Abstract

Several techniques have been used with Shack-Hartmann wave-front sensors to determine the local wave-front gradient across each lenslet. In this article we introduce an iterative weighted technique which is specifically targeted for open-loop applications such as aberrometers and metrology. In this article the iterative centroiding technique is compared to existing techniques such as center-of-mass with thresholding, weighted center-of-gravity, matched filter and cross-correlation. Under conditions of low signal-to-noise ratio, the iterative weighted centroiding algorithm is demonstrated to produce a lower variance in the reconstructed phase than existing techniques. The iteratively weighted algorithm was also compared in closed-loop and demonstrated to have the lowest error variance along with the weighted center-of-gravity, however, the iteratively weighted algorithm removes the bulk of the aberration in roughly half the iterations than the weighted center-of-gravity algorithm. This iterative weighted algorithm is also well suited to applications such as guiding on telescopes.

© 2007 Optical Society of America

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    [CrossRef]
  3. B. Schafer and K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71, 2663 (2000).
    [CrossRef]
  4. K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, “The use of a Shack-Hartmann wave front sensor for electron density characterization of high density plasmas,” Rev. Sci. Instrum. 73, 3784 (2002).
    [CrossRef]
  5. N. Qi, R. R. Prasad, K. Campbell, P. Coleman, M. Krishnan, B. V. Weber, S. J. Stephanakis, and D. Mosher, “Laser wave-front analyzer for imploding plasma density and current profile measurements,” Rev. Sci. Instrum. 75, 3442 (2004).
    [CrossRef]
  6. J. Arines and J. Ares, “Minimum variance centroid thresholding,” Opt. Lett. 27, 497 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. T. Rhoadarmer, “Laboratory Demonstration of a Correlation-Based AO System for Wave Front Sensing of Extended Objects,” AMOS Technical Conference, Maui, HI, 2006.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2006 (1)

S. S. Olivier, M. Jones, D. C. Chen, R. J. Zawadzki, S. S. Choi, S. P. Laut, and J. S. Werner, “Biomedical Optics: OCT sees the human retina sharply with adaptive optics,” Laser Focus World 42, 89 (2006).

2005 (3)

K. L. Baker, “Least-Squares Wave-Front Reconstruction of Shack-Hartmann Sensors and Shearing Interferometers using Multigrid Techniques,” Rev. Sci. Instrum. 76, 053502 (2005).
[CrossRef]

L. A. Poyneer, D. W. Palmer, K. N. LaFortune, and B. Bauman, “Experimental results for correlation-based wave-front sensing,” SPIE 5894, 58940N (2005).
[CrossRef]

S. Velghe, J. Primot, N. Guérineau, M. Cohen, and B. Wattellier, “Wave-front reconstruction from multidirectional phase derivatives generated by multilateral shearing interferometers,” Opt. Lett. 30, 245 (2005).
[CrossRef] [PubMed]

2004 (5)

N. Qi, R. R. Prasad, K. Campbell, P. Coleman, M. Krishnan, B. V. Weber, S. J. Stephanakis, and D. Mosher, “Laser wave-front analyzer for imploding plasma density and current profile measurements,” Rev. Sci. Instrum. 75, 3442 (2004).
[CrossRef]

T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, “Optimisation of a Shack-Hartmann-based wave-front sensor for XAO system,” SPIE 5490, 1155 (2004).
[CrossRef]

Y. Carmon and E. N. Ribak, “Fast Fourier demodulation,” Appl. Phys. Lett. 84, 4656 (2004).
[CrossRef]

A. Talmi and E. N. Ribak, “Direct demodulation of Hartmann-Shack patterns,” J. Opt. Soc. Am. A 21, 632 (2004).
[CrossRef]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, “Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics,” Opt. Lett. 29, 2743 (2004).
[CrossRef] [PubMed]

2003 (1)

Y. Carmon and E. N. Ribak, “Phase retrieval by demodulation of a Hartmann-Shack sensor,” Opt. Commun. 215, 285 (2003).
[CrossRef]

2002 (2)

K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, “The use of a Shack-Hartmann wave front sensor for electron density characterization of high density plasmas,” Rev. Sci. Instrum. 73, 3784 (2002).
[CrossRef]

J. Arines and J. Ares, “Minimum variance centroid thresholding,” Opt. Lett. 27, 497 (2002).
[CrossRef]

2000 (4)

1995 (1)

N. Kaiser, Squires, and T. Broadhurst, “A Method For Weak Lensing Observations,” ApJ 449, 460 (1995).
[CrossRef]

1986 (1)

Q. Tian and M. N. Huhns, “Algorithms for Subpixel Registration,” Comput. Vision Graph. Image Process. 35, 220 (1986).
[CrossRef]

1983 (1)

V. N. Dvornychenko, “Bounds on Deterministic Correlation Functions with Applications to Registration,” IEEE Trans. Pattern Anal. Mach. Intell. 5, 206 (1983).
[CrossRef] [PubMed]

Ares, J.

Arines, J.

Artal, P.

Asztalos,

W. de Vries, S. Olivier, Asztalos, Leslie Rosenberg, and Kevin Baker, “Image Ellipticity From Atmospheric Aberrations,” Publ. Astron. Soc. Of the Pacific (to be submitted in 2007).

Atta, L. Van

Baker, K. L.

K. L. Baker, “Least-Squares Wave-Front Reconstruction of Shack-Hartmann Sensors and Shearing Interferometers using Multigrid Techniques,” Rev. Sci. Instrum. 76, 053502 (2005).
[CrossRef]

K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, “The use of a Shack-Hartmann wave front sensor for electron density characterization of high density plasmas,” Rev. Sci. Instrum. 73, 3784 (2002).
[CrossRef]

Baker, Kevin

W. de Vries, S. Olivier, Asztalos, Leslie Rosenberg, and Kevin Baker, “Image Ellipticity From Atmospheric Aberrations,” Publ. Astron. Soc. Of the Pacific (to be submitted in 2007).

Bauman, B.

L. A. Poyneer, D. W. Palmer, K. N. LaFortune, and B. Bauman, “Experimental results for correlation-based wave-front sensing,” SPIE 5894, 58940N (2005).
[CrossRef]

Beuzit, J.-L.

T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, “Optimisation of a Shack-Hartmann-based wave-front sensor for XAO system,” SPIE 5490, 1155 (2004).
[CrossRef]

Bijaoui, A.

J.-L. Starck, F. Murtagh, and A. Bijaoui, Image Processing and Data Analysis: The Multiscale Approach. (Cambridge University Press, 1998).
[CrossRef]

Bliss, E. S.

Brase, J.

K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, “The use of a Shack-Hartmann wave front sensor for electron density characterization of high density plasmas,” Rev. Sci. Instrum. 73, 3784 (2002).
[CrossRef]

Broadhurst, T.

N. Kaiser, Squires, and T. Broadhurst, “A Method For Weak Lensing Observations,” ApJ 449, 460 (1995).
[CrossRef]

Campbell, K.

N. Qi, R. R. Prasad, K. Campbell, P. Coleman, M. Krishnan, B. V. Weber, S. J. Stephanakis, and D. Mosher, “Laser wave-front analyzer for imploding plasma density and current profile measurements,” Rev. Sci. Instrum. 75, 3442 (2004).
[CrossRef]

Carmon, Y.

Y. Carmon and E. N. Ribak, “Fast Fourier demodulation,” Appl. Phys. Lett. 84, 4656 (2004).
[CrossRef]

Y. Carmon and E. N. Ribak, “Phase retrieval by demodulation of a Hartmann-Shack sensor,” Opt. Commun. 215, 285 (2003).
[CrossRef]

Chen, D. C.

S. S. Olivier, M. Jones, D. C. Chen, R. J. Zawadzki, S. S. Choi, S. P. Laut, and J. S. Werner, “Biomedical Optics: OCT sees the human retina sharply with adaptive optics,” Laser Focus World 42, 89 (2006).

Choi, S. S.

S. S. Olivier, M. Jones, D. C. Chen, R. J. Zawadzki, S. S. Choi, S. P. Laut, and J. S. Werner, “Biomedical Optics: OCT sees the human retina sharply with adaptive optics,” Laser Focus World 42, 89 (2006).

Cohen, M.

Coleman, P.

N. Qi, R. R. Prasad, K. Campbell, P. Coleman, M. Krishnan, B. V. Weber, S. J. Stephanakis, and D. Mosher, “Laser wave-front analyzer for imploding plasma density and current profile measurements,” Rev. Sci. Instrum. 75, 3442 (2004).
[CrossRef]

Dailey, M. J.

de Vries, W.

W. de Vries, S. Olivier, Asztalos, Leslie Rosenberg, and Kevin Baker, “Image Ellipticity From Atmospheric Aberrations,” Publ. Astron. Soc. Of the Pacific (to be submitted in 2007).

Dvornychenko, V. N.

V. N. Dvornychenko, “Bounds on Deterministic Correlation Functions with Applications to Registration,” IEEE Trans. Pattern Anal. Mach. Intell. 5, 206 (1983).
[CrossRef] [PubMed]

Feldman, M.

Fusco, T.

T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, “Optimisation of a Shack-Hartmann-based wave-front sensor for XAO system,” SPIE 5490, 1155 (2004).
[CrossRef]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, “Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics,” Opt. Lett. 29, 2743 (2004).
[CrossRef] [PubMed]

Goelz, S.

Grey, A. A.

Guérineau, N.

Hardy, J. W.

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

Holdener, F. R.

Huhns, M. N.

Q. Tian and M. N. Huhns, “Algorithms for Subpixel Registration,” Comput. Vision Graph. Image Process. 35, 220 (1986).
[CrossRef]

Jones, M.

S. S. Olivier, M. Jones, D. C. Chen, R. J. Zawadzki, S. S. Choi, S. P. Laut, and J. S. Werner, “Biomedical Optics: OCT sees the human retina sharply with adaptive optics,” Laser Focus World 42, 89 (2006).

Kaiser, N.

N. Kaiser, Squires, and T. Broadhurst, “A Method For Weak Lensing Observations,” ApJ 449, 460 (1995).
[CrossRef]

Kartz, M.

K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, “The use of a Shack-Hartmann wave front sensor for electron density characterization of high density plasmas,” Rev. Sci. Instrum. 73, 3784 (2002).
[CrossRef]

Koch, J. A.

Krishnan, M.

N. Qi, R. R. Prasad, K. Campbell, P. Coleman, M. Krishnan, B. V. Weber, S. J. Stephanakis, and D. Mosher, “Laser wave-front analyzer for imploding plasma density and current profile measurements,” Rev. Sci. Instrum. 75, 3442 (2004).
[CrossRef]

Kujawinska, M.

M. Kujawinska, in Interferogram Analysis, edited by David W Robinson and Graeme T Reid (Institute of Physics Publishing, Bristol and Philadelphia, 1993).

LaFortune, K. N.

L. A. Poyneer, D. W. Palmer, K. N. LaFortune, and B. Bauman, “Experimental results for correlation-based wave-front sensing,” SPIE 5894, 58940N (2005).
[CrossRef]

Laut, S. P.

S. S. Olivier, M. Jones, D. C. Chen, R. J. Zawadzki, S. S. Choi, S. P. Laut, and J. S. Werner, “Biomedical Optics: OCT sees the human retina sharply with adaptive optics,” Laser Focus World 42, 89 (2006).

Mann, K.

B. Schafer and K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71, 2663 (2000).
[CrossRef]

Michau, V.

T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, “Optimisation of a Shack-Hartmann-based wave-front sensor for XAO system,” SPIE 5490, 1155 (2004).
[CrossRef]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, “Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics,” Opt. Lett. 29, 2743 (2004).
[CrossRef] [PubMed]

Mosher, D.

N. Qi, R. R. Prasad, K. Campbell, P. Coleman, M. Krishnan, B. V. Weber, S. J. Stephanakis, and D. Mosher, “Laser wave-front analyzer for imploding plasma density and current profile measurements,” Rev. Sci. Instrum. 75, 3442 (2004).
[CrossRef]

Mouillet, D.

T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, “Optimisation of a Shack-Hartmann-based wave-front sensor for XAO system,” SPIE 5490, 1155 (2004).
[CrossRef]

Murtagh, F.

J.-L. Starck, F. Murtagh, and A. Bijaoui, Image Processing and Data Analysis: The Multiscale Approach. (Cambridge University Press, 1998).
[CrossRef]

Nicolle, M.

T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, “Optimisation of a Shack-Hartmann-based wave-front sensor for XAO system,” SPIE 5490, 1155 (2004).
[CrossRef]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, “Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics,” Opt. Lett. 29, 2743 (2004).
[CrossRef] [PubMed]

Olivier, S.

W. de Vries, S. Olivier, Asztalos, Leslie Rosenberg, and Kevin Baker, “Image Ellipticity From Atmospheric Aberrations,” Publ. Astron. Soc. Of the Pacific (to be submitted in 2007).

Olivier, S. S.

S. S. Olivier, M. Jones, D. C. Chen, R. J. Zawadzki, S. S. Choi, S. P. Laut, and J. S. Werner, “Biomedical Optics: OCT sees the human retina sharply with adaptive optics,” Laser Focus World 42, 89 (2006).

K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, “The use of a Shack-Hartmann wave front sensor for electron density characterization of high density plasmas,” Rev. Sci. Instrum. 73, 3784 (2002).
[CrossRef]

Palmer, D. W.

L. A. Poyneer, D. W. Palmer, K. N. LaFortune, and B. Bauman, “Experimental results for correlation-based wave-front sensing,” SPIE 5894, 58940N (2005).
[CrossRef]

Poyneer, L. A.

L. A. Poyneer, D. W. Palmer, K. N. LaFortune, and B. Bauman, “Experimental results for correlation-based wave-front sensing,” SPIE 5894, 58940N (2005).
[CrossRef]

Prasad, R. R.

N. Qi, R. R. Prasad, K. Campbell, P. Coleman, M. Krishnan, B. V. Weber, S. J. Stephanakis, and D. Mosher, “Laser wave-front analyzer for imploding plasma density and current profile measurements,” Rev. Sci. Instrum. 75, 3442 (2004).
[CrossRef]

Presta, R. W.

Prieto, P. M.

Primot, J.

Qi, N.

N. Qi, R. R. Prasad, K. Campbell, P. Coleman, M. Krishnan, B. V. Weber, S. J. Stephanakis, and D. Mosher, “Laser wave-front analyzer for imploding plasma density and current profile measurements,” Rev. Sci. Instrum. 75, 3442 (2004).
[CrossRef]

Rhoadarmer, T.

T. Rhoadarmer, “Laboratory Demonstration of a Correlation-Based AO System for Wave Front Sensing of Extended Objects,” AMOS Technical Conference, Maui, HI, 2006.

Ribak, E. N.

Y. Carmon and E. N. Ribak, “Fast Fourier demodulation,” Appl. Phys. Lett. 84, 4656 (2004).
[CrossRef]

A. Talmi and E. N. Ribak, “Direct demodulation of Hartmann-Shack patterns,” J. Opt. Soc. Am. A 21, 632 (2004).
[CrossRef]

Y. Carmon and E. N. Ribak, “Phase retrieval by demodulation of a Hartmann-Shack sensor,” Opt. Commun. 215, 285 (2003).
[CrossRef]

Rimmele, T. R.

T. R. Rimmele, “Solar Adaptive Optics,” SPIE 4007, 218 (2000).
[CrossRef]

Rosenberg, Leslie

W. de Vries, S. Olivier, Asztalos, Leslie Rosenberg, and Kevin Baker, “Image Ellipticity From Atmospheric Aberrations,” Publ. Astron. Soc. Of the Pacific (to be submitted in 2007).

Rousset, G.

T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, “Optimisation of a Shack-Hartmann-based wave-front sensor for XAO system,” SPIE 5490, 1155 (2004).
[CrossRef]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, “Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics,” Opt. Lett. 29, 2743 (2004).
[CrossRef] [PubMed]

Sacks, R. A.

Salmon, J. T.

Sawvel, B.

K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, “The use of a Shack-Hartmann wave front sensor for electron density characterization of high density plasmas,” Rev. Sci. Instrum. 73, 3784 (2002).
[CrossRef]

Schafer, B.

B. Schafer and K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71, 2663 (2000).
[CrossRef]

Seppala, L. G.

Squires,

N. Kaiser, Squires, and T. Broadhurst, “A Method For Weak Lensing Observations,” ApJ 449, 460 (1995).
[CrossRef]

Starck, J.-L.

J.-L. Starck, F. Murtagh, and A. Bijaoui, Image Processing and Data Analysis: The Multiscale Approach. (Cambridge University Press, 1998).
[CrossRef]

Stephanakis, S. J.

N. Qi, R. R. Prasad, K. Campbell, P. Coleman, M. Krishnan, B. V. Weber, S. J. Stephanakis, and D. Mosher, “Laser wave-front analyzer for imploding plasma density and current profile measurements,” Rev. Sci. Instrum. 75, 3442 (2004).
[CrossRef]

Talmi, A.

Tian, Q.

Q. Tian and M. N. Huhns, “Algorithms for Subpixel Registration,” Comput. Vision Graph. Image Process. 35, 220 (1986).
[CrossRef]

Toeppen, J. S.

Tucker, J.

K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, “The use of a Shack-Hartmann wave front sensor for electron density characterization of high density plasmas,” Rev. Sci. Instrum. 73, 3784 (2002).
[CrossRef]

Vargas-Martin, F.

Velghe, S.

Wattellier, B.

Weber, B. V.

N. Qi, R. R. Prasad, K. Campbell, P. Coleman, M. Krishnan, B. V. Weber, S. J. Stephanakis, and D. Mosher, “Laser wave-front analyzer for imploding plasma density and current profile measurements,” Rev. Sci. Instrum. 75, 3442 (2004).
[CrossRef]

Werner, J. S.

S. S. Olivier, M. Jones, D. C. Chen, R. J. Zawadzki, S. S. Choi, S. P. Laut, and J. S. Werner, “Biomedical Optics: OCT sees the human retina sharply with adaptive optics,” Laser Focus World 42, 89 (2006).

Whistler, W. T.

Winters, S. E.

Wonterghem, B. M. Van

Woods, B. W.

Zacharias, R. A.

Zawadzki, R. J.

S. S. Olivier, M. Jones, D. C. Chen, R. J. Zawadzki, S. S. Choi, S. P. Laut, and J. S. Werner, “Biomedical Optics: OCT sees the human retina sharply with adaptive optics,” Laser Focus World 42, 89 (2006).

ApJ (1)

N. Kaiser, Squires, and T. Broadhurst, “A Method For Weak Lensing Observations,” ApJ 449, 460 (1995).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

Y. Carmon and E. N. Ribak, “Fast Fourier demodulation,” Appl. Phys. Lett. 84, 4656 (2004).
[CrossRef]

Comput. Vision Graph. Image Process. (1)

Q. Tian and M. N. Huhns, “Algorithms for Subpixel Registration,” Comput. Vision Graph. Image Process. 35, 220 (1986).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

V. N. Dvornychenko, “Bounds on Deterministic Correlation Functions with Applications to Registration,” IEEE Trans. Pattern Anal. Mach. Intell. 5, 206 (1983).
[CrossRef] [PubMed]

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

Laser Focus World (1)

S. S. Olivier, M. Jones, D. C. Chen, R. J. Zawadzki, S. S. Choi, S. P. Laut, and J. S. Werner, “Biomedical Optics: OCT sees the human retina sharply with adaptive optics,” Laser Focus World 42, 89 (2006).

Opt. Commun. (1)

Y. Carmon and E. N. Ribak, “Phase retrieval by demodulation of a Hartmann-Shack sensor,” Opt. Commun. 215, 285 (2003).
[CrossRef]

Opt. Lett. (3)

Rev. Sci. Instrum. (4)

B. Schafer and K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71, 2663 (2000).
[CrossRef]

K. L. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, “The use of a Shack-Hartmann wave front sensor for electron density characterization of high density plasmas,” Rev. Sci. Instrum. 73, 3784 (2002).
[CrossRef]

N. Qi, R. R. Prasad, K. Campbell, P. Coleman, M. Krishnan, B. V. Weber, S. J. Stephanakis, and D. Mosher, “Laser wave-front analyzer for imploding plasma density and current profile measurements,” Rev. Sci. Instrum. 75, 3442 (2004).
[CrossRef]

K. L. Baker, “Least-Squares Wave-Front Reconstruction of Shack-Hartmann Sensors and Shearing Interferometers using Multigrid Techniques,” Rev. Sci. Instrum. 76, 053502 (2005).
[CrossRef]

SPIE (3)

T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, “Optimisation of a Shack-Hartmann-based wave-front sensor for XAO system,” SPIE 5490, 1155 (2004).
[CrossRef]

T. R. Rimmele, “Solar Adaptive Optics,” SPIE 4007, 218 (2000).
[CrossRef]

L. A. Poyneer, D. W. Palmer, K. N. LaFortune, and B. Bauman, “Experimental results for correlation-based wave-front sensing,” SPIE 5894, 58940N (2005).
[CrossRef]

Other (5)

T. Rhoadarmer, “Laboratory Demonstration of a Correlation-Based AO System for Wave Front Sensing of Extended Objects,” AMOS Technical Conference, Maui, HI, 2006.

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

M. Kujawinska, in Interferogram Analysis, edited by David W Robinson and Graeme T Reid (Institute of Physics Publishing, Bristol and Philadelphia, 1993).

J.-L. Starck, F. Murtagh, and A. Bijaoui, Image Processing and Data Analysis: The Multiscale Approach. (Cambridge University Press, 1998).
[CrossRef]

W. de Vries, S. Olivier, Asztalos, Leslie Rosenberg, and Kevin Baker, “Image Ellipticity From Atmospheric Aberrations,” Publ. Astron. Soc. Of the Pacific (to be submitted in 2007).

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Figures (6)

Fig. 1.
Fig. 1.

Residual variance as a function of the number of iterations performed with the iteratively weighted algorithm.

Fig. 2.
Fig. 2.

Weighting function σ and reconstructed wavefront variance after four iterations as a function of the initial starting value, σinit, for the Gaussian width.

Fig. 3.
Fig. 3.

Residual variance as a function of noise for the three different filtering techniques and the unfiltered case.

Fig. 4.
Fig. 4.

Residual variance as a function of noise for the three different reference generation methods.

Fig. 5.
Fig. 5.

Comparison of the different centroid locating algorithms in open-loop.

Fig. 6.
Fig. 6.

Comparison between different algorithms in closed-loop. Figure 4a illustrates the results with 105 photons/sub-aperture and Fig. 4b represents the case of 500 photons/sub-aperture.

Equations (11)

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w x y = 1 2 π π 2 e 1 2 σ 2 ( x x c ) 2 e 1 2 σ 2 ( y y c ) 2 ,
S w = x , y I x y w x y ,
S x = x , y xI x y w x y ,
S y = x , y yI x y w x y ,
S xx = x , y x 2 I x y w x y ,
S yy = x , y y 2 I x y w x y ,
x c = S x S w , y c = S y S w
σ = ( 1 S w ) S xx S w S x S x + S yy S w S y S y
σ ph 2 = π 2 2 ln ( 2 ) N ph ( N T N D ) 2 ( N T 2 + N W 2 2 N T 2 + N W 2 ) 2 and
σ det 2 = π 3 32 [ ln ( 2 ) ] 2 ( d det ector N ph ) 2 ( N T 2 + N W 2 N D ) 2 ,
( 1 16 1 4 3 8 1 4 1 16 ) ( 1 16 1 4 3 8 1 4 1 16 ) ,

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