Abstract

In this paper we derive an analytical model of a long-exposure star image for an adaptive-optics(AO)-corrected coronagraphic imaging system. This expression accounts for static aberrations upstream and downstream of the coronagraphic mask as well as turbulence residuals. It is based on the perfect coronagraph model. The analytical model is validated by means of simulations using the design and parameters of the SPHERE instrument. The analytical model is also compared to a simulated four-quadrant phase-mask coronagraph. Then, its sensitivity to a miscalibration of structure function and upstream static aberrations is studied, and the impact on exoplanet detectability is quantified. Last, a first inversion method is presented for a simulation case using a single monochromatic image with no reference. The obtained result shows a planet detectability increase by two orders of magnitude with respect to the raw image. This analytical model presents numerous potential applications in coronographic imaging, such as exoplanet direct detection, and circumstellar disk observation.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. J. M. Conan, P. Y. Madec, and G. Rousset, “Evaluation of image quality obtained with adaptive optics partial correction,” in Progress in Telescope and Instrumentation Technologies, ESO Conference and Workshop Proceedings, M.-H. Ulrich, ed. (ESO, 1992), p. 475.
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  5. E. E. Bloemhof, R. G. Dekany, M. Troy, and B. R. Oppenheimer, “Behavior of remnant speckles in an adaptively corrected imaging system,” Astrophys. J. 558, L71–L74 (2001).
    [CrossRef]
  6. A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552, 397–408 (2001).
    [CrossRef]
  7. M. D. Perrin, A. Sivaramakrishnan, R. B. Makidon, B. R. Oppenheimer, and J. R. Graham, “The structure of high Strehl ratio point-spread functions,” Astrophys. J. 596, 702–712 (2003).
    [CrossRef]
  8. C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescopes,” Astron. Astrophys. 447, 397–403 (2006).
    [CrossRef]
  9. C. Marois, D. Lafrenière, R. Doyon, B. Macintosh, and D. Nadeau, “Angular differential imaging: A powerful high-contrast imaging technique,” Astrophys. J. 641, 556–564 (2006).
    [CrossRef]
  10. D. Lafrenière, C. Marois, R. Doyon, D. Nadeau, and É. Artigau, “A new algorithm for point-spread function subtraction in high-contrast imaging: A demonstration with angular differential imaging,” Astrophys. J. 660, 770–780 (2007).
    [CrossRef]
  11. L. M. Mugnier, A. Cornia, J.-F. Sauvage, G. Rousset, T. Fusco, and N. Védrenne, “Optimal method for exoplanet detection by angular differential imaging,” J. Opt. Soc. Am. A 26, 1326–1334 (2009).
    [CrossRef]
  12. C. Marois, R. Doyon, D. Nadeau, R. Racine, M. Riopel, P. Vallée, and D. Lafrenière, “TRIDENT: an infrared differential imaging camera optimized for the detection of methanated substellar companions,” Publ. Astron. Soc. Pac. 117, 745–756 (2005).
    [CrossRef]
  13. A. Boccaletti, D. Mouillet, T. Fusco, P. Baudoz, C. Cavarroc, J.-L. Beuzit, C. Moutou, and K. Dohlen, “Analysis of ground-based differential imager performance,” presented at IAUC 200, Direct Imaging of Exoplanets: Science and Techniques,” Nice, France, October 2005 (2005).
  14. I. Smith, M. Carbillet, A. Ferrari, D. Mouillet, A. Boccaletti, and K. Dohlen, “Simulation of moving exoplanets detection using the VLT instrument SPHERE/IRDIS,” Proc. SPIE 7015, 70156F (2008).
  15. C. Aime and R. Soummer, “The usefulness and limits of coronagraphy in the presence of pinned speckles,” Astrophys. J. Lett. 612, L85–L88 (2004).
    [CrossRef]
  16. R. Soummer, K. Dohlen, and C. Aime, “Achromatic dual-zone phase mask stellar coronagraph,” Astron. Astrophys. 403, 369–381 (2003).
    [CrossRef]
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  21. L. A. Poyneer and B. Macintosh, “Spatially filtered wave-front sensor for high-order adaptive optics,” J. Opt. Soc. Am. A 21, 810–819 (2004).
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  22. T. Fusco, C. Petit, G. Rousset, J.-M. Conan, and J.-L. Beuzit, “Closed-loop experimental validation of the spatially filtered Shack–Hartmann concept,” Opt. Lett. 30, 1255–1257 (2005).
    [CrossRef] [PubMed]
  23. J.-F. Sauvage, T. Fusco, G. Rousset, and C. Petit, “Calibration and pre-compensation of non-common path aberrations for extreme adaptive optics,” J. Opt. Soc. Am. A 24, 2334–2346 (2007).
    [CrossRef]
  24. D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
    [CrossRef]
  25. F. Malbet, “High angular resolution coronography for adaptive optics,” Astron. Astrophys. Suppl. Ser. 115, 161–174 (1996).
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    [CrossRef]
  27. J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, and 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]
  28. L. M. Mugnier, T. Fusco, and J.-M. Conan, “MISTRAL: a myopic edge-preserving image restoration method with application to astronomical adaptive-optics-corrected long-exposure images,” J. Opt. Soc. Am. A 21, 1841–1854 (2004).
    [CrossRef]
  29. D. Gratadour, D. Rouan, L. M. Mugnier, T. Fusco, Y. Clénet, E. Gendron, and F. Lacombe, “Near-IR AO dissection of the core of NGC 1068 with NaCo,” Astron. Astrophys. 446, 813–825 (2006).
    [CrossRef]
  30. T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P.-Y. Madec, A.-M. Lagrange, J. Charton, D. Rouan, H. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
    [CrossRef]
  31. J.-F. Sauvage, L. Mugnier, T. Fusco, and G. Rousset, “Post processing of differential images for direct extrasolar planet detection from the ground,” Proc. SPIE 6272, 62722B (2006).
    [CrossRef]
  32. J. K. Wallace, J. J. Green, M. Shao, M. Troy, J. P. Lloyd, and B. Macintosh, “Science camera calibration for extreme adaptive optics,” Proc. SPIE 5490, 370–378 (2004).
  33. A. Sivaramakrishnan, R. Soummer, L. Pueyo, J. K. Wallace, and M. Shao, “Sensing phase aberrations behind Lyot coronagraphs,” Astrophys. J. 688, 701–708 (2008).
    [CrossRef]

2009 (1)

L. M. Mugnier, A. Cornia, J.-F. Sauvage, G. Rousset, T. Fusco, and N. Védrenne, “Optimal method for exoplanet detection by angular differential imaging,” J. Opt. Soc. Am. A 26, 1326–1334 (2009).
[CrossRef]

2008 (4)

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, and F. Wildi, “SPHERE: a ‘planet finder’ instrument for the VLT,” Proc. SPIE 7014, 701418 (2008).
[CrossRef]

I. Smith, M. Carbillet, A. Ferrari, D. Mouillet, A. Boccaletti, and K. Dohlen, “Simulation of moving exoplanets detection using the VLT instrument SPHERE/IRDIS,” Proc. SPIE 7015, 70156F (2008).

A. Sivaramakrishnan, R. Soummer, L. Pueyo, J. K. Wallace, and M. Shao, “Sensing phase aberrations behind Lyot coronagraphs,” Astrophys. J. 688, 701–708 (2008).
[CrossRef]

2007 (2)

J.-F. Sauvage, T. Fusco, G. Rousset, and C. Petit, “Calibration and pre-compensation of non-common path aberrations for extreme adaptive optics,” J. Opt. Soc. Am. A 24, 2334–2346 (2007).
[CrossRef]

D. Lafrenière, C. Marois, R. Doyon, D. Nadeau, and É. Artigau, “A new algorithm for point-spread function subtraction in high-contrast imaging: A demonstration with angular differential imaging,” Astrophys. J. 660, 770–780 (2007).
[CrossRef]

2006 (6)

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescopes,” Astron. Astrophys. 447, 397–403 (2006).
[CrossRef]

C. Marois, D. Lafrenière, R. Doyon, B. Macintosh, and D. Nadeau, “Angular differential imaging: A powerful high-contrast imaging technique,” Astrophys. J. 641, 556–564 (2006).
[CrossRef]

D. Gratadour, D. Rouan, L. M. Mugnier, T. Fusco, Y. Clénet, E. Gendron, and F. Lacombe, “Near-IR AO dissection of the core of NGC 1068 with NaCo,” Astron. Astrophys. 446, 813–825 (2006).
[CrossRef]

L. Jolissaint, J.-P. Véran, and R. Conan, “Analytical modeling of adaptive optics: foundations of the phase spatial power spectrum approach,” J. Opt. Soc. Am. A 23, 382–394 (2006).
[CrossRef]

T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, and P. Puget, “High order adaptive optics requirements for direct detection of extra-solar planets. application to the sphere instrument,” Opt. Express 14, 7515–7534 (2006).
[CrossRef] [PubMed]

J.-F. Sauvage, L. Mugnier, T. Fusco, and G. Rousset, “Post processing of differential images for direct extrasolar planet detection from the ground,” Proc. SPIE 6272, 62722B (2006).
[CrossRef]

2005 (2)

T. Fusco, C. Petit, G. Rousset, J.-M. Conan, and J.-L. Beuzit, “Closed-loop experimental validation of the spatially filtered Shack–Hartmann concept,” Opt. Lett. 30, 1255–1257 (2005).
[CrossRef] [PubMed]

C. Marois, R. Doyon, D. Nadeau, R. Racine, M. Riopel, P. Vallée, and D. Lafrenière, “TRIDENT: an infrared differential imaging camera optimized for the detection of methanated substellar companions,” Publ. Astron. Soc. Pac. 117, 745–756 (2005).
[CrossRef]

2004 (5)

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P.-Y. Madec, A.-M. Lagrange, J. Charton, D. Rouan, H. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

C. Aime and R. Soummer, “The usefulness and limits of coronagraphy in the presence of pinned speckles,” Astrophys. J. Lett. 612, L85–L88 (2004).
[CrossRef]

L. A. Poyneer and B. Macintosh, “Spatially filtered wave-front sensor for high-order adaptive optics,” J. Opt. Soc. Am. A 21, 810–819 (2004).
[CrossRef]

L. M. Mugnier, T. Fusco, and J.-M. Conan, “MISTRAL: a myopic edge-preserving image restoration method with application to astronomical adaptive-optics-corrected long-exposure images,” J. Opt. Soc. Am. A 21, 1841–1854 (2004).
[CrossRef]

J. K. Wallace, J. J. Green, M. Shao, M. Troy, J. P. Lloyd, and B. Macintosh, “Science camera calibration for extreme adaptive optics,” Proc. SPIE 5490, 370–378 (2004).

2003 (2)

R. Soummer, K. Dohlen, and C. Aime, “Achromatic dual-zone phase mask stellar coronagraph,” Astron. Astrophys. 403, 369–381 (2003).
[CrossRef]

M. D. Perrin, A. Sivaramakrishnan, R. B. Makidon, B. R. Oppenheimer, and J. R. Graham, “The structure of high Strehl ratio point-spread functions,” Astrophys. J. 596, 702–712 (2003).
[CrossRef]

2001 (2)

E. E. Bloemhof, R. G. Dekany, M. Troy, and B. R. Oppenheimer, “Behavior of remnant speckles in an adaptively corrected imaging system,” Astrophys. J. 558, L71–L74 (2001).
[CrossRef]

A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552, 397–408 (2001).
[CrossRef]

2000 (1)

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

1999 (1)

R. Racine, G. A. Walker, D. Nadeau, and C. Marois, “Speckle noise and the detection of faint companions’,” Publ. Astron. Soc. Pac. 112, 587 (1999).
[CrossRef]

1998 (1)

1997 (1)

1996 (1)

F. Malbet, “High angular resolution coronography for adaptive optics,” Astron. Astrophys. Suppl. Ser. 115, 161–174 (1996).

Ageorges, N.

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P.-Y. Madec, A.-M. Lagrange, J. Charton, D. Rouan, H. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

Aime, C.

C. Aime and R. Soummer, “The usefulness and limits of coronagraphy in the presence of pinned speckles,” Astrophys. J. Lett. 612, L85–L88 (2004).
[CrossRef]

R. Soummer, K. Dohlen, and C. Aime, “Achromatic dual-zone phase mask stellar coronagraph,” Astron. Astrophys. 403, 369–381 (2003).
[CrossRef]

Artigau, É.

D. Lafrenière, C. Marois, R. Doyon, D. Nadeau, and É. Artigau, “A new algorithm for point-spread function subtraction in high-contrast imaging: A demonstration with angular differential imaging,” Astrophys. J. 660, 770–780 (2007).
[CrossRef]

Baudoz, P.

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescopes,” Astron. Astrophys. 447, 397–403 (2006).
[CrossRef]

A. Boccaletti, D. Mouillet, T. Fusco, P. Baudoz, C. Cavarroc, J.-L. Beuzit, C. Moutou, and K. Dohlen, “Analysis of ground-based differential imager performance,” presented at IAUC 200, Direct Imaging of Exoplanets: Science and Techniques,” Nice, France, October 2005 (2005).

Bauman, B.

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

Berkefeld, T.

A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552, 397–408 (2001).
[CrossRef]

Beuzit, J.-L.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, and F. Wildi, “SPHERE: a ‘planet finder’ instrument for the VLT,” Proc. SPIE 7014, 701418 (2008).
[CrossRef]

T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, and P. Puget, “High order adaptive optics requirements for direct detection of extra-solar planets. application to the sphere instrument,” Opt. Express 14, 7515–7534 (2006).
[CrossRef] [PubMed]

T. Fusco, C. Petit, G. Rousset, J.-M. Conan, and J.-L. Beuzit, “Closed-loop experimental validation of the spatially filtered Shack–Hartmann concept,” Opt. Lett. 30, 1255–1257 (2005).
[CrossRef] [PubMed]

A. Boccaletti, D. Mouillet, T. Fusco, P. Baudoz, C. Cavarroc, J.-L. Beuzit, C. Moutou, and K. Dohlen, “Analysis of ground-based differential imager performance,” presented at IAUC 200, Direct Imaging of Exoplanets: Science and Techniques,” Nice, France, October 2005 (2005).

Bloemhof, E. E.

E. E. Bloemhof, R. G. Dekany, M. Troy, and B. R. Oppenheimer, “Behavior of remnant speckles in an adaptively corrected imaging system,” Astrophys. J. 558, L71–L74 (2001).
[CrossRef]

Boccaletti, A.

I. Smith, M. Carbillet, A. Ferrari, D. Mouillet, A. Boccaletti, and K. Dohlen, “Simulation of moving exoplanets detection using the VLT instrument SPHERE/IRDIS,” Proc. SPIE 7015, 70156F (2008).

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescopes,” Astron. Astrophys. 447, 397–403 (2006).
[CrossRef]

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

A. Boccaletti, D. Mouillet, T. Fusco, P. Baudoz, C. Cavarroc, J.-L. Beuzit, C. Moutou, and K. Dohlen, “Analysis of ground-based differential imager performance,” presented at IAUC 200, Direct Imaging of Exoplanets: Science and Techniques,” Nice, France, October 2005 (2005).

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th (corrected) ed. (Pergamon Press, 1993).

Carbillet, M.

I. Smith, M. Carbillet, A. Ferrari, D. Mouillet, A. Boccaletti, and K. Dohlen, “Simulation of moving exoplanets detection using the VLT instrument SPHERE/IRDIS,” Proc. SPIE 7015, 70156F (2008).

Cavarroc, C.

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescopes,” Astron. Astrophys. 447, 397–403 (2006).
[CrossRef]

A. Boccaletti, D. Mouillet, T. Fusco, P. Baudoz, C. Cavarroc, J.-L. Beuzit, C. Moutou, and K. Dohlen, “Analysis of ground-based differential imager performance,” presented at IAUC 200, Direct Imaging of Exoplanets: Science and Techniques,” Nice, France, October 2005 (2005).

Charton, J.

T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, and P. Puget, “High order adaptive optics requirements for direct detection of extra-solar planets. application to the sphere instrument,” Opt. Express 14, 7515–7534 (2006).
[CrossRef] [PubMed]

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P.-Y. Madec, A.-M. Lagrange, J. Charton, D. Rouan, H. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

Clénet, Y.

D. Gratadour, D. Rouan, L. M. Mugnier, T. Fusco, Y. Clénet, E. Gendron, and F. Lacombe, “Near-IR AO dissection of the core of NGC 1068 with NaCo,” Astron. Astrophys. 446, 813–825 (2006).
[CrossRef]

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

Conan, J. M.

J. M. Conan, P. Y. Madec, and G. Rousset, “Evaluation of image quality obtained with adaptive optics partial correction,” in Progress in Telescope and Instrumentation Technologies, ESO Conference and Workshop Proceedings, M.-H. Ulrich, ed. (ESO, 1992), p. 475.

Conan, J.-M.

Conan, R.

Cornia, A.

L. M. Mugnier, A. Cornia, J.-F. Sauvage, G. Rousset, T. Fusco, and N. Védrenne, “Optimal method for exoplanet detection by angular differential imaging,” J. Opt. Soc. Am. A 26, 1326–1334 (2009).
[CrossRef]

Dekany, R. G.

E. E. Bloemhof, R. G. Dekany, M. Troy, and B. R. Oppenheimer, “Behavior of remnant speckles in an adaptively corrected imaging system,” Astrophys. J. 558, L71–L74 (2001).
[CrossRef]

Dohlen, K.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, and F. Wildi, “SPHERE: a ‘planet finder’ instrument for the VLT,” Proc. SPIE 7014, 701418 (2008).
[CrossRef]

I. Smith, M. Carbillet, A. Ferrari, D. Mouillet, A. Boccaletti, and K. Dohlen, “Simulation of moving exoplanets detection using the VLT instrument SPHERE/IRDIS,” Proc. SPIE 7015, 70156F (2008).

T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, and P. Puget, “High order adaptive optics requirements for direct detection of extra-solar planets. application to the sphere instrument,” Opt. Express 14, 7515–7534 (2006).
[CrossRef] [PubMed]

R. Soummer, K. Dohlen, and C. Aime, “Achromatic dual-zone phase mask stellar coronagraph,” Astron. Astrophys. 403, 369–381 (2003).
[CrossRef]

A. Boccaletti, D. Mouillet, T. Fusco, P. Baudoz, C. Cavarroc, J.-L. Beuzit, C. Moutou, and K. Dohlen, “Analysis of ground-based differential imager performance,” presented at IAUC 200, Direct Imaging of Exoplanets: Science and Techniques,” Nice, France, October 2005 (2005).

Doyon, R.

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

D. Lafrenière, C. Marois, R. Doyon, D. Nadeau, and É. Artigau, “A new algorithm for point-spread function subtraction in high-contrast imaging: A demonstration with angular differential imaging,” Astrophys. J. 660, 770–780 (2007).
[CrossRef]

C. Marois, D. Lafrenière, R. Doyon, B. Macintosh, and D. Nadeau, “Angular differential imaging: A powerful high-contrast imaging technique,” Astrophys. J. 641, 556–564 (2006).
[CrossRef]

C. Marois, R. Doyon, D. Nadeau, R. Racine, M. Riopel, P. Vallée, and D. Lafrenière, “TRIDENT: an infrared differential imaging camera optimized for the detection of methanated substellar companions,” Publ. Astron. Soc. Pac. 117, 745–756 (2005).
[CrossRef]

Dunn, J.

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

Erickson, D. A.

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

Feldt, M.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, and F. Wildi, “SPHERE: a ‘planet finder’ instrument for the VLT,” Proc. SPIE 7014, 701418 (2008).
[CrossRef]

Ferrari, A.

I. Smith, M. Carbillet, A. Ferrari, D. Mouillet, A. Boccaletti, and K. Dohlen, “Simulation of moving exoplanets detection using the VLT instrument SPHERE/IRDIS,” Proc. SPIE 7015, 70156F (2008).

Fusco, T.

L. M. Mugnier, A. Cornia, J.-F. Sauvage, G. Rousset, T. Fusco, and N. Védrenne, “Optimal method for exoplanet detection by angular differential imaging,” J. Opt. Soc. Am. A 26, 1326–1334 (2009).
[CrossRef]

J.-F. Sauvage, T. Fusco, G. Rousset, and C. Petit, “Calibration and pre-compensation of non-common path aberrations for extreme adaptive optics,” J. Opt. Soc. Am. A 24, 2334–2346 (2007).
[CrossRef]

T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, and P. Puget, “High order adaptive optics requirements for direct detection of extra-solar planets. application to the sphere instrument,” Opt. Express 14, 7515–7534 (2006).
[CrossRef] [PubMed]

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescopes,” Astron. Astrophys. 447, 397–403 (2006).
[CrossRef]

J.-F. Sauvage, L. Mugnier, T. Fusco, and G. Rousset, “Post processing of differential images for direct extrasolar planet detection from the ground,” Proc. SPIE 6272, 62722B (2006).
[CrossRef]

D. Gratadour, D. Rouan, L. M. Mugnier, T. Fusco, Y. Clénet, E. Gendron, and F. Lacombe, “Near-IR AO dissection of the core of NGC 1068 with NaCo,” Astron. Astrophys. 446, 813–825 (2006).
[CrossRef]

T. Fusco, C. Petit, G. Rousset, J.-M. Conan, and J.-L. Beuzit, “Closed-loop experimental validation of the spatially filtered Shack–Hartmann concept,” Opt. Lett. 30, 1255–1257 (2005).
[CrossRef] [PubMed]

L. M. Mugnier, T. Fusco, and J.-M. Conan, “MISTRAL: a myopic edge-preserving image restoration method with application to astronomical adaptive-optics-corrected long-exposure images,” J. Opt. Soc. Am. A 21, 1841–1854 (2004).
[CrossRef]

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P.-Y. Madec, A.-M. Lagrange, J. Charton, D. Rouan, H. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, and 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]

A. Boccaletti, D. Mouillet, T. Fusco, P. Baudoz, C. Cavarroc, J.-L. Beuzit, C. Moutou, and K. Dohlen, “Analysis of ground-based differential imager performance,” presented at IAUC 200, Direct Imaging of Exoplanets: Science and Techniques,” Nice, France, October 2005 (2005).

Gavel, D. T.

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

Gendron, E.

D. Gratadour, D. Rouan, L. M. Mugnier, T. Fusco, Y. Clénet, E. Gendron, and F. Lacombe, “Near-IR AO dissection of the core of NGC 1068 with NaCo,” Astron. Astrophys. 446, 813–825 (2006).
[CrossRef]

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P.-Y. Madec, A.-M. Lagrange, J. Charton, D. Rouan, H. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

Graham, J. R.

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

M. D. Perrin, A. Sivaramakrishnan, R. B. Makidon, B. R. Oppenheimer, and J. R. Graham, “The structure of high Strehl ratio point-spread functions,” Astrophys. J. 596, 702–712 (2003).
[CrossRef]

Gratadour, D.

D. Gratadour, D. Rouan, L. M. Mugnier, T. Fusco, Y. Clénet, E. Gendron, and F. Lacombe, “Near-IR AO dissection of the core of NGC 1068 with NaCo,” Astron. Astrophys. 446, 813–825 (2006).
[CrossRef]

Green, J. J.

J. K. Wallace, J. J. Green, M. Shao, M. Troy, J. P. Lloyd, and B. Macintosh, “Science camera calibration for extreme adaptive optics,” Proc. SPIE 5490, 370–378 (2004).

Hubin, H.

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P.-Y. Madec, A.-M. Lagrange, J. Charton, D. Rouan, H. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

Jolissaint, L.

Kasper, M.

Koresko, C. D.

A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552, 397–408 (2001).
[CrossRef]

Kuchner, M. J.

A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552, 397–408 (2001).
[CrossRef]

Labeyrie, A.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

Lacombe, F.

D. Gratadour, D. Rouan, L. M. Mugnier, T. Fusco, Y. Clénet, E. Gendron, and F. Lacombe, “Near-IR AO dissection of the core of NGC 1068 with NaCo,” Astron. Astrophys. 446, 813–825 (2006).
[CrossRef]

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P.-Y. Madec, A.-M. Lagrange, J. Charton, D. Rouan, H. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

Lafrenière, D.

D. Lafrenière, C. Marois, R. Doyon, D. Nadeau, and É. Artigau, “A new algorithm for point-spread function subtraction in high-contrast imaging: A demonstration with angular differential imaging,” Astrophys. J. 660, 770–780 (2007).
[CrossRef]

C. Marois, D. Lafrenière, R. Doyon, B. Macintosh, and D. Nadeau, “Angular differential imaging: A powerful high-contrast imaging technique,” Astrophys. J. 641, 556–564 (2006).
[CrossRef]

C. Marois, R. Doyon, D. Nadeau, R. Racine, M. Riopel, P. Vallée, and D. Lafrenière, “TRIDENT: an infrared differential imaging camera optimized for the detection of methanated substellar companions,” Publ. Astron. Soc. Pac. 117, 745–756 (2005).
[CrossRef]

Lagrange, A.-M.

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P.-Y. Madec, A.-M. Lagrange, J. Charton, D. Rouan, H. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

Larkin, J.

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

Lloyd, J. P.

J. K. Wallace, J. J. Green, M. Shao, M. Troy, J. P. Lloyd, and B. Macintosh, “Science camera calibration for extreme adaptive optics,” Proc. SPIE 5490, 370–378 (2004).

Macintosh, B.

C. Marois, D. Lafrenière, R. Doyon, B. Macintosh, and D. Nadeau, “Angular differential imaging: A powerful high-contrast imaging technique,” Astrophys. J. 641, 556–564 (2006).
[CrossRef]

L. A. Poyneer and B. Macintosh, “Spatially filtered wave-front sensor for high-order adaptive optics,” J. Opt. Soc. Am. A 21, 810–819 (2004).
[CrossRef]

J. K. Wallace, J. J. Green, M. Shao, M. Troy, J. P. Lloyd, and B. Macintosh, “Science camera calibration for extreme adaptive optics,” Proc. SPIE 5490, 370–378 (2004).

Macintosh, B. A.

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

Madec, P. Y.

J. M. Conan, P. Y. Madec, and G. Rousset, “Evaluation of image quality obtained with adaptive optics partial correction,” in Progress in Telescope and Instrumentation Technologies, ESO Conference and Workshop Proceedings, M.-H. Ulrich, ed. (ESO, 1992), p. 475.

Madec, P.-Y.

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P.-Y. Madec, A.-M. Lagrange, J. Charton, D. Rouan, H. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

Maître, H.

Makidon, R. B.

M. D. Perrin, A. Sivaramakrishnan, R. B. Makidon, B. R. Oppenheimer, and J. R. Graham, “The structure of high Strehl ratio point-spread functions,” Astrophys. J. 596, 702–712 (2003).
[CrossRef]

A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552, 397–408 (2001).
[CrossRef]

Malbet, F.

F. Malbet, “High angular resolution coronography for adaptive optics,” Astron. Astrophys. Suppl. Ser. 115, 161–174 (1996).

Marois, C.

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

D. Lafrenière, C. Marois, R. Doyon, D. Nadeau, and É. Artigau, “A new algorithm for point-spread function subtraction in high-contrast imaging: A demonstration with angular differential imaging,” Astrophys. J. 660, 770–780 (2007).
[CrossRef]

C. Marois, D. Lafrenière, R. Doyon, B. Macintosh, and D. Nadeau, “Angular differential imaging: A powerful high-contrast imaging technique,” Astrophys. J. 641, 556–564 (2006).
[CrossRef]

C. Marois, R. Doyon, D. Nadeau, R. Racine, M. Riopel, P. Vallée, and D. Lafrenière, “TRIDENT: an infrared differential imaging camera optimized for the detection of methanated substellar companions,” Publ. Astron. Soc. Pac. 117, 745–756 (2005).
[CrossRef]

R. Racine, G. A. Walker, D. Nadeau, and C. Marois, “Speckle noise and the detection of faint companions’,” Publ. Astron. Soc. Pac. 112, 587 (1999).
[CrossRef]

Michau, V.

Mouillet, D.

I. Smith, M. Carbillet, A. Ferrari, D. Mouillet, A. Boccaletti, and K. Dohlen, “Simulation of moving exoplanets detection using the VLT instrument SPHERE/IRDIS,” Proc. SPIE 7015, 70156F (2008).

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, and F. Wildi, “SPHERE: a ‘planet finder’ instrument for the VLT,” Proc. SPIE 7014, 701418 (2008).
[CrossRef]

T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, and P. Puget, “High order adaptive optics requirements for direct detection of extra-solar planets. application to the sphere instrument,” Opt. Express 14, 7515–7534 (2006).
[CrossRef] [PubMed]

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P.-Y. Madec, A.-M. Lagrange, J. Charton, D. Rouan, H. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

A. Boccaletti, D. Mouillet, T. Fusco, P. Baudoz, C. Cavarroc, J.-L. Beuzit, C. Moutou, and K. Dohlen, “Analysis of ground-based differential imager performance,” presented at IAUC 200, Direct Imaging of Exoplanets: Science and Techniques,” Nice, France, October 2005 (2005).

Moutou, C.

A. Boccaletti, D. Mouillet, T. Fusco, P. Baudoz, C. Cavarroc, J.-L. Beuzit, C. Moutou, and K. Dohlen, “Analysis of ground-based differential imager performance,” presented at IAUC 200, Direct Imaging of Exoplanets: Science and Techniques,” Nice, France, October 2005 (2005).

Mugnier, L.

J.-F. Sauvage, L. Mugnier, T. Fusco, and G. Rousset, “Post processing of differential images for direct extrasolar planet detection from the ground,” Proc. SPIE 6272, 62722B (2006).
[CrossRef]

Mugnier, L. M.

L. M. Mugnier, A. Cornia, J.-F. Sauvage, G. Rousset, T. Fusco, and N. Védrenne, “Optimal method for exoplanet detection by angular differential imaging,” J. Opt. Soc. Am. A 26, 1326–1334 (2009).
[CrossRef]

D. Gratadour, D. Rouan, L. M. Mugnier, T. Fusco, Y. Clénet, E. Gendron, and F. Lacombe, “Near-IR AO dissection of the core of NGC 1068 with NaCo,” Astron. Astrophys. 446, 813–825 (2006).
[CrossRef]

L. M. Mugnier, T. Fusco, and J.-M. Conan, “MISTRAL: a myopic edge-preserving image restoration method with application to astronomical adaptive-optics-corrected long-exposure images,” J. Opt. Soc. Am. A 21, 1841–1854 (2004).
[CrossRef]

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, and 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]

Nadeau, D.

D. Lafrenière, C. Marois, R. Doyon, D. Nadeau, and É. Artigau, “A new algorithm for point-spread function subtraction in high-contrast imaging: A demonstration with angular differential imaging,” Astrophys. J. 660, 770–780 (2007).
[CrossRef]

C. Marois, D. Lafrenière, R. Doyon, B. Macintosh, and D. Nadeau, “Angular differential imaging: A powerful high-contrast imaging technique,” Astrophys. J. 641, 556–564 (2006).
[CrossRef]

C. Marois, R. Doyon, D. Nadeau, R. Racine, M. Riopel, P. Vallée, and D. Lafrenière, “TRIDENT: an infrared differential imaging camera optimized for the detection of methanated substellar companions,” Publ. Astron. Soc. Pac. 117, 745–756 (2005).
[CrossRef]

R. Racine, G. A. Walker, D. Nadeau, and C. Marois, “Speckle noise and the detection of faint companions’,” Publ. Astron. Soc. Pac. 112, 587 (1999).
[CrossRef]

Nicolle, M.

Oppenheimer, B.

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

Oppenheimer, B. R.

M. D. Perrin, A. Sivaramakrishnan, R. B. Makidon, B. R. Oppenheimer, and J. R. Graham, “The structure of high Strehl ratio point-spread functions,” Astrophys. J. 596, 702–712 (2003).
[CrossRef]

E. E. Bloemhof, R. G. Dekany, M. Troy, and B. R. Oppenheimer, “Behavior of remnant speckles in an adaptively corrected imaging system,” Astrophys. J. 558, L71–L74 (2001).
[CrossRef]

Palmer, D. W.

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

Perrin, M. D.

M. D. Perrin, A. Sivaramakrishnan, R. B. Makidon, B. R. Oppenheimer, and J. R. Graham, “The structure of high Strehl ratio point-spread functions,” Astrophys. J. 596, 702–712 (2003).
[CrossRef]

Petit, C.

Poyneer, L. A.

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

L. A. Poyneer and B. Macintosh, “Spatially filtered wave-front sensor for high-order adaptive optics,” J. Opt. Soc. Am. A 21, 810–819 (2004).
[CrossRef]

Pueyo, L.

A. Sivaramakrishnan, R. Soummer, L. Pueyo, J. K. Wallace, and M. Shao, “Sensing phase aberrations behind Lyot coronagraphs,” Astrophys. J. 688, 701–708 (2008).
[CrossRef]

Puget, P.

Rabaud, D.

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P.-Y. Madec, A.-M. Lagrange, J. Charton, D. Rouan, H. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

Racine, R.

C. Marois, R. Doyon, D. Nadeau, R. Racine, M. Riopel, P. Vallée, and D. Lafrenière, “TRIDENT: an infrared differential imaging camera optimized for the detection of methanated substellar companions,” Publ. Astron. Soc. Pac. 117, 745–756 (2005).
[CrossRef]

R. Racine, G. A. Walker, D. Nadeau, and C. Marois, “Speckle noise and the detection of faint companions’,” Publ. Astron. Soc. Pac. 112, 587 (1999).
[CrossRef]

Riaud, P.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

Rigaut, F.

Riopel, M.

C. Marois, R. Doyon, D. Nadeau, R. Racine, M. Riopel, P. Vallée, and D. Lafrenière, “TRIDENT: an infrared differential imaging camera optimized for the detection of methanated substellar companions,” Publ. Astron. Soc. Pac. 117, 745–756 (2005).
[CrossRef]

Roddier, F.

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

Rouan, D.

D. Gratadour, D. Rouan, L. M. Mugnier, T. Fusco, Y. Clénet, E. Gendron, and F. Lacombe, “Near-IR AO dissection of the core of NGC 1068 with NaCo,” Astron. Astrophys. 446, 813–825 (2006).
[CrossRef]

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescopes,” Astron. Astrophys. 447, 397–403 (2006).
[CrossRef]

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P.-Y. Madec, A.-M. Lagrange, J. Charton, D. Rouan, H. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

J.-P. Véran, F. Rigaut, H. Maître, and 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]

Rousset, G.

L. M. Mugnier, A. Cornia, J.-F. Sauvage, G. Rousset, T. Fusco, and N. Védrenne, “Optimal method for exoplanet detection by angular differential imaging,” J. Opt. Soc. Am. A 26, 1326–1334 (2009).
[CrossRef]

J.-F. Sauvage, T. Fusco, G. Rousset, and C. Petit, “Calibration and pre-compensation of non-common path aberrations for extreme adaptive optics,” J. Opt. Soc. Am. A 24, 2334–2346 (2007).
[CrossRef]

T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, and P. Puget, “High order adaptive optics requirements for direct detection of extra-solar planets. application to the sphere instrument,” Opt. Express 14, 7515–7534 (2006).
[CrossRef] [PubMed]

J.-F. Sauvage, L. Mugnier, T. Fusco, and G. Rousset, “Post processing of differential images for direct extrasolar planet detection from the ground,” Proc. SPIE 6272, 62722B (2006).
[CrossRef]

T. Fusco, C. Petit, G. Rousset, J.-M. Conan, and J.-L. Beuzit, “Closed-loop experimental validation of the spatially filtered Shack–Hartmann concept,” Opt. Lett. 30, 1255–1257 (2005).
[CrossRef] [PubMed]

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P.-Y. Madec, A.-M. Lagrange, J. Charton, D. Rouan, H. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, and 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, P. Y. Madec, and G. Rousset, “Evaluation of image quality obtained with adaptive optics partial correction,” in Progress in Telescope and Instrumentation Technologies, ESO Conference and Workshop Proceedings, M.-H. Ulrich, ed. (ESO, 1992), p. 475.

Saddlemyer, L.

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

Sauvage, J.-F.

L. M. Mugnier, A. Cornia, J.-F. Sauvage, G. Rousset, T. Fusco, and N. Védrenne, “Optimal method for exoplanet detection by angular differential imaging,” J. Opt. Soc. Am. A 26, 1326–1334 (2009).
[CrossRef]

J.-F. Sauvage, T. Fusco, G. Rousset, and C. Petit, “Calibration and pre-compensation of non-common path aberrations for extreme adaptive optics,” J. Opt. Soc. Am. A 24, 2334–2346 (2007).
[CrossRef]

T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, and P. Puget, “High order adaptive optics requirements for direct detection of extra-solar planets. application to the sphere instrument,” Opt. Express 14, 7515–7534 (2006).
[CrossRef] [PubMed]

J.-F. Sauvage, L. Mugnier, T. Fusco, and G. Rousset, “Post processing of differential images for direct extrasolar planet detection from the ground,” Proc. SPIE 6272, 62722B (2006).
[CrossRef]

Shao, M.

A. Sivaramakrishnan, R. Soummer, L. Pueyo, J. K. Wallace, and M. Shao, “Sensing phase aberrations behind Lyot coronagraphs,” Astrophys. J. 688, 701–708 (2008).
[CrossRef]

J. K. Wallace, J. J. Green, M. Shao, M. Troy, J. P. Lloyd, and B. Macintosh, “Science camera calibration for extreme adaptive optics,” Proc. SPIE 5490, 370–378 (2004).

Sivaramakrishnan, A.

A. Sivaramakrishnan, R. Soummer, L. Pueyo, J. K. Wallace, and M. Shao, “Sensing phase aberrations behind Lyot coronagraphs,” Astrophys. J. 688, 701–708 (2008).
[CrossRef]

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

M. D. Perrin, A. Sivaramakrishnan, R. B. Makidon, B. R. Oppenheimer, and J. R. Graham, “The structure of high Strehl ratio point-spread functions,” Astrophys. J. 596, 702–712 (2003).
[CrossRef]

A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552, 397–408 (2001).
[CrossRef]

Smith, I.

I. Smith, M. Carbillet, A. Ferrari, D. Mouillet, A. Boccaletti, and K. Dohlen, “Simulation of moving exoplanets detection using the VLT instrument SPHERE/IRDIS,” Proc. SPIE 7015, 70156F (2008).

Soummer, R.

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

A. Sivaramakrishnan, R. Soummer, L. Pueyo, J. K. Wallace, and M. Shao, “Sensing phase aberrations behind Lyot coronagraphs,” Astrophys. J. 688, 701–708 (2008).
[CrossRef]

C. Aime and R. Soummer, “The usefulness and limits of coronagraphy in the presence of pinned speckles,” Astrophys. J. Lett. 612, L85–L88 (2004).
[CrossRef]

R. Soummer, K. Dohlen, and C. Aime, “Achromatic dual-zone phase mask stellar coronagraph,” Astron. Astrophys. 403, 369–381 (2003).
[CrossRef]

Troy, M.

J. K. Wallace, J. J. Green, M. Shao, M. Troy, J. P. Lloyd, and B. Macintosh, “Science camera calibration for extreme adaptive optics,” Proc. SPIE 5490, 370–378 (2004).

E. E. Bloemhof, R. G. Dekany, M. Troy, and B. R. Oppenheimer, “Behavior of remnant speckles in an adaptively corrected imaging system,” Astrophys. J. 558, L71–L74 (2001).
[CrossRef]

Vallée, P.

C. Marois, R. Doyon, D. Nadeau, R. Racine, M. Riopel, P. Vallée, and D. Lafrenière, “TRIDENT: an infrared differential imaging camera optimized for the detection of methanated substellar companions,” Publ. Astron. Soc. Pac. 117, 745–756 (2005).
[CrossRef]

Védrenne, N.

L. M. Mugnier, A. Cornia, J.-F. Sauvage, G. Rousset, T. Fusco, and N. Védrenne, “Optimal method for exoplanet detection by angular differential imaging,” J. Opt. Soc. Am. A 26, 1326–1334 (2009).
[CrossRef]

Véran, J.-P.

Walker, G. A.

R. Racine, G. A. Walker, D. Nadeau, and C. Marois, “Speckle noise and the detection of faint companions’,” Publ. Astron. Soc. Pac. 112, 587 (1999).
[CrossRef]

Wallace, J. K.

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

A. Sivaramakrishnan, R. Soummer, L. Pueyo, J. K. Wallace, and M. Shao, “Sensing phase aberrations behind Lyot coronagraphs,” Astrophys. J. 688, 701–708 (2008).
[CrossRef]

J. K. Wallace, J. J. Green, M. Shao, M. Troy, J. P. Lloyd, and B. Macintosh, “Science camera calibration for extreme adaptive optics,” Proc. SPIE 5490, 370–378 (2004).

Wildi, F.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, and F. Wildi, “SPHERE: a ‘planet finder’ instrument for the VLT,” Proc. SPIE 7014, 701418 (2008).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th (corrected) ed. (Pergamon Press, 1993).

Zins, G.

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P.-Y. Madec, A.-M. Lagrange, J. Charton, D. Rouan, H. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

Appl. Opt. (1)

Astron. Astrophys. (3)

D. Gratadour, D. Rouan, L. M. Mugnier, T. Fusco, Y. Clénet, E. Gendron, and F. Lacombe, “Near-IR AO dissection of the core of NGC 1068 with NaCo,” Astron. Astrophys. 446, 813–825 (2006).
[CrossRef]

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescopes,” Astron. Astrophys. 447, 397–403 (2006).
[CrossRef]

R. Soummer, K. Dohlen, and C. Aime, “Achromatic dual-zone phase mask stellar coronagraph,” Astron. Astrophys. 403, 369–381 (2003).
[CrossRef]

Astron. Astrophys. Suppl. Ser. (1)

F. Malbet, “High angular resolution coronography for adaptive optics,” Astron. Astrophys. Suppl. Ser. 115, 161–174 (1996).

Astrophys. J. (2)

C. Marois, D. Lafrenière, R. Doyon, B. Macintosh, and D. Nadeau, “Angular differential imaging: A powerful high-contrast imaging technique,” Astrophys. J. 641, 556–564 (2006).
[CrossRef]

E. E. Bloemhof, R. G. Dekany, M. Troy, and B. R. Oppenheimer, “Behavior of remnant speckles in an adaptively corrected imaging system,” Astrophys. J. 558, L71–L74 (2001).
[CrossRef]

Astrophys. J. Lett. (1)

C. Aime and R. Soummer, “The usefulness and limits of coronagraphy in the presence of pinned speckles,” Astrophys. J. Lett. 612, L85–L88 (2004).
[CrossRef]

Astrophys. J. (4)

A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552, 397–408 (2001).
[CrossRef]

M. D. Perrin, A. Sivaramakrishnan, R. B. Makidon, B. R. Oppenheimer, and J. R. Graham, “The structure of high Strehl ratio point-spread functions,” Astrophys. J. 596, 702–712 (2003).
[CrossRef]

D. Lafrenière, C. Marois, R. Doyon, D. Nadeau, and É. Artigau, “A new algorithm for point-spread function subtraction in high-contrast imaging: A demonstration with angular differential imaging,” Astrophys. J. 660, 770–780 (2007).
[CrossRef]

A. Sivaramakrishnan, R. Soummer, L. Pueyo, J. K. Wallace, and M. Shao, “Sensing phase aberrations behind Lyot coronagraphs,” Astrophys. J. 688, 701–708 (2008).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P.-Y. Madec, A.-M. Lagrange, J. Charton, D. Rouan, H. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

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

L. M. Mugnier, A. Cornia, J.-F. Sauvage, G. Rousset, T. Fusco, and N. Védrenne, “Optimal method for exoplanet detection by angular differential imaging,” J. Opt. Soc. Am. A 26, 1326–1334 (2009).
[CrossRef]

L. A. Poyneer and B. Macintosh, “Spatially filtered wave-front sensor for high-order adaptive optics,” J. Opt. Soc. Am. A 21, 810–819 (2004).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (3)

B. A. Macintosh, J. R. Graham, D. W. Palmer, R. Doyon, J. Dunn, D. T. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, A. Sivaramakrishnan, J. K. Wallace, B. Bauman, D. A. Erickson, C. Marois, L. A. Poyneer, and R. Soummer, “The Gemini Planet Imager: from science to design to construction,” Proc. SPIE 7015, 701518 (2008).
[CrossRef]

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, and F. Wildi, “SPHERE: a ‘planet finder’ instrument for the VLT,” Proc. SPIE 7014, 701418 (2008).
[CrossRef]

J.-F. Sauvage, L. Mugnier, T. Fusco, and G. Rousset, “Post processing of differential images for direct extrasolar planet detection from the ground,” Proc. SPIE 6272, 62722B (2006).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

R. Racine, G. A. Walker, D. Nadeau, and C. Marois, “Speckle noise and the detection of faint companions’,” Publ. Astron. Soc. Pac. 112, 587 (1999).
[CrossRef]

Publ. Astron. Soc. Pac. (2)

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

C. Marois, R. Doyon, D. Nadeau, R. Racine, M. Riopel, P. Vallée, and D. Lafrenière, “TRIDENT: an infrared differential imaging camera optimized for the detection of methanated substellar companions,” Publ. Astron. Soc. Pac. 117, 745–756 (2005).
[CrossRef]

Other (6)

A. Boccaletti, D. Mouillet, T. Fusco, P. Baudoz, C. Cavarroc, J.-L. Beuzit, C. Moutou, and K. Dohlen, “Analysis of ground-based differential imager performance,” presented at IAUC 200, Direct Imaging of Exoplanets: Science and Techniques,” Nice, France, October 2005 (2005).

I. Smith, M. Carbillet, A. Ferrari, D. Mouillet, A. Boccaletti, and K. Dohlen, “Simulation of moving exoplanets detection using the VLT instrument SPHERE/IRDIS,” Proc. SPIE 7015, 70156F (2008).

J. M. Conan, P. Y. Madec, and G. Rousset, “Evaluation of image quality obtained with adaptive optics partial correction,” in Progress in Telescope and Instrumentation Technologies, ESO Conference and Workshop Proceedings, M.-H. Ulrich, ed. (ESO, 1992), p. 475.

M. Born and E. Wolf, Principles of Optics, 6th (corrected) ed. (Pergamon Press, 1993).

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

J. K. Wallace, J. J. Green, M. Shao, M. Troy, J. P. Lloyd, and B. Macintosh, “Science camera calibration for extreme adaptive optics,” Proc. SPIE 5490, 370–378 (2004).

Cited By

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Figures (12)

Fig. 1
Fig. 1

Optical scheme of a coronagraphic imager. The upstream and downstream static aberrations as well as the adopted notations are φ u and φ d respectively. A i ( α ) denote focal plane complex amplitudes, while Ψ i ( ρ ) denote pupil plane amplitudes.

Fig. 2
Fig. 2

Coronagraph response for a system comprising pure tip–tilt from 1.6 to 1.6  rad . Central PSF is completely obscured as the perfect coronagraph presents an infinite extinction for a non-aberrant system.

Fig. 3
Fig. 3

Static aberrations spectrum upstream of the coronagraph mask. Low frequencies are assumed to be pre-compensated down to a residual of 5 mm . The medium frequencies follow a 1 f 2 shaped spectrum, with an RMS value of 35 nm . The total RMS value of the OPD of the upstream aberrations is σ u = 35.3 nm .

Fig. 4
Fig. 4

Profiles of long-exposure star images with and without coronagraph for the conditions given in Subsection , including AO residuals (SPHERE case), upstream and downstream aberrations, perfect coronagraph, at wavelength λ = 1.6 μ m . Profiles normalized to 1 photon in the entrance pupil. Horizontal dotted–dashed lines: maximum intensity for a planet of contrast 2.10 4 (centered on 1  pixel and between 4  pixels ). Vertical dotted–dashed line: cutoff of the AO correction ( 20 λ D ) .

Fig. 5
Fig. 5

(Left) Analytical model, (center) simulated coronagraphic PSF with N = 1000 turbulence realizations, and (right) absolute value of difference in log-scale and same dynamic. The image formation includes residual turbulence and static aberrations. The conditions of simulation are the ones explained in Subsection 3A.

Fig. 6
Fig. 6

Circularly averaged profiles of error between the analytical model and the simulated star image. The profiles are plotted for different cases of long-exposure convergence. The image formation includes residual turbulence and static aberrations. The simulation conditions are explained in Subsection 3A.

Fig. 7
Fig. 7

(Left) Analytical model , (center left) FQPM coronagraphic PSF simulated, (center right) absolute value of difference, and (right) the same without accounting for the biquadrants points (log-scale, same dynamic). The image formation includes residual turbulence and static aberrations. The conditions of simulation are the ones explained in Subsection 3A.

Fig. 8
Fig. 8

Circularly averaged profiles of error between the analytical model and the simulated star image with FPQM coronagraph. The image formation includes residual turbulence and static aberrations. The simulation conditions are explained in Subsection 3A.

Fig. 9
Fig. 9

Profiles of the difference h Δ for different error levels on the miscalibration of the structure function. Dotted curve, β = 0.8 . Dashed curve, β = 0.9 . Dotted–dashed curve, β = 0.95 . Continuous curve, profile of h c . For lines and conditions see caption of Fig. 4.

Fig. 10
Fig. 10

Profiles of the difference h Δ for different calibration errors of the upstream aberrations. Dotted curve, ε = 0.05 ( 1.75 nm ) . Dashed curve, ε = 0.10 ( 3.5 nm ) . Dotted–dashed, ε = 0.20 ( 7.0 nm ) . Dot dot dot–dash, ε = 0.30 ( 10.5 nm ) . Continuous curve, profile of h c . For lines and conditions see caption of Fig. 4.

Fig. 11
Fig. 11

(Left) Simulated empirical long-exposure coronagraphic star image with a companion of contrast 2.10 4 and separation 14 λ D , sum of 1000 short exposures, star photon flux F 0 = 10 10 , perfect coronagraph; (center) differential image i Δ of the star environment after subtraction of the star response F ̂ 0 h c computed with miscalibrated D φ r ( β = 0.95 ) and φ u ( ε = 0.05 ) ; (right) object map after MAP deconvolution. Images are in linear scale, the star residual is saturated, only the AO-corrected area is shown, up to 20 λ D . For the detailed simulation conditions see Subsection 3A.

Fig. 12
Fig. 12

Horizontal profile of Fig. 11, linear scale.

Equations (37)

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

Ψ 0 ( ρ , t ) = P u ( ρ ) e j ( φ r ( ρ , t ) + φ u ( ρ ) ) ,
A 1 ( α , t ) = FT 1 ( Ψ 0 ( ρ , t ) ) = FT 1 ( P u ( ρ ) e j ( φ r ( ρ , t ) + φ u ( ρ ) ) ) ,
A 1 ( α , t ) = + + Ψ 0 ( ρ , t ) e 2 j π α ρ d 2 ρ .
A 1 + ( α , t ) = A 1 ( α , t ) η ( t ) FT 1 ( P u ( ρ ) ) .
η 0 ( t ) = arg min η ( t ) A 1 ( α , t ) η ( t ) FT 1 ( P u ( ρ ) ) 2 ,
η 0 ( t ) = Ψ 0 ( ρ , t ) | P u ( ρ ) ,
f | g = 1 S S f ( ρ ) g ( ρ ) d 2 ρ .
Ψ 2 ( ρ , t ) = FT ( A 1 + ( α , t ) ) = e j ( φ r ( ρ , t ) + φ u ( ρ ) ) P u ( ρ ) η 0 ( t ) P u ( ρ ) .
Ψ 2 + ( t ) = Ψ 2 ( t ) P d e j φ d = P d e j ( φ r ( t ) + φ u + φ d ) η 0 ( t ) P d e j φ d ,
A 3 ( t ) = FT 1 ( Ψ 2 + ( t ) ) = A n ( t ) η 0 ( t ) A d ,
A n ( t ) = FT 1 ( P d e j ( φ r ( t ) + φ u + φ d ) ) ,
A d = FT 1 ( P d e j φ d ) ,
h 3 ( t ) = A 3 ( t ) A 3 ( t ) = | A n ( t ) η 0 ( t ) A d | 2 = A n ( t ) A n ( t ) + | η 0 ( t ) | 2 A d A d 2 R ( η 0 ( t ) A n ( t ) A d ) .
h c = h 3 ( t ) = h n + | η 0 ( t ) | 2 A d A d 2 R ( η 0 ( t ) A n ( t ) A d ) ,
h n A n ( t ) A n ( t ) .
h ̃ n = ( P d e j ( φ u + φ d ) P d e j ( φ u + φ d ) ) e 1 2 D φ r ,
| η 0 ( t ) | 2 = 1 S 2 P u ( ρ ) P u ( ρ ) × e ( j ( φ r ( ρ , t ) + φ u ( ρ ) ) j ( φ r ( ρ , t ) + φ u ( ρ ) ) ) d ρ d ρ = 1 S 2 P u ( ρ ) P u ( ρ ) e 1 2 D φ r ( ρ ρ ) + j ( φ u ( ρ ) φ u ( ρ ) ) d ρ d ρ ,
= 1 S 2 ( e 1 2 D φ Ψ u ) ( ρ ) Ψ u ( ρ ) d ρ ,
Ψ u = P u e j φ u .
η 0 ( t ) A n ( α , t ) = 1 S ρ P u ( ρ ) e j ( φ u ( ρ ) + φ r ( ρ , t ) ) × ρ P d ( ρ ) e j ( φ r ( ρ , t ) + φ u ( ρ ) + φ d ( ρ ) ) × e 2 j π α ρ d ρ d ρ .
η 0 ( t ) A n ( α , t ) = 1 S ρ , ρ e j ( φ r ( ρ , t ) φ r ( ρ , t ) ) × P u ( ρ ) P d ( ρ ) e j φ u ( ρ ) e j ( φ u ( ρ ) + φ d ( ρ ) ) × e 2 j π α ρ d ρ d ρ .
η 0 ( t ) A n ( α , t ) = 1 S ρ , ρ e 1 2 D φ r ( ρ ρ ) P u ( ρ ) P d ( ρ ) × e j φ u ( ρ ) e j ( φ u ( ρ ) + φ d ( ρ ) ) e 2 j π α ρ d ρ d ρ .
η 0 ( t ) A n ( α , t ) = 1 S FT 1 [ Ψ u d ( ρ ) ( e 1 2 D φ Ψ u ) ( ρ ) ] ,
Ψ u d ( ρ ) = P d ( ρ ) e j ( φ u ( ρ ) + φ d ( ρ ) ) .
h c = h n + | η 0 ( t ) | 2 h d 2 S R { FT 1 [ Ψ u d × ( e 1 2 D φ r Ψ u ) ] A d } .
h 3 N = 1 N k = 1 N h 3 ( φ r , k ) .
ε ( α ) = 1 2 π 0 2 π ( h c ( α , θ ) h 3 N ( α , θ ) ) 2 d θ ,
D ̂ φ = β D φ r ,
φ ̂ = ( 1 + ε ) φ u ,
h ( α , α ) h n ( α α ) for | α | > λ D .
i = F 0 h c + h n o ,
J ( F 0 , o ) = ( i F 0 h c ) ( h n o ) σ b 2 + J F 0 ( F 0 ) + J o ( o ) ,
F ̂ 0 ( o ) = α ( i h n o ) h c ( α ) σ b 2 ( α ) α h c ( α ) σ b 2 ( α ) .
J ( o , F ̂ 0 ) = i Δ ( F ̂ 0 ) h n o σ b 2 + J o ( o ) +       constant
i Δ ( F ̂ 0 ) = i F ̂ 0 h c .
E c = e σ φ r ( ρ , t ) + φ u 2 ,
σ f 2 = 1 S S ( f 2 ( ρ ) ( 1 S S f ( ρ ) d 2 ρ ) ) 2 d 2 ρ ,

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