Abstract

The phase diversity technique is a useful tool to measure and pre-compensate for quasi-static aberrations, in particular non-common path aberrations, in an adaptive optics corrected imaging system. In this paper, we propose and validate by simulations an extension of the phase diversity technique that uses long exposure adaptive optics corrected images for sensing quasi-static aberrations during the scientific observation, in particular for high-contrast imaging. The principle of the method is that, for a sufficiently long exposure time, the residual turbulence is averaged into a convolutive component of the image and that phase diversity estimates the sole static aberrations of interest.

The advantages of such a procedure, compared to the processing of short-exposure image pairs, are that the separation between static aberrations and turbulence-induced ones is performed by the long-exposure itself and not numerically, that only one image pair must be processed, that the estimation benefits from the high SNR of long-exposure images, and that only the static aberrations of interest are to be estimated. Long-exposure phase diversity can also be used as a phasing sensor for a segmented aperture telescope. Thus, it may be particularly useful for future planet finder projects such as EPICS on the European ELT.

© 2008 Optical Society of America

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  1. F. Roddier, ed., Adaptive Optics in Astronomy (Cambridge University Press, Cambridge, 1999).
    [CrossRef]
  2. A. Blanc, T. Fusco, M. Hartung, L. M. Mugnier, and G. Rousset, "Calibration of NAOS and CONICA static aberrations. Application of the phase diversity technique," Astron. Astrophys. 399, 373-383 (2003).
    [CrossRef]
  3. M. Hartung, A. Blanc, T. Fusco, F. Lacombe, L. M. Mugnier, G. Rousset, and R. Lenzen, "Calibration of NAOS and CONICA static aberrations. Experimental results," Astron. Astrophys. 399, 385-394 (2003).
    [CrossRef]
  4. J.-F. Sauvage, T. Fusco, G. Rousset, and C. Petit, "Calibration and Pre-Compensation of Non-Common Path Aberrations for eXtreme Adaptive Optics," J. Opt. Soc. Am. A 24, 2334-2346 (2007).
    [CrossRef]
  5. G. Rousset, "Wave-front sensors," in Roddier [1], chap. 5, pp. 91-130.
  6. R. A. Gonsalves, "Phase retrieval and diversity in adaptive optics," Opt. Eng. 21, 829-832 (1982).
  7. R. G. Paxman and J. R. Fienup, "Optical misalignment sensing and image reconstruction using phase diversity," J. Opt. Soc. Am. A 5, 914-923 (1988).
    [CrossRef]
  8. R. G. Paxman, T. J. Schulz, and J. R. Fienup, "Joint estimation of object and aberrations by using phase diversity," J. Opt. Soc. Am. A 9, 1072-1085 (1992).
    [CrossRef]
  9. M. G. L¨ofdahl and G. B. Scharmer, "Wavefront sensing and image restoration from focused and defocused solar images," Astron. Astrophys. 107, 243-264 (1994).
  10. D. J. Lee, M. C. Roggemann, B. M. Welsh, and E. R. Crosby, "Evaluation of least-squares phase-diversity technique for space telescope wave-front sensing," Appl. Opt. 36, 9186-9197 (1997).
    [CrossRef]
  11. B. J. Thelen, R. G. Paxman, D. A. Carrara, and J. H. Seldin, "Maximum a posteriori estimation of fixed aberrations, dynamic aberrations, and the object from phase-diverse speckle data," J. Opt. Soc. Am. A 16, 1016-1025 (1999).
    [CrossRef]
  12. A. Blanc, L. M. Mugnier, and J. Idier, "Marginal estimation of aberrations and image restoration by use of phase diversity," J. Opt. Soc. Am. A 20, 1035-1045 (2003).
    [CrossRef]
  13. L.M. Mugnier, A. Blanc, and J. Idier, "Phase Diversity: a Technique forWave-Front Sensing and for Diffraction- Limited Imaging," in Advances in Imaging and Electron Physics, P. Hawkes, ed., vol. 141, chap. 1, pp. 1-76 (Elsevier, 2006).
    [CrossRef]
  14. D. S. Acton, D. Soltau, and W. Schmidt, "Full-field wavefront measurements with phase diversity," Astron. Astrophys. 309, 661-672 (1996).
  15. N. Baba and K. Mutoh, "Measurement of telescope aberrations through atmospheric turbulence by use of phase diversity," Appl. Opt. 40, 544-552 (2001).
    [CrossRef]
  16. D. J. Lee, B. M. Welsh, and M. C. Roggemann, "Diagnosing unknown aberrations in an adaptive optics system by use of phase diversity," Opt. Lett. 22, 952-954 (1997).
    [CrossRef] [PubMed]
  17. F. Roddier, "The effects of atmospherical turbulence in optical astronomy," in Progress in Optics, E. Wolf, ed., vol. XIX, pp. 281-376 (North Holland, Amsterdam, 1981).
    [CrossRef]
  18. G. Demoment, "Image Reconstruction and Restoration: Overview of Common Estimation Structures and Problems," IEEE Trans. Acoust. Speech Signal Process. 37, 2024-2036 (1989).
    [CrossRef]
  19. A. Blanc, "Identification de r’eponse impulsionnelle et restauration d’images : apports de la diversit’e de phase," Ph.D. thesis, Universit’e Paris XI Orsay (2002).
  20. J. Idier, L. Mugnier, and A. Blanc, "Statistical behavior of joint least square estimation in the phase diversity context," IEEE Trans. Image Processing 14, 2107-2116 (2005).
    [CrossRef]
  21. L. Meynadier, V. Michau, M.-T. Velluet, J.-M. Conan, L. M. Mugnier, and G. Rousset, "Noise propagation in wave-front sensing with phase diversity," Appl. Opt. 38, 4967-4979 (1999).
    [CrossRef]
  22. 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]
  23. 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, and 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).
    [PubMed]
  24. L. Jolissaint, J.-P. V’eran, 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]
  25. 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," in Advancements in Adaptive Optics, vol. 5490 (Proc. Soc. Photo-Opt. Instrum. Eng., 2004). Conference date: Jun. 2004, Glasgow, UK.
  26. M. Kasper, C. Verinaud, J.-L. Beuzit, N. Yaitskova, N. Hubin, A. Boccaletti, K. Dohlen, T. Fusco, A. Glindemann, R. Gratton, and N. Thatte, "EPICS: A Planet Hunter for the European ELT," 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). Conference date: Jun. 2007,
  27. J.-F. Sauvage, L. Mugnier, T. Fusco, and G. Rousset, "Post processing of differential images for direct extrasolar planet detection from the ground," in Advances in Adaptive Optics II, L. Ellerbroek, B. and D. Bonaccini Calia, eds., vol. 6272 (Proc. Soc. Photo-Opt. Instrum. Eng., 2006).
  28. J.-F. Sauvage, "Calibration et m’ethodes d’inversion en imagerie haute dynamique pour la d’etection directe d’exoplan`etes." Ph.D. thesis, Universit’e Paris VII (2007).

2007 (1)

2006 (2)

2005 (1)

J. Idier, L. Mugnier, and A. Blanc, "Statistical behavior of joint least square estimation in the phase diversity context," IEEE Trans. Image Processing 14, 2107-2116 (2005).
[CrossRef]

2003 (3)

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

M. Hartung, A. Blanc, T. Fusco, F. Lacombe, L. M. Mugnier, G. Rousset, and R. Lenzen, "Calibration of NAOS and CONICA static aberrations. Experimental results," Astron. Astrophys. 399, 385-394 (2003).
[CrossRef]

A. Blanc, L. M. Mugnier, and J. Idier, "Marginal estimation of aberrations and image restoration by use of phase diversity," J. Opt. Soc. Am. A 20, 1035-1045 (2003).
[CrossRef]

2001 (1)

1999 (2)

1997 (2)

1996 (1)

D. S. Acton, D. Soltau, and W. Schmidt, "Full-field wavefront measurements with phase diversity," Astron. Astrophys. 309, 661-672 (1996).

1994 (1)

M. G. L¨ofdahl and G. B. Scharmer, "Wavefront sensing and image restoration from focused and defocused solar images," Astron. Astrophys. 107, 243-264 (1994).

1992 (1)

1989 (1)

G. Demoment, "Image Reconstruction and Restoration: Overview of Common Estimation Structures and Problems," IEEE Trans. Acoust. Speech Signal Process. 37, 2024-2036 (1989).
[CrossRef]

1988 (1)

1982 (1)

R. A. Gonsalves, "Phase retrieval and diversity in adaptive optics," Opt. Eng. 21, 829-832 (1982).

Acton, D. S.

D. S. Acton, D. Soltau, and W. Schmidt, "Full-field wavefront measurements with phase diversity," Astron. Astrophys. 309, 661-672 (1996).

Baba, N.

Beuzit, J.-L.

Blanc, A.

J. Idier, L. Mugnier, and A. Blanc, "Statistical behavior of joint least square estimation in the phase diversity context," IEEE Trans. Image Processing 14, 2107-2116 (2005).
[CrossRef]

A. Blanc, L. M. Mugnier, and J. Idier, "Marginal estimation of aberrations and image restoration by use of phase diversity," J. Opt. Soc. Am. A 20, 1035-1045 (2003).
[CrossRef]

M. Hartung, A. Blanc, T. Fusco, F. Lacombe, L. M. Mugnier, G. Rousset, and R. Lenzen, "Calibration of NAOS and CONICA static aberrations. Experimental results," Astron. Astrophys. 399, 385-394 (2003).
[CrossRef]

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

Carrara, D. A.

Charton, J.

Conan, J.-M.

Crosby, E. R.

Demoment, G.

G. Demoment, "Image Reconstruction and Restoration: Overview of Common Estimation Structures and Problems," IEEE Trans. Acoust. Speech Signal Process. 37, 2024-2036 (1989).
[CrossRef]

Dohlen, K.

Fienup, J. R.

Fusco, T.

J.-F. Sauvage, T. Fusco, G. Rousset, and C. Petit, "Calibration and Pre-Compensation of Non-Common Path Aberrations for eXtreme Adaptive Optics," J. Opt. Soc. Am. A 24, 2334-2346 (2007).
[CrossRef]

T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, and P. Puget, "High order Adaptive Optics requirements for direct detection of Extra-solar planets. Application to the SPHERE instrument." Opt. Express 14, 7515-7534 (2006).
[CrossRef] [PubMed]

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

M. Hartung, A. Blanc, T. Fusco, F. Lacombe, L. M. Mugnier, G. Rousset, and R. Lenzen, "Calibration of NAOS and CONICA static aberrations. Experimental results," Astron. Astrophys. 399, 385-394 (2003).
[CrossRef]

Gonsalves, R. A.

R. A. Gonsalves, "Phase retrieval and diversity in adaptive optics," Opt. Eng. 21, 829-832 (1982).

Hartung, M.

M. Hartung, A. Blanc, T. Fusco, F. Lacombe, L. M. Mugnier, G. Rousset, and R. Lenzen, "Calibration of NAOS and CONICA static aberrations. Experimental results," Astron. Astrophys. 399, 385-394 (2003).
[CrossRef]

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

Idier, J.

J. Idier, L. Mugnier, and A. Blanc, "Statistical behavior of joint least square estimation in the phase diversity context," IEEE Trans. Image Processing 14, 2107-2116 (2005).
[CrossRef]

A. Blanc, L. M. Mugnier, and J. Idier, "Marginal estimation of aberrations and image restoration by use of phase diversity," J. Opt. Soc. Am. A 20, 1035-1045 (2003).
[CrossRef]

Jolissaint, L.

Kasper, M.

L¨ofdahl, M. G.

M. G. L¨ofdahl and G. B. Scharmer, "Wavefront sensing and image restoration from focused and defocused solar images," Astron. Astrophys. 107, 243-264 (1994).

Lacombe, F.

M. Hartung, A. Blanc, T. Fusco, F. Lacombe, L. M. Mugnier, G. Rousset, and R. Lenzen, "Calibration of NAOS and CONICA static aberrations. Experimental results," Astron. Astrophys. 399, 385-394 (2003).
[CrossRef]

Lee, D. J.

Lenzen, R.

M. Hartung, A. Blanc, T. Fusco, F. Lacombe, L. M. Mugnier, G. Rousset, and R. Lenzen, "Calibration of NAOS and CONICA static aberrations. Experimental results," Astron. Astrophys. 399, 385-394 (2003).
[CrossRef]

Meynadier, L.

Michau, V.

Mouillet, D.

Mugnier, L.

J. Idier, L. Mugnier, and A. Blanc, "Statistical behavior of joint least square estimation in the phase diversity context," IEEE Trans. Image Processing 14, 2107-2116 (2005).
[CrossRef]

Mugnier, L. M.

A. Blanc, L. M. Mugnier, and J. Idier, "Marginal estimation of aberrations and image restoration by use of phase diversity," J. Opt. Soc. Am. A 20, 1035-1045 (2003).
[CrossRef]

M. Hartung, A. Blanc, T. Fusco, F. Lacombe, L. M. Mugnier, G. Rousset, and R. Lenzen, "Calibration of NAOS and CONICA static aberrations. Experimental results," Astron. Astrophys. 399, 385-394 (2003).
[CrossRef]

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

L. Meynadier, V. Michau, M.-T. Velluet, J.-M. Conan, L. M. Mugnier, and G. Rousset, "Noise propagation in wave-front sensing with phase diversity," Appl. Opt. 38, 4967-4979 (1999).
[CrossRef]

Mutoh, K.

Nicolle, M.

Paxman, R. G.

Petit, C.

Puget, P.

Roggemann, M. C.

Rousset, G.

Sauvage, J.-F.

Scharmer, G. B.

M. G. L¨ofdahl and G. B. Scharmer, "Wavefront sensing and image restoration from focused and defocused solar images," Astron. Astrophys. 107, 243-264 (1994).

Schmidt, W.

D. S. Acton, D. Soltau, and W. Schmidt, "Full-field wavefront measurements with phase diversity," Astron. Astrophys. 309, 661-672 (1996).

Schulz, T. J.

Seldin, J. H.

Soltau, D.

D. S. Acton, D. Soltau, and W. Schmidt, "Full-field wavefront measurements with phase diversity," Astron. Astrophys. 309, 661-672 (1996).

Thelen, B. J.

Velluet, M.-T.

Welsh, B. M.

Appl. Opt. (3)

Astron. Astrophys. (4)

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

M. Hartung, A. Blanc, T. Fusco, F. Lacombe, L. M. Mugnier, G. Rousset, and R. Lenzen, "Calibration of NAOS and CONICA static aberrations. Experimental results," Astron. Astrophys. 399, 385-394 (2003).
[CrossRef]

M. G. L¨ofdahl and G. B. Scharmer, "Wavefront sensing and image restoration from focused and defocused solar images," Astron. Astrophys. 107, 243-264 (1994).

D. S. Acton, D. Soltau, and W. Schmidt, "Full-field wavefront measurements with phase diversity," Astron. Astrophys. 309, 661-672 (1996).

IEEE Trans. Acoust. Speech Signal Process. (1)

G. Demoment, "Image Reconstruction and Restoration: Overview of Common Estimation Structures and Problems," IEEE Trans. Acoust. Speech Signal Process. 37, 2024-2036 (1989).
[CrossRef]

IEEE Trans. Image Processing (1)

J. Idier, L. Mugnier, and A. Blanc, "Statistical behavior of joint least square estimation in the phase diversity context," IEEE Trans. Image Processing 14, 2107-2116 (2005).
[CrossRef]

J. Opt. Soc. Am. A (6)

Opt. Eng. (1)

R. A. Gonsalves, "Phase retrieval and diversity in adaptive optics," Opt. Eng. 21, 829-832 (1982).

Opt. Express (1)

Opt. Lett. (1)

Other (10)

L.M. Mugnier, A. Blanc, and J. Idier, "Phase Diversity: a Technique forWave-Front Sensing and for Diffraction- Limited Imaging," in Advances in Imaging and Electron Physics, P. Hawkes, ed., vol. 141, chap. 1, pp. 1-76 (Elsevier, 2006).
[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, and 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).
[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," in Advancements in Adaptive Optics, vol. 5490 (Proc. Soc. Photo-Opt. Instrum. Eng., 2004). Conference date: Jun. 2004, Glasgow, UK.

M. Kasper, C. Verinaud, J.-L. Beuzit, N. Yaitskova, N. Hubin, A. Boccaletti, K. Dohlen, T. Fusco, A. Glindemann, R. Gratton, and N. Thatte, "EPICS: A Planet Hunter for the European ELT," 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). Conference date: Jun. 2007,

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

J.-F. Sauvage, "Calibration et m’ethodes d’inversion en imagerie haute dynamique pour la d’etection directe d’exoplan`etes." Ph.D. thesis, Universit’e Paris VII (2007).

F. Roddier, ed., Adaptive Optics in Astronomy (Cambridge University Press, Cambridge, 1999).
[CrossRef]

G. Rousset, "Wave-front sensors," in Roddier [1], chap. 5, pp. 91-130.

A. Blanc, "Identification de r’eponse impulsionnelle et restauration d’images : apports de la diversit’e de phase," Ph.D. thesis, Universit’e Paris XI Orsay (2002).

F. Roddier, "The effects of atmospherical turbulence in optical astronomy," in Progress in Optics, E. Wolf, ed., vol. XIX, pp. 281-376 (North Holland, Amsterdam, 1981).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Evolution of the reconstruction error with the exposure time (in number of independent turbulence realizations). Static aberrations are randomly generated according to conditions described in Subsection 4.1. AO correction is assumed to be performed by a SAXO-like system.

Fig. 2.
Fig. 2.

Evolution of the reconstruction error with the exposure time, for several levels of AO correction. Static aberrations are randomly generated according to conditions described in Subsection 4.1.

Fig. 3.
Fig. 3.

Spatial spectrum of the estimated aberrations, in the case of a NAOS-7 correction. The vertical line represents the maximum spatial frequency that is corrected by the AO system.

Fig. 4.
Fig. 4.

Spatial spectrum of the estimated aberrations, in the case of a NAOS-14 correction. The vertical line represents the maximum spatial frequency that is corrected by the AO system.

Fig. 5.
Fig. 5.

Spatial spectrum of the estimated aberrations, in the case of a SAXO/SPHERE correction. The vertical line represents the maximum spatial frequency that is corrected by the AO system.

Equations (9)

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

h ˜ o = h ˜ s h ˜ a .
h ˜ s ( φ ) = P e i φ P e i φ
h ˜ a ( f ) = e 1 2 D ϕ ( λ f )
h le = h d h o = h d h s h a ,
i f = h le o + n ,
i f = h d h s ( ϕ ) ( h a o ) + n
i d = h d h s ( ϕ + ϕ d ) ( h a o ) + n ' ,
o ' = h a o
J ( o ' , ϕ ) = 1 2 σ n 2 i f h d h s ( ϕ ) o ' + 1 2 σ n ' 2 i d h d h s ( ϕ + ϕ d ) o ' + R o ( o ' ) + R ϕ ( ϕ ) ,

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