Abstract

A number of techniques used for high-resolution speckle imaging in astronomy generate average spatial-correlation spectra of objects. Here a straightforward method for iteratively deconvolving these noisy spectra to obtain high-resolution images is described.

© 1989 Optical Society of America

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References

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  1. J. C. Dainty, J. R. Fienup, in Image Recovery, H. Stark, ed. (Academic, New York, 1987), pp. 231–275.
  2. K. T. Knox, B. J. Thompson, Astron. J. 193, L45 (1974).
  3. A. W. Lohmann, G. P. Weigelt, B. Wirnitzer, Appl. Opt. 22, 4028 (1983).
    [CrossRef] [PubMed]
  4. A. Labeyrie, Astron. Astrophys. 6, 85 (1970).
  5. G. R. Ayers, J. C. Dainty, Opt. Lett. 13, 547 (1988).
    [CrossRef] [PubMed]
  6. J. R. Fienup, Opt. Lett. 3, 27 (1978).
    [CrossRef] [PubMed]
  7. B. L. Davey, R. G. Lane, R. H. T. Bates, Opt. Commun. 69, 353 (1989).
    [CrossRef]
  8. G. R. Ayers, M. J. Northcott, J. C. Dainty, J. Opt. Soc. Am. A 5, 963 (1988).
    [CrossRef]
  9. G. R. Ayers, Ph.D. dissertation (Imperial College, University of London, London, 1988).
  10. J. R. Taylor, An Introduction to Error Analysis (University Science Books, Mill Valley, Calif., 1982).
  11. B. J. Brames, J. C. Dainty, J. Opt. Soc. Am. 71, 1542 (1981).
    [CrossRef]

1989

B. L. Davey, R. G. Lane, R. H. T. Bates, Opt. Commun. 69, 353 (1989).
[CrossRef]

1988

1983

1981

1978

1974

K. T. Knox, B. J. Thompson, Astron. J. 193, L45 (1974).

1970

A. Labeyrie, Astron. Astrophys. 6, 85 (1970).

Ayers, G. R.

Bates, R. H. T.

B. L. Davey, R. G. Lane, R. H. T. Bates, Opt. Commun. 69, 353 (1989).
[CrossRef]

Brames, B. J.

Dainty, J. C.

Davey, B. L.

B. L. Davey, R. G. Lane, R. H. T. Bates, Opt. Commun. 69, 353 (1989).
[CrossRef]

Fienup, J. R.

J. R. Fienup, Opt. Lett. 3, 27 (1978).
[CrossRef] [PubMed]

J. C. Dainty, J. R. Fienup, in Image Recovery, H. Stark, ed. (Academic, New York, 1987), pp. 231–275.

Knox, K. T.

K. T. Knox, B. J. Thompson, Astron. J. 193, L45 (1974).

Labeyrie, A.

A. Labeyrie, Astron. Astrophys. 6, 85 (1970).

Lane, R. G.

B. L. Davey, R. G. Lane, R. H. T. Bates, Opt. Commun. 69, 353 (1989).
[CrossRef]

Lohmann, A. W.

Northcott, M. J.

Taylor, J. R.

J. R. Taylor, An Introduction to Error Analysis (University Science Books, Mill Valley, Calif., 1982).

Thompson, B. J.

K. T. Knox, B. J. Thompson, Astron. J. 193, L45 (1974).

Weigelt, G. P.

Wirnitzer, B.

Appl. Opt.

Astron. Astrophys.

A. Labeyrie, Astron. Astrophys. 6, 85 (1970).

Astron. J.

K. T. Knox, B. J. Thompson, Astron. J. 193, L45 (1974).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

B. L. Davey, R. G. Lane, R. H. T. Bates, Opt. Commun. 69, 353 (1989).
[CrossRef]

Opt. Lett.

Other

G. R. Ayers, Ph.D. dissertation (Imperial College, University of London, London, 1988).

J. R. Taylor, An Introduction to Error Analysis (University Science Books, Mill Valley, Calif., 1982).

J. C. Dainty, J. R. Fienup, in Image Recovery, H. Stark, ed. (Academic, New York, 1987), pp. 231–275.

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Figures (4)

Fig. 1
Fig. 1

(a) Diffraction-limited image of the object used in the computer simulations; (b), (c), respectively, the object reconstructions obtained using the conventional KT reconstruction process and the described deconvolution process.

Fig. 2
Fig. 2

Reconstructed Fourier moduli obtained from the average power spectrum (filled circles) and from the deconvolution process (open circles). The solid curve corresponds to the correct object Fourier modulus, and the error bars plotted correspond to a single standard deviation.

Fig. 3
Fig. 3

Reconstructed Fourier phase obtained from the conventional KT reconstruction (filled circles) procedure and from the deconvolution process (open circles). The solid curve corresponds to the correct object Fourier phase, and the error bars plotted correspond to a single standard deviation.

Fig. 4
Fig. 4

Plot on a logarithmic scale of the error measure estimated at each iteration. The measure corresponds to the absolute value of the total amount of negative energy present in the object estimate at the end of step 8 of each iteration.

Equations (5)

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O KT ( u 1 , Δ u ) = O ( u 1 ) O * ( u 1 + Δ u ) ,
O TC ( u 1 , u 2 ) = O ( u 1 ) O * ( u 1 + u 2 ) O ( u 2 ) .
| O KT ( u 1 , Δ u ) O i KT ( u 1 , Δ u ) | .
χ 2 = u 1 Δ u | O KT ( u 1 , Δ u ) O i KT ( u 1 , Δ u ) σ KT ( u 1 , Δ u ) | 2 ,
O i ( u 1 ) = O KT ( u 1 , Δ u ) O i * ( u 1 + Δ u ) , | u 1 + Δ u | < | u 1 | .

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