Abstract

We study different possibilities to use adaptive optics (AO) and phase diversity (PD) together in a jointly optimized system. The potential of the joint system is demonstrated through numerical simulations. We find that the most significant benefits are obtained from the improved deconvolution of AO-corrected wavefronts and the additional wavefront sensor (WFS) information that reduces the computational demands of PD algorithms. When applied together, it is seen that the image error can be reduced by 20% compared to traditional PD, working with one focused and one defocused camera image, and the computational load is reduced by a factor of 20 compared to a more reliable PD algorithm requiring more camera images. In addition, we find that the system performance can be optimized by adjusting the magnitude of the applied diversity wavefronts.

© 2012 Optical Society of America

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  2. R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).
  3. 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]
  4. M. G. Löfdahl and G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).
  5. R. G. Paxman, J. H. Seldin, M. G. Löfdahl, G. B. Scharmer, and C. U. Keller, “Evaluation of phase-diversity techniques for solar-image restoration,” Astrophys. J. 466, 1087–1099(1996).
    [CrossRef]
  6. M. G. Löfdahl, “Multi-frame blind deconvolution with linear equality constraints,” Proc. SPIE 4792, 146–155 (2002).
    [CrossRef]
  7. M. van Noort, L. R. van der Voort, and M. G. Löfdahl, “Solar image restoration by use of multi-frame blind de-convolution with multiple objects and phase diversity,” Sol. Phys. 228, 191–215 (2005).
    [CrossRef]
  8. J. Sauvage, T. Fusco, G. Rousset, and C. Petit, “Calibration and precompensation of noncommon path aberrations for extreme adaptive optics,” J. Opt. Soc. Am. A 24, 2334–2346 (2007).
    [CrossRef]
  9. S. M. Jefferies, M. Lloyd-Hart, E. K. Hege, and J. Georges, “Sensing wave-front amplitude and phase with phase diversity,” Appl. Opt. 41, 2095–2102 (2002).
    [CrossRef]
  10. T. Berkefeld, “Solar adaptive optics,” in Modern Solar Facilities—Advanced Solar Science, F. Kneer, K. G. Puschmann, and A. D. Wittmann, eds. (Universitätsverlag Göttingen, 2007), pp. 107–113.
  11. F. J. Rigaut, B. L. Ellerbroek, and R. Flicker, “Principles, limitations, and performance of multiconjugate adaptive optics,” Proc. SPIE 4007, 1022–1031 (2000).
    [CrossRef]
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    [CrossRef]
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  14. M. G. Löfdahl and G. B. Scharmer, “Phase diverse speckle inversion applied to data from the Swedish 1-meter solar telescope,” Proc. SPIE 4853, 567–575 (2003).
    [CrossRef]
  15. K. G. Puschmann and M. Sailer, “Speckle reconstruction of photometric data observed with adaptive optics,” Astron. Astrophys. 454, 1011–1019 (2006).
    [CrossRef]
  16. J. H. Seldin, R. G. Paxman, D. A. Carrara, C. U. Keller, and T. R. Rimmele, “Deconvolution of narrowband solar images using aberrations estimated from phase-diverse imagery,” Proc. SPIE 3815, 155–163 (1999).
    [CrossRef]
  17. 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]
  18. R. A. Gonsalves, “Adaptive optics by sequential diversity imaging,” in Beyond Conventional Optics, E. Vernet, R. Ragazzoni, S. Esposito, and N. Hubin, eds. (European Southern Observatory, 2002), Vol. 58, pp. 121–124.
  19. R. A. Gonsalves, “Sequential diversity imaging: phase diversity with AO changes as the diversities,” in Frontiers in Optics, Technical Digest (CD) (Optical Society of America, 2010) p. FWV1.
  20. A. W. van Eekeren, K. Schutte, J. Dijk, and P. B. Schwering, “Time-varying phase diversity turbulence compensation,” Proc. SPIE 8012, 80120D (2011).
    [CrossRef]
  21. F. Roddier, “Theoretical aspects,” in Adaptive Optics in Astronomy, F. Roddier, ed. (Cambridge University, 1999), pp. 25–56.
  22. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. A 66, 207–211 (1976).
    [CrossRef]
  23. E. Peli, “Contrast in complex images,” J. Opt. Soc. Am. A 7, 2032–2040 (1990).
    [CrossRef]
  24. E. V. Khomenko, S. Shelyag, S. K. Solanki, and A. Vögler, “Stokes diagnostics of simulations of magnetoconvection of mixed-polarity quiet-Sun regions,” Astron. Astrophys. 442, 1059–1078 (2005).
    [CrossRef]
  25. V. Korkiakoski, C. Vérinaud, and M. Le Louarn, “Improving the performance of a pyramid wavefront sensor with modal sensitivity compensation,” Appl. Opt. 47, 79–87 (2008).
    [CrossRef]
  26. M. W. Smith, “Use of adaptive optics to implement nonquadratic phase diversity imaging,” Proc. SPIE 5524, 66–77 (2004).
    [CrossRef]
  27. D. J. Lee, M. C. Roggemann, and B. M. Welsh, “Cramér–Rao analysis of phase-diverse wave-front sensing,” J. Opt. Soc. Am. A 16, 1005–1015 (1999).
    [CrossRef]
  28. 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]
  29. J. J. Dolne, R. J. Tansey, K. A. Black, J. H. Deville, P. R. Cunningham, K. C. Widen, and P. S. Idell, “Practical issues in wave-front sensing by use of phase diversity,” Appl. Opt. 42, 5284–5289 (2003).
    [CrossRef]
  30. M. Carbillet, C. Vérinaud, B. Femenía, A. Riccardi, and L. Fini, “Modelling astronomical adaptive optics—I. The software package CAOS,” Mon. Not. R. Astron. Soc. 356, 1263–1275 (2005).
    [CrossRef]
  31. G. B. Scharmer, M. G. Löfdahl, T. I. M. van Werkhoven, and J. de la Cruz Rodríguez, “High-order aberration compensation with multi-frame blind deconvolution and phase diversity image restoration techniques,” Astron. Astrophys. 521, A68 (2010).
    [CrossRef]

2011

A. W. van Eekeren, K. Schutte, J. Dijk, and P. B. Schwering, “Time-varying phase diversity turbulence compensation,” Proc. SPIE 8012, 80120D (2011).
[CrossRef]

2010

G. B. Scharmer, M. G. Löfdahl, T. I. M. van Werkhoven, and J. de la Cruz Rodríguez, “High-order aberration compensation with multi-frame blind deconvolution and phase diversity image restoration techniques,” Astron. Astrophys. 521, A68 (2010).
[CrossRef]

2008

2007

2006

K. G. Puschmann and M. Sailer, “Speckle reconstruction of photometric data observed with adaptive optics,” Astron. Astrophys. 454, 1011–1019 (2006).
[CrossRef]

2005

M. van Noort, L. R. van der Voort, and M. G. Löfdahl, “Solar image restoration by use of multi-frame blind de-convolution with multiple objects and phase diversity,” Sol. Phys. 228, 191–215 (2005).
[CrossRef]

E. V. Khomenko, S. Shelyag, S. K. Solanki, and A. Vögler, “Stokes diagnostics of simulations of magnetoconvection of mixed-polarity quiet-Sun regions,” Astron. Astrophys. 442, 1059–1078 (2005).
[CrossRef]

M. Carbillet, C. Vérinaud, B. Femenía, A. Riccardi, and L. Fini, “Modelling astronomical adaptive optics—I. The software package CAOS,” Mon. Not. R. Astron. Soc. 356, 1263–1275 (2005).
[CrossRef]

2004

M. W. Smith, “Use of adaptive optics to implement nonquadratic phase diversity imaging,” Proc. SPIE 5524, 66–77 (2004).
[CrossRef]

2003

J. J. Dolne, R. J. Tansey, K. A. Black, J. H. Deville, P. R. Cunningham, K. C. Widen, and P. S. Idell, “Practical issues in wave-front sensing by use of phase diversity,” Appl. Opt. 42, 5284–5289 (2003).
[CrossRef]

M. G. Löfdahl and G. B. Scharmer, “Phase diverse speckle inversion applied to data from the Swedish 1-meter solar telescope,” Proc. SPIE 4853, 567–575 (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]

2002

M. G. Löfdahl, “Multi-frame blind deconvolution with linear equality constraints,” Proc. SPIE 4792, 146–155 (2002).
[CrossRef]

S. M. Jefferies, M. Lloyd-Hart, E. K. Hege, and J. Georges, “Sensing wave-front amplitude and phase with phase diversity,” Appl. Opt. 41, 2095–2102 (2002).
[CrossRef]

2000

F. J. Rigaut, B. L. Ellerbroek, and R. Flicker, “Principles, limitations, and performance of multiconjugate adaptive optics,” Proc. SPIE 4007, 1022–1031 (2000).
[CrossRef]

1999

1997

1996

R. G. Paxman, J. H. Seldin, M. G. Löfdahl, G. B. Scharmer, and C. U. Keller, “Evaluation of phase-diversity techniques for solar-image restoration,” Astrophys. J. 466, 1087–1099(1996).
[CrossRef]

1994

M. G. Löfdahl and G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).

1992

1990

1982

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

1976

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. A 66, 207–211 (1976).
[CrossRef]

Berkefeld, T.

T. Berkefeld, “Solar adaptive optics,” in Modern Solar Facilities—Advanced Solar Science, F. Kneer, K. G. Puschmann, and A. D. Wittmann, eds. (Universitätsverlag Göttingen, 2007), pp. 107–113.

Black, K. A.

Blanc, A.

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]

Carbillet, M.

M. Carbillet, C. Vérinaud, B. Femenía, A. Riccardi, and L. Fini, “Modelling astronomical adaptive optics—I. The software package CAOS,” Mon. Not. R. Astron. Soc. 356, 1263–1275 (2005).
[CrossRef]

Carrara, D.

C. U. Keller, T. R. Rimmele, R. G. Paxman, J. H. Seldin, D. Carrara, and K. Gleichman, “Evolution of small-scale magnetic fields from combined adaptive optics and phase-diverse speckle imaging,” in AAS/Solar Physics Division Meeting #31, vol. 32 of Bulletin of the American Astronomical Society (American Astronomical Society, 2000), p. 833.

Carrara, D. A.

J. H. Seldin, R. G. Paxman, D. A. Carrara, C. U. Keller, and T. R. Rimmele, “Deconvolution of narrowband solar images using aberrations estimated from phase-diverse imagery,” Proc. SPIE 3815, 155–163 (1999).
[CrossRef]

Conan, J.-M.

Cunningham, P. R.

de la Cruz Rodríguez, J.

G. B. Scharmer, M. G. Löfdahl, T. I. M. van Werkhoven, and J. de la Cruz Rodríguez, “High-order aberration compensation with multi-frame blind deconvolution and phase diversity image restoration techniques,” Astron. Astrophys. 521, A68 (2010).
[CrossRef]

Deville, J. H.

Dijk, J.

A. W. van Eekeren, K. Schutte, J. Dijk, and P. B. Schwering, “Time-varying phase diversity turbulence compensation,” Proc. SPIE 8012, 80120D (2011).
[CrossRef]

Dolne, J. J.

Ellerbroek, B. L.

F. J. Rigaut, B. L. Ellerbroek, and R. Flicker, “Principles, limitations, and performance of multiconjugate adaptive optics,” Proc. SPIE 4007, 1022–1031 (2000).
[CrossRef]

Femenía, B.

M. Carbillet, C. Vérinaud, B. Femenía, A. Riccardi, and L. Fini, “Modelling astronomical adaptive optics—I. The software package CAOS,” Mon. Not. R. Astron. Soc. 356, 1263–1275 (2005).
[CrossRef]

Fienup, J. R.

Fini, L.

M. Carbillet, C. Vérinaud, B. Femenía, A. Riccardi, and L. Fini, “Modelling astronomical adaptive optics—I. The software package CAOS,” Mon. Not. R. Astron. Soc. 356, 1263–1275 (2005).
[CrossRef]

Flicker, R.

F. J. Rigaut, B. L. Ellerbroek, and R. Flicker, “Principles, limitations, and performance of multiconjugate adaptive optics,” Proc. SPIE 4007, 1022–1031 (2000).
[CrossRef]

Fusco, T.

J. Sauvage, T. Fusco, G. Rousset, and C. Petit, “Calibration and precompensation of noncommon path aberrations for extreme adaptive optics,” J. Opt. Soc. Am. A 24, 2334–2346 (2007).
[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]

Georges, J.

Gleichman, K.

C. U. Keller, T. R. Rimmele, R. G. Paxman, J. H. Seldin, D. Carrara, and K. Gleichman, “Evolution of small-scale magnetic fields from combined adaptive optics and phase-diverse speckle imaging,” in AAS/Solar Physics Division Meeting #31, vol. 32 of Bulletin of the American Astronomical Society (American Astronomical Society, 2000), p. 833.

Gonsalves, R. A.

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

R. A. Gonsalves, “Sequential diversity imaging: phase diversity with AO changes as the diversities,” in Frontiers in Optics, Technical Digest (CD) (Optical Society of America, 2010) p. FWV1.

R. A. Gonsalves, “Adaptive optics by sequential diversity imaging,” in Beyond Conventional Optics, E. Vernet, R. Ragazzoni, S. Esposito, and N. Hubin, eds. (European Southern Observatory, 2002), Vol. 58, pp. 121–124.

Hartung, M.

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]

Hege, E. K.

Idell, P. S.

Jefferies, S. M.

Keller, C. U.

J. H. Seldin, R. G. Paxman, D. A. Carrara, C. U. Keller, and T. R. Rimmele, “Deconvolution of narrowband solar images using aberrations estimated from phase-diverse imagery,” Proc. SPIE 3815, 155–163 (1999).
[CrossRef]

R. G. Paxman, J. H. Seldin, M. G. Löfdahl, G. B. Scharmer, and C. U. Keller, “Evaluation of phase-diversity techniques for solar-image restoration,” Astrophys. J. 466, 1087–1099(1996).
[CrossRef]

C. U. Keller, T. R. Rimmele, R. G. Paxman, J. H. Seldin, D. Carrara, and K. Gleichman, “Evolution of small-scale magnetic fields from combined adaptive optics and phase-diverse speckle imaging,” in AAS/Solar Physics Division Meeting #31, vol. 32 of Bulletin of the American Astronomical Society (American Astronomical Society, 2000), p. 833.

Khomenko, E. V.

E. V. Khomenko, S. Shelyag, S. K. Solanki, and A. Vögler, “Stokes diagnostics of simulations of magnetoconvection of mixed-polarity quiet-Sun regions,” Astron. Astrophys. 442, 1059–1078 (2005).
[CrossRef]

Korkiakoski, V.

Le Louarn, M.

Lee, D. J.

Lloyd-Hart, M.

Löfdahl, M. G.

G. B. Scharmer, M. G. Löfdahl, T. I. M. van Werkhoven, and J. de la Cruz Rodríguez, “High-order aberration compensation with multi-frame blind deconvolution and phase diversity image restoration techniques,” Astron. Astrophys. 521, A68 (2010).
[CrossRef]

M. van Noort, L. R. van der Voort, and M. G. Löfdahl, “Solar image restoration by use of multi-frame blind de-convolution with multiple objects and phase diversity,” Sol. Phys. 228, 191–215 (2005).
[CrossRef]

M. G. Löfdahl and G. B. Scharmer, “Phase diverse speckle inversion applied to data from the Swedish 1-meter solar telescope,” Proc. SPIE 4853, 567–575 (2003).
[CrossRef]

M. G. Löfdahl, “Multi-frame blind deconvolution with linear equality constraints,” Proc. SPIE 4792, 146–155 (2002).
[CrossRef]

R. G. Paxman, J. H. Seldin, M. G. Löfdahl, G. B. Scharmer, and C. U. Keller, “Evaluation of phase-diversity techniques for solar-image restoration,” Astrophys. J. 466, 1087–1099(1996).
[CrossRef]

M. G. Löfdahl and G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).

Maître, H.

Meynadier, L.

Michau, V.

Mugnier, L. M.

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]

Noll, R. J.

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. A 66, 207–211 (1976).
[CrossRef]

Paxman, R. G.

J. H. Seldin, R. G. Paxman, D. A. Carrara, C. U. Keller, and T. R. Rimmele, “Deconvolution of narrowband solar images using aberrations estimated from phase-diverse imagery,” Proc. SPIE 3815, 155–163 (1999).
[CrossRef]

R. G. Paxman, J. H. Seldin, M. G. Löfdahl, G. B. Scharmer, and C. U. Keller, “Evaluation of phase-diversity techniques for solar-image restoration,” Astrophys. J. 466, 1087–1099(1996).
[CrossRef]

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]

C. U. Keller, T. R. Rimmele, R. G. Paxman, J. H. Seldin, D. Carrara, and K. Gleichman, “Evolution of small-scale magnetic fields from combined adaptive optics and phase-diverse speckle imaging,” in AAS/Solar Physics Division Meeting #31, vol. 32 of Bulletin of the American Astronomical Society (American Astronomical Society, 2000), p. 833.

Peli, E.

Petit, C.

Puschmann, K. G.

K. G. Puschmann and M. Sailer, “Speckle reconstruction of photometric data observed with adaptive optics,” Astron. Astrophys. 454, 1011–1019 (2006).
[CrossRef]

Riccardi, A.

M. Carbillet, C. Vérinaud, B. Femenía, A. Riccardi, and L. Fini, “Modelling astronomical adaptive optics—I. The software package CAOS,” Mon. Not. R. Astron. Soc. 356, 1263–1275 (2005).
[CrossRef]

Rigaut, F.

Rigaut, F. J.

F. J. Rigaut, B. L. Ellerbroek, and R. Flicker, “Principles, limitations, and performance of multiconjugate adaptive optics,” Proc. SPIE 4007, 1022–1031 (2000).
[CrossRef]

Rimmele, T. R.

J. H. Seldin, R. G. Paxman, D. A. Carrara, C. U. Keller, and T. R. Rimmele, “Deconvolution of narrowband solar images using aberrations estimated from phase-diverse imagery,” Proc. SPIE 3815, 155–163 (1999).
[CrossRef]

C. U. Keller, T. R. Rimmele, R. G. Paxman, J. H. Seldin, D. Carrara, and K. Gleichman, “Evolution of small-scale magnetic fields from combined adaptive optics and phase-diverse speckle imaging,” in AAS/Solar Physics Division Meeting #31, vol. 32 of Bulletin of the American Astronomical Society (American Astronomical Society, 2000), p. 833.

Roddier, F.

F. Roddier, Adaptive Optics in Astronomy (Cambridge University, 1999).

F. Roddier, “Theoretical aspects,” in Adaptive Optics in Astronomy, F. Roddier, ed. (Cambridge University, 1999), pp. 25–56.

Roggemann, M. C.

Rouan, D.

Rousset, G.

Sailer, M.

K. G. Puschmann and M. Sailer, “Speckle reconstruction of photometric data observed with adaptive optics,” Astron. Astrophys. 454, 1011–1019 (2006).
[CrossRef]

Sauvage, J.

Scharmer, G. B.

G. B. Scharmer, M. G. Löfdahl, T. I. M. van Werkhoven, and J. de la Cruz Rodríguez, “High-order aberration compensation with multi-frame blind deconvolution and phase diversity image restoration techniques,” Astron. Astrophys. 521, A68 (2010).
[CrossRef]

M. G. Löfdahl and G. B. Scharmer, “Phase diverse speckle inversion applied to data from the Swedish 1-meter solar telescope,” Proc. SPIE 4853, 567–575 (2003).
[CrossRef]

R. G. Paxman, J. H. Seldin, M. G. Löfdahl, G. B. Scharmer, and C. U. Keller, “Evaluation of phase-diversity techniques for solar-image restoration,” Astrophys. J. 466, 1087–1099(1996).
[CrossRef]

M. G. Löfdahl and G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).

Schulz, T. J.

Schutte, K.

A. W. van Eekeren, K. Schutte, J. Dijk, and P. B. Schwering, “Time-varying phase diversity turbulence compensation,” Proc. SPIE 8012, 80120D (2011).
[CrossRef]

Schwering, P. B.

A. W. van Eekeren, K. Schutte, J. Dijk, and P. B. Schwering, “Time-varying phase diversity turbulence compensation,” Proc. SPIE 8012, 80120D (2011).
[CrossRef]

Seldin, J. H.

J. H. Seldin, R. G. Paxman, D. A. Carrara, C. U. Keller, and T. R. Rimmele, “Deconvolution of narrowband solar images using aberrations estimated from phase-diverse imagery,” Proc. SPIE 3815, 155–163 (1999).
[CrossRef]

R. G. Paxman, J. H. Seldin, M. G. Löfdahl, G. B. Scharmer, and C. U. Keller, “Evaluation of phase-diversity techniques for solar-image restoration,” Astrophys. J. 466, 1087–1099(1996).
[CrossRef]

C. U. Keller, T. R. Rimmele, R. G. Paxman, J. H. Seldin, D. Carrara, and K. Gleichman, “Evolution of small-scale magnetic fields from combined adaptive optics and phase-diverse speckle imaging,” in AAS/Solar Physics Division Meeting #31, vol. 32 of Bulletin of the American Astronomical Society (American Astronomical Society, 2000), p. 833.

Shelyag, S.

E. V. Khomenko, S. Shelyag, S. K. Solanki, and A. Vögler, “Stokes diagnostics of simulations of magnetoconvection of mixed-polarity quiet-Sun regions,” Astron. Astrophys. 442, 1059–1078 (2005).
[CrossRef]

Smith, M. W.

M. W. Smith, “Use of adaptive optics to implement nonquadratic phase diversity imaging,” Proc. SPIE 5524, 66–77 (2004).
[CrossRef]

Solanki, S. K.

E. V. Khomenko, S. Shelyag, S. K. Solanki, and A. Vögler, “Stokes diagnostics of simulations of magnetoconvection of mixed-polarity quiet-Sun regions,” Astron. Astrophys. 442, 1059–1078 (2005).
[CrossRef]

Tansey, R. J.

van der Voort, L. R.

M. van Noort, L. R. van der Voort, and M. G. Löfdahl, “Solar image restoration by use of multi-frame blind de-convolution with multiple objects and phase diversity,” Sol. Phys. 228, 191–215 (2005).
[CrossRef]

van Eekeren, A. W.

A. W. van Eekeren, K. Schutte, J. Dijk, and P. B. Schwering, “Time-varying phase diversity turbulence compensation,” Proc. SPIE 8012, 80120D (2011).
[CrossRef]

van Noort, M.

M. van Noort, L. R. van der Voort, and M. G. Löfdahl, “Solar image restoration by use of multi-frame blind de-convolution with multiple objects and phase diversity,” Sol. Phys. 228, 191–215 (2005).
[CrossRef]

van Werkhoven, T. I. M.

G. B. Scharmer, M. G. Löfdahl, T. I. M. van Werkhoven, and J. de la Cruz Rodríguez, “High-order aberration compensation with multi-frame blind deconvolution and phase diversity image restoration techniques,” Astron. Astrophys. 521, A68 (2010).
[CrossRef]

Velluet, M.-T.

Véran, J.-P.

Vérinaud, C.

V. Korkiakoski, C. Vérinaud, and M. Le Louarn, “Improving the performance of a pyramid wavefront sensor with modal sensitivity compensation,” Appl. Opt. 47, 79–87 (2008).
[CrossRef]

M. Carbillet, C. Vérinaud, B. Femenía, A. Riccardi, and L. Fini, “Modelling astronomical adaptive optics—I. The software package CAOS,” Mon. Not. R. Astron. Soc. 356, 1263–1275 (2005).
[CrossRef]

Vögler, A.

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[CrossRef]

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Appl. Opt.

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Figures (4)

Fig. 1.
Fig. 1.

Data collection scheme in our PD algorithm.

Fig. 2.
Fig. 2.

Relative image reconstruction error as a function of applied diversity rms. M=36, M=0. Horizontal lines show the original image error. Error bars show the range of image error in terms of rms computed from different realizations (9 WFs times 9 images). Thin lines: 2-image PD used. Thick gray lines: 4-image PD used. Upper plot: r0 is 0.08 m (the range of original image error shown by dashed lines). Lower plot: r0 is 0.05, 0.08, and 0.15 m.

Fig. 3.
Fig. 3.

The number of required FFTs as a function of reconstruction error. Solid lines show the pure PD; dashed lines are made with additional WF information. Thin lines are made with 2-image PD, thick lines with 4-image PD. The lines connect points with 26–126 estimated modal coefficients with the other simulation parameters fixed. The circles around the points show the rms computed over 32 random WF realizations and nine different subimages of the object. Upper plot: Kolmogorov-style turbulence (r0=0.08m at 0.5 μm). Seeing-limited image error ϵs0.11. Lower plot: WFs typical for an AO system. AO-corrected image error ϵs0.09.

Fig. 4.
Fig. 4.

Illustration of performance. All images have a dimension of 384×384 pixels, showing the region PD has reconstructed. Upper row: original object (having no spatial frequencies above the system diffraction limit), seeing-limited image, and AO-corrected image. Images 1–6 show examples of PD performance. See text for details.

Tables (3)

Tables Icon

Table 1. Used Notations

Tables Icon

Table 2. AO Simulation Parameters

Tables Icon

Table 3. PD Performance on AO Sequences

Equations (17)

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L=k=1Nu,vγk|DkF^T^k|2+Z,
Z=l=1Ki=1Mri2cil2,
tk(x,y)=|F{P(x,y)exp[i(ϕl(x,y)+ψk(x,y))]}|2,
ϕl(x,y)=i=1MMi(x,y)cil+i=1MMi(x,y)cil,
FM=Q2k=1NγkDkT^k*,
Q=(k=1Nγk|Tk|2)1/2,
LM=j=1N1k=j+1Nu,vQ2γjγk|DjT^kDkT^j|2+l=1Ki=1Mri2cil2.
LM=j=1N1k=j+1Nu,v|Ejk|2+l=1Ki=1Mri2cil2,
Ejk=Q(γjγk)1/2(DjT^kDkT^j).
Ejkcil=(γjγk)1/2[Dj(QT^kcil+QcilT^k)Dk(QT^jcil+QcilT^j)],
Qcil=Q3Re(k=1NγkT^k*T^kcil)
T^kcil=0ifkl.
j=1N1k=j+1Nu,v|Ejk+l=1Ki=1MEjkcilΔcil|2+l=1Ki=1Mri2(cil+Δcil)2.
AΔc+b=0,
A(m,m)=j=1N1k=j+1N(Ejkcil|Ejkcil)+δ(m,m)ri2
b(m)=j=1N1k=j+1N(Ejkcil|Ejk)+ri2cil,
ϵ=[(IrI)2I2]1/2,

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