Abstract

Space-variant blur is encountered when objects extend beyond the isoplanatic patch associated with the intervening atmospheric turbulence. The method of phase diversity, used to estimate jointly the object and the aberrations, is generalized to accommodate turbulence-induced space-variant blur. This generalization utilizes a parametric model for the blur function that is constructed with multiple phase screens. Simulation results are presented that demonstrate the recovery of near-diffraction-limited imagery from phase-diversity imagery that has been degraded with rather severe anisoplanatism.

© 1994 Optical Society of America

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References

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  1. R. G. Paxman, in Proceedings on Wavefront Supported Post-Facto Image Correction, Anderson, ed. (Nordic Optical Telescope Workshop, Risø, Roskilde, Denmark, 1992), p. 1.
  2. R. A. Gonsalves, R. Chidlaw, Proc. Soc. Photo-Opt. Instrum. Eng. 207, 32 (1979).
  3. R. G. Paxman, J. R. Fienup, J. Opt. Soc. Am. A 5, 914 (1988).
    [CrossRef]
  4. R. G. Paxman, T. J. Schulz, J. R. Fienup, J. Opt. Soc. Am. A 9, 1072 (1992).
    [CrossRef]
  5. R. A. Gonsalves, Opt. Lett. 19, 493 (1994).
    [CrossRef] [PubMed]
  6. R. G. Paxman, J. H. Seldin, Proc. Soc. Photo-Opt. Instrum. Eng. 2029, 287 (1993).
  7. F. Roddier, M. J. Northcott, J. E. Graves, D. L. McKenna, J. Opt. Soc. Am. A 10, 957 (1993).
    [CrossRef]
  8. D. L. Fried, J. Opt. Soc. Am. 72, 52 (1982).
    [CrossRef]

1994 (1)

1993 (2)

R. G. Paxman, J. H. Seldin, Proc. Soc. Photo-Opt. Instrum. Eng. 2029, 287 (1993).

F. Roddier, M. J. Northcott, J. E. Graves, D. L. McKenna, J. Opt. Soc. Am. A 10, 957 (1993).
[CrossRef]

1992 (1)

1988 (1)

1982 (1)

1979 (1)

R. A. Gonsalves, R. Chidlaw, Proc. Soc. Photo-Opt. Instrum. Eng. 207, 32 (1979).

Chidlaw, R.

R. A. Gonsalves, R. Chidlaw, Proc. Soc. Photo-Opt. Instrum. Eng. 207, 32 (1979).

Fienup, J. R.

Fried, D. L.

Gonsalves, R. A.

R. A. Gonsalves, Opt. Lett. 19, 493 (1994).
[CrossRef] [PubMed]

R. A. Gonsalves, R. Chidlaw, Proc. Soc. Photo-Opt. Instrum. Eng. 207, 32 (1979).

Graves, J. E.

McKenna, D. L.

Northcott, M. J.

Paxman, R. G.

R. G. Paxman, J. H. Seldin, Proc. Soc. Photo-Opt. Instrum. Eng. 2029, 287 (1993).

R. G. Paxman, T. J. Schulz, J. R. Fienup, J. Opt. Soc. Am. A 9, 1072 (1992).
[CrossRef]

R. G. Paxman, J. R. Fienup, J. Opt. Soc. Am. A 5, 914 (1988).
[CrossRef]

R. G. Paxman, in Proceedings on Wavefront Supported Post-Facto Image Correction, Anderson, ed. (Nordic Optical Telescope Workshop, Risø, Roskilde, Denmark, 1992), p. 1.

Roddier, F.

Schulz, T. J.

Seldin, J. H.

R. G. Paxman, J. H. Seldin, Proc. Soc. Photo-Opt. Instrum. Eng. 2029, 287 (1993).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

R. G. Paxman, J. H. Seldin, Proc. Soc. Photo-Opt. Instrum. Eng. 2029, 287 (1993).

R. A. Gonsalves, R. Chidlaw, Proc. Soc. Photo-Opt. Instrum. Eng. 207, 32 (1979).

Other (1)

R. G. Paxman, in Proceedings on Wavefront Supported Post-Facto Image Correction, Anderson, ed. (Nordic Optical Telescope Workshop, Risø, Roskilde, Denmark, 1992), p. 1.

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Figures (4)

Fig. 1
Fig. 1

Optical layout of a phase-diversity system.

Fig. 2
Fig. 2

Two-phase-screen model.

Fig. 3
Fig. 3

Images of regular arrays of point objects: (a) diffraction-limited image, (b) array viewed through two phase screens.

Fig. 4
Fig. 4

Phase-diversity correction of the space-variant blur: (a) noisy conventional image of a jet with space-variant blur, (b) noisy diversity image with a 0.5-wave defocus, (c) phase-diversity estimate of the diffraction-limited image, (d) noiseless diffraction-limited image of the jet, (e) and (f) upsampled versions of (c) and (d), respectively.

Equations (5)

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g ( x ) = x f ( x ) s ( x , x ) ,
ϕ ( u , x ) = l = 1 L ϕ l ( u + x h l f 0 ) ,
s k ( x , x ) = | F { H ( u ) exp { i [ ϕ ( u , x ) + θ k ( u ) ] } } | 2 ,
ϕ l ( u ) = m α l m ψ l m ( u ) ,
L ( f , { α l m } ) = k = 1 K x [ d k ( x ) ln g k ( x ) - g k ( x ) ] ,

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