Abstract

In many situations it is not possible for an adaptive optics system to use a point source to measure the phase derivative, such as imaging along slant paths through the atmosphere and observation of the earth from space with a lightweight optic. Instead, small subimages of the observed scene can be used in a scene-based wave-front sensing technique. This study presents three important advances in the understanding of this technique. Rigorous analysis shows how slope estimation performance depends precisely on scene content and illumination. Scaling laws for changes in illumination are derived. The technique, when applied to point sources, is more robust to detect size changes and background levels than current methods.

© 2003 Optical Society of America

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  1. P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
    [CrossRef]
  2. P. C. Chen, C. W. Bowers, D. A. Content, M. Marzouk, R. C. Romeo, “Advances in very lightweight composite mirror technology,” Opt. Eng. 39, 2320–2329 (2000).
    [CrossRef]
  3. M. G. Lofdahl, G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).
  4. R. G. Paxman, J. H. Seldin, M. G. Lofdahl, G. B. Scharmer, C. U. Keller, “Evaluation of phase-diversity techniques for solar-image restoration,” Astrophys. J. 466, 1087–1099 (1996).
    [CrossRef]
  5. T. R. Rimmele, “Solar adaptive optics,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 218–231 (2000).
    [CrossRef]
  6. T. R. Rimmele, O. von der Luehe, P. H. Wiborg, A. L. Widener, R. B. Dunn, G. Spence, “Solar feature correlation tracker,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE1542, 186–193 (1991).
    [CrossRef]
  7. L. G. Brown, “A survey of image registration techniques,” ACM Comp. Surveys 24, 325–376 (1992).
    [CrossRef]
  8. M. A. van Dam, R. G. Lane, “Wave-front slope estimation,” J. Opt. Soc. Am. A 17, 1319–1324 (2000).
    [CrossRef]
  9. H. Foroosh, J. B. Zerubia, M. Berthod, “Extension of phase correlation to subpixel registration,” IEEE Trans. Image Process. 11, 188–200 (2002).
    [CrossRef]
  10. G. A. Tyler, D. L. Fried, “Image-position error associated with a quadrant detector,” J. Opt. Soc. Am. A 72, 804–808 (1982).
    [CrossRef]
  11. W. L. Wolfe, G. J. Zissis, eds., The Infrared Handbook, revised ed. (Office of Naval Research, Washington, D.C., 1978).
  12. L. A. Poyneer, D. T. Gavel, J. M. Brase, “Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform,” J. Opt. Soc. Am. A 19, 2100–2111 (2002).
    [CrossRef]
  13. J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University, New York, 1998).
  14. J.-P. Veran, G. Herriot, “Centroid gain compensation in Shack-Hartmann adaptive optics systems with natural or laser guide star,” J. Opt. Soc. Am. A 17, 1430–1439 (2000).
    [CrossRef]
  15. I. de Pater, S. G. Gibbard, B. A. Macintosh, H. G. Roe, D. T. Gavel, C. E. Max, “Keck adaptive optics images of Uranus and its rings,” Icarus 160, 359–374 (2002).
    [CrossRef]

2002

H. Foroosh, J. B. Zerubia, M. Berthod, “Extension of phase correlation to subpixel registration,” IEEE Trans. Image Process. 11, 188–200 (2002).
[CrossRef]

L. A. Poyneer, D. T. Gavel, J. M. Brase, “Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform,” J. Opt. Soc. Am. A 19, 2100–2111 (2002).
[CrossRef]

I. de Pater, S. G. Gibbard, B. A. Macintosh, H. G. Roe, D. T. Gavel, C. E. Max, “Keck adaptive optics images of Uranus and its rings,” Icarus 160, 359–374 (2002).
[CrossRef]

2000

M. A. van Dam, R. G. Lane, “Wave-front slope estimation,” J. Opt. Soc. Am. A 17, 1319–1324 (2000).
[CrossRef]

J.-P. Veran, G. Herriot, “Centroid gain compensation in Shack-Hartmann adaptive optics systems with natural or laser guide star,” J. Opt. Soc. Am. A 17, 1430–1439 (2000).
[CrossRef]

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

P. C. Chen, C. W. Bowers, D. A. Content, M. Marzouk, R. C. Romeo, “Advances in very lightweight composite mirror technology,” Opt. Eng. 39, 2320–2329 (2000).
[CrossRef]

1996

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

1994

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

1992

L. G. Brown, “A survey of image registration techniques,” ACM Comp. Surveys 24, 325–376 (1992).
[CrossRef]

1982

G. A. Tyler, D. L. Fried, “Image-position error associated with a quadrant detector,” J. Opt. Soc. Am. A 72, 804–808 (1982).
[CrossRef]

Acton, D. S.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

An, J.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Avicola, K.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Berthod, M.

H. Foroosh, J. B. Zerubia, M. Berthod, “Extension of phase correlation to subpixel registration,” IEEE Trans. Image Process. 11, 188–200 (2002).
[CrossRef]

Bowers, C. W.

P. C. Chen, C. W. Bowers, D. A. Content, M. Marzouk, R. C. Romeo, “Advances in very lightweight composite mirror technology,” Opt. Eng. 39, 2320–2329 (2000).
[CrossRef]

Brase, J.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Brase, J. M.

Brown, L. G.

L. G. Brown, “A survey of image registration techniques,” ACM Comp. Surveys 24, 325–376 (1992).
[CrossRef]

Chen, P. C.

P. C. Chen, C. W. Bowers, D. A. Content, M. Marzouk, R. C. Romeo, “Advances in very lightweight composite mirror technology,” Opt. Eng. 39, 2320–2329 (2000).
[CrossRef]

Content, D. A.

P. C. Chen, C. W. Bowers, D. A. Content, M. Marzouk, R. C. Romeo, “Advances in very lightweight composite mirror technology,” Opt. Eng. 39, 2320–2329 (2000).
[CrossRef]

de Pater, I.

I. de Pater, S. G. Gibbard, B. A. Macintosh, H. G. Roe, D. T. Gavel, C. E. Max, “Keck adaptive optics images of Uranus and its rings,” Icarus 160, 359–374 (2002).
[CrossRef]

Dunn, R. B.

T. R. Rimmele, O. von der Luehe, P. H. Wiborg, A. L. Widener, R. B. Dunn, G. Spence, “Solar feature correlation tracker,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE1542, 186–193 (1991).
[CrossRef]

Foroosh, H.

H. Foroosh, J. B. Zerubia, M. Berthod, “Extension of phase correlation to subpixel registration,” IEEE Trans. Image Process. 11, 188–200 (2002).
[CrossRef]

Fried, D. L.

G. A. Tyler, D. L. Fried, “Image-position error associated with a quadrant detector,” J. Opt. Soc. Am. A 72, 804–808 (1982).
[CrossRef]

Gathright, J.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Gavel, D.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Gavel, D. T.

L. A. Poyneer, D. T. Gavel, J. M. Brase, “Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform,” J. Opt. Soc. Am. A 19, 2100–2111 (2002).
[CrossRef]

I. de Pater, S. G. Gibbard, B. A. Macintosh, H. G. Roe, D. T. Gavel, C. E. Max, “Keck adaptive optics images of Uranus and its rings,” Icarus 160, 359–374 (2002).
[CrossRef]

Ghez, A.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Gibbard, S. G.

I. de Pater, S. G. Gibbard, B. A. Macintosh, H. G. Roe, D. T. Gavel, C. E. Max, “Keck adaptive optics images of Uranus and its rings,” Icarus 160, 359–374 (2002).
[CrossRef]

Hardy, J. W.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University, New York, 1998).

Herriot, G.

Ho, K.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Keller, C. U.

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

Lai, O.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Lane, R. G.

Larkin, J.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Lofdahl, M. G.

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

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

Lupton, W.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Macintosh, B.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Macintosh, B. A.

I. de Pater, S. G. Gibbard, B. A. Macintosh, H. G. Roe, D. T. Gavel, C. E. Max, “Keck adaptive optics images of Uranus and its rings,” Icarus 160, 359–374 (2002).
[CrossRef]

Marzouk, M.

P. C. Chen, C. W. Bowers, D. A. Content, M. Marzouk, R. C. Romeo, “Advances in very lightweight composite mirror technology,” Opt. Eng. 39, 2320–2329 (2000).
[CrossRef]

Max, C.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Max, C. E.

I. de Pater, S. G. Gibbard, B. A. Macintosh, H. G. Roe, D. T. Gavel, C. E. Max, “Keck adaptive optics images of Uranus and its rings,” Icarus 160, 359–374 (2002).
[CrossRef]

Olivier, S.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Paxman, R. G.

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

Poyneer, L. A.

Rimmele, T. R.

T. R. Rimmele, “Solar adaptive optics,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 218–231 (2000).
[CrossRef]

T. R. Rimmele, O. von der Luehe, P. H. Wiborg, A. L. Widener, R. B. Dunn, G. Spence, “Solar feature correlation tracker,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE1542, 186–193 (1991).
[CrossRef]

Roe, H. G.

I. de Pater, S. G. Gibbard, B. A. Macintosh, H. G. Roe, D. T. Gavel, C. E. Max, “Keck adaptive optics images of Uranus and its rings,” Icarus 160, 359–374 (2002).
[CrossRef]

Romeo, R. C.

P. C. Chen, C. W. Bowers, D. A. Content, M. Marzouk, R. C. Romeo, “Advances in very lightweight composite mirror technology,” Opt. Eng. 39, 2320–2329 (2000).
[CrossRef]

Scharmer, G. B.

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

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

Seldin, J. H.

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

Shelton, C.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Spence, G.

T. R. Rimmele, O. von der Luehe, P. H. Wiborg, A. L. Widener, R. B. Dunn, G. Spence, “Solar feature correlation tracker,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE1542, 186–193 (1991).
[CrossRef]

Stomski, P.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Tsubota, K.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Tyler, G. A.

G. A. Tyler, D. L. Fried, “Image-position error associated with a quadrant detector,” J. Opt. Soc. Am. A 72, 804–808 (1982).
[CrossRef]

van Dam, M. A.

Veran, J.-P.

von der Luehe, O.

T. R. Rimmele, O. von der Luehe, P. H. Wiborg, A. L. Widener, R. B. Dunn, G. Spence, “Solar feature correlation tracker,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE1542, 186–193 (1991).
[CrossRef]

Wiborg, P. H.

T. R. Rimmele, O. von der Luehe, P. H. Wiborg, A. L. Widener, R. B. Dunn, G. Spence, “Solar feature correlation tracker,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE1542, 186–193 (1991).
[CrossRef]

Widener, A. L.

T. R. Rimmele, O. von der Luehe, P. H. Wiborg, A. L. Widener, R. B. Dunn, G. Spence, “Solar feature correlation tracker,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE1542, 186–193 (1991).
[CrossRef]

Wizinowich, P.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Zerubia, J. B.

H. Foroosh, J. B. Zerubia, M. Berthod, “Extension of phase correlation to subpixel registration,” IEEE Trans. Image Process. 11, 188–200 (2002).
[CrossRef]

ACM Comp. Surveys

L. G. Brown, “A survey of image registration techniques,” ACM Comp. Surveys 24, 325–376 (1992).
[CrossRef]

Astron. Astrophys. Suppl. Ser.

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

Astrophys. J.

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

Icarus

I. de Pater, S. G. Gibbard, B. A. Macintosh, H. G. Roe, D. T. Gavel, C. E. Max, “Keck adaptive optics images of Uranus and its rings,” Icarus 160, 359–374 (2002).
[CrossRef]

IEEE Trans. Image Process.

H. Foroosh, J. B. Zerubia, M. Berthod, “Extension of phase correlation to subpixel registration,” IEEE Trans. Image Process. 11, 188–200 (2002).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

P. C. Chen, C. W. Bowers, D. A. Content, M. Marzouk, R. C. Romeo, “Advances in very lightweight composite mirror technology,” Opt. Eng. 39, 2320–2329 (2000).
[CrossRef]

Publ. Astron. Soc. Pac.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Other

T. R. Rimmele, “Solar adaptive optics,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 218–231 (2000).
[CrossRef]

T. R. Rimmele, O. von der Luehe, P. H. Wiborg, A. L. Widener, R. B. Dunn, G. Spence, “Solar feature correlation tracker,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE1542, 186–193 (1991).
[CrossRef]

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University, New York, 1998).

W. L. Wolfe, G. J. Zissis, eds., The Infrared Handbook, revised ed. (Office of Naval Research, Washington, D.C., 1978).

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Figures (3)

Fig. 1
Fig. 1

Periodic correlation has competitive performance with the MSE method for a good image. In this case, Monte Carlo simulation results for slope estimation of a shift in the x direction are shown: (a) Error of estimation in both cases is small, (b) the standard deviation of the estimates are comparable.

Fig. 2
Fig. 2

For the zero-shift case, the bias and standard deviation (st dev) of the estimate can be explicitly calculated from the image itself a priori. The predicted standard deviation σ vs. simulation results for a shift of zero. For high-quality images, the prediction is extremely accurate. It starts to under predict for poorer images.

Fig. 3
Fig. 3

Scene performance varies with the total amount and type of illumination. Simulation results are shown for the x- and y-slope estimate in the zero-shift case. In both panels the open symbols are simulation results. The solid curves are exact calculations of scene quality. The dashed curves are predictions based on the scaling law [Eq. (24)] and a single copy of the image: (a) Variation in total amount of light. Reduction in the total amount of light causes a fall-off inversely proportional to the SNR. (b) Increasing background and constant total amount of light. Performance falls off rapidly once the amount of background light is equal to or greater than image light. For this image, 100 photons per pixel of image and no background gets comparable performance to 250 photons background and 250 photons image. St dev is standard deviation.

Tables (1)

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Table 1 Total kFLOPsa per Cycle for Slope Estimation and Phase Reconstruction

Equations (32)

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rm, n=imD, nD.
sm, n=imD-x0D, nD-y0D.
sm, n=rm-x0, n-y0
R˜ϕx, ϕy=1T2ĨϕxD, ϕyD,
S˜ϕx, ϕy=R˜ϕx, ϕyexp-j2πx0ϕx+y0ϕy.
S˜k, l=R˜k, lexp-j2πx0k+y0lN.
F˜k, l=exp-j2πx0k+y0lN.
em, n= ri-m, j-n-si, j2×N-mN-n-1,
em, n=  ri-m, j-n2+si, j2-2ri-m, j-nsi, j×N-mN-n-1.
em, n=i=0N-1j=0N-1 ri-m, j-n2+si, j2-2ri-m, j-nsi, jN-2.
em, n -i=0N-1j=0N-1 ri-m, j-nsi, j,
Cm, n=1D2 Cx, y|x=mD-x0D,y=nD-y0D.
xˆ0=Δx+0.5CΔx-1, Δy-CΔx+1, ΔyCΔx-1, Δy+CΔx+1, Δy-2CΔx, Δy.
Cm, n=ij ri-m, j-nsi, j
xˆ0=Δx+0.5C-1-C1C-1+C1-2C0.
f˜C-1, C0, C1=fm-1, m0, m1+C-1-m-1f-1m-1, m0, m1+C0-m0f0m-1, m0, m1+C1-m1f1m-1, m0, m1.
xˆ0Δx+C-1m1-m0+C0m-1-m1+C1m0-m-1+0.5m-1-m1m-1+m1-2m0×m-1+m1-2m0-2.
Exˆ0=Δx+0.5m1-m-1m-1+m1-2m0.
σx2=σ-12m1-m02+σ02m-1-m12+σ12m0-m-12+2m1-m0m-1-m1σ-1,02+2m1-m0m0-m-1σ-1,12+2m-1-m1m0-m-1σ0,12×m-1+m1-2m0-4.
xˆ0Δx+C-1-C14m1-m0.
Exˆ0=0.
σx2=σ12-σ-1,128m0-m12.
σx2f=σ˜12-f-1f-1m˜1-σ˜-1,128fm˜0-m˜12.
σxf=1fσ˜12-m˜1-σ˜-1,121/222m˜0-m˜1.
σxb, f=Nb2+2bf2m˜0-m˜2+t˜f-1+f3σ˜12-f-1f-1m˜1-σ˜-1,121/222f2m˜0-m˜1,
Ck=ij ri-k, jsi, j.
ECk=mk=ij mri-k, jmsi, j
VarCk=σk2=ijσr2i-k, jσs2i, j+σr2i-k, jms2i, j+mr2i-k, jσs2i, j.
CovarCk, Cl=σk,l2=ijσs2i, jmri-k, j×mri-l, j+σr2i, jmsi+k, jmsi+l, j.
mk=ij λri-k, jλsi, j,
σk2=ij λri-k, jλsi, j×1+λsi, j+λri-k, j.
σk,l2=ijλsi, jλri-k, jλri-l, j+λri, jλsi+k, jλsi+l, j.

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