. Moutou, T. Fusco, L. Abé, T. Gillot, R. Soummer, P. Riaud, “VLT-‘Planet Finder’: specifications for a ground-based high contrast imager,” in Scientific Highlights 2002, F. Combes, D. Barret, eds. (EDP Sciences, Les Ulis, France, 2002).

Merkle, F.

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, 29–32 (1990).

Michau, V.

Molodij, G.

Mouillet, D.

T. Fusco, L. M. Mugnier, J.-M. Conan, F. Marchis, G. Chauvin, G. Rousset, A.-M. Lagrange, D. Mouillet, F. Roddier, “Deconvolution of astronomical images obtained from ground-based telescopes with adaptive optics,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 1065–1075 (2002).
[CrossRef]

D. Mouillet, A.-M. Lagrange, J.-L. Beuzit, F. Ménard, C. Moutou, T. Fusco, L. Abé, T. Gillot, R. Soummer, P. Riaud, “VLT-‘Planet Finder’: specifications for a ground-based high contrast imager,” in Scientific Highlights 2002, F. Combes, D. Barret, eds. (EDP Sciences, Les Ulis, France, 2002).

D. Mouillet, T. Fusco, A.-M. Lagrange, J.-L. Beuzit, “ ‘Planet Finder’ on the VLT: context, goals and critical specification for adaptive optics,” in Astronomy with High Contrast Imaging: From Planetary Systems to Active Galactic Nuclei, C. Aime, R. Soummer, eds., EAS Publication Series (EDP Sciences, Les Ulis, France, 2002).

Moutou, C.

D. Mouillet, A.-M. Lagrange, J.-L. Beuzit, F. Ménard, C. Moutou, T. Fusco, L. Abé, T. Gillot, R. Soummer, P. Riaud, “VLT-‘Planet Finder’: specifications for a ground-based high contrast imager,” in Scientific Highlights 2002, F. Combes, D. Barret, eds. (EDP Sciences, Les Ulis, France, 2002).

Mugnier, L.

T. Fusco, J.-P. Véran, J.-M. Conan, L. Mugnier, “Myopic deconvolution method for adaptive optics images of stellar fields,” 134, 1–10 (1999).

J.-M. Conan, T. Fusco, L. Mugnier, F. Marchis, C. Roddier, F. Roddier, “Deconvolution of adaptive optics images: from theory to practice,” in Adaptive Optical Systems Tech-nology, P. Wizinowich, ed., Proc. SPIE4007, 913–924 (2000).
[CrossRef]

Mugnier, L. M.

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998).
[CrossRef]

T. Fusco, L. M. Mugnier, J.-M. Conan, F. Marchis, G. Chauvin, G. Rousset, A.-M. Lagrange, D. Mouillet, F. Roddier, “Deconvolution of astronomical images obtained from ground-based telescopes with adaptive optics,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 1065–1075 (2002).
[CrossRef]

Noll, R. J.

Rabaud, D.

G. Rousset, P. Y. Madec, D. Rabaud, “Adaptive optics partial correction simulation for two telescopes,” in High Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1991), pp. 1095–1104.

Riaud, P.

D. Mouillet, A.-M. Lagrange, J.-L. Beuzit, F. Ménard, C. Moutou, T. Fusco, L. Abé, T. Gillot, R. Soummer, P. Riaud, “VLT-‘Planet Finder’: specifications for a ground-based high contrast imager,” in Scientific Highlights 2002, F. Combes, D. Barret, eds. (EDP Sciences, Les Ulis, France, 2002).

Rigaut, F.

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]

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, 29–32 (1990).

Roddier, C.

J.-M. Conan, T. Fusco, L. Mugnier, F. Marchis, C. Roddier, F. Roddier, “Deconvolution of adaptive optics images: from theory to practice,” in Adaptive Optical Systems Tech-nology, P. Wizinowich, ed., Proc. SPIE4007, 913–924 (2000).
[CrossRef]

F. Roddier, C. Roddier, “NOAO infrared adaptive optics program II: modeling atmospheric effects in adaptive optics systems for astronomical telescopes,” in Advanced Technology Optical Telescopes III, L. D. Barr, ed., Proc. SPIE628, 298–304 (1986).
[CrossRef]

Roddier, F.

F. Roddier, J. M. Gilli, G. Lund, “On the origin of speckle boilding and its effects in stellar speckle interferometry,” J. Opt. (Paris) 13, 263–271 (1982).
[CrossRef]

F. Roddier, J. M. Gilli, J. Vernin, “On the isoplanatic patch size in stellar speckle interferometry,” J. Opt. (Paris) 13, 63–70 (1982).
[CrossRef]

J.-M. Conan, T. Fusco, L. Mugnier, F. Marchis, C. Roddier, F. Roddier, “Deconvolution of adaptive optics images: from theory to practice,” in Adaptive Optical Systems Tech-nology, P. Wizinowich, ed., Proc. SPIE4007, 913–924 (2000).
[CrossRef]

F. Roddier, “The effects of atmospherical turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1981), Vol. 19, pp. 281–376.

F. Roddier, C. Roddier, “NOAO infrared adaptive optics program II: modeling atmospheric effects in adaptive optics systems for astronomical telescopes,” in Advanced Technology Optical Telescopes III, L. D. Barr, ed., Proc. SPIE628, 298–304 (1986).
[CrossRef]

T. Fusco, L. M. Mugnier, J.-M. Conan, F. Marchis, G. Chauvin, G. Rousset, A.-M. Lagrange, D. Mouillet, F. Roddier, “Deconvolution of astronomical images obtained from ground-based telescopes with adaptive optics,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 1065–1075 (2002).
[CrossRef]

Roddier, N.

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

Roggemann, M. C.

Rouan, D.

Rousset, G.

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998).
[CrossRef]

G. Molodij, G. Rousset, “Angular correlation of Zernike polynomials for a laser guide star in adaptive optics,” J. Opt. Soc. Am. A 14, 1949–1966 (1997).
[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]

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, 29–32 (1990).

G. Rousset, P. Y. Madec, D. Rabaud, “Adaptive optics partial correction simulation for two telescopes,” in High Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1991), pp. 1095–1104.

J. M. Conan, P. Y. Madec, G. Rousset, “Evaluation of image quality obtained with adaptive optics partial correction,” in Progress in Telescope and Instrumentation Technologies, M.-H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1992), pp. 471–474.

T. Fusco, L. M. Mugnier, J.-M. Conan, F. Marchis, G. Chauvin, G. Rousset, A.-M. Lagrange, D. Mouillet, F. Roddier, “Deconvolution of astronomical images obtained from ground-based telescopes with adaptive optics,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 1065–1075 (2002).
[CrossRef]

Ruilier, C.

Sandler, D.

S. Stahl, D. Sandler, “Optimization and performance of adaptive optics for imaging extrasolar planets,” Astrophys. J. Lett. 454, L153–L156 (1995).

Sasiela, R. J.

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence Evaluation and Application of Mellin Transforms (Springer-Verlag, Berlin, 1995).

Soummer, R.

D. Mouillet, A.-M. Lagrange, J.-L. Beuzit, F. Ménard, C. Moutou, T. Fusco, L. Abé, T. Gillot, R. Soummer, P. Riaud, “VLT-‘Planet Finder’: specifications for a ground-based high contrast imager,” in Scientific Highlights 2002, F. Combes, D. Barret, eds. (EDP Sciences, Les Ulis, France, 2002).

Stahl, S.

S. Stahl, D. Sandler, “Optimization and performance of adaptive optics for imaging extrasolar planets,” Astrophys. J. Lett. 454, L153–L156 (1995).

Véran, J.-P.

T. Fusco, J.-P. Véran, J.-M. Conan, L. Mugnier, “Myopic deconvolution method for adaptive optics images of stellar fields,” 134, 1–10 (1999).

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]

Vernin, J.

F. Roddier, J. M. Gilli, J. Vernin, “On the isoplanatic patch size in stellar speckle interferometry,” J. Opt. (Paris) 13, 63–70 (1982).
[CrossRef]

Appl. Opt. (3)

Astron. Astrophys. (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, 29–32 (1990).

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).

Astrophys. J. Lett. (1)

S. Stahl, D. Sandler, “Optimization and performance of adaptive optics for imaging extrasolar planets,” Astrophys. J. Lett. 454, L153–L156 (1995).

J. Opt. (Paris) (3)

F. Roddier, J. M. Gilli, J. Vernin, “On the isoplanatic patch size in stellar speckle interferometry,” J. Opt. (Paris) 13, 63–70 (1982).
[CrossRef]

F. Roddier, J. M. Gilli, G. Lund, “On the origin of speckle boilding and its effects in stellar speckle interferometry,” J. Opt. (Paris) 13, 263–271 (1982).
[CrossRef]

F. Chassat, “Calcul du domaine d’isoplanétisme d’un système d’optique adaptative fonctionnant à travers la turbulence atmosphérique,” J. Opt. (Paris) 20, 13–23 (1989).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (5)

Myopic deconvolution method for adaptive optics images of stellar fields (1)

T. Fusco, J.-P. Véran, J.-M. Conan, L. Mugnier, “Myopic deconvolution method for adaptive optics images of stellar fields,” 134, 1–10 (1999).

Opt. Eng. (1)

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

Opt. Lett. (1)

Publ. Astron. Soc. Pac. (1)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229 (1953).
[CrossRef]

Other (14)

J. M. Conan, P. Y. Madec, G. Rousset, “Evaluation of image quality obtained with adaptive optics partial correction,” in Progress in Telescope and Instrumentation Technologies, M.-H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1992), pp. 471–474.

G. Rousset, P. Y. Madec, D. Rabaud, “Adaptive optics partial correction simulation for two telescopes,” in High Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1991), pp. 1095–1104.

F. Roddier, ed., Adaptive Optics in Astronomy (Cambridge U. Press, Cambridge, UK, 1999).

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence Evaluation and Application of Mellin Transforms (Springer-Verlag, Berlin, 1995).

T. Fusco, L. M. Mugnier, J.-M. Conan, F. Marchis, G. Chauvin, G. Rousset, A.-M. Lagrange, D. Mouillet, F. Roddier, “Deconvolution of astronomical images obtained from ground-based telescopes with adaptive optics,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 1065–1075 (2002).
[CrossRef]

J. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 255–280.

J. C. Dainty, “Stellar speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 255–280.

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

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

J.-M. Conan, T. Fusco, L. Mugnier, F. Marchis, C. Roddier, F. Roddier, “Deconvolution of adaptive optics images: from theory to practice,” in Adaptive Optical Systems Tech-nology, P. Wizinowich, ed., Proc. SPIE4007, 913–924 (2000).
[CrossRef]

D. Mouillet, A.-M. Lagrange, J.-L. Beuzit, F. Ménard, C. Moutou, T. Fusco, L. Abé, T. Gillot, R. Soummer, P. Riaud, “VLT-‘Planet Finder’: specifications for a ground-based high contrast imager,” in Scientific Highlights 2002, F. Combes, D. Barret, eds. (EDP Sciences, Les Ulis, France, 2002).

D. Mouillet, T. Fusco, A.-M. Lagrange, J.-L. Beuzit, “ ‘Planet Finder’ on the VLT: context, goals and critical specification for adaptive optics,” in Astronomy with High Contrast Imaging: From Planetary Systems to Active Galactic Nuclei, C. Aime, R. Soummer, eds., EAS Publication Series (EDP Sciences, Les Ulis, France, 2002).

F. Roddier, “The effects of atmospherical turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1981), Vol. 19, pp. 281–376.

F. Roddier, C. Roddier, “NOAO infrared adaptive optics program II: modeling atmospheric effects in adaptive optics systems for astronomical telescopes,” in Advanced Technology Optical Telescopes III, L. D. Barr, ed., Proc. SPIE628, 298–304 (1986).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Cross section of the long-exposure PSF: full correction of 36 Zernike modes with D/r0=40 (solid curve), no correction with D/r0=40 (dashed curve), and no correction with D/r0,eq=23 (dotted curve).

Fig. 2
Fig. 2

Intensity fluctuation rate (σISR0/ISR0) as a function of D/r0 for different kinds of correction (one to seven corrected radial orders). Symbols, computed ISR0 rates from simulation; solid lines, predicted the ISR0 fluctuation rate from the analytical expression. One can note that all the simulated curves saturate to 1 for large D/r0 values that are large residual phase fluctuations.

Fig. 3
Fig. 3

SR fluctuation rate as a function of angle. Three correction degrees are considered: 35 (asterisks) 66 (pluses) and 120 (diamonds) Zernike polynomials. In all the cases D/r0 is equal to 14. The theoretical curves are plotted (solid curves) for comparison.

Fig. 4
Fig. 4

SR Strehl ratio fluctuation rate as a function of angle. Three D/r0 values are considered: 14 (asterisks), 10 (pluses), and 5 (diamonds). For each case, the correction degree is equal to 66 corrected Zernike polynomials. The theoretical curves are plotted (solid curves) for comparison.

Fig. 5
Fig. 5

Angular correlations: comparison between simulations and analytical results. C(α) is plotted in the case of three D/r0—14 (asterisks), 10 (pluses), and 5 (diamonds)—and one correction degree (66 corrected Zernike polynomials). The analytical results are plotted for each case (solid curve) (the same turbulence screens are used in each correction case).

Fig. 6
Fig. 6

ISR angular correlations: comparison between simulations and analytical results. C(α) is plotted in the case of three correction degrees: 35 (asterisks), 66 (pluses), and 120 (diamonds) corrected Zernike polynomials. For each case, D/r0=14. The analytical results are plotted for each case (solid curve) (the same turbulence screens are used in each correction case).

Fig. 7
Fig. 7

θs (FWHM of the ISR correlation) as a function of the correction degree. The fit by a n-6/5 law is plotted (dashed line) for comparison.

Fig. 8
Fig. 8

X-axis cut of a PSF mean and a PSF root-mean-square for a correction of four radial orders. D/r0=10, SR=30%.

Fig. 9
Fig. 9

X-axis cut of σI/I for a correction of four radial orders and for different D/r0=[5, 10, 15, 20], i.e., SR=[68%, 30%, 11%, 3%].

Fig. 10
Fig. 10

Residual variance after a perfect correction of the n first radial orders. Noll expression [expression (A9)] (asterisks) and asymptotic expression [expression (A6)] (solid line) D/r0=1.

Equations (82)

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

Iα(ρ)=|FT{P(r)A(r, α)exp[iΦres(r, α)]}|2,
Φres(r, α)=Φturb(r, α)-Φcorr(r, 0).
Φres(r, α)=i=2i0[ai,turb(α)-ai,corr(0)]Zi(r)+i=i0+1ai,turb(α)Zi(r).
Φres(r, 0)=i=i0+1ai,turb(0)Zi(r).
CoEn(α)=exp[-σres2(α)],
Iα(ρ)Iαcoh(ρ)+Iαhalo(ρ),
λD2Iα(0)λD2Iαcoh(0)+Lhalo2Iαhalo(0),
SR(α)=CoEn(α)+[1-CoEn(α)] (λ/D)2Lhalo2.
ISRα=Iα(0)Airy(0).
Iα(ρ)FTΠ(r, α)1+iφ(r, α)-φ(r, α)22ρ2,
Iα(ρ)|FT[Π(r)]ρ+i{FT[Πφ(r, α)]ρ}-{FT[Πφ(r, α)2]ρ}/2|2,
Iα(0)Π(r)dr2+Π(r)φ(r, α)dr2-Π(r)drΠ(r)φ2(r, α)dr,
Iα(0)Airy(0){1-var[Φ(r, α)]},
Iα(0)Airy(0){1-var[Φ(r, α)]}
(second-orderexpansion),
Iα(0)2Airy(0)2{1-2var[Φ(r, α)]+var[Φ(r, α)]2}
(fourth-orderexpansion).
ISRα{1-var[Φ(r, α)]},
ISRα2{1-2var[Φ(r, α)]+var[Φ(r, α)]2},
σISRασvar[Φ(r,α)](fourth-orderexpansion).
var(Φ)=1Si=i0+1+MyaiZi(r)×j=i0+1+ajZj(r)dr=i=i0+1+j=i0+aiaj1SZi(r)Zj(r)dr,
1SZi(r)Zj(r)dr=δij,
var(Φ)=i=i0+1+ai2.
var(Φ)=i=i0+ai2=σΦ2,
σΦ2=0.458 * (n0+1)-5/3(D/r0)5/3.
var(Φ)2=i=i0+1+j=j0+1ai2aj2i=i0+1+ai4+j=i0+1+ij+ai2aj2.
var(Φ)23i=i0+1+σai4+j=i0+1+ij+σai2σai2,
var(Φ)2=i=i0+1+j=i0+1+σai2σaj2=i=i0+1+σai4+ij+σai4.
σvarΦ22i=i0+1+σai4.
σvarΦ22m=n0+1+(m+1)σm4.
σvarΦ20.218(n0+1)-16/3Dr010/31.04 σΦ4(n0+1)2,
ISR0(1-σΦ2)1-0.458(n0+1)-5/3Dr05/3,
σISR02σvarΦ21.04 σΦ4(n0+1)2,
σISR0ISR01.02 σΦ2(n0+1),
σISR0ISR00.467(n0+1)-8/3Dr05/3.
PB(I)=1/Iexp(-I/I),
σI/I=1.
σI0/I0=1.
Φ(r,α)=i=2i0(ai,α-ai,0)Zi(r)anisoplanatic error+i=i0+1∞;ai,αZi(r)fitting error,
var[Φ(r, α)]=i=2i0(ai,α-ai,0)2+i=i0+1ai,α2.
var[Φ(r, α)]=2i=2i0(σai2-ai,αai,0)+i=i0+1σai2.
var[Φ(r, α)]=2i=2i0[σai2-Ci(α)]+i=i0+1σai2.
{var[Φ(r, α)]}2
=i=i0+1j=i0+1ai,α2aj,α2+i=2i0j=2i0(ai,α2+ai,02-2ai,αai,0)(aj,α2+aj,02-2aj,αaj,0)+2i=i0+1j=2i0ai,α2(aj,α2+aj,02-2aj,0aj,α)+2j=i0+1i=2i0ai,α2(aj,α2+aj,02-2aj,0aj,α).
σvar[Φ(r,α)]2=2i=i0+1σai4+4i=2i0[σai2-Ci(α)]2.
ISRα1-i=i0+1σai2+2i=2i0[σai2-Ci(α)],
σISRα22i=i0+1σai4+4i=2i0[σai2-Ci(α)]2.
C(α)=I0(0)I0(α)-I0(0)I0(α)[σI0(0)2σI0(α)2]1/2,
C(α)=var[Φ(r, 0)]var[Φ(r, α)]-var[Φ(r, 0)]var[Φ(r, α)]{σvar[Φ(r,0)]2σvar[Φ(r,α)]2}1/2.
var[Φ(r, 0)]var[Φ(r, α)]
=i=i0+1ai,02j=i0+1aj,α2+j=2i0(aj,α-aj,0)2=i=i0+1j=i0+1ai,02aj,α2+i=i0+1j=2i0ai,02aj,α2+i=i0+1j=2i0ai,02aj,02-2i=i0+1j=2i0ai,02aj,0aj,α.
C(α)=2i=i0+1[Ci(α)]2{σvar[Φ(r,0)]2σvar[Φ(r,α)]2}1/2.
σI2(T)=τT σI2,
σI(T)=1.02τTσΦ2(n+1).
σn2=2.2698(n+1) Γn-(56)[Γ(17 6)]2Γ(n+236)Dr05/3.
σn20.7632(n+1)-11/3Dr05/3,
σn40.5824(n+1)-22/3Dr010/3.
σΦ2=n=n+1+(n+1)σn2,
σvarΦ2=2n=n+1+(n+1)σn4.
σΦ20.458(n+1)-5/3Dr05/3,
σvarΦ2=0.218(n+1)-16/3Dr010/3.
σΦ20.257(jmax)-5/6Dr05/3.
σΦ,Noll20.2944(jmax)-3/2Dr05/3.
{var[Φ(r, α)]}2
=i=i0+1j=i0+1ai,α2aj,α2+i=2i0j=2i0(ai,α2+ai,02-2ai,αai,0)(aj,α2+aj,02-2aj,αaj,0)+2i=i0+1j=2i0ai,α2(aj,α2+aj,02-2aj,0aj,α)+2j=i0+1i=2i0ai,α2(aj,α2+aj,02-2aj,0aj,α).
(1)=3i=i0+1σai4+ijσai2σaj2.
(2)=2i=2i0j=2i0ai,α2aj,α2+ai,02aj,α2-4aj,α2ai,0ai,α+2aj,0aj,αai,0ai,α.
(2)=6i=2i0σai4+4ijσai2σaj2+2i=2i0σai2+4i=2i0Ci2(α)-24i=2i0σaj2Ci(α)-8ijσai2Cj(α)+4i=2i0σai4+8i=2i0Ci2(α)+4ijCi(α)Cj(α),
(2)=43i=2i0[σai2-Ci(α)]2+ij[σai2-Ci(α)][σaj2-Cj(α)].
(3, 4)=4i=i0+1j=2i0σai2[σaj2-Cj(α)].
σvar[Φ(r,α)]2=2i=i0+1σai4+4i=2i0[σai2-Ci(α)]2.
var[Φ(r, 0)]var[Φ(r, α)]
=i=i0+1ai,02j=i0+1aj,α2+j=2i0(aj,α-aj,0)2=i=i0+1j=i0+1ai,02aj,α2+i=i0+1j=2i0ai,02aj,α2+i=i0+1j=2i0ai,02aj,02-2i=i0+1j=2i0ai,02aj,0aj,α.
i=i0+1j=i0+1ai,02aj,α2
=i=i0+1ai,02ai,α2+2i=i0+1Ci2(α)+i=i0+1ijai,02aj,α2=i=i0+1σai4+2i=i0+1Ci2(α)+i=i0+1ijσai2σaj2.
2i=i0+1j=2i0ai,02aj,α2=2i=i0+1j=2i0σai2σaj2.
-2i=i0+1j=2i0ai,02aj,0aj,α=-2i=i0+1j=2i0σai2Cj(α).
var[Φ(r, 0)]var[Φ(r, α)]
=i=i0+1[σai4+2Ci2(α)]+i=i0+1ijσai2σaj2+2i=i0+1j=2i0+1σai2[σaj2-Cj(α)].
var[Φ(r, 0)]var[Φ(r, α)]
=i=i0+1j=i0+1σai2σaj2+2i=i0+1j=2i0σai2[σaj2-Cj(α)].
C(α)=2i=i0+1[Ci(α)]2{σvar[Φ(r,0)]2σvar[Φ(r,α)]2}1/2.

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