Abstract

Deconvolution from wave front sensing (DWFS) is an image-reconstruction technique for compensating the image degradation due to atmospheric turbulence. DWFS requires the simultaneous recording of high cadence short-exposure images and wave-front sensor (WFS) data. A deconvolution algorithm is then used to estimate both the target object and the wave front phases from the images, subject to constraints imposed by the WFS data and a model of the optical system. Here we show that by capturing the inherent temporal correlations present in the consecutive wave fronts, using the frozen flow hypothesis (FFH) during the modeling, high-quality object estimates may be recovered in much worse conditions than when the correlations are ignored.

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  1. L. A. Poyneer, M. van Dam, and J.-P. Véran, “Experimental verification of the frozen flow atmospheric turbulence assumption with use of astronomical adaptive optics telemetry,” J. Opt. Soc. Am. A 26(4), 833–846 (2009).
    [CrossRef]
  2. E. Gendron and P. Léna, “Single layer atmospheric turbulence demonstrated by adaptive optics observations,” Astrophys. Space Sci. 239(2), 221–228 (1996).
    [CrossRef]
  3. M. Schöck and E. J. Spillar, “Method for a quantitative investigation of the frozen flow hypothesis,” J. Opt. Soc. Am. A 17(9), 1650–1658 (2000).
    [CrossRef]
  4. D. L. Fried, “Time-delay-induced mean-square error in adaptive optics,” J. Opt. Soc. Am. A 7(7), 1224–1225 (1990).
    [CrossRef]
  5. D. F. Buscher, J. T. Armstrong, C. A. Hummel, A. Quirrenbach, D. Mozurkewich, K. J. Johnston, C. S. Denison, M. M. Colavita, and M. Shao, “Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales,” Appl. Opt. 34(6), 1081–1096 (1995).
    [CrossRef] [PubMed]
  6. J. W. Hardy, “Adaptive optics for astronomical telescopes,” Oxford Series in Optical and Imaging Science, Oxford University Press, §9.4.3 (1998)
  7. K. A. Page, “Exploiting the frozen flow hypothesis for linear predictions in adaptive optics,” presented in Session 145 on Astronomical Instruments and Analytical Tools at the AAS 199th meeting, Washington DC, Jan 10, 2002.
  8. L. A. Poyneer, B. A. Macintosh, and J.-P. Véran, “Fourier transform wavefront control with adaptive prediction of the atmosphere,” J. Opt. Soc. Am. A 24(9), 2645–2660 (2007).
    [CrossRef]
  9. J. Primot, G. Rousset, and J. C. Fontanella, “Deconvolution from wave front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7(9), 1598–1608 (1990).
    [CrossRef]
  10. B. M. Welsh and M. C. Roggemann, “Signal-to-noise comparison of deconvolution from wave-front sensing with traditional linear and speckle image reconstruction,” Appl. Opt. 34(12), 2111–2119 (1995).
    [CrossRef] [PubMed]
  11. L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, and S. Salem, “Myopic deconvolution from wave front sensing,” J. Opt. Soc. Am. A 18(4), 862–872 (2001).
    [CrossRef]
  12. S. M. Jefferies, M. Lloyd-Hart, E. K. Hege, and J. Georges, “Sensing wave-front amplitude and phase with phase diversity,” Appl. Opt. 41(11), 2095–2102 (2002).
    [CrossRef] [PubMed]
  13. R. H. T. Bates, and M. J. McDonnell, Image Restoration and Reconstruction, Chapter 3, Oxford University Press, p 77 (1986)
  14. L. C. Roberts and C. R. Neyman, “Characterization of the AEOS adaptive optics system,” Publ. Astron. Soc. Pac. 114(801), 1260–1266 (2002).
    [CrossRef]
  15. F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
    [CrossRef]
  16. N. M. Milton, M. Lloyd-Hart, J. Bernier, and C. Baranec, “Real-time atmospheric turbulence profile estimation using modal covariance measurements from multiple guide stars,” in Astronomical Adaptive Optics Systems and Applications III (Proc. SPIE) eds. Tyson, R. K. & Lloyd-Hart, M., 6691, 66910B (2007).
  17. S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
    [CrossRef] [PubMed]
  18. S. E. Egner, E. Masciadri, and D. McKenna, “Generalized SCIDAR measurements at Mount Graham,” Publ. Astron. Soc. Pac. 119(856), 669–686 (2007).
    [CrossRef]
  19. T. Rimmele, “Haleakala turbulence and wind profiles used for adaptive optics performance modeling,” ATST Project Document RPT-0300 (1996).
  20. S. R. Maethner, Deconvolution from wave-front sensing using optimal wave-front estimators, Thesis, Air Force Institute of Technology, AFIT/GSO/ENP/96D–01, p 42–43 (1996)
  21. R. B. Makidon, A. Sivaramakrishnan, M. D. Perrin, L. C. Roberts, B. R. Oppenheimer, R. Soummer, and J. R. Graham, “An Analysis of Fundamental Waffle Mode in Early AEOS Adaptive Optics Images,” Publ. Astron. Soc. Pac. 117(834), 831–846 (2005).
    [CrossRef]
  22. D. A. Hope, and S. M. Jefferies, “A Fourier-based constraint for blind restoration of imagery obtained through strong turbulence”, Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, held in Wailea, Maui, Hawaii, September 10–14, 2006, Ed.: S. Ryan, The Maui Economic Development Board, p. E26 (2006).

2009

L. A. Poyneer, M. van Dam, and J.-P. Véran, “Experimental verification of the frozen flow atmospheric turbulence assumption with use of astronomical adaptive optics telemetry,” J. Opt. Soc. Am. A 26(4), 833–846 (2009).
[CrossRef]

2008

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

2007

S. E. Egner, E. Masciadri, and D. McKenna, “Generalized SCIDAR measurements at Mount Graham,” Publ. Astron. Soc. Pac. 119(856), 669–686 (2007).
[CrossRef]

L. A. Poyneer, B. A. Macintosh, and J.-P. Véran, “Fourier transform wavefront control with adaptive prediction of the atmosphere,” J. Opt. Soc. Am. A 24(9), 2645–2660 (2007).
[CrossRef]

2005

R. B. Makidon, A. Sivaramakrishnan, M. D. Perrin, L. C. Roberts, B. R. Oppenheimer, R. Soummer, and J. R. Graham, “An Analysis of Fundamental Waffle Mode in Early AEOS Adaptive Optics Images,” Publ. Astron. Soc. Pac. 117(834), 831–846 (2005).
[CrossRef]

2002

S. M. Jefferies, M. Lloyd-Hart, E. K. Hege, and J. Georges, “Sensing wave-front amplitude and phase with phase diversity,” Appl. Opt. 41(11), 2095–2102 (2002).
[CrossRef] [PubMed]

L. C. Roberts and C. R. Neyman, “Characterization of the AEOS adaptive optics system,” Publ. Astron. Soc. Pac. 114(801), 1260–1266 (2002).
[CrossRef]

2001

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, and S. Salem, “Myopic deconvolution from wave front sensing,” J. Opt. Soc. Am. A 18(4), 862–872 (2001).
[CrossRef]

2000

M. Schöck and E. J. Spillar, “Method for a quantitative investigation of the frozen flow hypothesis,” J. Opt. Soc. Am. A 17(9), 1650–1658 (2000).
[CrossRef]

1996

E. Gendron and P. Léna, “Single layer atmospheric turbulence demonstrated by adaptive optics observations,” Astrophys. Space Sci. 239(2), 221–228 (1996).
[CrossRef]

1995

D. F. Buscher, J. T. Armstrong, C. A. Hummel, A. Quirrenbach, D. Mozurkewich, K. J. Johnston, C. S. Denison, M. M. Colavita, and M. Shao, “Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales,” Appl. Opt. 34(6), 1081–1096 (1995).
[CrossRef] [PubMed]

B. M. Welsh and M. C. Roggemann, “Signal-to-noise comparison of deconvolution from wave-front sensing with traditional linear and speckle image reconstruction,” Appl. Opt. 34(12), 2111–2119 (1995).
[CrossRef] [PubMed]

1991

F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

1990

J. Primot, G. Rousset, and J. C. Fontanella, “Deconvolution from wave front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7(9), 1598–1608 (1990).
[CrossRef]

D. L. Fried, “Time-delay-induced mean-square error in adaptive optics,” J. Opt. Soc. Am. A 7(7), 1224–1225 (1990).
[CrossRef]

Armstrong, J. T.

D. F. Buscher, J. T. Armstrong, C. A. Hummel, A. Quirrenbach, D. Mozurkewich, K. J. Johnston, C. S. Denison, M. M. Colavita, and M. Shao, “Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales,” Appl. Opt. 34(6), 1081–1096 (1995).
[CrossRef] [PubMed]

Blum, R.

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

Buscher, D. F.

D. F. Buscher, J. T. Armstrong, C. A. Hummel, A. Quirrenbach, D. Mozurkewich, K. J. Johnston, C. S. Denison, M. M. Colavita, and M. Shao, “Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales,” Appl. Opt. 34(6), 1081–1096 (1995).
[CrossRef] [PubMed]

Bustos, E.

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

Colavita, M. M.

D. F. Buscher, J. T. Armstrong, C. A. Hummel, A. Quirrenbach, D. Mozurkewich, K. J. Johnston, C. S. Denison, M. M. Colavita, and M. Shao, “Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales,” Appl. Opt. 34(6), 1081–1096 (1995).
[CrossRef] [PubMed]

Conan, J.-M.

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, and S. Salem, “Myopic deconvolution from wave front sensing,” J. Opt. Soc. Am. A 18(4), 862–872 (2001).
[CrossRef]

Denison, C. S.

D. F. Buscher, J. T. Armstrong, C. A. Hummel, A. Quirrenbach, D. Mozurkewich, K. J. Johnston, C. S. Denison, M. M. Colavita, and M. Shao, “Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales,” Appl. Opt. 34(6), 1081–1096 (1995).
[CrossRef] [PubMed]

Egner, S. E.

S. E. Egner, E. Masciadri, and D. McKenna, “Generalized SCIDAR measurements at Mount Graham,” Publ. Astron. Soc. Pac. 119(856), 669–686 (2007).
[CrossRef]

Els, S. G.

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

Fontanella, J. C.

J. Primot, G. Rousset, and J. C. Fontanella, “Deconvolution from wave front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7(9), 1598–1608 (1990).
[CrossRef]

Fried, D. L.

D. L. Fried, “Time-delay-induced mean-square error in adaptive optics,” J. Opt. Soc. Am. A 7(7), 1224–1225 (1990).
[CrossRef]

Gendron, E.

E. Gendron and P. Léna, “Single layer atmospheric turbulence demonstrated by adaptive optics observations,” Astrophys. Space Sci. 239(2), 221–228 (1996).
[CrossRef]

Georges, J.

S. M. Jefferies, M. Lloyd-Hart, E. K. Hege, and J. Georges, “Sensing wave-front amplitude and phase with phase diversity,” Appl. Opt. 41(11), 2095–2102 (2002).
[CrossRef] [PubMed]

Gillett, P.

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

Graham, J. R.

R. B. Makidon, A. Sivaramakrishnan, M. D. Perrin, L. C. Roberts, B. R. Oppenheimer, R. Soummer, and J. R. Graham, “An Analysis of Fundamental Waffle Mode in Early AEOS Adaptive Optics Images,” Publ. Astron. Soc. Pac. 117(834), 831–846 (2005).
[CrossRef]

Graves, J. E.

F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Gregory, B.

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

Hege, E. K.

S. M. Jefferies, M. Lloyd-Hart, E. K. Hege, and J. Georges, “Sensing wave-front amplitude and phase with phase diversity,” Appl. Opt. 41(11), 2095–2102 (2002).
[CrossRef] [PubMed]

Hummel, C. A.

D. F. Buscher, J. T. Armstrong, C. A. Hummel, A. Quirrenbach, D. Mozurkewich, K. J. Johnston, C. S. Denison, M. M. Colavita, and M. Shao, “Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales,” Appl. Opt. 34(6), 1081–1096 (1995).
[CrossRef] [PubMed]

Jefferies, S. M.

S. M. Jefferies, M. Lloyd-Hart, E. K. Hege, and J. Georges, “Sensing wave-front amplitude and phase with phase diversity,” Appl. Opt. 41(11), 2095–2102 (2002).
[CrossRef] [PubMed]

Johnston, K. J.

D. F. Buscher, J. T. Armstrong, C. A. Hummel, A. Quirrenbach, D. Mozurkewich, K. J. Johnston, C. S. Denison, M. M. Colavita, and M. Shao, “Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales,” Appl. Opt. 34(6), 1081–1096 (1995).
[CrossRef] [PubMed]

Kornilov, V.

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

Léna, P.

E. Gendron and P. Léna, “Single layer atmospheric turbulence demonstrated by adaptive optics observations,” Astrophys. Space Sci. 239(2), 221–228 (1996).
[CrossRef]

Lloyd-Hart, M.

S. M. Jefferies, M. Lloyd-Hart, E. K. Hege, and J. Georges, “Sensing wave-front amplitude and phase with phase diversity,” Appl. Opt. 41(11), 2095–2102 (2002).
[CrossRef] [PubMed]

Macintosh, B. A.

L. A. Poyneer, B. A. Macintosh, and J.-P. Véran, “Fourier transform wavefront control with adaptive prediction of the atmosphere,” J. Opt. Soc. Am. A 24(9), 2645–2660 (2007).
[CrossRef]

Makidon, R. B.

R. B. Makidon, A. Sivaramakrishnan, M. D. Perrin, L. C. Roberts, B. R. Oppenheimer, R. Soummer, and J. R. Graham, “An Analysis of Fundamental Waffle Mode in Early AEOS Adaptive Optics Images,” Publ. Astron. Soc. Pac. 117(834), 831–846 (2005).
[CrossRef]

Masciadri, E.

S. E. Egner, E. Masciadri, and D. McKenna, “Generalized SCIDAR measurements at Mount Graham,” Publ. Astron. Soc. Pac. 119(856), 669–686 (2007).
[CrossRef]

McKenna, D.

S. E. Egner, E. Masciadri, and D. McKenna, “Generalized SCIDAR measurements at Mount Graham,” Publ. Astron. Soc. Pac. 119(856), 669–686 (2007).
[CrossRef]

Michau, V.

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, and S. Salem, “Myopic deconvolution from wave front sensing,” J. Opt. Soc. Am. A 18(4), 862–872 (2001).
[CrossRef]

Mozurkewich, D.

D. F. Buscher, J. T. Armstrong, C. A. Hummel, A. Quirrenbach, D. Mozurkewich, K. J. Johnston, C. S. Denison, M. M. Colavita, and M. Shao, “Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales,” Appl. Opt. 34(6), 1081–1096 (1995).
[CrossRef] [PubMed]

Mugnier, L. M.

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, and S. Salem, “Myopic deconvolution from wave front sensing,” J. Opt. Soc. Am. A 18(4), 862–872 (2001).
[CrossRef]

Neyman, C. R.

L. C. Roberts and C. R. Neyman, “Characterization of the AEOS adaptive optics system,” Publ. Astron. Soc. Pac. 114(801), 1260–1266 (2002).
[CrossRef]

Northcott, M.

F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Oppenheimer, B. R.

R. B. Makidon, A. Sivaramakrishnan, M. D. Perrin, L. C. Roberts, B. R. Oppenheimer, R. Soummer, and J. R. Graham, “An Analysis of Fundamental Waffle Mode in Early AEOS Adaptive Optics Images,” Publ. Astron. Soc. Pac. 117(834), 831–846 (2005).
[CrossRef]

Perrin, M. D.

R. B. Makidon, A. Sivaramakrishnan, M. D. Perrin, L. C. Roberts, B. R. Oppenheimer, R. Soummer, and J. R. Graham, “An Analysis of Fundamental Waffle Mode in Early AEOS Adaptive Optics Images,” Publ. Astron. Soc. Pac. 117(834), 831–846 (2005).
[CrossRef]

Poyneer, L. A.

L. A. Poyneer, M. van Dam, and J.-P. Véran, “Experimental verification of the frozen flow atmospheric turbulence assumption with use of astronomical adaptive optics telemetry,” J. Opt. Soc. Am. A 26(4), 833–846 (2009).
[CrossRef]

L. A. Poyneer, B. A. Macintosh, and J.-P. Véran, “Fourier transform wavefront control with adaptive prediction of the atmosphere,” J. Opt. Soc. Am. A 24(9), 2645–2660 (2007).
[CrossRef]

Primot, J.

J. Primot, G. Rousset, and J. C. Fontanella, “Deconvolution from wave front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7(9), 1598–1608 (1990).
[CrossRef]

Quirrenbach, A.

D. F. Buscher, J. T. Armstrong, C. A. Hummel, A. Quirrenbach, D. Mozurkewich, K. J. Johnston, C. S. Denison, M. M. Colavita, and M. Shao, “Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales,” Appl. Opt. 34(6), 1081–1096 (1995).
[CrossRef] [PubMed]

Riddle, R.

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

Robert, C.

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, and S. Salem, “Myopic deconvolution from wave front sensing,” J. Opt. Soc. Am. A 18(4), 862–872 (2001).
[CrossRef]

Roberts, L. C.

R. B. Makidon, A. Sivaramakrishnan, M. D. Perrin, L. C. Roberts, B. R. Oppenheimer, R. Soummer, and J. R. Graham, “An Analysis of Fundamental Waffle Mode in Early AEOS Adaptive Optics Images,” Publ. Astron. Soc. Pac. 117(834), 831–846 (2005).
[CrossRef]

L. C. Roberts and C. R. Neyman, “Characterization of the AEOS adaptive optics system,” Publ. Astron. Soc. Pac. 114(801), 1260–1266 (2002).
[CrossRef]

Roddier, F.

F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Roggemann, M. C.

B. M. Welsh and M. C. Roggemann, “Signal-to-noise comparison of deconvolution from wave-front sensing with traditional linear and speckle image reconstruction,” Appl. Opt. 34(12), 2111–2119 (1995).
[CrossRef] [PubMed]

Rousset, G.

J. Primot, G. Rousset, and J. C. Fontanella, “Deconvolution from wave front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7(9), 1598–1608 (1990).
[CrossRef]

Salem, S.

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, and S. Salem, “Myopic deconvolution from wave front sensing,” J. Opt. Soc. Am. A 18(4), 862–872 (2001).
[CrossRef]

Schöck, M.

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

M. Schöck and E. J. Spillar, “Method for a quantitative investigation of the frozen flow hypothesis,” J. Opt. Soc. Am. A 17(9), 1650–1658 (2000).
[CrossRef]

Seguel, J.

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

Shao, M.

D. F. Buscher, J. T. Armstrong, C. A. Hummel, A. Quirrenbach, D. Mozurkewich, K. J. Johnston, C. S. Denison, M. M. Colavita, and M. Shao, “Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales,” Appl. Opt. 34(6), 1081–1096 (1995).
[CrossRef] [PubMed]

Sivaramakrishnan, A.

R. B. Makidon, A. Sivaramakrishnan, M. D. Perrin, L. C. Roberts, B. R. Oppenheimer, R. Soummer, and J. R. Graham, “An Analysis of Fundamental Waffle Mode in Early AEOS Adaptive Optics Images,” Publ. Astron. Soc. Pac. 117(834), 831–846 (2005).
[CrossRef]

Skidmore, W.

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

Soummer, R.

R. B. Makidon, A. Sivaramakrishnan, M. D. Perrin, L. C. Roberts, B. R. Oppenheimer, R. Soummer, and J. R. Graham, “An Analysis of Fundamental Waffle Mode in Early AEOS Adaptive Optics Images,” Publ. Astron. Soc. Pac. 117(834), 831–846 (2005).
[CrossRef]

Spillar, E. J.

M. Schöck and E. J. Spillar, “Method for a quantitative investigation of the frozen flow hypothesis,” J. Opt. Soc. Am. A 17(9), 1650–1658 (2000).
[CrossRef]

Tokovinin, A.

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

Travouillon, T.

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

van Dam, M.

L. A. Poyneer, M. van Dam, and J.-P. Véran, “Experimental verification of the frozen flow atmospheric turbulence assumption with use of astronomical adaptive optics telemetry,” J. Opt. Soc. Am. A 26(4), 833–846 (2009).
[CrossRef]

Vasquez, J.

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

Véran, J.-P.

L. A. Poyneer, M. van Dam, and J.-P. Véran, “Experimental verification of the frozen flow atmospheric turbulence assumption with use of astronomical adaptive optics telemetry,” J. Opt. Soc. Am. A 26(4), 833–846 (2009).
[CrossRef]

L. A. Poyneer, B. A. Macintosh, and J.-P. Véran, “Fourier transform wavefront control with adaptive prediction of the atmosphere,” J. Opt. Soc. Am. A 24(9), 2645–2660 (2007).
[CrossRef]

Vogiatzis, K.

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

Walker, D.

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

Welsh, B. M.

B. M. Welsh and M. C. Roggemann, “Signal-to-noise comparison of deconvolution from wave-front sensing with traditional linear and speckle image reconstruction,” Appl. Opt. 34(12), 2111–2119 (1995).
[CrossRef] [PubMed]

Appl. Opt.

D. F. Buscher, J. T. Armstrong, C. A. Hummel, A. Quirrenbach, D. Mozurkewich, K. J. Johnston, C. S. Denison, M. M. Colavita, and M. Shao, “Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales,” Appl. Opt. 34(6), 1081–1096 (1995).
[CrossRef] [PubMed]

B. M. Welsh and M. C. Roggemann, “Signal-to-noise comparison of deconvolution from wave-front sensing with traditional linear and speckle image reconstruction,” Appl. Opt. 34(12), 2111–2119 (1995).
[CrossRef] [PubMed]

S. M. Jefferies, M. Lloyd-Hart, E. K. Hege, and J. Georges, “Sensing wave-front amplitude and phase with phase diversity,” Appl. Opt. 41(11), 2095–2102 (2002).
[CrossRef] [PubMed]

S. G. Els, M. Schöck, J. Seguel, A. Tokovinin, V. Kornilov, R. Riddle, W. Skidmore, T. Travouillon, K. Vogiatzis, R. Blum, E. Bustos, B. Gregory, J. Vasquez, D. Walker, and P. Gillett, “Study on the precision of the multiaperture scintillation sensor turbulence profiler (MASS) employed in the site testing campaign for the Thirty Meter Telescope,” Appl. Opt. 47(14), 2610–2618 (2008).
[CrossRef] [PubMed]

Astrophys. Space Sci.

E. Gendron and P. Léna, “Single layer atmospheric turbulence demonstrated by adaptive optics observations,” Astrophys. Space Sci. 239(2), 221–228 (1996).
[CrossRef]

J. Opt. Soc. Am. A

M. Schöck and E. J. Spillar, “Method for a quantitative investigation of the frozen flow hypothesis,” J. Opt. Soc. Am. A 17(9), 1650–1658 (2000).
[CrossRef]

D. L. Fried, “Time-delay-induced mean-square error in adaptive optics,” J. Opt. Soc. Am. A 7(7), 1224–1225 (1990).
[CrossRef]

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, and S. Salem, “Myopic deconvolution from wave front sensing,” J. Opt. Soc. Am. A 18(4), 862–872 (2001).
[CrossRef]

L. A. Poyneer, B. A. Macintosh, and J.-P. Véran, “Fourier transform wavefront control with adaptive prediction of the atmosphere,” J. Opt. Soc. Am. A 24(9), 2645–2660 (2007).
[CrossRef]

J. Primot, G. Rousset, and J. C. Fontanella, “Deconvolution from wave front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7(9), 1598–1608 (1990).
[CrossRef]

L. A. Poyneer, M. van Dam, and J.-P. Véran, “Experimental verification of the frozen flow atmospheric turbulence assumption with use of astronomical adaptive optics telemetry,” J. Opt. Soc. Am. A 26(4), 833–846 (2009).
[CrossRef]

Publ. Astron. Soc. Pac.

R. B. Makidon, A. Sivaramakrishnan, M. D. Perrin, L. C. Roberts, B. R. Oppenheimer, R. Soummer, and J. R. Graham, “An Analysis of Fundamental Waffle Mode in Early AEOS Adaptive Optics Images,” Publ. Astron. Soc. Pac. 117(834), 831–846 (2005).
[CrossRef]

S. E. Egner, E. Masciadri, and D. McKenna, “Generalized SCIDAR measurements at Mount Graham,” Publ. Astron. Soc. Pac. 119(856), 669–686 (2007).
[CrossRef]

L. C. Roberts and C. R. Neyman, “Characterization of the AEOS adaptive optics system,” Publ. Astron. Soc. Pac. 114(801), 1260–1266 (2002).
[CrossRef]

F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Other

N. M. Milton, M. Lloyd-Hart, J. Bernier, and C. Baranec, “Real-time atmospheric turbulence profile estimation using modal covariance measurements from multiple guide stars,” in Astronomical Adaptive Optics Systems and Applications III (Proc. SPIE) eds. Tyson, R. K. & Lloyd-Hart, M., 6691, 66910B (2007).

R. H. T. Bates, and M. J. McDonnell, Image Restoration and Reconstruction, Chapter 3, Oxford University Press, p 77 (1986)

T. Rimmele, “Haleakala turbulence and wind profiles used for adaptive optics performance modeling,” ATST Project Document RPT-0300 (1996).

S. R. Maethner, Deconvolution from wave-front sensing using optimal wave-front estimators, Thesis, Air Force Institute of Technology, AFIT/GSO/ENP/96D–01, p 42–43 (1996)

J. W. Hardy, “Adaptive optics for astronomical telescopes,” Oxford Series in Optical and Imaging Science, Oxford University Press, §9.4.3 (1998)

K. A. Page, “Exploiting the frozen flow hypothesis for linear predictions in adaptive optics,” presented in Session 145 on Astronomical Instruments and Analytical Tools at the AAS 199th meeting, Washington DC, Jan 10, 2002.

D. A. Hope, and S. M. Jefferies, “A Fourier-based constraint for blind restoration of imagery obtained through strong turbulence”, Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, held in Wailea, Maui, Hawaii, September 10–14, 2006, Ed.: S. Ryan, The Maui Economic Development Board, p. E26 (2006).

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Figures (5)

Fig. 1
Fig. 1

Cartoon of a phase screen representing a single atmospheric layer propagating across the telescope pupil, depicted as the heavy black circle, with wind velocity v indicated by the arrow. The light and medium gray areas represent adjacent regions of wave-front phase for which the FFH is valid, each of length |v|τFFH. The phases in the dark gray area, the overlap between the two, are independently estimated for both screens.

Fig. 2
Fig. 2

The object estimates of a point source obtained from (left) DWFS using the FFH to model the inherent temporal correlations in the wave-front phases and (right) DWFS assuming no temporal correlation. Note, as Eq. (7) does not enforce positivity, negative values can be present in the restored object. Both images are shown with square root scaling.

Fig. 3
Fig. 3

Top Left: truth point spread function (PSF) for first frame. Top Middle: estimated PSF using the FFH. The absence of speckle structure at large radial distances reflects the lack of high-spatial frequencies in the reconstructed wave-front phase estimates. Top Right: estimated PSF without using the FFH. Bottom row: wave front phases corresponding to the PSFs directly above. The top row is shown with square root scaling to emphasize the complex speckle structure. The bottom row is displayed with linear scaling (see color bar for scaling in radians).

Fig. 4
Fig. 4

Left: Diffraction-limited image of the truth object, a model of the Hubble Space Telescope. Middle Left: Image after convolution of truth object with truth PSF shown in Fig. 3 and addition of photon noise. Middle Right: Restored image from 80 ms of focal plane and WFS data when using the FFH. Right: Restored image without use of the FFH. All images are shown with linear scaling.

Fig. 5
Fig. 5

Top row: the point source and extended object estimates obtained from inverse Fourier transforming the spectra of the truth objects multiplied by the binary masks shown beneath. These panels are of the central region of the frames displayed in Figs. 2 and 4 and show the best recovery that can be expected with the given data. Bottom row: the Fourier plane coverage of the object spectrum provided by the ensemble of data used in each restoration, defined as frequencies where the signal-to-noise ratio is > 1. The black circles indicate the Nyquist cut-off frequency for the observations.

Tables (4)

Tables Icon

Table 1 Atmospheric parameters used in the simulations. The values for r0 and τ0 are given for a wavelength of 0.5 μm.

Tables Icon

Table 2 Optical system and object parameters used in the simulations. Photon fluxes were calculated using [20]: Ω= Esun 1.944e-11 10-0.4mv A t Δλ Δt / (hc/λ), where Esun= 813 J/s m2 μm at 0.94 μm, and 1750 J/s m2 μm at 0.6μm, mv is the visual magnitude of the target, A is the area of the aperture, Δλ is the band pass (in μm), Δt is the integration time, t is the efficiency (assumed = 0.5), h is Planck’s constant, c is the velocity of light and λ is the imaging wavelength.

Tables Icon

Table 3 Residual wave-front phase errors (in nm) for the point source for tests both with and without the FFH. Top row shows rms values averaged over the pupil and all frames for the full wave-front error. Bottom row shows values with tip and tilt explicitly removed.

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Table 4 Residual wave-front phase errors for the HST extended source in nm for tests both with and without the FFH.

Equations (7)

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

g ( x ) = ( f h ) x
Φ ( x , t + Δ t ) = Σ i α i ( x - v i Δ t , t ) ,
ε c o n v = Σ k Σ x ( g k o b s ( x ) g k ( x ) ) 2 ,
g k o b s ( x ) = ( f o h k o ) x + n k ( x ) ,
ε w f s = k j x M [ ( x Φ j k S j k x ) 2 + ( y Φ j k S j k y ) 2 ]
h k ( x ) = ( 1 / J ) j | F T 1 { P j k ( u ) exp [ i Φ j k ( u ) ] } | 2
f ( x ) F T 1 { k G k o b s ( u ) H k * ( u ) [ k H k ( u ) H k * ( u ) + γ ] 1 }

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