Abstract

Scene-based wavefront sensing currently uses the periodic-correlation algorithm based on fast Fourier transforms. However, when the object scene contains features at the field edges, the performance of the algorithm is poor due to the periodicity of fast Fourier transforms, called wraparound effect. In this paper, we propose an algorithm based on the gradient cross-correlation. Both simulation and experiment results show its dramatic effectiveness against the wraparound effect, and a considerable improvement is obtained in image resolution with closed loop adaptive optics correction.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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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, and 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(769), 315–319 (2000).
    [Crossref]
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    [Crossref]
  3. M. J. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light Sci. Appl. 3(4), e165 (2014).
    [Crossref]
  4. R. K. Tyson, “Adaptive optics and ground-to-space laser communications,” Appl. Opt. 35(19), 3640–3646 (1996).
    [Crossref] [PubMed]
  5. B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
    [PubMed]
  6. S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
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  11. E. Sidick, J. J. Green, R. M. Morgan, C. M. Ohara, and D. C. Redding, “Adaptive cross-correlation algorithm for extended scene Shack-Hartmann wavefront sensing,” Opt. Lett. 33(3), 213–215 (2008).
    [Crossref] [PubMed]
  12. M. J. Townson, A. Kellerer, and C. D. Saunter, “Improved shift estimates on extended Shack–Hartmann wavefront sensor images,” Mon. Not. R. Astron. Soc. 452(4), 4022–4028 (2015).
    [Crossref]
  13. D. I. Barnea and H. F. Silverman, “A class of algorithms for fast digital image registration,” IEEE Trans. Comput. C-21(2), 179–186 (1972).
    [Crossref]
  14. J. F. Andrus, C. W. Campbell, and R. R. Jayroe, “Digital image registration algorithm using boundaly maps,” IEEE Trans. Comput. C-24(9), 935–940 (1975).
    [Crossref]
  15. X. Peng, M. Li, and C. Rao, “Architecture Design of FPGA-Based Wavefront Processor for Correlating Shack-Hartmann Sensor,” Proc. SPIE 7156, 71561B (2008).
    [Crossref]

2015 (1)

M. J. Townson, A. Kellerer, and C. D. Saunter, “Improved shift estimates on extended Shack–Hartmann wavefront sensor images,” Mon. Not. R. Astron. Soc. 452(4), 4022–4028 (2015).
[Crossref]

2014 (2)

M. J. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light Sci. Appl. 3(4), e165 (2014).
[Crossref]

A. Montmerle Bonnefois, T. Fusco, S. Meimon, L. Mugnier, J. F. Sauvage, C. Engel, C. Escolle, M. Ferrari, E. Hugot, A. Liotard, M. Bernot, M. Carlavan, F. Falzon, T. Bret-Dibat, and D. Laubier, “Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity Sensor, for high-precision wavefront sensing dedicated to Space Active Optics,” Proc. SPIE 10563, 105634B (2014).

2008 (2)

E. Sidick, J. J. Green, R. M. Morgan, C. M. Ohara, and D. C. Redding, “Adaptive cross-correlation algorithm for extended scene Shack-Hartmann wavefront sensing,” Opt. Lett. 33(3), 213–215 (2008).
[Crossref] [PubMed]

X. Peng, M. Li, and C. Rao, “Architecture Design of FPGA-Based Wavefront Processor for Correlating Shack-Hartmann Sensor,” Proc. SPIE 7156, 71561B (2008).
[Crossref]

2006 (1)

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

2003 (1)

2001 (1)

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

2000 (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, and 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(769), 315–319 (2000).
[Crossref]

1996 (2)

R. W. Wilson and C. R. Jenkins, “Adaptive optics for astronomy theoretical performance and limitations,” Mon. Not. R. Astron. Soc. 278(1), 39–61 (1996).
[Crossref]

R. K. Tyson, “Adaptive optics and ground-to-space laser communications,” Appl. Opt. 35(19), 3640–3646 (1996).
[Crossref] [PubMed]

1975 (1)

J. F. Andrus, C. W. Campbell, and R. R. Jayroe, “Digital image registration algorithm using boundaly maps,” IEEE Trans. Comput. C-24(9), 935–940 (1975).
[Crossref]

1972 (1)

D. I. Barnea and H. F. Silverman, “A class of algorithms for fast digital image registration,” IEEE Trans. Comput. C-21(2), 179–186 (1972).
[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, and 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(769), 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, and 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(769), 315–319 (2000).
[Crossref]

Andrus, J. F.

J. F. Andrus, C. W. Campbell, and R. R. Jayroe, “Digital image registration algorithm using boundaly maps,” IEEE Trans. Comput. C-24(9), 935–940 (1975).
[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, and 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(769), 315–319 (2000).
[Crossref]

Barnea, D. I.

D. I. Barnea and H. F. Silverman, “A class of algorithms for fast digital image registration,” IEEE Trans. Comput. C-21(2), 179–186 (1972).
[Crossref]

Bernot, M.

A. Montmerle Bonnefois, T. Fusco, S. Meimon, L. Mugnier, J. F. Sauvage, C. Engel, C. Escolle, M. Ferrari, E. Hugot, A. Liotard, M. Bernot, M. Carlavan, F. Falzon, T. Bret-Dibat, and D. Laubier, “Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity Sensor, for high-precision wavefront sensing dedicated to Space Active Optics,” Proc. SPIE 10563, 105634B (2014).

Booth, M. J.

M. J. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light Sci. Appl. 3(4), e165 (2014).
[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, and 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(769), 315–319 (2000).
[Crossref]

Bret-Dibat, T.

A. Montmerle Bonnefois, T. Fusco, S. Meimon, L. Mugnier, J. F. Sauvage, C. Engel, C. Escolle, M. Ferrari, E. Hugot, A. Liotard, M. Bernot, M. Carlavan, F. Falzon, T. Bret-Dibat, and D. Laubier, “Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity Sensor, for high-precision wavefront sensing dedicated to Space Active Optics,” Proc. SPIE 10563, 105634B (2014).

Campbell, C. W.

J. F. Andrus, C. W. Campbell, and R. R. Jayroe, “Digital image registration algorithm using boundaly maps,” IEEE Trans. Comput. C-24(9), 935–940 (1975).
[Crossref]

Carlavan, M.

A. Montmerle Bonnefois, T. Fusco, S. Meimon, L. Mugnier, J. F. Sauvage, C. Engel, C. Escolle, M. Ferrari, E. Hugot, A. Liotard, M. Bernot, M. Carlavan, F. Falzon, T. Bret-Dibat, and D. Laubier, “Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity Sensor, for high-precision wavefront sensing dedicated to Space Active Optics,” Proc. SPIE 10563, 105634B (2014).

Engel, C.

A. Montmerle Bonnefois, T. Fusco, S. Meimon, L. Mugnier, J. F. Sauvage, C. Engel, C. Escolle, M. Ferrari, E. Hugot, A. Liotard, M. Bernot, M. Carlavan, F. Falzon, T. Bret-Dibat, and D. Laubier, “Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity Sensor, for high-precision wavefront sensing dedicated to Space Active Optics,” Proc. SPIE 10563, 105634B (2014).

Escolle, C.

A. Montmerle Bonnefois, T. Fusco, S. Meimon, L. Mugnier, J. F. Sauvage, C. Engel, C. Escolle, M. Ferrari, E. Hugot, A. Liotard, M. Bernot, M. Carlavan, F. Falzon, T. Bret-Dibat, and D. Laubier, “Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity Sensor, for high-precision wavefront sensing dedicated to Space Active Optics,” Proc. SPIE 10563, 105634B (2014).

Falzon, F.

A. Montmerle Bonnefois, T. Fusco, S. Meimon, L. Mugnier, J. F. Sauvage, C. Engel, C. Escolle, M. Ferrari, E. Hugot, A. Liotard, M. Bernot, M. Carlavan, F. Falzon, T. Bret-Dibat, and D. Laubier, “Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity Sensor, for high-precision wavefront sensing dedicated to Space Active Optics,” Proc. SPIE 10563, 105634B (2014).

Ferrari, M.

A. Montmerle Bonnefois, T. Fusco, S. Meimon, L. Mugnier, J. F. Sauvage, C. Engel, C. Escolle, M. Ferrari, E. Hugot, A. Liotard, M. Bernot, M. Carlavan, F. Falzon, T. Bret-Dibat, and D. Laubier, “Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity Sensor, for high-precision wavefront sensing dedicated to Space Active Optics,” Proc. SPIE 10563, 105634B (2014).

Fusco, T.

A. Montmerle Bonnefois, T. Fusco, S. Meimon, L. Mugnier, J. F. Sauvage, C. Engel, C. Escolle, M. Ferrari, E. Hugot, A. Liotard, M. Bernot, M. Carlavan, F. Falzon, T. Bret-Dibat, and D. Laubier, “Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity Sensor, for high-precision wavefront sensing dedicated to Space Active Optics,” Proc. SPIE 10563, 105634B (2014).

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[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, and 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(769), 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, and 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(769), 315–319 (2000).
[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, and 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(769), 315–319 (2000).
[Crossref]

Green, J. J.

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, and 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(769), 315–319 (2000).
[Crossref]

Hugot, E.

A. Montmerle Bonnefois, T. Fusco, S. Meimon, L. Mugnier, J. F. Sauvage, C. Engel, C. Escolle, M. Ferrari, E. Hugot, A. Liotard, M. Bernot, M. Carlavan, F. Falzon, T. Bret-Dibat, and D. Laubier, “Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity Sensor, for high-precision wavefront sensing dedicated to Space Active Optics,” Proc. SPIE 10563, 105634B (2014).

Jayroe, R. R.

J. F. Andrus, C. W. Campbell, and R. R. Jayroe, “Digital image registration algorithm using boundaly maps,” IEEE Trans. Comput. C-24(9), 935–940 (1975).
[Crossref]

Jenkins, C. R.

R. W. Wilson and C. R. Jenkins, “Adaptive optics for astronomy theoretical performance and limitations,” Mon. Not. R. Astron. Soc. 278(1), 39–61 (1996).
[Crossref]

Kellerer, A.

M. J. Townson, A. Kellerer, and C. D. Saunter, “Improved shift estimates on extended Shack–Hartmann wavefront sensor images,” Mon. Not. R. Astron. Soc. 452(4), 4022–4028 (2015).
[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, and 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(769), 315–319 (2000).
[Crossref]

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, and 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(769), 315–319 (2000).
[Crossref]

Laubier, D.

A. Montmerle Bonnefois, T. Fusco, S. Meimon, L. Mugnier, J. F. Sauvage, C. Engel, C. Escolle, M. Ferrari, E. Hugot, A. Liotard, M. Bernot, M. Carlavan, F. Falzon, T. Bret-Dibat, and D. Laubier, “Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity Sensor, for high-precision wavefront sensing dedicated to Space Active Optics,” Proc. SPIE 10563, 105634B (2014).

Li, M.

X. Peng, M. Li, and C. Rao, “Architecture Design of FPGA-Based Wavefront Processor for Correlating Shack-Hartmann Sensor,” Proc. SPIE 7156, 71561B (2008).
[Crossref]

Liotard, A.

A. Montmerle Bonnefois, T. Fusco, S. Meimon, L. Mugnier, J. F. Sauvage, C. Engel, C. Escolle, M. Ferrari, E. Hugot, A. Liotard, M. Bernot, M. Carlavan, F. Falzon, T. Bret-Dibat, and D. Laubier, “Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity Sensor, for high-precision wavefront sensing dedicated to Space Active Optics,” Proc. SPIE 10563, 105634B (2014).

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, and 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(769), 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, and 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(769), 315–319 (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, and 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(769), 315–319 (2000).
[Crossref]

Meimon, S.

A. Montmerle Bonnefois, T. Fusco, S. Meimon, L. Mugnier, J. F. Sauvage, C. Engel, C. Escolle, M. Ferrari, E. Hugot, A. Liotard, M. Bernot, M. Carlavan, F. Falzon, T. Bret-Dibat, and D. Laubier, “Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity Sensor, for high-precision wavefront sensing dedicated to Space Active Optics,” Proc. SPIE 10563, 105634B (2014).

Michau, V.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Montmerle Bonnefois, A.

A. Montmerle Bonnefois, T. Fusco, S. Meimon, L. Mugnier, J. F. Sauvage, C. Engel, C. Escolle, M. Ferrari, E. Hugot, A. Liotard, M. Bernot, M. Carlavan, F. Falzon, T. Bret-Dibat, and D. Laubier, “Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity Sensor, for high-precision wavefront sensing dedicated to Space Active Optics,” Proc. SPIE 10563, 105634B (2014).

Morgan, R. M.

Mugnier, L.

A. Montmerle Bonnefois, T. Fusco, S. Meimon, L. Mugnier, J. F. Sauvage, C. Engel, C. Escolle, M. Ferrari, E. Hugot, A. Liotard, M. Bernot, M. Carlavan, F. Falzon, T. Bret-Dibat, and D. Laubier, “Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity Sensor, for high-precision wavefront sensing dedicated to Space Active Optics,” Proc. SPIE 10563, 105634B (2014).

Nicolle, M.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Ohara, C. M.

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, and 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(769), 315–319 (2000).
[Crossref]

Peng, X.

X. Peng, M. Li, and C. Rao, “Architecture Design of FPGA-Based Wavefront Processor for Correlating Shack-Hartmann Sensor,” Proc. SPIE 7156, 71561B (2008).
[Crossref]

Platt, B. C.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

Poyneer, L. A.

Rao, C.

X. Peng, M. Li, and C. Rao, “Architecture Design of FPGA-Based Wavefront Processor for Correlating Shack-Hartmann Sensor,” Proc. SPIE 7156, 71561B (2008).
[Crossref]

Redding, D. C.

Rousset, G.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Saunter, C. D.

M. J. Townson, A. Kellerer, and C. D. Saunter, “Improved shift estimates on extended Shack–Hartmann wavefront sensor images,” Mon. Not. R. Astron. Soc. 452(4), 4022–4028 (2015).
[Crossref]

Sauvage, J. F.

A. Montmerle Bonnefois, T. Fusco, S. Meimon, L. Mugnier, J. F. Sauvage, C. Engel, C. Escolle, M. Ferrari, E. Hugot, A. Liotard, M. Bernot, M. Carlavan, F. Falzon, T. Bret-Dibat, and D. Laubier, “Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity Sensor, for high-precision wavefront sensing dedicated to Space Active Optics,” Proc. SPIE 10563, 105634B (2014).

Shack, R.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

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, and 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(769), 315–319 (2000).
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D. I. Barnea and H. F. Silverman, “A class of algorithms for fast digital image registration,” IEEE Trans. Comput. C-21(2), 179–186 (1972).
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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, and 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(769), 315–319 (2000).
[Crossref]

Thomas, S.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
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Tokovinin, A.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Townson, M. J.

M. J. Townson, A. Kellerer, and C. D. Saunter, “Improved shift estimates on extended Shack–Hartmann wavefront sensor images,” Mon. Not. R. Astron. Soc. 452(4), 4022–4028 (2015).
[Crossref]

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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, and 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(769), 315–319 (2000).
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Wilson, R. W.

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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, and 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(769), 315–319 (2000).
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Appl. Opt. (2)

IEEE Trans. Comput. (2)

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[Crossref]

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M. J. Townson, A. Kellerer, and C. D. Saunter, “Improved shift estimates on extended Shack–Hartmann wavefront sensor images,” Mon. Not. R. Astron. Soc. 452(4), 4022–4028 (2015).
[Crossref]

R. W. Wilson and C. R. Jenkins, “Adaptive optics for astronomy theoretical performance and limitations,” Mon. Not. R. Astron. Soc. 278(1), 39–61 (1996).
[Crossref]

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Opt. Lett. (1)

Proc. SPIE (2)

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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, and 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(769), 315–319 (2000).
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Figures (14)

Fig. 1
Fig. 1 (a) The object scene image. (b) The reference sub-image. It is the part used for correlation calculation of the object scene image. (c) A test sub-image indicating y-axis shift relative to the reference sub-image which is the lower part of the object scene image. (d) The periodic extension test sub-image with the reference sub-image moving on it. The red and green sections indicate two different locations the reference sub-image moves to. (e) The section of the periodic extension test sub-image located at the green section for cross-correlation calculation with the reference sub-image. (f) The section of the periodic extension test sub-image located at the red section for cross-correlation calculation with the reference sub-image.
Fig. 2
Fig. 2 (a) The object scene image. (b) The y-axis gradient of the reference sub-image in Fig. 1(b). The part of the object characterizing the motion is emphasized in the gradient image. (c) The y-axis gradient of the test sub-image in Fig. 1(c). (d) The periodic extension y-axis gradient of the test sub-image with the y-axis gradient of reference sub-image moving on it. The red and green sections indicate two different locations the y-axis gradient reference sub-image moves to. (e) The section of the periodic extension y-axis gradient test sub-image located at the green section for cross-correlation calculation with the y-axis gradient reference sub-image. (f) The section of the periodic extension y-axis gradient test sub-image located at the red section for cross-correlation calculation with the y-axis gradient reference sub-image.
Fig. 3
Fig. 3 Procedure of the simulation for two sub-apertures shift estimation
Fig. 4
Fig. 4 (a) The object scene image with fiber beam background. (b) An original reference sub-image. (c) An original test sub-image. (d) The 2-D periodic correlation function image of (b) and (c). (e) The 3-D periodic correlation function image of (b) and (c). The blue circle stresses the top section of the function. (f) The y-axis gradient sub-image of (b) with thresholding operation. The red circle stresses the characteristic of the image. (g) The y-axis gradient sub-image of (c). The red circle stresses the characteristic of the image. (h) The 2-D periodic correlation function image of (f) and (g). The red circle stresses the biggest correlation value. (i) The 3-D periodic correlation function image of (f) and (g). The blue circle stresses the top of the function.
Fig. 5
Fig. 5 (a) Comparison of estimate shifts and (c) estimate errors corresponding to the periodic-correlation algorithm and the gradient cross-correlation algorithm respectively for the object scene in Fig. 1(a). (b) Comparison of estimate shifts and (d) estimate errors corresponding to the periodic-correlation algorithm and the gradient cross-correlation algorithm respectively for the object scene with fiber beam background.
Fig. 6
Fig. 6 (a) The simulated distorted spot image array of a Shark-Hartmann sensor. (b) The object scene image with fiber beam background used to create an S-H WFS extended-scene image array. (c) The S-H WFS extended-scene image array created by convolving (a) with (b). The pink pentagram marks the reference sub-aperture.
Fig. 7
Fig. 7 The added distorted wavefront and its Zernike coefficients.
Fig. 8
Fig. 8 (a) The reconstructed distorted wavefront employing the periodic-correlation algorithm for shifts estimation and its Zernike coefficients. (b) The reconstructed distorted wavefront employing the gradient cross-correlation algorithm for shifts estimation and its Zernike coefficients.
Fig. 9
Fig. 9 Optical layout for the object scene wavefront aberration detection and correction.
Fig. 10
Fig. 10 (a) The S-H WFS extended-scene sub-image array obtained in the experiment. (b) One sub-image of the SH extended-scene. The blue-colored box shows a 28x28 pixels sub-aperture, and the yellow-colored box a 16x16 pixels sub-aperture. The latter is the size we used for correlation calculation.
Fig. 11
Fig. 11 (a) The reconstructed distorted wavefront employing the periodic-correlation algorithm for shifts estimation and its Zernike coefficients. (b) The reconstructed distorted wavefront employing the gradient cross-correlation algorithm for shifts estimation and its Zernike coefficients.
Fig. 12
Fig. 12 The residual wavefronts for defocus reconstrcted of different PV value. (a) 2λ defocus reconstructed error employing the periodic-correlation algorithm and (e) employing the gradient cross-correlation algorithm. (b) 4λ defocus reconstructed error employing the periodic-correlation algorithm and (f) employing the gradient cross-correlation algorithm. (c) 6λ defocus reconstructed error employing the periodic-correlation algorithm and (g) employing the gradient cross-correlation algorithm. (d) 8λ defocus reconstructed error employing the periodic-correlation algorithm and (h) employing the gradient cross-correlation algorithm.
Fig. 13
Fig. 13 Comparison of residual errors corresponding to the periodic-correlation algorithm and the gradient cross-correlation algorithm respectively.
Fig. 14
Fig. 14 Images and wavefronts of the object. (a) Images of the object without aberration plate. (e) Images of the object with aberration plate before correction and the corresponding distorted wavefront (b) detected by the periodic-correlation algorithm and (f) by the gradient cross-correlation algorithm; (c) Images and (d) wavefronts of the object after correction with the periodic-correlation algorithm; (g) Images and (h) wavefronts of the object after correction with the gradient cross-correlation algorithm.

Equations (12)

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C( x,y )= i=0 N1 j=0 N1 r * (ix,jy)s( i,j )
C( x,y )= F 1 [ R * ( u,v )S( u,v ) ].
S( u,v )=R( u,v ) e j( u x 0 +v y 0 ) .
C( x,y )= F 1 { | R( u,v ) | 2 e j( u x 0 +v y 0 ) }.
C(x,y)=w(x x 0 ,y y 0 )
x 0 = Δ x + 0.5[ C( Δ x 1, Δ y )C( Δ x +1, Δ y ) ] C( Δ x 1, Δ y )+C( Δ x +1, Δ y )2C( Δ x , Δ y ) .
s G x ( x,y )=| s( x+1,y )s( x,y ) |.
r G x ( x,y )=| r( x+1,y )r( x,y ) |.
C G x ( x,y )= i=0 N1 j=0 N1 r G x * ( ix,jy ) s G x ( i,j )
C G x ( x,y )= F 1 [ R G x * ( u,v ) S G x ( u,v ) ].
C G x (x,y)= w G x (x x 0 ,y y 0 )
x 0 = Δ x + 0.5[ C G x ( Δ x 1, Δ y ) C G x ( Δ x +1, Δ y ) ] C G x ( Δ x 1, Δ y )+ C G x ( Δ x +1, Δ y )2 C G x ( Δ x , Δ y ) .

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