Abstract

The estimation and compensation of quasi-static aberrations is mandatory to reach the ultimate performance of high-contrast imaging systems. COFFEE is a focal plane wave-front sensing method that consists in the extension of phase diversity to high-contrast imaging systems. Based on a Bayesian approach, it estimates the quasi-static aberrations from two focal plane images recorded from the scientific camera itself. In this paper, we present COFFEE’s extension which allows an estimation of low and high order aberrations with nanometric precision for any coronagraphic device. The performance is evaluated by realistic simulations, performed in the SPHERE instrument framework. We develop a myopic estimation that allows us to take into account an imperfect knowledge on the used diversity phase. Lastly, we evaluate COFFEE’s performance in a compensation process, to optimize the contrast on the detector, and show it allows one to reach the 10−6 contrast required by SPHERE at a few resolution elements from the star. Notably, we present a non-linear energy minimization method which can be used to reach very high contrast levels (better than 107 in a SPHERE-like context).

© 2013 Optical Society of America

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2013 (1)

B. Paul, J.-F. Sauvage, L. M. Mugnier, “Coronagraphic phase diversity: performance study and laboratory demonstration,” Astron. Astrophys. 552(2013).
[CrossRef]

2012 (1)

J.-F. Sauvage, L. M. Mugnier, B. Paul, R. Villecroze, “Coronagraphic phase diversity: a simple focal-plane wavefront sensor,” Opt. Lett. 37(2012).
[CrossRef]

2011 (2)

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
[CrossRef]

S. Bongard, F. Soulez, E. Thiébaut, E. Pecontal, “3D deconvolution of hyper-spectral astronomical data,” Mon. Not. R. Astr. Soc. 418(2011).
[CrossRef]

2009 (1)

2007 (3)

R. Soummer, L. Pueyo, A. Sivaramakrishnan, R. J. Vanderbei, “Fast computation of lyot-style coronagraph propagation,” Opt. Express 15(2007).
[CrossRef] [PubMed]

R. Soummer, A. Ferrari, C. Aime, L. Jolissaint, “Speckle noise and dynamic range in coronagraphic images,” Astrophys. J. 669(2007).
[CrossRef]

A. Give’on, R. Belikov, S. Shaklan, J. Kasdin, “Closed loop, DM diversity based, wave-front correction algorithm for high contrast imaging systems,” Opt. Express 15(2007).

2006 (1)

P. J. Bordé, W. A. Traub, “High constrast imaging from space : speckle-nulling in a low-aberration regime,” Astrophys. J. 638(2006).
[CrossRef]

2003 (1)

A. Blanc, T. Fusco, M. Hartung, L. M. Mugnier, G. Rousset, “Calibration of NAOS and CONICA static aberrations. Application of the phase diversity technique,” Astron. Astrophys. 399, 373–383 (2003).
[CrossRef]

1997 (1)

D. J. Lee, M. C. Roggemann, B. M. Welsh, E. R. Crosby, “Evaluation of least-squares phase-diversity technique for space telescope wave-front sensing,” Astrophys. J. 36(1997).

Aime, C.

R. Soummer, A. Ferrari, C. Aime, L. Jolissaint, “Speckle noise and dynamic range in coronagraphic images,” Astrophys. J. 669(2007).
[CrossRef]

Angione, J. R.

J. K. Wallace, R. S. Burruss, R. D. Bartos, T. Q. Trinh, L. A. Pueyo, S. F. Fregoso, J. R. Angione, J. C. Shelton, “the gemini planet imager calibration wavefront sensor instrument,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
[CrossRef]

Antici, J.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

Bartos, R. D.

J. K. Wallace, R. S. Burruss, R. D. Bartos, T. Q. Trinh, L. A. Pueyo, S. F. Fregoso, J. R. Angione, J. C. Shelton, “the gemini planet imager calibration wavefront sensor instrument,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
[CrossRef]

Baruffolo, A.

K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

Baudoz, P.

P. Baudoz, A. Boccaletti, J. Baudrand, D. Rouan, “The self-coherent camera : a new tool for exoplanet detection,” in “Proc. IAU Colloquium,” (2006).

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

P. Baudoz, J. Mazoyer, M. Mas, R. Galicher, G. Rousset, “Dark hole and planet detection: laboratory results using the self-coherent camera,” in “Ground-based and Airborn Intrusmentation for Astronomy IV,”, vol. 8446 (Proc. Soc. Photo-Opt. Instrum. Eng., 2012), vol. 8446.
[CrossRef]

Baudrand, J.

P. Baudoz, A. Boccaletti, J. Baudrand, D. Rouan, “The self-coherent camera : a new tool for exoplanet detection,” in “Proc. IAU Colloquium,” (2006).

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, R. Soummer, “the gemini planet imager: from sience to design to construction,” in “Adaptive Optics Systems,”, vol. 7015 (Proc. Soc. Photo-Opt. Instrum. Eng., 2008), vol. 7015.
[CrossRef]

Beichman, C.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
[CrossRef]

Belikov, R.

A. Give’on, R. Belikov, S. Shaklan, J. Kasdin, “Closed loop, DM diversity based, wave-front correction algorithm for high contrast imaging systems,” Opt. Express 15(2007).

Beuzit, J.

K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

Beuzit, J.-L.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

Blanc, A.

A. Blanc, T. Fusco, M. Hartung, L. M. Mugnier, G. Rousset, “Calibration of NAOS and CONICA static aberrations. Application of the phase diversity technique,” Astron. Astrophys. 399, 373–383 (2003).
[CrossRef]

L. M. Mugnier, A. Blanc, J. Idier, “Phase diversity: a technique for wave-front sensing and for diffraction-limited imaging,” in “Advances in Imaging and Electron Physics,”, vol. 141, P. Hawkes, ed. (Elsevier, 2006), chap. 1, pp. 1–76.
[CrossRef]

Boccaletti, A.

P. Baudoz, A. Boccaletti, J. Baudrand, D. Rouan, “The self-coherent camera : a new tool for exoplanet detection,” in “Proc. IAU Colloquium,” (2006).

K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

Bongard, S.

S. Bongard, F. Soulez, E. Thiébaut, E. Pecontal, “3D deconvolution of hyper-spectral astronomical data,” Mon. Not. R. Astr. Soc. 418(2011).
[CrossRef]

Bordé, P. J.

P. J. Bordé, W. A. Traub, “High constrast imaging from space : speckle-nulling in a low-aberration regime,” Astrophys. J. 638(2006).
[CrossRef]

Bouchez, A.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
[CrossRef]

Brenner, D.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
[CrossRef]

Burrows, C.

J. Trauger, A. Give’on, B. Gordon, B. Kern, A. Kuhnert, D. Moody, A. Niesser, F. Shi, D. Wilson, C. Burrows, “Laboratory demonstration of high-contrast imaging for space coronagraphy,” in “Tecniques and Instrumentation for Detection of Exoplanets III,”, vol. 6693 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 6693.

Burruss, R.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
[CrossRef]

Burruss, R. S.

J. K. Wallace, R. S. Burruss, R. D. Bartos, T. Q. Trinh, L. A. Pueyo, S. F. Fregoso, J. R. Angione, J. C. Shelton, “the gemini planet imager calibration wavefront sensor instrument,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
[CrossRef]

Carbillet, M.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

Cassaing, F.

Charton, J.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

Claudi, R.

K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

Costille, A.

J.-F. Sauvage, T. Fusco, C. Petit, L. M. Mugnier, B. Paul, A. Costille, “Focal-plane wave front sensing strategies for high-contrast imaging. experimantal validations on SPHERE,” in “Adaptive Optics Systems III,”, vol. 8447 (Proc. Soc. Photo-Opt. Instrum. Eng., 2012), vol. 8447.
[CrossRef]

K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

Crepp, J. R.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
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D. J. Lee, M. C. Roggemann, B. M. Welsh, E. R. Crosby, “Evaluation of least-squares phase-diversity technique for space telescope wave-front sensing,” Astrophys. J. 36(1997).

Dekany, R.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
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Dillon, D.

S. J. Thomas, A. A. Give’On, D. Dillon, B. Macintosh, D. Gavel, R. Soummer, “Laboratory test of aplication of electric field conjugation image-sharpening to ground-based adaptive optics,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
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K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

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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, R. Soummer, “the gemini planet imager: from sience to design to construction,” in “Adaptive Optics Systems,”, vol. 7015 (Proc. Soc. Photo-Opt. Instrum. Eng., 2008), vol. 7015.
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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, R. Soummer, “the gemini planet imager: from sience to design to construction,” in “Adaptive Optics Systems,”, vol. 7015 (Proc. Soc. Photo-Opt. Instrum. Eng., 2008), vol. 7015.
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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, R. Soummer, “the gemini planet imager: from sience to design to construction,” in “Adaptive Optics Systems,”, vol. 7015 (Proc. Soc. Photo-Opt. Instrum. Eng., 2008), vol. 7015.
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K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

Feldt, M.

K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

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Fusco, T.

A. Blanc, T. Fusco, M. Hartung, L. M. Mugnier, G. Rousset, “Calibration of NAOS and CONICA static aberrations. Application of the phase diversity technique,” Astron. Astrophys. 399, 373–383 (2003).
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K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

J.-F. Sauvage, L. Mugnier, T. Fusco, G. Rousset, “Post processing of differential images for direct extrasolar planet detection from the ground,” in “Advances in Adaptive Optics II,”, vol. 6272, L. Ellerbroek, B. Bonaccini Calia, D. Bonaccini Calia, eds. (Proc. Soc. Photo-Opt. Instrum. Eng., 2006), vol. 6272.
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J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

J.-F. Sauvage, T. Fusco, C. Petit, L. M. Mugnier, B. Paul, A. Costille, “Focal-plane wave front sensing strategies for high-contrast imaging. experimantal validations on SPHERE,” in “Adaptive Optics Systems III,”, vol. 8447 (Proc. Soc. Photo-Opt. Instrum. Eng., 2012), vol. 8447.
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Galicher, R.

P. Baudoz, J. Mazoyer, M. Mas, R. Galicher, G. Rousset, “Dark hole and planet detection: laboratory results using the self-coherent camera,” in “Ground-based and Airborn Intrusmentation for Astronomy IV,”, vol. 8446 (Proc. Soc. Photo-Opt. Instrum. Eng., 2012), vol. 8446.
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Garrel, V.

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Gavel, D.

S. J. Thomas, A. A. Give’On, D. Dillon, B. Macintosh, D. Gavel, R. Soummer, “Laboratory test of aplication of electric field conjugation image-sharpening to ground-based adaptive optics,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
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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, R. Soummer, “the gemini planet imager: from sience to design to construction,” in “Adaptive Optics Systems,”, vol. 7015 (Proc. Soc. Photo-Opt. Instrum. Eng., 2008), vol. 7015.
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Give’on, A.

A. Give’on, R. Belikov, S. Shaklan, J. Kasdin, “Closed loop, DM diversity based, wave-front correction algorithm for high contrast imaging systems,” Opt. Express 15(2007).

J. Trauger, A. Give’on, B. Gordon, B. Kern, A. Kuhnert, D. Moody, A. Niesser, F. Shi, D. Wilson, C. Burrows, “Laboratory demonstration of high-contrast imaging for space coronagraphy,” in “Tecniques and Instrumentation for Detection of Exoplanets III,”, vol. 6693 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 6693.

Give’On, A. A.

S. J. Thomas, A. A. Give’On, D. Dillon, B. Macintosh, D. Gavel, R. Soummer, “Laboratory test of aplication of electric field conjugation image-sharpening to ground-based adaptive optics,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
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Gordon, B.

J. Trauger, A. Give’on, B. Gordon, B. Kern, A. Kuhnert, D. Moody, A. Niesser, F. Shi, D. Wilson, C. Burrows, “Laboratory demonstration of high-contrast imaging for space coronagraphy,” in “Tecniques and Instrumentation for Detection of Exoplanets III,”, vol. 6693 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 6693.

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, R. Soummer, “the gemini planet imager: from sience to design to construction,” in “Adaptive Optics Systems,”, vol. 7015 (Proc. Soc. Photo-Opt. Instrum. Eng., 2008), vol. 7015.
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Gratton, R.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

Guyon, O.

O. Guyon, F. Martinache, V. Garrel, F. Vogt, K. Yokochi, T. Yoshikawa, “The subaru coronagraphic extreme ao (SCExAO) system: wavefront control and detection of exoplanets with coherent light modulation in the focal plane,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
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Hartung, M.

A. Blanc, T. Fusco, M. Hartung, L. M. Mugnier, G. Rousset, “Calibration of NAOS and CONICA static aberrations. Application of the phase diversity technique,” Astron. Astrophys. 399, 373–383 (2003).
[CrossRef]

Henning, T.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

Hinkley, S.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
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Hubin, N.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

Idier, J.

L. M. Mugnier, A. Blanc, J. Idier, “Phase diversity: a technique for wave-front sensing and for diffraction-limited imaging,” in “Advances in Imaging and Electron Physics,”, vol. 141, P. Hawkes, ed. (Elsevier, 2006), chap. 1, pp. 1–76.
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Jolissaint, L.

R. Soummer, A. Ferrari, C. Aime, L. Jolissaint, “Speckle noise and dynamic range in coronagraphic images,” Astrophys. J. 669(2007).
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Joos, F.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

Kasdin, J.

A. Give’on, R. Belikov, S. Shaklan, J. Kasdin, “Closed loop, DM diversity based, wave-front correction algorithm for high contrast imaging systems,” Opt. Express 15(2007).

Kasper, M.

K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

Kern, B.

J. Trauger, A. Give’on, B. Gordon, B. Kern, A. Kuhnert, D. Moody, A. Niesser, F. Shi, D. Wilson, C. Burrows, “Laboratory demonstration of high-contrast imaging for space coronagraphy,” in “Tecniques and Instrumentation for Detection of Exoplanets III,”, vol. 6693 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 6693.

King, D.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
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Kuhnert, A.

J. Trauger, A. Give’on, B. Gordon, B. Kern, A. Kuhnert, D. Moody, A. Niesser, F. Shi, D. Wilson, C. Burrows, “Laboratory demonstration of high-contrast imaging for space coronagraphy,” in “Tecniques and Instrumentation for Detection of Exoplanets III,”, vol. 6693 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 6693.

Langlois, M.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

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, R. Soummer, “the gemini planet imager: from sience to design to construction,” in “Adaptive Optics Systems,”, vol. 7015 (Proc. Soc. Photo-Opt. Instrum. Eng., 2008), vol. 7015.
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Lee, D. J.

D. J. Lee, M. C. Roggemann, B. M. Welsh, E. R. Crosby, “Evaluation of least-squares phase-diversity technique for space telescope wave-front sensing,” Astrophys. J. 36(1997).

Ligon, E.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
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Lizon, J.

K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

Lockhart, T.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
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J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

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S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
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A. Give’on, R. Belikov, S. Shaklan, J. Kasdin, “Closed loop, DM diversity based, wave-front correction algorithm for high contrast imaging systems,” Opt. Express 15(2007).

Shao, M.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
[CrossRef]

Shelton, C.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
[CrossRef]

Shelton, J. C.

J. K. Wallace, R. S. Burruss, R. D. Bartos, T. Q. Trinh, L. A. Pueyo, S. F. Fregoso, J. R. Angione, J. C. Shelton, “the gemini planet imager calibration wavefront sensor instrument,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
[CrossRef]

Shi, F.

J. Trauger, A. Give’on, B. Gordon, B. Kern, A. Kuhnert, D. Moody, A. Niesser, F. Shi, D. Wilson, C. Burrows, “Laboratory demonstration of high-contrast imaging for space coronagraphy,” in “Tecniques and Instrumentation for Detection of Exoplanets III,”, vol. 6693 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 6693.

Sivaramakrishnan, A.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
[CrossRef]

R. Soummer, L. Pueyo, A. Sivaramakrishnan, R. J. Vanderbei, “Fast computation of lyot-style coronagraph propagation,” Opt. Express 15(2007).
[CrossRef] [PubMed]

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, R. Soummer, “the gemini planet imager: from sience to design to construction,” in “Adaptive Optics Systems,”, vol. 7015 (Proc. Soc. Photo-Opt. Instrum. Eng., 2008), vol. 7015.
[CrossRef]

Soulez, F.

S. Bongard, F. Soulez, E. Thiébaut, E. Pecontal, “3D deconvolution of hyper-spectral astronomical data,” Mon. Not. R. Astr. Soc. 418(2011).
[CrossRef]

Soummer, R.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
[CrossRef]

R. Soummer, A. Ferrari, C. Aime, L. Jolissaint, “Speckle noise and dynamic range in coronagraphic images,” Astrophys. J. 669(2007).
[CrossRef]

R. Soummer, L. Pueyo, A. Sivaramakrishnan, R. J. Vanderbei, “Fast computation of lyot-style coronagraph propagation,” Opt. Express 15(2007).
[CrossRef] [PubMed]

S. J. Thomas, A. A. Give’On, D. Dillon, B. Macintosh, D. Gavel, R. Soummer, “Laboratory test of aplication of electric field conjugation image-sharpening to ground-based adaptive optics,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
[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, R. Soummer, “the gemini planet imager: from sience to design to construction,” in “Adaptive Optics Systems,”, vol. 7015 (Proc. Soc. Photo-Opt. Instrum. Eng., 2008), vol. 7015.
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes : the Art of Scientific Computing (Cambridge University, 2007).

Thiébaut, E.

S. Bongard, F. Soulez, E. Thiébaut, E. Pecontal, “3D deconvolution of hyper-spectral astronomical data,” Mon. Not. R. Astr. Soc. 418(2011).
[CrossRef]

E. Thiébaut, “Optimization issues in blind deconvolution algorithms,” in “Astronomical Data Analysis II,”, vol. 4847 (Proc. Soc. Photo-Opt. Instrum. Eng., 2002), vol. 4847, pp. 174–183.
[CrossRef]

Thomas, S. J.

S. J. Thomas, A. A. Give’On, D. Dillon, B. Macintosh, D. Gavel, R. Soummer, “Laboratory test of aplication of electric field conjugation image-sharpening to ground-based adaptive optics,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
[CrossRef]

Traub, W. A.

P. J. Bordé, W. A. Traub, “High constrast imaging from space : speckle-nulling in a low-aberration regime,” Astrophys. J. 638(2006).
[CrossRef]

Trauger, J.

J. Trauger, A. Give’on, B. Gordon, B. Kern, A. Kuhnert, D. Moody, A. Niesser, F. Shi, D. Wilson, C. Burrows, “Laboratory demonstration of high-contrast imaging for space coronagraphy,” in “Tecniques and Instrumentation for Detection of Exoplanets III,”, vol. 6693 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 6693.

Trinh, T. Q.

J. K. Wallace, R. S. Burruss, R. D. Bartos, T. Q. Trinh, L. A. Pueyo, S. F. Fregoso, J. R. Angione, J. C. Shelton, “the gemini planet imager calibration wavefront sensor instrument,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
[CrossRef]

Turatto, M.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

Udry, S.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

Vakili, F.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

Vanderbei, R. J.

R. Soummer, L. Pueyo, A. Sivaramakrishnan, R. J. Vanderbei, “Fast computation of lyot-style coronagraph propagation,” Opt. Express 15(2007).
[CrossRef] [PubMed]

Vasisht, G.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes : the Art of Scientific Computing (Cambridge University, 2007).

Villecroze, R.

J.-F. Sauvage, L. M. Mugnier, B. Paul, R. Villecroze, “Coronagraphic phase diversity: a simple focal-plane wavefront sensor,” Opt. Lett. 37(2012).
[CrossRef]

Vogt, F.

O. Guyon, F. Martinache, V. Garrel, F. Vogt, K. Yokochi, T. Yoshikawa, “The subaru coronagraphic extreme ao (SCExAO) system: wavefront control and detection of exoplanets with coherent light modulation in the focal plane,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
[CrossRef]

Wallace, J. K.

J. K. Wallace, R. S. Burruss, R. D. Bartos, T. Q. Trinh, L. A. Pueyo, S. F. Fregoso, J. R. Angione, J. C. Shelton, “the gemini planet imager calibration wavefront sensor instrument,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
[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, R. Soummer, “the gemini planet imager: from sience to design to construction,” in “Adaptive Optics Systems,”, vol. 7015 (Proc. Soc. Photo-Opt. Instrum. Eng., 2008), vol. 7015.
[CrossRef]

Waters, R.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

Welsh, B. M.

D. J. Lee, M. C. Roggemann, B. M. Welsh, E. R. Crosby, “Evaluation of least-squares phase-diversity technique for space telescope wave-front sensing,” Astrophys. J. 36(1997).

Wildi, F.

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

Wilson, D.

J. Trauger, A. Give’on, B. Gordon, B. Kern, A. Kuhnert, D. Moody, A. Niesser, F. Shi, D. Wilson, C. Burrows, “Laboratory demonstration of high-contrast imaging for space coronagraphy,” in “Tecniques and Instrumentation for Detection of Exoplanets III,”, vol. 6693 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 6693.

Yokochi, K.

O. Guyon, F. Martinache, V. Garrel, F. Vogt, K. Yokochi, T. Yoshikawa, “The subaru coronagraphic extreme ao (SCExAO) system: wavefront control and detection of exoplanets with coherent light modulation in the focal plane,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
[CrossRef]

Yoshikawa, T.

O. Guyon, F. Martinache, V. Garrel, F. Vogt, K. Yokochi, T. Yoshikawa, “The subaru coronagraphic extreme ao (SCExAO) system: wavefront control and detection of exoplanets with coherent light modulation in the focal plane,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
[CrossRef]

Zhai, C.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
[CrossRef]

Zimmerman, N.

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
[CrossRef]

Astron. Astrophys. (2)

B. Paul, J.-F. Sauvage, L. M. Mugnier, “Coronagraphic phase diversity: performance study and laboratory demonstration,” Astron. Astrophys. 552(2013).
[CrossRef]

A. Blanc, T. Fusco, M. Hartung, L. M. Mugnier, G. Rousset, “Calibration of NAOS and CONICA static aberrations. Application of the phase diversity technique,” Astron. Astrophys. 399, 373–383 (2003).
[CrossRef]

Astrophys. J. (3)

D. J. Lee, M. C. Roggemann, B. M. Welsh, E. R. Crosby, “Evaluation of least-squares phase-diversity technique for space telescope wave-front sensing,” Astrophys. J. 36(1997).

R. Soummer, A. Ferrari, C. Aime, L. Jolissaint, “Speckle noise and dynamic range in coronagraphic images,” Astrophys. J. 669(2007).
[CrossRef]

P. J. Bordé, W. A. Traub, “High constrast imaging from space : speckle-nulling in a low-aberration regime,” Astrophys. J. 638(2006).
[CrossRef]

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

S. Bongard, F. Soulez, E. Thiébaut, E. Pecontal, “3D deconvolution of hyper-spectral astronomical data,” Mon. Not. R. Astr. Soc. 418(2011).
[CrossRef]

Opt. Express (2)

R. Soummer, L. Pueyo, A. Sivaramakrishnan, R. J. Vanderbei, “Fast computation of lyot-style coronagraph propagation,” Opt. Express 15(2007).
[CrossRef] [PubMed]

A. Give’on, R. Belikov, S. Shaklan, J. Kasdin, “Closed loop, DM diversity based, wave-front correction algorithm for high contrast imaging systems,” Opt. Express 15(2007).

Opt. Lett. (2)

J.-F. Sauvage, L. M. Mugnier, B. Paul, R. Villecroze, “Coronagraphic phase diversity: a simple focal-plane wavefront sensor,” Opt. Lett. 37(2012).
[CrossRef]

I. Mocœur, L. M. Mugnier, F. Cassaing, “Analytical solution to the phase-diversity problem for real-time wavefront sensing,” Opt. Lett. 34, 3487–3489 (2009).
[CrossRef]

Pub. Astron. Soc. Pacific (1)

S. Hinkley, B. R. Oppenheimer, N. Zimmerman, D. Brenner, I. R. Parry, J. R. Crepp, G. Vasisht, E. Ligon, D. King, R. Soummer, A. Sivaramakrishnan, C. Beichman, M. Shao, L. C. Roberts, A. Bouchez, R. Dekany, L. Pueyo, J. E. Roberts, T. Lockhart, C. Zhai, C. Shelton, R. Burruss, “A new high contrast imaging program at palomar observatory,” Pub. Astron. Soc. Pacific 123(2011).
[CrossRef]

Other (14)

L. M. Mugnier, A. Blanc, J. Idier, “Phase diversity: a technique for wave-front sensing and for diffraction-limited imaging,” in “Advances in Imaging and Electron Physics,”, vol. 141, P. Hawkes, ed. (Elsevier, 2006), chap. 1, pp. 1–76.
[CrossRef]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes : the Art of Scientific Computing (Cambridge University, 2007).

E. Thiébaut, “Optimization issues in blind deconvolution algorithms,” in “Astronomical Data Analysis II,”, vol. 4847 (Proc. Soc. Photo-Opt. Instrum. Eng., 2002), vol. 4847, pp. 174–183.
[CrossRef]

K. Dohlen, F. Wildi, J. Beuzit, P. Puget, D. Mouillet, A. Baruffolo, A. Boccaletti, J. Charton, R. Claudi, A. Costille, P. Feautrier, M. Feldt, T. Fusco, R. Gratton, M. Kasper, M. Langlois, D. L. Mignant, J. Lizon, N. Hubin, A. Pavlov, C. Petit, J. Pragt, P. Rabou, S. Rochat, R. Roelfsema, J. Sauvage, H. Schmid, “Sphere system analysis predictions,” (AO4ELT 2, 2011).

J.-F. Sauvage, L. Mugnier, T. Fusco, G. Rousset, “Post processing of differential images for direct extrasolar planet detection from the ground,” in “Advances in Adaptive Optics II,”, vol. 6272, L. Ellerbroek, B. Bonaccini Calia, D. Bonaccini Calia, eds. (Proc. Soc. Photo-Opt. Instrum. Eng., 2006), vol. 6272.
[CrossRef]

J. Trauger, A. Give’on, B. Gordon, B. Kern, A. Kuhnert, D. Moody, A. Niesser, F. Shi, D. Wilson, C. Burrows, “Laboratory demonstration of high-contrast imaging for space coronagraphy,” in “Tecniques and Instrumentation for Detection of Exoplanets III,”, vol. 6693 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 6693.

S. J. Thomas, A. A. Give’On, D. Dillon, B. Macintosh, D. Gavel, R. Soummer, “Laboratory test of aplication of electric field conjugation image-sharpening to ground-based adaptive optics,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
[CrossRef]

P. Baudoz, J. Mazoyer, M. Mas, R. Galicher, G. Rousset, “Dark hole and planet detection: laboratory results using the self-coherent camera,” in “Ground-based and Airborn Intrusmentation for Astronomy IV,”, vol. 8446 (Proc. Soc. Photo-Opt. Instrum. Eng., 2012), vol. 8446.
[CrossRef]

P. Baudoz, A. Boccaletti, J. Baudrand, D. Rouan, “The self-coherent camera : a new tool for exoplanet detection,” in “Proc. IAU Colloquium,” (2006).

J.-F. Sauvage, T. Fusco, C. Petit, L. M. Mugnier, B. Paul, A. Costille, “Focal-plane wave front sensing strategies for high-contrast imaging. experimantal validations on SPHERE,” in “Adaptive Optics Systems III,”, vol. 8447 (Proc. Soc. Photo-Opt. Instrum. Eng., 2012), vol. 8447.
[CrossRef]

J. K. Wallace, R. S. Burruss, R. D. Bartos, T. Q. Trinh, L. A. Pueyo, S. F. Fregoso, J. R. Angione, J. C. Shelton, “the gemini planet imager calibration wavefront sensor instrument,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
[CrossRef]

J.-L. Beuzit, M. Feldt, K. Dohlen, D. Mouillet, P. Puget, J. Antici, P. Baudoz, A. Boccaletti, M. Carbillet, J. Charton, R. Claudi, T. Fusco, R. Gratton, T. Henning, N. Hubin, F. Joos, M. Kasper, M. Langlois, C. Moutou, J. Pragt, P. Rabou, M. Saisse, H. M. Schmid, M. Turatto, S. Udry, F. Vakili, R. Waters, F. Wildi, “SPHERE: A Planet Finder Instrument for the VLT,” in “Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.”,, P. Kalas, ed. (University of California, Berkeley, CA, USA, 2007).

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, R. Soummer, “the gemini planet imager: from sience to design to construction,” in “Adaptive Optics Systems,”, vol. 7015 (Proc. Soc. Photo-Opt. Instrum. Eng., 2008), vol. 7015.
[CrossRef]

O. Guyon, F. Martinache, V. Garrel, F. Vogt, K. Yokochi, T. Yoshikawa, “The subaru coronagraphic extreme ao (SCExAO) system: wavefront control and detection of exoplanets with coherent light modulation in the focal plane,” in “Adaptive Optics Systems II,”, vol. 7736 (Proc. Soc. Photo-Opt. Instrum. Eng., 2010), vol. 7736.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Apodized Lyot coronagraph: apodization function used in this paper, computed from an experimental image recorded on SPHERE

Fig. 2
Fig. 2

Regularization metrics : reconstruction error upstream (red line) and downstream (blue line) of the coronagraph as functions of the hyperparameter value

Fig. 3
Fig. 3

Reconstruction error (solid red line) upstream (left) and downstream (right) as a function of the incoming flux α. For comparison, 1 / α (magenta dashed line) theoretical behaviour is plotted for photon noise only. The dotted-dashed black line represent the WFE value upstream and downstream of the coronagraph.

Fig. 4
Fig. 4

Reconstruction errors upstream (left) and downstream (right) of the coronagraph as functions of the amplitude adiv of a diversity phase composed of defocus only (Z4, dashed lines), or composed of a mix of defocus and astigmatism (Z4 + Z5, solid lines).

Fig. 5
Fig. 5

COFFEE : simulation of aberration compensation using classical phase conjugation. Left : coronagraphic images before (top) and after five iterations of the closed loop process (bottom, logarithmic scale for both images). Right: normalized average raw contrast computed from the images without coronagraph (solid red line), with coronagraph before (solid green line) and after compensation (solid blue line). For comparison, the contrast computed from a coronagraphic image computed without any aberrations is plotted as well (dashed black line).

Fig. 6
Fig. 6

COFFEE : simulation of aberration compensation by minimizing the energy in a chosen area (between 5 λ D and 20 λ D in the right part of the focal plane). Left : coronagraphic images before (top) and after five iterations of the closed loop process (bottom, logarithmic scale for both images). Right: normalized average raw contrast computed in the dark hole area from the images without coronagraph (solid red line), with coronagraph before (solid green line) and after compensation. After minimization, the average contrast in the Dark Hole is 3.1 10−8 when the myopic approach is used (solid blue line), and 6.6 10−8 otherwise (solid cyan line). For comparison, the contrast computed from a coronagraphic image computed without any aberrations is plotted as well (dashed black line).

Tables (4)

Tables Icon

Table 1 COFFEE: simulation parameters

Tables Icon

Table 2 Comparison of COFFEE’s estimation accuracy when the a priori knowledge on the aberration’s PSD is not perfectly accurate. As previously, k stands for u (upstream) or d (downstream).

Tables Icon

Table 3 Comparison of COFFEE estimation accuracy with and without myopic estimation of ϕε when the diversity phase is not perfectly known.

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Table 4 COFFEE: parameters used for the compensation simulations of Section 5

Equations (24)

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i c foc = α foc h det h c ( ϕ u , ϕ d ) + n foc + β foc i c div = α div h det h c ( ϕ u + ϕ div , ϕ d ) + n div + β div
( α ^ , β ^ , ϕ ^ u , ϕ ^ d ) = argmin α , β , ϕ u , ϕ d [ J ( α , β , ϕ u , ϕ d ) ]
J ( α , β , ϕ u , ϕ d ) = 1 2 i c foc ( α foc h det h c ( ϕ u , ϕ d ) + β foc ) σ n foc 2 + 1 2 i c div ( α div h det h c ( ϕ u + ϕ div , ϕ d ) + β div ) σ n div 2 + ( ϕ u ) + ( ϕ d )
{ S ϕ k 1 ν n ϕ k = 0
( ϕ k ) = 1 2 ν | [ ϕ k ] ( ν ) | 2 S ϕ k ( ν ) ,
( ϕ k ) = μ k 2 ϕ k ( r ) 2 .
( ϕ k ) = μ k 2 Δ ϕ k ( r ) 2 .
μ k = 1 σ ϕ k 2 ,
P u ( r ) = Π ( 2 r D u ) Φ ( r ) ,
Ψ A ( r ) = P u ( r ) e j ϕ u ( r ) .
Ψ d ( γ ) = 1 { [ 1 ( Ψ A ( r ) ) ] P d ( r ) e j ϕ d ( r ) } ,
h c = | 1 { [ 1 ( Ψ A ) ] P d e j ϕ d } | 2
J ( α , β , ϕ u , ϕ d , ϕ ε ) = 1 2 i c foc ( α foc h det h c ( ϕ u , ϕ d ) + β foc ) σ n foc 2 + 1 2 i c div ( α div h det h c ( ϕ u + ϕ div cal + ϕ ε , ϕ d ) + β div ) σ n div 2 + ( ϕ u ) + ( ϕ d ) + ( ϕ ε ) ,
ϕ u i + 1 = ϕ u i g ϕ ^ u DM ,
ϕ ^ u DM = F T ϕ ^ u .
DH = α m , n DH | Ψ DH ( m , n ) | 2
Ψ DH ( v ) = 1 { [ 1 ( P u e j ( ϕ u + ψ ( v ) ) ) ] P d e j ϕ d } .
Ψ DH ( v ) = 1 { [ 1 ( P u e j ( ϕ u + ψ ( v ) ) + ξ ) ] P d e j ϕ d }
ϕ u i + 1 = ϕ u i + g F v DH .
J ( α , β , ϕ u , ϕ d ) = 1 2 i c foc ( α foc h det h c foc + β foc ) σ n foc 2 + 1 2 i c div ( α div h det h c div + β div ) σ n div 2 + ( ϕ u ) + ( ϕ d ) = J foc + J div + ( ϕ u ) + ( ϕ d )
J foc ϕ d = 2 { ψ 0 * ε ψ d [ 1 ( ψ u ) ] * × [ J foc h c foc ( Ψ 0 ε Ψ c ) ] } J foc ϕ u = 2 { ψ 0 * [ J foc h c foc ( Ψ 0 ε Ψ c ) ] } ε Ψ u * [ * 1 ( Ψ d * { J foc h foc [ Ψ 0 ε Ψ c ] } ) ]
J foc h c foc = 1 σ n foc 2 [ α h det ( α h det h c foc i c foc ) ]
ψ u = P u e j ϕ u ψ d = P d e j ϕ d Ψ d = 1 ( ψ d ) ψ 0 = P u e j ( ϕ u + ϕ d ) Ψ 0 = 1 ( ψ 0 ) Ψ c = 1 { ψ d [ 1 ( ψ u ) ] }
ϕ k = μ k Δ ϕ k ( r ) .

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