Abstract

Calibration experiments with a bimorph mirror are presented. Phase-diversity wave-front sensing is used for measuring the control matrix, nulling wave-front errors in the optical setup, including the mirror, and measuring Strehl ratios and residual higher-order aberrations. The Strehl ratio of the calibrated system is measured to be 0.975, corresponding to 1/40 wave rms in the residual wave front. The conclusion is that a phase-diversity wave-front sensor is easier to install and use than interferometers and can replace them in optical setups for testing adaptive optics systems.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. B. Scharmer, D. S. Brown, L. Pettersson, J. Rehn, “Concepts for the Swedish 50-cm Vacuum Solar Telescope,” Appl. Opt. 24, 2558–2564 (1985).
    [CrossRef] [PubMed]
  2. M. Shand, G. Scharmer, “The Swedish Vacuum Solar Telescope data acquisition and control systems,” in Site Properties of the Canarian Observatories, C. Muñoz-Tuñón, ed., Vol. 42 of New Astronomy Reviews (Elsevier, Amsterdam, 1998), pp. 481–484.
  3. M. Shand, G. B. Scharmer, W. Wei, “Correlation tracking and adaptive optics control using off-the-shelf workstation technology,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Proceedings of the Nineteenth Sacramento Peak Summer Workshop, Vol. 183 of the Astronomical Society of the Pacific Conference Series (ASP, San Francisco, Calif., 1999), p. 231.
  4. M. G. Löfdahl, G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).
  5. M. G. Löfdahl, T. E. Berger, R. A. Shine, A. M. Title, “Preparation of a dual wave-length sequence of high-resolution solar photospheric images using phase diversity,” Astrophys. J. 495, 965–972 (1998).
    [CrossRef]
  6. G. B. Scharmer, M. Owner-Petersen, T. Korhonen, A. Title, “The new Swedish solar telescope,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Proceedings of the Nineteenth Sacramento Peak Summer Workshop, Vol. 183 of the Astronomical Society of the Pacific Conference Series (ASP, San Francisco, Calif., 1999), p. 157.
  7. G. B. Scharmer, M. Shand, M. G. Löfdahl, W. Wei are preparing a manuscript to be called “A workstation based solar adaptive optics system.”
  8. G. B. Scharmer, “Object-independent fast phase-diversity,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Proceedings of the Nineteenth Sacramento Peak Summer Workshop, Vol. 183 of the Astronomical Society of the Pacific Conference Series (ASP, San Francisco, Calif., 1999), p. 330.
  9. R. G. Paxman, J. H. Seldin, M. G. Löfdahl, G. B. Scharmer, C. U. Keller, “Evaluation of phase-diverse techniques for solar-image restoration,” Astrophys. J. 466, 1087–1099 (1996).
    [CrossRef]
  10. R. L. Kendrick, D. S. Acton, A. L. Duncan, “Phase-diversity wave-front sensor for imaging systems,” Appl. Opt. 33, 6533–6546 (1994).
    [CrossRef] [PubMed]
  11. R. G. Paxman, T. J. Schulz, J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072–1085 (1992).
    [CrossRef]
  12. R. G. Paxman, J. R. Fienup, “Optical misalignment sensing and image reconstruction using phase diversity,” J. Opt. Soc. Am. A 5, 914–923 (1988).
    [CrossRef]
  13. R. A. Gonsalves, R. Chidlaw, “Wavefront sensing by phase retrieval,” in Applications of Digital Image Processing III, A. G. Tescher, ed., Proc. SPIE207, 32–39 (1979).
    [CrossRef]
  14. M. G. Löfdahl, A. L. Duncan, G. B. Scharmer, “Fast phase diversity wavefront sensing for mirror control,” in Adaptive Optical System Technologies, D. Bonnaccini, R. K. Tyson, eds., Proc. SPIE3353, 952–963 (1998).
    [CrossRef]
  15. R. G. Paxman, J. H. Seldin, “Fine-resolution astronomical imaging with phase-diverse speckle,” in Digital Recovery and Synthesis II, P. S. Idell, ed., Proc. SPIE2029, 287–298 (1993).
    [CrossRef]
  16. R. L. Kendrick, R. Bell, A. L. Duncan, G. D. Love, D. S. Acton, “Closed loop wavefront correction using phase diversity,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 844–853 (1998).
    [CrossRef]
  17. M. G. Löfdahl, R. L. Kendrick, A. Harwit, K. E. Mitchell, A. L. Duncan, J. H. Seldin, R. G. Paxman, D. S. Acton, “A phase diversity experiment to measure piston misalignment on the segmented primary mirror of the Keck II telescope,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 1190–1201 (1998).
    [CrossRef]
  18. D. J. Lee, B. M. Welsh, M. C. Roggemann, B. L. Ellerbroek, “Diagnosing unknown aberrations in an adaptive optics system by use of phase diversity,” Opt. Lett. 22, 952–954 (1997).
    [CrossRef] [PubMed]
  19. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  20. C. L. Lawson, R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974).
  21. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).
  22. M. J. Northcott, Laplacian Optics, Inc., Suite 134, 2800 Woodlawn Drive, Honolulu, HI 96822 (personal communication, 1999).
  23. F. Roddier, “The problematic of adaptive optics design,” in Adaptive Optics for Astronomy, D. M. Alloin, J.-M. Mariotti, eds., NATO ASI Series423, 89–112 (1994).
  24. E. G. Stevens, J. P. Lavine, “An analytical, aperture, and two-layer carrier diffusion MTF and quantum efficiency model for solid-state image sensors,” IEEE Trans. Electron. Dev. 41, 1753–1760 (1994).
    [CrossRef]
  25. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  26. R. N. Bracewell, Two-Dimensional Imaging (Prentice-Hall, Englewood Cliffs, N.J., 1995).
  27. V. N. Mahajan, “Strehl ratio for primary aberrations: some analytical results for circular and annular pupils,” J. Opt. Soc. Am. 72, 1258–1266 (1982).
    [CrossRef]
  28. W. J. Smith, Modern Optical Engineering: The Design of Optical Systems, 2nd ed. (McGraw-Hill, New York, 1990).
  29. R. G. Paxman, T. J. Schulz, J. R. Fienup, “Phase-diverse speckle interferometry,” in Signal Recovery and Synthesis IV, Vol. 11 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 5–7.
  30. B. L. Ellerbroek, B. J. Thelen, D. J. Lee, D. A. Carrara, R. G. Paxman, “Comparison of Shack–Hartmann wavefront sensing and phase-diverse phase retrieval,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 307–320 (1997).
    [CrossRef]

1998 (1)

M. G. Löfdahl, T. E. Berger, R. A. Shine, A. M. Title, “Preparation of a dual wave-length sequence of high-resolution solar photospheric images using phase diversity,” Astrophys. J. 495, 965–972 (1998).
[CrossRef]

1997 (1)

1996 (1)

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

1994 (3)

R. L. Kendrick, D. S. Acton, A. L. Duncan, “Phase-diversity wave-front sensor for imaging systems,” Appl. Opt. 33, 6533–6546 (1994).
[CrossRef] [PubMed]

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

E. G. Stevens, J. P. Lavine, “An analytical, aperture, and two-layer carrier diffusion MTF and quantum efficiency model for solid-state image sensors,” IEEE Trans. Electron. Dev. 41, 1753–1760 (1994).
[CrossRef]

1992 (1)

1988 (1)

1985 (1)

1982 (1)

1976 (1)

Acton, D. S.

R. L. Kendrick, D. S. Acton, A. L. Duncan, “Phase-diversity wave-front sensor for imaging systems,” Appl. Opt. 33, 6533–6546 (1994).
[CrossRef] [PubMed]

R. L. Kendrick, R. Bell, A. L. Duncan, G. D. Love, D. S. Acton, “Closed loop wavefront correction using phase diversity,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 844–853 (1998).
[CrossRef]

M. G. Löfdahl, R. L. Kendrick, A. Harwit, K. E. Mitchell, A. L. Duncan, J. H. Seldin, R. G. Paxman, D. S. Acton, “A phase diversity experiment to measure piston misalignment on the segmented primary mirror of the Keck II telescope,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 1190–1201 (1998).
[CrossRef]

Bell, R.

R. L. Kendrick, R. Bell, A. L. Duncan, G. D. Love, D. S. Acton, “Closed loop wavefront correction using phase diversity,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 844–853 (1998).
[CrossRef]

Berger, T. E.

M. G. Löfdahl, T. E. Berger, R. A. Shine, A. M. Title, “Preparation of a dual wave-length sequence of high-resolution solar photospheric images using phase diversity,” Astrophys. J. 495, 965–972 (1998).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, Two-Dimensional Imaging (Prentice-Hall, Englewood Cliffs, N.J., 1995).

Brown, D. S.

Carrara, D. A.

B. L. Ellerbroek, B. J. Thelen, D. J. Lee, D. A. Carrara, R. G. Paxman, “Comparison of Shack–Hartmann wavefront sensing and phase-diverse phase retrieval,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 307–320 (1997).
[CrossRef]

Chidlaw, R.

R. A. Gonsalves, R. Chidlaw, “Wavefront sensing by phase retrieval,” in Applications of Digital Image Processing III, A. G. Tescher, ed., Proc. SPIE207, 32–39 (1979).
[CrossRef]

Duncan, A. L.

R. L. Kendrick, D. S. Acton, A. L. Duncan, “Phase-diversity wave-front sensor for imaging systems,” Appl. Opt. 33, 6533–6546 (1994).
[CrossRef] [PubMed]

M. G. Löfdahl, A. L. Duncan, G. B. Scharmer, “Fast phase diversity wavefront sensing for mirror control,” in Adaptive Optical System Technologies, D. Bonnaccini, R. K. Tyson, eds., Proc. SPIE3353, 952–963 (1998).
[CrossRef]

R. L. Kendrick, R. Bell, A. L. Duncan, G. D. Love, D. S. Acton, “Closed loop wavefront correction using phase diversity,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 844–853 (1998).
[CrossRef]

M. G. Löfdahl, R. L. Kendrick, A. Harwit, K. E. Mitchell, A. L. Duncan, J. H. Seldin, R. G. Paxman, D. S. Acton, “A phase diversity experiment to measure piston misalignment on the segmented primary mirror of the Keck II telescope,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 1190–1201 (1998).
[CrossRef]

Ellerbroek, B. L.

D. J. Lee, B. M. Welsh, M. C. Roggemann, B. L. Ellerbroek, “Diagnosing unknown aberrations in an adaptive optics system by use of phase diversity,” Opt. Lett. 22, 952–954 (1997).
[CrossRef] [PubMed]

B. L. Ellerbroek, B. J. Thelen, D. J. Lee, D. A. Carrara, R. G. Paxman, “Comparison of Shack–Hartmann wavefront sensing and phase-diverse phase retrieval,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 307–320 (1997).
[CrossRef]

Fienup, J. R.

R. G. Paxman, T. J. Schulz, J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072–1085 (1992).
[CrossRef]

R. G. Paxman, J. R. Fienup, “Optical misalignment sensing and image reconstruction using phase diversity,” J. Opt. Soc. Am. A 5, 914–923 (1988).
[CrossRef]

R. G. Paxman, T. J. Schulz, J. R. Fienup, “Phase-diverse speckle interferometry,” in Signal Recovery and Synthesis IV, Vol. 11 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 5–7.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Gonsalves, R. A.

R. A. Gonsalves, R. Chidlaw, “Wavefront sensing by phase retrieval,” in Applications of Digital Image Processing III, A. G. Tescher, ed., Proc. SPIE207, 32–39 (1979).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Hanson, R. J.

C. L. Lawson, R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974).

Harwit, A.

M. G. Löfdahl, R. L. Kendrick, A. Harwit, K. E. Mitchell, A. L. Duncan, J. H. Seldin, R. G. Paxman, D. S. Acton, “A phase diversity experiment to measure piston misalignment on the segmented primary mirror of the Keck II telescope,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 1190–1201 (1998).
[CrossRef]

Keller, C. U.

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

Kendrick, R. L.

R. L. Kendrick, D. S. Acton, A. L. Duncan, “Phase-diversity wave-front sensor for imaging systems,” Appl. Opt. 33, 6533–6546 (1994).
[CrossRef] [PubMed]

M. G. Löfdahl, R. L. Kendrick, A. Harwit, K. E. Mitchell, A. L. Duncan, J. H. Seldin, R. G. Paxman, D. S. Acton, “A phase diversity experiment to measure piston misalignment on the segmented primary mirror of the Keck II telescope,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 1190–1201 (1998).
[CrossRef]

R. L. Kendrick, R. Bell, A. L. Duncan, G. D. Love, D. S. Acton, “Closed loop wavefront correction using phase diversity,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 844–853 (1998).
[CrossRef]

Korhonen, T.

G. B. Scharmer, M. Owner-Petersen, T. Korhonen, A. Title, “The new Swedish solar telescope,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Proceedings of the Nineteenth Sacramento Peak Summer Workshop, Vol. 183 of the Astronomical Society of the Pacific Conference Series (ASP, San Francisco, Calif., 1999), p. 157.

Lavine, J. P.

E. G. Stevens, J. P. Lavine, “An analytical, aperture, and two-layer carrier diffusion MTF and quantum efficiency model for solid-state image sensors,” IEEE Trans. Electron. Dev. 41, 1753–1760 (1994).
[CrossRef]

Lawson, C. L.

C. L. Lawson, R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974).

Lee, D. J.

D. J. Lee, B. M. Welsh, M. C. Roggemann, B. L. Ellerbroek, “Diagnosing unknown aberrations in an adaptive optics system by use of phase diversity,” Opt. Lett. 22, 952–954 (1997).
[CrossRef] [PubMed]

B. L. Ellerbroek, B. J. Thelen, D. J. Lee, D. A. Carrara, R. G. Paxman, “Comparison of Shack–Hartmann wavefront sensing and phase-diverse phase retrieval,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 307–320 (1997).
[CrossRef]

Löfdahl, M. G.

M. G. Löfdahl, T. E. Berger, R. A. Shine, A. M. Title, “Preparation of a dual wave-length sequence of high-resolution solar photospheric images using phase diversity,” Astrophys. J. 495, 965–972 (1998).
[CrossRef]

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

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

G. B. Scharmer, M. Shand, M. G. Löfdahl, W. Wei are preparing a manuscript to be called “A workstation based solar adaptive optics system.”

M. G. Löfdahl, R. L. Kendrick, A. Harwit, K. E. Mitchell, A. L. Duncan, J. H. Seldin, R. G. Paxman, D. S. Acton, “A phase diversity experiment to measure piston misalignment on the segmented primary mirror of the Keck II telescope,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 1190–1201 (1998).
[CrossRef]

M. G. Löfdahl, A. L. Duncan, G. B. Scharmer, “Fast phase diversity wavefront sensing for mirror control,” in Adaptive Optical System Technologies, D. Bonnaccini, R. K. Tyson, eds., Proc. SPIE3353, 952–963 (1998).
[CrossRef]

Love, G. D.

R. L. Kendrick, R. Bell, A. L. Duncan, G. D. Love, D. S. Acton, “Closed loop wavefront correction using phase diversity,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 844–853 (1998).
[CrossRef]

Mahajan, V. N.

Mitchell, K. E.

M. G. Löfdahl, R. L. Kendrick, A. Harwit, K. E. Mitchell, A. L. Duncan, J. H. Seldin, R. G. Paxman, D. S. Acton, “A phase diversity experiment to measure piston misalignment on the segmented primary mirror of the Keck II telescope,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 1190–1201 (1998).
[CrossRef]

Noll, R. J.

Northcott, M. J.

M. J. Northcott, Laplacian Optics, Inc., Suite 134, 2800 Woodlawn Drive, Honolulu, HI 96822 (personal communication, 1999).

Owner-Petersen, M.

G. B. Scharmer, M. Owner-Petersen, T. Korhonen, A. Title, “The new Swedish solar telescope,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Proceedings of the Nineteenth Sacramento Peak Summer Workshop, Vol. 183 of the Astronomical Society of the Pacific Conference Series (ASP, San Francisco, Calif., 1999), p. 157.

Paxman, R. G.

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

R. G. Paxman, T. J. Schulz, J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072–1085 (1992).
[CrossRef]

R. G. Paxman, J. R. Fienup, “Optical misalignment sensing and image reconstruction using phase diversity,” J. Opt. Soc. Am. A 5, 914–923 (1988).
[CrossRef]

R. G. Paxman, J. H. Seldin, “Fine-resolution astronomical imaging with phase-diverse speckle,” in Digital Recovery and Synthesis II, P. S. Idell, ed., Proc. SPIE2029, 287–298 (1993).
[CrossRef]

M. G. Löfdahl, R. L. Kendrick, A. Harwit, K. E. Mitchell, A. L. Duncan, J. H. Seldin, R. G. Paxman, D. S. Acton, “A phase diversity experiment to measure piston misalignment on the segmented primary mirror of the Keck II telescope,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 1190–1201 (1998).
[CrossRef]

B. L. Ellerbroek, B. J. Thelen, D. J. Lee, D. A. Carrara, R. G. Paxman, “Comparison of Shack–Hartmann wavefront sensing and phase-diverse phase retrieval,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 307–320 (1997).
[CrossRef]

R. G. Paxman, T. J. Schulz, J. R. Fienup, “Phase-diverse speckle interferometry,” in Signal Recovery and Synthesis IV, Vol. 11 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 5–7.

Pettersson, L.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Rehn, J.

Roddier, F.

F. Roddier, “The problematic of adaptive optics design,” in Adaptive Optics for Astronomy, D. M. Alloin, J.-M. Mariotti, eds., NATO ASI Series423, 89–112 (1994).

Roggemann, M. C.

Scharmer, G.

M. Shand, G. Scharmer, “The Swedish Vacuum Solar Telescope data acquisition and control systems,” in Site Properties of the Canarian Observatories, C. Muñoz-Tuñón, ed., Vol. 42 of New Astronomy Reviews (Elsevier, Amsterdam, 1998), pp. 481–484.

Scharmer, G. B.

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

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

G. B. Scharmer, D. S. Brown, L. Pettersson, J. Rehn, “Concepts for the Swedish 50-cm Vacuum Solar Telescope,” Appl. Opt. 24, 2558–2564 (1985).
[CrossRef] [PubMed]

G. B. Scharmer, M. Owner-Petersen, T. Korhonen, A. Title, “The new Swedish solar telescope,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Proceedings of the Nineteenth Sacramento Peak Summer Workshop, Vol. 183 of the Astronomical Society of the Pacific Conference Series (ASP, San Francisco, Calif., 1999), p. 157.

M. Shand, G. B. Scharmer, W. Wei, “Correlation tracking and adaptive optics control using off-the-shelf workstation technology,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Proceedings of the Nineteenth Sacramento Peak Summer Workshop, Vol. 183 of the Astronomical Society of the Pacific Conference Series (ASP, San Francisco, Calif., 1999), p. 231.

G. B. Scharmer, M. Shand, M. G. Löfdahl, W. Wei are preparing a manuscript to be called “A workstation based solar adaptive optics system.”

G. B. Scharmer, “Object-independent fast phase-diversity,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Proceedings of the Nineteenth Sacramento Peak Summer Workshop, Vol. 183 of the Astronomical Society of the Pacific Conference Series (ASP, San Francisco, Calif., 1999), p. 330.

M. G. Löfdahl, A. L. Duncan, G. B. Scharmer, “Fast phase diversity wavefront sensing for mirror control,” in Adaptive Optical System Technologies, D. Bonnaccini, R. K. Tyson, eds., Proc. SPIE3353, 952–963 (1998).
[CrossRef]

Schulz, T. J.

R. G. Paxman, T. J. Schulz, J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072–1085 (1992).
[CrossRef]

R. G. Paxman, T. J. Schulz, J. R. Fienup, “Phase-diverse speckle interferometry,” in Signal Recovery and Synthesis IV, Vol. 11 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 5–7.

Seldin, J. H.

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

R. G. Paxman, J. H. Seldin, “Fine-resolution astronomical imaging with phase-diverse speckle,” in Digital Recovery and Synthesis II, P. S. Idell, ed., Proc. SPIE2029, 287–298 (1993).
[CrossRef]

M. G. Löfdahl, R. L. Kendrick, A. Harwit, K. E. Mitchell, A. L. Duncan, J. H. Seldin, R. G. Paxman, D. S. Acton, “A phase diversity experiment to measure piston misalignment on the segmented primary mirror of the Keck II telescope,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 1190–1201 (1998).
[CrossRef]

Shand, M.

G. B. Scharmer, M. Shand, M. G. Löfdahl, W. Wei are preparing a manuscript to be called “A workstation based solar adaptive optics system.”

M. Shand, G. B. Scharmer, W. Wei, “Correlation tracking and adaptive optics control using off-the-shelf workstation technology,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Proceedings of the Nineteenth Sacramento Peak Summer Workshop, Vol. 183 of the Astronomical Society of the Pacific Conference Series (ASP, San Francisco, Calif., 1999), p. 231.

M. Shand, G. Scharmer, “The Swedish Vacuum Solar Telescope data acquisition and control systems,” in Site Properties of the Canarian Observatories, C. Muñoz-Tuñón, ed., Vol. 42 of New Astronomy Reviews (Elsevier, Amsterdam, 1998), pp. 481–484.

Shine, R. A.

M. G. Löfdahl, T. E. Berger, R. A. Shine, A. M. Title, “Preparation of a dual wave-length sequence of high-resolution solar photospheric images using phase diversity,” Astrophys. J. 495, 965–972 (1998).
[CrossRef]

Smith, W. J.

W. J. Smith, Modern Optical Engineering: The Design of Optical Systems, 2nd ed. (McGraw-Hill, New York, 1990).

Stevens, E. G.

E. G. Stevens, J. P. Lavine, “An analytical, aperture, and two-layer carrier diffusion MTF and quantum efficiency model for solid-state image sensors,” IEEE Trans. Electron. Dev. 41, 1753–1760 (1994).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Thelen, B. J.

B. L. Ellerbroek, B. J. Thelen, D. J. Lee, D. A. Carrara, R. G. Paxman, “Comparison of Shack–Hartmann wavefront sensing and phase-diverse phase retrieval,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 307–320 (1997).
[CrossRef]

Title, A.

G. B. Scharmer, M. Owner-Petersen, T. Korhonen, A. Title, “The new Swedish solar telescope,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Proceedings of the Nineteenth Sacramento Peak Summer Workshop, Vol. 183 of the Astronomical Society of the Pacific Conference Series (ASP, San Francisco, Calif., 1999), p. 157.

Title, A. M.

M. G. Löfdahl, T. E. Berger, R. A. Shine, A. M. Title, “Preparation of a dual wave-length sequence of high-resolution solar photospheric images using phase diversity,” Astrophys. J. 495, 965–972 (1998).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Wei, W.

M. Shand, G. B. Scharmer, W. Wei, “Correlation tracking and adaptive optics control using off-the-shelf workstation technology,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Proceedings of the Nineteenth Sacramento Peak Summer Workshop, Vol. 183 of the Astronomical Society of the Pacific Conference Series (ASP, San Francisco, Calif., 1999), p. 231.

G. B. Scharmer, M. Shand, M. G. Löfdahl, W. Wei are preparing a manuscript to be called “A workstation based solar adaptive optics system.”

Welsh, B. M.

Appl. Opt. (2)

Astron. Astrophys. Suppl. Ser. (1)

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

Astrophys. J. (2)

M. G. Löfdahl, T. E. Berger, R. A. Shine, A. M. Title, “Preparation of a dual wave-length sequence of high-resolution solar photospheric images using phase diversity,” Astrophys. J. 495, 965–972 (1998).
[CrossRef]

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

IEEE Trans. Electron. Dev. (1)

E. G. Stevens, J. P. Lavine, “An analytical, aperture, and two-layer carrier diffusion MTF and quantum efficiency model for solid-state image sensors,” IEEE Trans. Electron. Dev. 41, 1753–1760 (1994).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Opt. Lett. (1)

Other (19)

M. Shand, G. Scharmer, “The Swedish Vacuum Solar Telescope data acquisition and control systems,” in Site Properties of the Canarian Observatories, C. Muñoz-Tuñón, ed., Vol. 42 of New Astronomy Reviews (Elsevier, Amsterdam, 1998), pp. 481–484.

M. Shand, G. B. Scharmer, W. Wei, “Correlation tracking and adaptive optics control using off-the-shelf workstation technology,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Proceedings of the Nineteenth Sacramento Peak Summer Workshop, Vol. 183 of the Astronomical Society of the Pacific Conference Series (ASP, San Francisco, Calif., 1999), p. 231.

G. B. Scharmer, M. Owner-Petersen, T. Korhonen, A. Title, “The new Swedish solar telescope,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Proceedings of the Nineteenth Sacramento Peak Summer Workshop, Vol. 183 of the Astronomical Society of the Pacific Conference Series (ASP, San Francisco, Calif., 1999), p. 157.

G. B. Scharmer, M. Shand, M. G. Löfdahl, W. Wei are preparing a manuscript to be called “A workstation based solar adaptive optics system.”

G. B. Scharmer, “Object-independent fast phase-diversity,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Proceedings of the Nineteenth Sacramento Peak Summer Workshop, Vol. 183 of the Astronomical Society of the Pacific Conference Series (ASP, San Francisco, Calif., 1999), p. 330.

R. A. Gonsalves, R. Chidlaw, “Wavefront sensing by phase retrieval,” in Applications of Digital Image Processing III, A. G. Tescher, ed., Proc. SPIE207, 32–39 (1979).
[CrossRef]

M. G. Löfdahl, A. L. Duncan, G. B. Scharmer, “Fast phase diversity wavefront sensing for mirror control,” in Adaptive Optical System Technologies, D. Bonnaccini, R. K. Tyson, eds., Proc. SPIE3353, 952–963 (1998).
[CrossRef]

R. G. Paxman, J. H. Seldin, “Fine-resolution astronomical imaging with phase-diverse speckle,” in Digital Recovery and Synthesis II, P. S. Idell, ed., Proc. SPIE2029, 287–298 (1993).
[CrossRef]

R. L. Kendrick, R. Bell, A. L. Duncan, G. D. Love, D. S. Acton, “Closed loop wavefront correction using phase diversity,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 844–853 (1998).
[CrossRef]

M. G. Löfdahl, R. L. Kendrick, A. Harwit, K. E. Mitchell, A. L. Duncan, J. H. Seldin, R. G. Paxman, D. S. Acton, “A phase diversity experiment to measure piston misalignment on the segmented primary mirror of the Keck II telescope,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 1190–1201 (1998).
[CrossRef]

W. J. Smith, Modern Optical Engineering: The Design of Optical Systems, 2nd ed. (McGraw-Hill, New York, 1990).

R. G. Paxman, T. J. Schulz, J. R. Fienup, “Phase-diverse speckle interferometry,” in Signal Recovery and Synthesis IV, Vol. 11 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 5–7.

B. L. Ellerbroek, B. J. Thelen, D. J. Lee, D. A. Carrara, R. G. Paxman, “Comparison of Shack–Hartmann wavefront sensing and phase-diverse phase retrieval,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 307–320 (1997).
[CrossRef]

C. L. Lawson, R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

M. J. Northcott, Laplacian Optics, Inc., Suite 134, 2800 Woodlawn Drive, Honolulu, HI 96822 (personal communication, 1999).

F. Roddier, “The problematic of adaptive optics design,” in Adaptive Optics for Astronomy, D. M. Alloin, J.-M. Mariotti, eds., NATO ASI Series423, 89–112 (1994).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

R. N. Bracewell, Two-Dimensional Imaging (Prentice-Hall, Englewood Cliffs, N.J., 1995).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Electrode configuration of the bimorph mirror. The thick circle inside the outer ring of electrodes indicates the 34-mm diameter of the active area. Courtesy of Laplacian Optics, Inc.

Fig. 2
Fig. 2

Optical setup.

Fig. 3
Fig. 3

Sample electrode response wave fronts. Top row, ϕ p , raw, estimated with PD. Bottom row, ϕp, averaged responses.

Fig. 4
Fig. 4

Graphic representation of electrode voltages to make Zernike mirror modes. Compare Fig. 1. The electrode maps are scaled individually. White is positive voltage, and black is negative.

Fig. 5
Fig. 5

Out-of-focus images from the closed loop. From the left, 0, 1, … , 5 corrections. Top row, observed data, g 1. Bottom row, corresponding PD estimates, ĝ 1(α, D), with Zernike coefficients 4–15 and 19 and D = 40 mm.

Fig. 6
Fig. 6

Simulated aberration-free out-of-focus channel image, 1(0, D); D = 33.25 mm.

Fig. 7
Fig. 7

Top, simulated out-of-focus images, 1(α, D), corresponding to the closed-loop data. The wave-front coefficients α are PD estimates of Zernike coefficients 4–55 with 35 SV’s and D = 33.25 mm. Note in particular the excellent agreement with the observed defocused images, g 1 in Fig. 5. Bottom, corresponding wave-front estimates scaled as a set. From the left, 0, 1, … , 5 corrections.

Fig. 8
Fig. 8

SR’s from closed-loop data: (a) after 5 corrections, for 35 SV’s as a function of pupil diameter D; (b) after 5 corrections, for D = 33.25 mm as a function of the number of SV’s; (c) for D = 33.25 mm and 35 SV’s, as a function of the number of corrections. Solid lines, measured directly from observed images (So); dashed–dotted–dotted lines, measured from simulated images (Ss); dashed lines, from wave-front rms (Sσ); dotted lines, observed images and PD object in the denominator (SOPD). The circles group the two observed image SR’s, So and SOPD, together. Note that in (b) SV’s do not enter into the calculation of the constant So.

Equations (16)

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

gkx=fx * skx+nkx=F-1FuSku+Nku,
ϕ=jJ αjψj.
L=x|g0-gˆ0α, D|2+|g1-gˆ1α, D|2,
gˆkα, D=F-1Fˆα, DSˆkα, D.
Fˆ=H G0Sˆ0+G1Sˆ1|Sˆ0|2+|Sˆ1|2,
h=Cα=jJ αjvj.
C=MTM-1MT,
α=Mh.
Mjp=αjhp
g˜kα, D=F-1HSkα, DTλ, ρjincρR,
So=peak g0peak g˜00, D,
peak g=maxx g-bgx g-bg.
Sσ=exp-4π2σ2,
Ss=peak g˜0α, Dpeak g˜00, D,
SOPD=peak g0peak gˆ00, D,
SSPD=peak gˆ0α, Dpeak gˆ00, D,

Metrics