Abstract

We demonstrate that high-resolution imaging through strong atmospheric turbulence can be achieved by acquiring data with a system that captures short exposure (“speckle”) images using a range of aperture sizes and then using a bootstrap multi-frame blind deconvolution restoration process that starts with the smallest aperture data. Our results suggest a potential paradigm shift in how we image through atmospheric turbulence. No longer should image acquisition and post processing be treated as two independent processes: they should be considered as intimately related.

© 2016 Optical Society of America

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References

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    [Crossref]

2015 (1)

J. P. Bos and B. Calef, “Using aperture partitioning to improve scene recovery in horizontal long-path speckle imaging,” Proc. SPIE 9614, 961407 (2015).
[Crossref]

2012 (2)

A. Polo, N. van Marrewijk, S. F. Pereira, and H. P. Urbach, “Sub-aperture phase reconstruction from a Hartmann wave front sensor by phase retrieval method for application in EUV adaptive optics,” Proc. SPIE 8322, 832219 (2012).
[Crossref]

M. Aubailly and M. A. Vorontsov, “Scintillation resistant wavefront sensing based on multi-aperture phase reconstruction technique,” J. Opt. Soc. Am. A 29(8), 1707–1716 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (1)

B. Calef, “Improving imaging through turbulence via aperture partitioning,” Proc. SPIE 7701, 77010G (2010).
[Crossref]

2009 (1)

2008 (1)

A. Foi, M. Trimeche, V. Katkovnik, and K. Egiazarian, “Practical Poissonian-Gaussian noise modeling and fitting for single-image raw-data,” IEEE Trans. Image Process. 17(10), 1737–1754 (2008).
[Crossref] [PubMed]

2005 (1)

R. Vio, J. Bardsley, and W. Wamsteker, “Least-squares methods with Poissonian noise: analysis and comparison with the Richardson-Lucy algorithm,” Astron. Astrophys. 436(2), 741–755 (2005).
[Crossref]

2004 (1)

2003 (1)

2002 (1)

2000 (1)

W.-Y. V. Leung and R. G. Lane, “Blind deconvolution of images blurred by atmospheric speckle,” Proc. SPIE 4123, 73–83 (2000).
[Crossref]

1999 (1)

1998 (1)

1997 (1)

M. R. Stoneking and D. J. Den Hartog, “Maximum-likelihood fitting of data dominated by Poisson statistical uncertainties,” Rev. Sci. Instrum. 68(1), 914–917 (1997).
[Crossref]

1995 (1)

1993 (2)

T. Schulz, “Multiframe blind deconvolution of astronomical images,” J. Opt. Soc. Am. A 10(5), 1064–1073 (1993).
[Crossref]

S. M. Jefferies and J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astrophys. J. 415, 862–864 (1993).
[Crossref]

1966 (1)

Aubailly, M.

Bardsley, J.

R. Vio, J. Bardsley, and W. Wamsteker, “Least-squares methods with Poissonian noise: analysis and comparison with the Richardson-Lucy algorithm,” Astron. Astrophys. 436(2), 741–755 (2005).
[Crossref]

Barraza-Felix, S.

Beckner, C. C.

Borelli, K.

Bos, J. P.

J. P. Bos and B. Calef, “Using aperture partitioning to improve scene recovery in horizontal long-path speckle imaging,” Proc. SPIE 9614, 961407 (2015).
[Crossref]

Calef, B.

J. P. Bos and B. Calef, “Using aperture partitioning to improve scene recovery in horizontal long-path speckle imaging,” Proc. SPIE 9614, 961407 (2015).
[Crossref]

B. Calef, “Improving imaging through turbulence via aperture partitioning,” Proc. SPIE 7701, 77010G (2010).
[Crossref]

Christou, J. C.

S. M. Jefferies and J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astrophys. J. 415, 862–864 (1993).
[Crossref]

Conan, J. M.

Conan, J.-M.

Den Hartog, D. J.

M. R. Stoneking and D. J. Den Hartog, “Maximum-likelihood fitting of data dominated by Poisson statistical uncertainties,” Rev. Sci. Instrum. 68(1), 914–917 (1997).
[Crossref]

Egiazarian, K.

A. Foi, M. Trimeche, V. Katkovnik, and K. Egiazarian, “Practical Poissonian-Gaussian noise modeling and fitting for single-image raw-data,” IEEE Trans. Image Process. 17(10), 1737–1754 (2008).
[Crossref] [PubMed]

Foi, A.

A. Foi, M. Trimeche, V. Katkovnik, and K. Egiazarian, “Practical Poissonian-Gaussian noise modeling and fitting for single-image raw-data,” IEEE Trans. Image Process. 17(10), 1737–1754 (2008).
[Crossref] [PubMed]

Fried, D.

Frieden, B. R.

Fusco, T.

Georges, J.

Hart, M.

Hege, E. K.

Hope, D. A.

Ivanov, J. M.

J. M. Ivanov and D. McGaughey, “Image reconstruction by aperture diversity blind deconvolution,” in Proceedings of the AMOS Conference (2007).

Jefferies, S.

Jefferies, S. M.

Katkovnik, V.

A. Foi, M. Trimeche, V. Katkovnik, and K. Egiazarian, “Practical Poissonian-Gaussian noise modeling and fitting for single-image raw-data,” IEEE Trans. Image Process. 17(10), 1737–1754 (2008).
[Crossref] [PubMed]

Lane, R. G.

W.-Y. V. Leung and R. G. Lane, “Blind deconvolution of images blurred by atmospheric speckle,” Proc. SPIE 4123, 73–83 (2000).
[Crossref]

Leung, W.-Y. V.

W.-Y. V. Leung and R. G. Lane, “Blind deconvolution of images blurred by atmospheric speckle,” Proc. SPIE 4123, 73–83 (2000).
[Crossref]

Lloyd-Hart, M.

Matson, C. L.

McGaughey, D.

J. M. Ivanov and D. McGaughey, “Image reconstruction by aperture diversity blind deconvolution,” in Proceedings of the AMOS Conference (2007).

Michau, V.

Miura, N.

Mugnier, L. M.

Pereira, S. F.

A. Polo, N. van Marrewijk, S. F. Pereira, and H. P. Urbach, “Sub-aperture phase reconstruction from a Hartmann wave front sensor by phase retrieval method for application in EUV adaptive optics,” Proc. SPIE 8322, 832219 (2012).
[Crossref]

Polo, A.

A. Polo, N. van Marrewijk, S. F. Pereira, and H. P. Urbach, “Sub-aperture phase reconstruction from a Hartmann wave front sensor by phase retrieval method for application in EUV adaptive optics,” Proc. SPIE 8322, 832219 (2012).
[Crossref]

Rousset, G.

Schulz, T.

Stoneking, M. R.

M. R. Stoneking and D. J. Den Hartog, “Maximum-likelihood fitting of data dominated by Poisson statistical uncertainties,” Rev. Sci. Instrum. 68(1), 914–917 (1997).
[Crossref]

Thiebaut, E.

Trimeche, M.

A. Foi, M. Trimeche, V. Katkovnik, and K. Egiazarian, “Practical Poissonian-Gaussian noise modeling and fitting for single-image raw-data,” IEEE Trans. Image Process. 17(10), 1737–1754 (2008).
[Crossref] [PubMed]

Urbach, H. P.

A. Polo, N. van Marrewijk, S. F. Pereira, and H. P. Urbach, “Sub-aperture phase reconstruction from a Hartmann wave front sensor by phase retrieval method for application in EUV adaptive optics,” Proc. SPIE 8322, 832219 (2012).
[Crossref]

van Marrewijk, N.

A. Polo, N. van Marrewijk, S. F. Pereira, and H. P. Urbach, “Sub-aperture phase reconstruction from a Hartmann wave front sensor by phase retrieval method for application in EUV adaptive optics,” Proc. SPIE 8322, 832219 (2012).
[Crossref]

Vio, R.

R. Vio, J. Bardsley, and W. Wamsteker, “Least-squares methods with Poissonian noise: analysis and comparison with the Richardson-Lucy algorithm,” Astron. Astrophys. 436(2), 741–755 (2005).
[Crossref]

Vorontsov, M. A.

Wamsteker, W.

R. Vio, J. Bardsley, and W. Wamsteker, “Least-squares methods with Poissonian noise: analysis and comparison with the Richardson-Lucy algorithm,” Astron. Astrophys. 436(2), 741–755 (2005).
[Crossref]

Appl. Opt. (4)

Astron. Astrophys. (1)

R. Vio, J. Bardsley, and W. Wamsteker, “Least-squares methods with Poissonian noise: analysis and comparison with the Richardson-Lucy algorithm,” Astron. Astrophys. 436(2), 741–755 (2005).
[Crossref]

Astrophys. J. (1)

S. M. Jefferies and J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astrophys. J. 415, 862–864 (1993).
[Crossref]

IEEE Trans. Image Process. (1)

A. Foi, M. Trimeche, V. Katkovnik, and K. Egiazarian, “Practical Poissonian-Gaussian noise modeling and fitting for single-image raw-data,” IEEE Trans. Image Process. 17(10), 1737–1754 (2008).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Opt. Express (1)

Opt. Lett. (2)

Proc. SPIE (4)

B. Calef, “Improving imaging through turbulence via aperture partitioning,” Proc. SPIE 7701, 77010G (2010).
[Crossref]

J. P. Bos and B. Calef, “Using aperture partitioning to improve scene recovery in horizontal long-path speckle imaging,” Proc. SPIE 9614, 961407 (2015).
[Crossref]

W.-Y. V. Leung and R. G. Lane, “Blind deconvolution of images blurred by atmospheric speckle,” Proc. SPIE 4123, 73–83 (2000).
[Crossref]

A. Polo, N. van Marrewijk, S. F. Pereira, and H. P. Urbach, “Sub-aperture phase reconstruction from a Hartmann wave front sensor by phase retrieval method for application in EUV adaptive optics,” Proc. SPIE 8322, 832219 (2012).
[Crossref]

Rev. Sci. Instrum. (1)

M. R. Stoneking and D. J. Den Hartog, “Maximum-likelihood fitting of data dominated by Poisson statistical uncertainties,” Rev. Sci. Instrum. 68(1), 914–917 (1997).
[Crossref]

Other (3)

T. Rimmele, “Haleakala turbulence and wind profiles used for adaptive optics performance modeling”, ATST Project Document RPT-0030 (2006).

B. Calef, “Weak signals and strong turbulence,” presentation to the AFOSR PROTEA group, September 10, 2011.

J. M. Ivanov and D. McGaughey, “Image reconstruction by aperture diversity blind deconvolution,” in Proceedings of the AMOS Conference (2007).

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Figures (9)

Fig. 1
Fig. 1 The restoration of 17 frames of simulated D/r0 = 40 data (D = 3.6 m) without (bottom left) and with (bottom right) an initial high-quality, low-spatial frequency, estimate of the object. The restoration on the bottom left used the mean data frame (top left) as the initial estimate for the object and has a root mean-square error (RMSE) of 0.49. The restoration on the bottom right used a diffraction-limited image of the object as would be obtained through a 1.0-m aperture telescope (top right) as an initial estimate for the object, and has an RMSE of 0.29. All images are displayed on a linear intensity scale. The RMSE is calculated as Σ pixels (restored imagetrue image) 2 /true imag e 2 .
Fig. 2
Fig. 2 Here we use numerical simulations of observations of the Hubble Space Telescope taken through different levels of atmospheric turbulence with a 3.6 m telescope with a 0.4 m central obscuration (see §3 for details), to determine the performance of MFBD with changing turbulence conditions. In the top row (left to right) we show sample data frames for a range of turbulence levels indicated by D/r0. In the bottom row we show the MFBD restorations of 17 frames of the corresponding data shown in the row above. The RMSE is shown for each of the restored images. All frames are displayed on linear scales between each image’s minimum and maximum values.
Fig. 3
Fig. 3 Schematic of restoration algorithm. The boxes with dotted boundaries show an iterative process. The dark grey boxes show where there is human intervention. The thick arrows show the multi-pass loop (index j). The dotted rows show the (inner) multi-channel loop (index l).
Fig. 4
Fig. 4 Left-to-right: Restorations of 17 frames of D/r0 = 10, 20, 30, 40 and 60 data. The results using a single pass through our MFBD algorithm are shown in the top row, and after multiple passes in the bottom row. The improvement in RMSE in the bottom row is (left to right); 31%, 18%, 19%, 31% and 0%.
Fig. 5
Fig. 5 Top row: Sample data frames from numerical simulations of observations of the Hubble Space Telescope (mv = + 2) taken with different apertures, shown in the bottom row, through atmospheric turbulence with r0 = 9 cm. Left to right: 3.6 m full aperture, 1.0 m annulus, 1.6 m annulus (1.0 m inner diameter), and 3.6 m diameter annulus (1.6 m inner diameter). The data frames are displayed on linear scales between each image’s minimum and maximum values.
Fig. 6
Fig. 6 Restoration of 17 “full pupil” images obtained through turbulence with D/r0 = 40 (D = 3.6 m) using multiple MFBD passes (left) and 17 sets of three-annuli “aperture diverse” images obtained through the same conditions and processed using a bootstrap approach (right). The RMSE values are 0.34 (left) and 0.29 (right). Both images are displayed on linear scales between each image’s minimum and maximum values.
Fig. 7
Fig. 7 Snapshot of simulated HST images seen through the 32 subapertures of the imaging Shack-Hartmann sensor. The images are characterized by moderate seeing of D/r0 = 12 (D = 60 cm, r0 = 5 cm) in each sub-aperture but are badly affected by photon noise.
Fig. 8
Fig. 8 Left to right: a) example simulated data frame for D/r0 = 70 with a target brightness of mv = + 2 and a 5 ms exposure (x 0.5 zoom); b) MFBD restoration of 17 “full pupil” images and associated imaging Shack-Hartmann WFS data (32 images per full pupil image); c) MFBD “bootstrap” restoration of 17 sets of 35 “aperture diverse” images that include three annuli and an imaging Shack-Hartmann WFS configuration of 32 sub-apertures; d) simulated diffraction-limited image for a 3.6 m telescope. The RMSE values for (b), (c) and (d), with respect to the true image, are 0.33, 0.23 and 0.19, respectively.
Fig. 9
Fig. 9 The RMSE vs. spatial frequency based on 20 Monte Carlo trials of 6-frame blind restorations for simulated data of a target of brightness mv = + 2. The lower the RMSE value, the better the quality of the restoration. (a) Results from data from single apertures of 1.0 m (solid), 1.6 m (dotted) and 3.6 m (dashed) observing through the same atmosphere (r0 = 15 cm). (b) The RMSE of restorations using the data from all three annular apertures. The solid line represents the simultaneous restoration of the combined data. The dotted line shows the result from the bootstrap approach that starts with the smallest aperture data to achieve a good low-spatial frequency estimate, and then systematically updates the estimate through the addition of data from the larger apertures.

Equations (6)

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H ^ l,k (u)= B l (u)exp(i Φ ^ k (u)) B l (u)exp(i Φ ^ k (u))
ε= l k x w l,k | g l,k ( x ) g ^ l,k ( x ) | 2
g ^ l,k (x)= α l ( f ^ h ^ l,k ) x
w l,k (x)= { g ^ l,k (x)+ n l,k 2 (x) } 1
ε SR = l,l' k,k' u w l.l',k,k' (u) | χ l.l',k,k' (u) | 2
χ l.l',k,k' (u)= H ^ l,k (u) G l',k' (u) H ^ l',k' (u) G l,k (u)

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