Abstract

We explore the feasibility of post-detection restoration when imaging through deep turbulence characterized by extreme anisoplanatism. A wave-optics code was used to simulate relevant short-exposure point spread functions (PSFs) and their decorrelation as a function of point-source separation was computed. In addition, short-exposure images of minimally extended objects were simulated and shown to retain a central lobe that is clearly narrower than the long-exposure counterpart. This suggests that short-exposure image data are more informative than long-exposure data, even in the presence of extreme anisoplanatism. The implications of these findings for image restoration from a sequence of short-exposure images are discussed.

© 2016 Optical Society of America

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References

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2013 (1)

X. Zhu and P. Milanfar, “Removing atmospheric turbulence via space-invariant deconvolution,” IEEE Trans. Pattern Anal. Mach. Intell. 35(1), 157–170 (2013).
[Crossref] [PubMed]

2012 (1)

G. A. Tyler, “Adaptive optics compensation for propagation through deep turbulence: a study of some interesting approaches,” Opt. Eng. 52(2), 021011 (2012).
[Crossref]

2009 (2)

B. J. Thelen, R. G. Paxman, D. A. Carrara, and J. H. Seldin, “Overcoming turbulence-induced space-variant blur by using phase-diverse speckle,” J. Opt. Soc. Am. A 26(1), 206–218 (2009).
[Crossref] [PubMed]

M. Aubailly, M. A. Vorontsov, G. W. Carhart, and M. T. Valley, “Automated video enhancement from a stream of atmospherically distorted images: the lucky-region fusion approach,” Proc. SPIE 7463, 74630C (2009).
[Crossref]

2008 (1)

2003 (2)

C. J. Carrano, “Progress in horizontal and slant-path imaging using speckle imagery,” Proc. SPIE 5001, 56–64 (2003).
[Crossref]

C. J. Carrano, “Anisoplanatic performance of horizontal-path speckle imaging,” Proc. SPIE 5162, 14–27 (2003).
[Crossref]

2002 (1)

A. J. Lambert, D. Fraser, M. R. Sayyah Jahromi, and B. R. Hunt, “Superresolution in image restoration of wide area images viewed through atmospheric turbulence,” Proc. SPIE 4792, 35–43 (2002).
[Crossref]

1999 (2)

R. G. Paxman, B. J. Thelen, and J. J. Miller, “Optimal simulation of volume turbulence with phase screens,” Proc. SPIE 3763-01, 2–10 (1999).
[Crossref]

D. Fraser, G. Thorpe, and A. Lambert, “Atmospheric turbulence visualization with wide-area motion-blur restoration,” J. Opt. Soc. Am. A 16(7), 1751–1758 (1999).
[Crossref]

1998 (1)

W. van Kampen and R. G. Paxman, “Multiframe blind deconvolution of infinite-extent objects,” Proc. SPIE 3433, 296–307 (1998).
[Crossref]

1996 (1)

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

1994 (3)

D. G. Sandler, S. Stahl, J. R. P. Angel, M. Lloyd-Hart, and D. McCarthy, “Adaptive optics for diffraction-limited infrared imaging with 8-m telescopes,” J. Opt. Soc. Am. A 11(2), 925–945 (1994).
[Crossref]

D. J. Link, “Comparison of the effects of near-field and distributed atmospheric turbulence on the performance of an adaptive optics system,” Proc. SPIE 2120, 87–94 (1994).
[Crossref]

E. P. Waliner, “Optimizing the locations of multiconjugate wavefront correctors,” Proc. SPIE 2201, 110–116 (1994).
[Crossref]

1993 (1)

1992 (1)

1990 (1)

1983 (2)

1982 (1)

1979 (1)

R. A. Gonsalves and R. Chidlaw, “Wavefront sensing by phase retrieval,” Proc. SPIE 207, 32–39 (1979).
[Crossref]

Angel, J. R. P.

Aubailly, M.

M. Aubailly, M. A. Vorontsov, G. W. Carhart, and M. T. Valley, “Automated video enhancement from a stream of atmospherically distorted images: the lucky-region fusion approach,” Proc. SPIE 7463, 74630C (2009).
[Crossref]

Bates, R. H. T.

Carhart, G. W.

M. Aubailly, M. A. Vorontsov, G. W. Carhart, and M. T. Valley, “Automated video enhancement from a stream of atmospherically distorted images: the lucky-region fusion approach,” Proc. SPIE 7463, 74630C (2009).
[Crossref]

Carrano, C. J.

C. J. Carrano, “Progress in horizontal and slant-path imaging using speckle imagery,” Proc. SPIE 5001, 56–64 (2003).
[Crossref]

C. J. Carrano, “Anisoplanatic performance of horizontal-path speckle imaging,” Proc. SPIE 5162, 14–27 (2003).
[Crossref]

Carrara, D. A.

Charnotskii, M.

Chidlaw, R.

R. A. Gonsalves and R. Chidlaw, “Wavefront sensing by phase retrieval,” Proc. SPIE 207, 32–39 (1979).
[Crossref]

Fienup, J. R.

Fontanella, J. C.

Fraser, D.

A. J. Lambert, D. Fraser, M. R. Sayyah Jahromi, and B. R. Hunt, “Superresolution in image restoration of wide area images viewed through atmospheric turbulence,” Proc. SPIE 4792, 35–43 (2002).
[Crossref]

D. Fraser, G. Thorpe, and A. Lambert, “Atmospheric turbulence visualization with wide-area motion-blur restoration,” J. Opt. Soc. Am. A 16(7), 1751–1758 (1999).
[Crossref]

Fried, D. L.

Fright, W. R.

Gonsalves, R. A.

R. A. Gonsalves and R. Chidlaw, “Wavefront sensing by phase retrieval,” Proc. SPIE 207, 32–39 (1979).
[Crossref]

Hunt, B. R.

A. J. Lambert, D. Fraser, M. R. Sayyah Jahromi, and B. R. Hunt, “Superresolution in image restoration of wide area images viewed through atmospheric turbulence,” Proc. SPIE 4792, 35–43 (2002).
[Crossref]

B. R. Hunt, W. R. Fright, and R. H. T. Bates, “Analysis of the shift-and-add method for imaging through turbulent media,” J. Opt. Soc. Am. 73(4), 456–465 (1983).
[Crossref]

Keller, C. U.

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

Lambert, A.

Lambert, A. J.

A. J. Lambert, D. Fraser, M. R. Sayyah Jahromi, and B. R. Hunt, “Superresolution in image restoration of wide area images viewed through atmospheric turbulence,” Proc. SPIE 4792, 35–43 (2002).
[Crossref]

Link, D. J.

D. J. Link, “Comparison of the effects of near-field and distributed atmospheric turbulence on the performance of an adaptive optics system,” Proc. SPIE 2120, 87–94 (1994).
[Crossref]

Lloyd-Hart, M.

Löfdahl, M. G.

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

Mahajan, V. N.

McCarthy, D.

Milanfar, P.

X. Zhu and P. Milanfar, “Removing atmospheric turbulence via space-invariant deconvolution,” IEEE Trans. Pattern Anal. Mach. Intell. 35(1), 157–170 (2013).
[Crossref] [PubMed]

Miller, J. J.

R. G. Paxman, B. J. Thelen, and J. J. Miller, “Optimal simulation of volume turbulence with phase screens,” Proc. SPIE 3763-01, 2–10 (1999).
[Crossref]

Paxman, R. G.

B. J. Thelen, R. G. Paxman, D. A. Carrara, and J. H. Seldin, “Overcoming turbulence-induced space-variant blur by using phase-diverse speckle,” J. Opt. Soc. Am. A 26(1), 206–218 (2009).
[Crossref] [PubMed]

R. G. Paxman, B. J. Thelen, and J. J. Miller, “Optimal simulation of volume turbulence with phase screens,” Proc. SPIE 3763-01, 2–10 (1999).
[Crossref]

W. van Kampen and R. G. Paxman, “Multiframe blind deconvolution of infinite-extent objects,” Proc. SPIE 3433, 296–307 (1998).
[Crossref]

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

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9(7), 1072–1085 (1992).
[Crossref]

Primot, J.

Rousset, G.

Sandler, D. G.

Sayyah Jahromi, M. R.

A. J. Lambert, D. Fraser, M. R. Sayyah Jahromi, and B. R. Hunt, “Superresolution in image restoration of wide area images viewed through atmospheric turbulence,” Proc. SPIE 4792, 35–43 (2002).
[Crossref]

Scharmer, G. B.

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

Schulz, T. J.

Seldin, J. H.

B. J. Thelen, R. G. Paxman, D. A. Carrara, and J. H. Seldin, “Overcoming turbulence-induced space-variant blur by using phase-diverse speckle,” J. Opt. Soc. Am. A 26(1), 206–218 (2009).
[Crossref] [PubMed]

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

Stahl, S.

Thelen, B. J.

B. J. Thelen, R. G. Paxman, D. A. Carrara, and J. H. Seldin, “Overcoming turbulence-induced space-variant blur by using phase-diverse speckle,” J. Opt. Soc. Am. A 26(1), 206–218 (2009).
[Crossref] [PubMed]

R. G. Paxman, B. J. Thelen, and J. J. Miller, “Optimal simulation of volume turbulence with phase screens,” Proc. SPIE 3763-01, 2–10 (1999).
[Crossref]

Thorpe, G.

Tyler, G. A.

G. A. Tyler, “Adaptive optics compensation for propagation through deep turbulence: a study of some interesting approaches,” Opt. Eng. 52(2), 021011 (2012).
[Crossref]

Valley, M. T.

M. Aubailly, M. A. Vorontsov, G. W. Carhart, and M. T. Valley, “Automated video enhancement from a stream of atmospherically distorted images: the lucky-region fusion approach,” Proc. SPIE 7463, 74630C (2009).
[Crossref]

van Kampen, W.

W. van Kampen and R. G. Paxman, “Multiframe blind deconvolution of infinite-extent objects,” Proc. SPIE 3433, 296–307 (1998).
[Crossref]

Vorontsov, M. A.

M. Aubailly, M. A. Vorontsov, G. W. Carhart, and M. T. Valley, “Automated video enhancement from a stream of atmospherically distorted images: the lucky-region fusion approach,” Proc. SPIE 7463, 74630C (2009).
[Crossref]

Waliner, E. P.

E. P. Waliner, “Optimizing the locations of multiconjugate wavefront correctors,” Proc. SPIE 2201, 110–116 (1994).
[Crossref]

Zhu, X.

X. Zhu and P. Milanfar, “Removing atmospheric turbulence via space-invariant deconvolution,” IEEE Trans. Pattern Anal. Mach. Intell. 35(1), 157–170 (2013).
[Crossref] [PubMed]

Appl. Opt. (1)

Astrophys. J. (1)

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

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

X. Zhu and P. Milanfar, “Removing atmospheric turbulence via space-invariant deconvolution,” IEEE Trans. Pattern Anal. Mach. Intell. 35(1), 157–170 (2013).
[Crossref] [PubMed]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (6)

Opt. Eng. (1)

G. A. Tyler, “Adaptive optics compensation for propagation through deep turbulence: a study of some interesting approaches,” Opt. Eng. 52(2), 021011 (2012).
[Crossref]

Proc. SPIE (9)

D. J. Link, “Comparison of the effects of near-field and distributed atmospheric turbulence on the performance of an adaptive optics system,” Proc. SPIE 2120, 87–94 (1994).
[Crossref]

E. P. Waliner, “Optimizing the locations of multiconjugate wavefront correctors,” Proc. SPIE 2201, 110–116 (1994).
[Crossref]

R. G. Paxman, B. J. Thelen, and J. J. Miller, “Optimal simulation of volume turbulence with phase screens,” Proc. SPIE 3763-01, 2–10 (1999).
[Crossref]

A. J. Lambert, D. Fraser, M. R. Sayyah Jahromi, and B. R. Hunt, “Superresolution in image restoration of wide area images viewed through atmospheric turbulence,” Proc. SPIE 4792, 35–43 (2002).
[Crossref]

C. J. Carrano, “Progress in horizontal and slant-path imaging using speckle imagery,” Proc. SPIE 5001, 56–64 (2003).
[Crossref]

C. J. Carrano, “Anisoplanatic performance of horizontal-path speckle imaging,” Proc. SPIE 5162, 14–27 (2003).
[Crossref]

M. Aubailly, M. A. Vorontsov, G. W. Carhart, and M. T. Valley, “Automated video enhancement from a stream of atmospherically distorted images: the lucky-region fusion approach,” Proc. SPIE 7463, 74630C (2009).
[Crossref]

R. A. Gonsalves and R. Chidlaw, “Wavefront sensing by phase retrieval,” Proc. SPIE 207, 32–39 (1979).
[Crossref]

W. van Kampen and R. G. Paxman, “Multiframe blind deconvolution of infinite-extent objects,” Proc. SPIE 3433, 296–307 (1998).
[Crossref]

Other (5)

J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, 1975).

R. Tyson, Principles of Adaptive Optics (CRC, 2010).

R. R. Beland, “Propagation through atmospheric optical turbulence,” in Atmospheric Propagation of Radiation (Volume 2 of The Infrared & Electro-Optical systems Handbook), F.G. Smith, ed. (SPIE Optical Engineering, 1993).

M. C. Roggemann and B. M. Welsh, Imaging Through Turbulence, (CRC, 1996).

J. W. Godman, Statistical Optics (Wiley, 2015).

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Figures (11)

Fig. 1
Fig. 1 Light emanating from spatially separated object points encounters different volumes of turbulence yielding field-dependent blur in the image plane.
Fig. 2
Fig. 2 Reference-scenario simulated PSFs. The short-exposure PSF shown is for a single turbulence realization. The PSFs have been scaled to have the same peak value.
Fig. 3
Fig. 3 Short-exposure PSFs for four turbulence realizations in the reference imaging scenario (R1-R4, left) compared with the theoretical long-exposure PSF and the vacuum-diffraction-limit PSF. The image chips measure 25.4x25.4 μrad.
Fig. 4
Fig. 4 Average spatial correlation coefficient for PSFs as a function of angular separation, for the reference scenario. The mean and the 99% confidence limits are shown for two turbulence profiles (profile 1 is HV, profile 2 is 0.075 × HV). For both profiles, the Fried isoplanatic angle approximately corresponds to r ¯ Δ =0.86 .
Fig. 5
Fig. 5 Average spatial correlation coefficient for PSFs as a function of angular separation in the adaptive-optics case (both points are corrected using the phase aberration of the first point). The mean and the 99% confidence limits are shown for two turbulence profiles (profile 1 is HV, profile 2 is 0.075 × HV). The Fried isoplanatic angle approximately corresponds to r ¯ Δ =0.94 for profile 1 and r ¯ Δ =0.93 for profile 2.
Fig. 6
Fig. 6 Surface plots comparing short-exposure images of a point object (top row) with short-exposure images of a minimally extended object (middle row) for four independent volume-turbulence realizations (R1-R4). The long-exposure and diffraction-limited images of both a point and a minimally extended object are also shown (bottom row) for comparison. The image chips measure 25.4 × 25.4 μrad in extent.
Fig. 7
Fig. 7 Example image of minimally extended object showing the half-intensity contour (red pixels) surrounding the peak intensity. The arrow illustrates measurement of a single radius from the peak intensity pixel to a pixel located on the contour. This chip is sampled at 4 times the Nyquist rate.
Fig. 8
Fig. 8 Histograms showing the relative occurrence of main-lobe extent in 100 images of the minimally extended object, each derived using an independent volume-turbulence realization. Separate histograms are displayed for the area-weighted mean radius of each main lobe (red) and for all radii (blue) involving many radii per image over 100 images. The dashed lines indicate the associated cumulative probabilities. Radii associated with diffraction-limited and long-exposure images of the square object are indicated for comparison.
Fig. 9
Fig. 9 Example image of a minimally extended object (extended blur function) which exhibits minimal spatial structure along with fits to this image using Gaussian basis functions. The images are normalized so that the sum of squares of the pixel values is unity. The sum of the squared error (SSE) in the fits drops as the number of basis functions, K, increases.
Fig. 10
Fig. 10 Example image of a minimally extended object (extended blur function) which exhibits pronounced spatial structure along with fits to this image using Gaussian basis functions. The images are normalized so that the sum of the squares of the pixel values is unity. The sum of the squared error (SSE) in the fits drops as the number of basis functions, K, increases.
Fig. 11
Fig. 11 Distributed-phase-screen model that can be used to efficiently parameterize field-dependent blur.

Tables (2)

Tables Icon

Table 1 Parameters Characterizing Imaging Performance for Three Scenarios

Tables Icon

Table 2 Fitting Error (Sum of Squared Errors) for Images of a Minimally Extended Object as a Function of Number of Parameters

Equations (12)

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

  σ 2 = ( θ θ o ) 5/3 .
r o [ 0.422 ( 2π λ ) 2 0 L dz C n 2 ( z )  ( Lz L ) 5/3 ] 3/5
θ o [ 2.91 ( 2π λ ) 2 0 L  dz C n 2 ( z )  z 5/3 ] 3/5
σ χ 2 0.56 ( 2π λ ) 7/6 0 L dz C n 2 ( z ) ( Lz L ) 5/6 z 5/6  ,
ρ=λ/D .
IRR   θ o /ρ.
C n 2 ( h ) = 8.148x 10 26 * v 2 * ( h 1000 ) 10 exp( h 1000 ) +2.7x 10 16 exp( h 1500 )+ C n 2 o exp( h 100 ),
v = 21,
C n 2 o =1x 10 13  ,
r i,j x,y [ s i ( x,y ) s ¯ i ][ s j ( x x ij ,y y ij ) s ¯ j ] { x,y [ s i ( x,y ) s ¯ i ] 2 } 1 2 { x [ s j ( x,y ) s ¯ j ] 2 } 1 2  ,
g ^ (x,y)= k=1 K A k exp{ [ a k ( x x 0k ) 2 2 b k ( x x 0k )( y y 0k )+ c k ( y y 0k ) 2 ] } .
a k = cos 2 θ 2 σ xk 2 + sin 2 θ 2 σ yk 2 b k = sin( 2θ ) 4 σ xk 2 + sin( 2θ ) 4 σ yk 2 c k = sin 2 θ 2 σ xk 2 + cos 2 θ 2 σ yk 2

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