Abstract

We propose a novel method for the efficient direct detection of exoplanets from the ground using angular differential imaging. The method combines images appropriately, then uses the combined images jointly in a maximum-likelihood framework to estimate the position and intensity of potential planets orbiting the observed star. It takes into account the mixture of photon and detector noises and a positivity constraint on the planet’s intensity. A reasonable detection criterion is also proposed based on the computation of the noise propagation from the images to the estimated intensity of the potential planet. The implementation of this method is tested on simulated data that take into account static aberrations before and after the coronagraph, residual turbulence after adaptive optics correction, and noise.

© 2009 Optical Society of America

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  1. J. R. P. Angel, “Groundbased imaging of extrasolar planets using adaptive optics,” Nature (London) 368, 203-207 (1994).
    [CrossRef]
  2. A. Burrows and D. Sudarsky, “Models of irradiated extrasolar giant planets,” in Scientific Frontiers in Research on Extrasolar Planets, Vol. 294 of Astronomical Society of the Pacific Conference Series, D.Deming and S.Seager, eds. (Astronomical Society of the Pacific, 2003), pp. 491-498.
  3. 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]
  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]
  5. M. R. Swain, G. Vasisht, and G. Tinetti, “The presence of methane in the atmosphere of an extrasolar planet,” Nature (London) 452, 329-331 (2008).
    [CrossRef]
  6. 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]
  7. B. Lyot, “The study of the solar corona and prominences without eclipses (George Darwin Lecture, 1939),” Mon. Not. R. Astron. Soc. 99, 580-594 (1939).
  8. 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]
  9. R. Soummer, C. Aime, and P. E. Falloon, “Stellar coronagraphy with prolate apodized circular apertures,” Astron. Astrophys. 397, 1161-1172 (2003).
    [CrossRef]
  10. R. Racine, G. A. Walker, D. Nadeau, and C. Marois, “Speckle noise and the detection of faint companions,” Publ. Astron. Soc. Pac. 112, 587-594 (1999).
    [CrossRef]
  11. C. Marois, R. Doyon, D. Nadeau, R. Racine, and G. A. H. Walker, “Effects of quasi-static aberrations in faint companion searches,” in Astronomy with High-Contrast Imaging, Vol. 8 of EAS Publications Series, C.Aime and R.Soummer, eds. (EDP Sciences, 2003), pp. 233-243.
  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. K. Dohlen, M. Langlois, and M. Saisse, “The infrared dual imaging and spectrograph for SPHERE: design and performance,” Proc. SPIE 7014, 70143L (2008).
    [CrossRef]
  14. A. Labeyrie, “Detection of extra-solar planets,” in Formation of Planetary Systems, A.Brahic, ed. (Cepadues-Editions, Toulouse, 1982), pp. 883, 885-888.
  15. M. Mueller and G. Weigelt, “High-resolution astronomical imaging by roll deconvolution of space telescope data,” Astron. Astrophys. 175, 312-318 (1987).
  16. 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]
  17. 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]
  18. I. Smith, A. Ferrari, and M. Carbillet, “Detection algorithm of exoplanets in field-rotated images: preliminary results on simulated SPHERE coronographic images,” in Semaine de l'Astrophysique Française, SF2A (EDP Sciences, 2007).
  19. 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).
    [CrossRef]
  20. L. M. Mugnier, J.-F. Sauvage, T. Fusco, and G. Rousset, “Multi-channel planet detection algorithm for angular differential imaging,” in Adaptive Optics: Analysis and Methods, OSA Technical Digest (OSA, 2007), paper ATu A4.
  21. J.-F. Sauvage, L. Mugnier, A. Woelfflé, T. Fusco, and G. Rousset, “Multi-channel algorithm for exoplanets detection by angular differential imaging,” in Semaine de l'Astrophysique Française, SF2A (EDP Sciences, 2007).
  22. 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]
  23. 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]
  24. R. Conan, T. Fusco, G. Rousset, D. Mouillet, J.-L. Beuzit, M. Nicolle, and C. Petit, “Modeling and analysis of XAO systems. Application to VLT-Planet Finder,” Proc. SPIE 5490, pp. 602-608 (2004).
    [CrossRef]
  25. J.-F. Sauvage, “Calibration et méthodes d'inversion en imagerie haute dynamique pour la détection directe d'exoplanètes,” Ph.D. thesis (Université Paris VII, 2007).

2008 (5)

K. Dohlen, M. Langlois, and M. Saisse, “The infrared dual imaging and spectrograph for SPHERE: design and performance,” Proc. SPIE 7014, 70143L (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]

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. R. Swain, G. Vasisht, and G. Tinetti, “The presence of methane in the atmosphere of an extrasolar planet,” Nature (London) 452, 329-331 (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).
[CrossRef]

2007 (1)

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 (3)

2005 (1)

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 (2)

R. Conan, T. Fusco, G. Rousset, D. Mouillet, J.-L. Beuzit, M. Nicolle, and C. Petit, “Modeling and analysis of XAO systems. Application to VLT-Planet Finder,” Proc. SPIE 5490, pp. 602-608 (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]

2003 (1)

R. Soummer, C. Aime, and P. E. Falloon, “Stellar coronagraphy with prolate apodized circular apertures,” Astron. Astrophys. 397, 1161-1172 (2003).
[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, 587-594 (1999).
[CrossRef]

1994 (1)

J. R. P. Angel, “Groundbased imaging of extrasolar planets using adaptive optics,” Nature (London) 368, 203-207 (1994).
[CrossRef]

1987 (1)

M. Mueller and G. Weigelt, “High-resolution astronomical imaging by roll deconvolution of space telescope data,” Astron. Astrophys. 175, 312-318 (1987).

1939 (1)

B. Lyot, “The study of the solar corona and prominences without eclipses (George Darwin Lecture, 1939),” Mon. Not. R. Astron. Soc. 99, 580-594 (1939).

Aime, C.

R. Soummer, C. Aime, and P. E. Falloon, “Stellar coronagraphy with prolate apodized circular apertures,” Astron. Astrophys. 397, 1161-1172 (2003).
[CrossRef]

Angel, J. R. P.

J. R. P. Angel, “Groundbased imaging of extrasolar planets using adaptive optics,” Nature (London) 368, 203-207 (1994).
[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]

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]

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]

R. Conan, T. Fusco, G. Rousset, D. Mouillet, J.-L. Beuzit, M. Nicolle, and C. Petit, “Modeling and analysis of XAO systems. Application to VLT-Planet Finder,” Proc. SPIE 5490, pp. 602-608 (2004).
[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).
[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]

Burrows, A.

A. Burrows and D. Sudarsky, “Models of irradiated extrasolar giant planets,” in Scientific Frontiers in Research on Extrasolar Planets, Vol. 294 of Astronomical Society of the Pacific Conference Series, D.Deming and S.Seager, eds. (Astronomical Society of the Pacific, 2003), pp. 491-498.

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).
[CrossRef]

I. Smith, A. Ferrari, and M. Carbillet, “Detection algorithm of exoplanets in field-rotated images: preliminary results on simulated SPHERE coronographic images,” in Semaine de l'Astrophysique Française, SF2A (EDP Sciences, 2007).

Charton, J.

Clénet, Y.

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.

Conan, R.

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]

R. Conan, T. Fusco, G. Rousset, D. Mouillet, J.-L. Beuzit, M. Nicolle, and C. Petit, “Modeling and analysis of XAO systems. Application to VLT-Planet Finder,” Proc. SPIE 5490, pp. 602-608 (2004).
[CrossRef]

Dohlen, K.

K. Dohlen, M. Langlois, and M. Saisse, “The infrared dual imaging and spectrograph for SPHERE: design and performance,” Proc. SPIE 7014, 70143L (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).
[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]

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]

C. Marois, R. Doyon, D. Nadeau, R. Racine, and G. A. H. Walker, “Effects of quasi-static aberrations in faint companion searches,” in Astronomy with High-Contrast Imaging, Vol. 8 of EAS Publications Series, C.Aime and R.Soummer, eds. (EDP Sciences, 2003), pp. 233-243.

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]

Falloon, P. E.

R. Soummer, C. Aime, and P. E. Falloon, “Stellar coronagraphy with prolate apodized circular apertures,” Astron. Astrophys. 397, 1161-1172 (2003).
[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).
[CrossRef]

I. Smith, A. Ferrari, and M. Carbillet, “Detection algorithm of exoplanets in field-rotated images: preliminary results on simulated SPHERE coronographic images,” in Semaine de l'Astrophysique Française, SF2A (EDP Sciences, 2007).

Fusco, T.

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. Conan, T. Fusco, G. Rousset, D. Mouillet, J.-L. Beuzit, M. Nicolle, and C. Petit, “Modeling and analysis of XAO systems. Application to VLT-Planet Finder,” Proc. SPIE 5490, pp. 602-608 (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.-F. Sauvage, L. Mugnier, A. Woelfflé, T. Fusco, and G. Rousset, “Multi-channel algorithm for exoplanets detection by angular differential imaging,” in Semaine de l'Astrophysique Française, SF2A (EDP Sciences, 2007).

L. M. Mugnier, J.-F. Sauvage, T. Fusco, and G. Rousset, “Multi-channel planet detection algorithm for angular differential imaging,” in Adaptive Optics: Analysis and Methods, OSA Technical Digest (OSA, 2007), paper ATu A4.

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]

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]

Jolissaint, L.

Kasper, M.

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]

A. Labeyrie, “Detection of extra-solar planets,” in Formation of Planetary Systems, A.Brahic, ed. (Cepadues-Editions, Toulouse, 1982), pp. 883, 885-888.

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]

Langlois, M.

K. Dohlen, M. Langlois, and M. Saisse, “The infrared dual imaging and spectrograph for SPHERE: design and performance,” Proc. SPIE 7014, 70143L (2008).
[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]

Lyot, B.

B. Lyot, “The study of the solar corona and prominences without eclipses (George Darwin Lecture, 1939),” Mon. Not. R. Astron. Soc. 99, 580-594 (1939).

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]

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]

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, 587-594 (1999).
[CrossRef]

C. Marois, R. Doyon, D. Nadeau, R. Racine, and G. A. H. Walker, “Effects of quasi-static aberrations in faint companion searches,” in Astronomy with High-Contrast Imaging, Vol. 8 of EAS Publications Series, C.Aime and R.Soummer, eds. (EDP Sciences, 2003), pp. 233-243.

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).
[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]

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. Conan, T. Fusco, G. Rousset, D. Mouillet, J.-L. Beuzit, M. Nicolle, and C. Petit, “Modeling and analysis of XAO systems. Application to VLT-Planet Finder,” Proc. SPIE 5490, pp. 602-608 (2004).
[CrossRef]

Mueller, M.

M. Mueller and G. Weigelt, “High-resolution astronomical imaging by roll deconvolution of space telescope data,” Astron. Astrophys. 175, 312-318 (1987).

Mugnier, L.

J.-F. Sauvage, L. Mugnier, A. Woelfflé, T. Fusco, and G. Rousset, “Multi-channel algorithm for exoplanets detection by angular differential imaging,” in Semaine de l'Astrophysique Française, SF2A (EDP Sciences, 2007).

Mugnier, L. M.

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]

L. M. Mugnier, J.-F. Sauvage, T. Fusco, and G. Rousset, “Multi-channel planet detection algorithm for angular differential imaging,” in Adaptive Optics: Analysis and Methods, OSA Technical Digest (OSA, 2007), paper ATu A4.

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, 587-594 (1999).
[CrossRef]

C. Marois, R. Doyon, D. Nadeau, R. Racine, and G. A. H. Walker, “Effects of quasi-static aberrations in faint companion searches,” in Astronomy with High-Contrast Imaging, Vol. 8 of EAS Publications Series, C.Aime and R.Soummer, eds. (EDP Sciences, 2003), pp. 233-243.

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]

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]

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]

Puget, P.

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, 587-594 (1999).
[CrossRef]

C. Marois, R. Doyon, D. Nadeau, R. Racine, and G. A. H. Walker, “Effects of quasi-static aberrations in faint companion searches,” in Astronomy with High-Contrast Imaging, Vol. 8 of EAS Publications Series, C.Aime and R.Soummer, eds. (EDP Sciences, 2003), pp. 233-243.

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]

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]

Rouan, D.

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]

Rousset, G.

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. Conan, T. Fusco, G. Rousset, D. Mouillet, J.-L. Beuzit, M. Nicolle, and C. Petit, “Modeling and analysis of XAO systems. Application to VLT-Planet Finder,” Proc. SPIE 5490, pp. 602-608 (2004).
[CrossRef]

L. M. Mugnier, J.-F. Sauvage, T. Fusco, and G. Rousset, “Multi-channel planet detection algorithm for angular differential imaging,” in Adaptive Optics: Analysis and Methods, OSA Technical Digest (OSA, 2007), paper ATu A4.

J.-F. Sauvage, L. Mugnier, A. Woelfflé, T. Fusco, and G. Rousset, “Multi-channel algorithm for exoplanets detection by angular differential imaging,” in Semaine de l'Astrophysique Française, SF2A (EDP Sciences, 2007).

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]

Saisse, M.

K. Dohlen, M. Langlois, and M. Saisse, “The infrared dual imaging and spectrograph for SPHERE: design and performance,” Proc. SPIE 7014, 70143L (2008).
[CrossRef]

Sauvage, J.-F.

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]

L. M. Mugnier, J.-F. Sauvage, T. Fusco, and G. Rousset, “Multi-channel planet detection algorithm for angular differential imaging,” in Adaptive Optics: Analysis and Methods, OSA Technical Digest (OSA, 2007), paper ATu A4.

J.-F. Sauvage, “Calibration et méthodes d'inversion en imagerie haute dynamique pour la détection directe d'exoplanètes,” Ph.D. thesis (Université Paris VII, 2007).

J.-F. Sauvage, L. Mugnier, A. Woelfflé, T. Fusco, and G. Rousset, “Multi-channel algorithm for exoplanets detection by angular differential imaging,” in Semaine de l'Astrophysique Française, SF2A (EDP Sciences, 2007).

Sivaramakrishnan, 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]

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).
[CrossRef]

I. Smith, A. Ferrari, and M. Carbillet, “Detection algorithm of exoplanets in field-rotated images: preliminary results on simulated SPHERE coronographic images,” in Semaine de l'Astrophysique Française, SF2A (EDP Sciences, 2007).

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]

R. Soummer, C. Aime, and P. E. Falloon, “Stellar coronagraphy with prolate apodized circular apertures,” Astron. Astrophys. 397, 1161-1172 (2003).
[CrossRef]

Sudarsky, D.

A. Burrows and D. Sudarsky, “Models of irradiated extrasolar giant planets,” in Scientific Frontiers in Research on Extrasolar Planets, Vol. 294 of Astronomical Society of the Pacific Conference Series, D.Deming and S.Seager, eds. (Astronomical Society of the Pacific, 2003), pp. 491-498.

Swain, M. R.

M. R. Swain, G. Vasisht, and G. Tinetti, “The presence of methane in the atmosphere of an extrasolar planet,” Nature (London) 452, 329-331 (2008).
[CrossRef]

Tinetti, G.

M. R. Swain, G. Vasisht, and G. Tinetti, “The presence of methane in the atmosphere of an extrasolar planet,” Nature (London) 452, 329-331 (2008).
[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]

Vasisht, G.

M. R. Swain, G. Vasisht, and G. Tinetti, “The presence of methane in the atmosphere of an extrasolar planet,” Nature (London) 452, 329-331 (2008).
[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, 587-594 (1999).
[CrossRef]

Walker, G. A. H.

C. Marois, R. Doyon, D. Nadeau, R. Racine, and G. A. H. Walker, “Effects of quasi-static aberrations in faint companion searches,” in Astronomy with High-Contrast Imaging, Vol. 8 of EAS Publications Series, C.Aime and R.Soummer, eds. (EDP Sciences, 2003), pp. 233-243.

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]

Weigelt, G.

M. Mueller and G. Weigelt, “High-resolution astronomical imaging by roll deconvolution of space telescope data,” Astron. Astrophys. 175, 312-318 (1987).

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]

Woelfflé, A.

J.-F. Sauvage, L. Mugnier, A. Woelfflé, T. Fusco, and G. Rousset, “Multi-channel algorithm for exoplanets detection by angular differential imaging,” in Semaine de l'Astrophysique Française, SF2A (EDP Sciences, 2007).

Astron. Astrophys. (2)

R. Soummer, C. Aime, and P. E. Falloon, “Stellar coronagraphy with prolate apodized circular apertures,” Astron. Astrophys. 397, 1161-1172 (2003).
[CrossRef]

M. Mueller and G. Weigelt, “High-resolution astronomical imaging by roll deconvolution of space telescope data,” Astron. Astrophys. 175, 312-318 (1987).

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]

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]

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

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

B. Lyot, “The study of the solar corona and prominences without eclipses (George Darwin Lecture, 1939),” Mon. Not. R. Astron. Soc. 99, 580-594 (1939).

Nature (London) (2)

J. R. P. Angel, “Groundbased imaging of extrasolar planets using adaptive optics,” Nature (London) 368, 203-207 (1994).
[CrossRef]

M. R. Swain, G. Vasisht, and G. Tinetti, “The presence of methane in the atmosphere of an extrasolar planet,” Nature (London) 452, 329-331 (2008).
[CrossRef]

Opt. Express (1)

Proc. SPIE (5)

R. Conan, T. Fusco, G. Rousset, D. Mouillet, J.-L. Beuzit, M. Nicolle, and C. Petit, “Modeling and analysis of XAO systems. Application to VLT-Planet Finder,” Proc. SPIE 5490, pp. 602-608 (2004).
[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]

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]

K. Dohlen, M. Langlois, and M. Saisse, “The infrared dual imaging and spectrograph for SPHERE: design and performance,” Proc. SPIE 7014, 70143L (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).
[CrossRef]

Publ. Astron. Soc. Pac. (3)

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]

R. Racine, G. A. Walker, D. Nadeau, and C. Marois, “Speckle noise and the detection of faint companions,” Publ. Astron. Soc. Pac. 112, 587-594 (1999).
[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 (7)

J.-F. Sauvage, “Calibration et méthodes d'inversion en imagerie haute dynamique pour la détection directe d'exoplanètes,” Ph.D. thesis (Université Paris VII, 2007).

C. Marois, R. Doyon, D. Nadeau, R. Racine, and G. A. H. Walker, “Effects of quasi-static aberrations in faint companion searches,” in Astronomy with High-Contrast Imaging, Vol. 8 of EAS Publications Series, C.Aime and R.Soummer, eds. (EDP Sciences, 2003), pp. 233-243.

I. Smith, A. Ferrari, and M. Carbillet, “Detection algorithm of exoplanets in field-rotated images: preliminary results on simulated SPHERE coronographic images,” in Semaine de l'Astrophysique Française, SF2A (EDP Sciences, 2007).

L. M. Mugnier, J.-F. Sauvage, T. Fusco, and G. Rousset, “Multi-channel planet detection algorithm for angular differential imaging,” in Adaptive Optics: Analysis and Methods, OSA Technical Digest (OSA, 2007), paper ATu A4.

J.-F. Sauvage, L. Mugnier, A. Woelfflé, T. Fusco, and G. Rousset, “Multi-channel algorithm for exoplanets detection by angular differential imaging,” in Semaine de l'Astrophysique Française, SF2A (EDP Sciences, 2007).

A. Labeyrie, “Detection of extra-solar planets,” in Formation of Planetary Systems, A.Brahic, ed. (Cepadues-Editions, Toulouse, 1982), pp. 883, 885-888.

A. Burrows and D. Sudarsky, “Models of irradiated extrasolar giant planets,” in Scientific Frontiers in Research on Extrasolar Planets, Vol. 294 of Astronomical Society of the Pacific Conference Series, D.Deming and S.Seager, eds. (Astronomical Society of the Pacific, 2003), pp. 491-498.

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Figures (8)

Fig. 1
Fig. 1

Illustration of the angular differences performed on the raw data. Left and center: two noiseless raw coronagraphic images i t 1 and i t 2 of a star with a very bright planet ( 10 3 intensity ratio between star and planet). Right: difference Δ ( r , t 1 , t 2 ) , used as our new data, which completely removes the star signal in this case where the quasi-static aberrations have not evolved. The colormap is inverted for better legibility, with black corresponding to the maximum value.

Fig. 2
Fig. 2

Examples of planet signatures p ( r , k ; r 0 ) . Top: for one value of r 0 and three values of the time index k. Bottom: for another value of r 0 and the three same values of the time index k. The cross in the middle represents the center of the field rotation.

Fig. 3
Fig. 3

Intensity maps a ̂ ( r 0 ) and a ̂ pos ( r 0 ) estimated without (left) and with (right) the positivity constraint, respectively, in a noiseless case. The colormap is inverted for better legibility: the white sidelobes have the lowest, and negative, value; the gray background has zero value, and black corresponds to the highest value.

Fig. 4
Fig. 4

Log-likelihood maps of the position of the planet in the noiseless case of Fig. 3 without [ J ( r 0 ) , left] and with [ J ( r 0 ) , right] the positivity constraint on the estimated intensity. The colormap is inverted for better legibility: white is the lowest, and zero, value; black corresponds to the highest value.

Fig. 5
Fig. 5

Simulated PSFs with (left) and without (right) coronagraph in logarithmic scale. Note that for legibility the colormap is inverted, and each of these two images is represented with its own gray-level scale (with black corresponding to its maximum value).

Fig. 6
Fig. 6

Likelihood maps with 100 images and an exposure time of 1 h . Top row: homogeneous noise. Bottom row: inhomogeneous noise. Left column: without positivity constraint. Right column: with positivity constraint. For legibility the colormap is inverted: white corresponds to the minimum value of zero, and black to the highest value.

Fig. 7
Fig. 7

Detection maps obtained by thresholding the maps of the SNR of the estimated intensity of Fig. 6, for various thresholds mentioned in the left column. From left to right: homogeneous noise, no positivity; homogeneous noise and positivity; inhomogeneous noise, no positivity; inhomogeneous noise and positivity.

Fig. 8
Fig. 8

Likelihood and detection maps for different exposure times: 1 h (left) and 2 h (right) with 100 images in each case. The estimation is done with the inhomogeneous noise model and a positivity constraint.

Equations (13)

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

Δ ( r , t 1 , t 2 ) i t 1 ( r ) i t 2 ( r ) ,
Δ ( r , k ) = a p ( r , k ; r 0 ) + n ( r , k ) ,
L ( r 0 , a ) exp { 1 2 k r Δ ( r , k ) a p ( r , k ; r 0 ) 2 2 σ 2 ( r , k ) } .
J ( r 0 , a ) a 2 k , r p 2 ( r , k ; r 0 ) σ 2 ( r , k ) + 2 a k , r p ( r , k ; r 0 ) Δ ( r , k ) σ 2 ( r , k )
= 2 ln L ( r 0 , a ) + const .
a ̂ ( r 0 ) = k , r p ( r , k ; r 0 ) Δ ( r , k ) σ 2 ( r , k ) k , r p 2 ( r , k ; r 0 ) σ 2 ( r , k ) .
J ( r 0 ) J [ r 0 , a ̂ ( r 0 ) ] = [ k , r p ( r , k ; r 0 ) Δ ( r , k ) σ 2 ( r , k ) ] 2 k , r p 2 ( r , k ; r 0 ) σ 2 ( r , k ) .
a ̂ pos ( r 0 ) = max { a ̂ ( r 0 ) , 0 } .
J ( r 0 ) J [ r 0 , a ̂ pos ( r 0 ) ] = { J ( r 0 ) , if a ̂ ( r 0 ) > 0 0 , if a ̂ ( r 0 ) 0 } ,
SNR [ a ̂ ( r 0 ) ] a ̂ ( r 0 ) σ [ a ̂ ( r 0 ) ] .
σ 2 [ a ̂ ( r 0 ) ] = 1 [ r , k p 2 ( r , k ; r 0 ) σ 2 ( r , k ) ] 2 r , k [ p ( r , k ; r 0 ) σ 2 ( r , k ) ] 2 σ 2 ( r , k ) ,
σ 2 [ a ̂ ( r 0 ) ] = [ r , k p 2 ( r , k ; r 0 ) σ 2 ( r , k ) ] 1 .
J ( r 0 ) = { a ̂ ( r 0 ) σ [ a ̂ ( r 0 ) ] } 2 = { SNR [ a ̂ ( r 0 ) ] } 2 .

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