Abstract

A technique has recently been proposed for processing astronomical photographs to remove the effects of turbulence. The method involves averaging over many short-exposure photographs of an object to reconstruct a diffraction-limited image of the object. A two-dimensional computer simulation of the reconstruction technique is presented. The results indicate that diffraction-limited imaging with a 100 in. telescope is possible even with 2 arc sec seeing conditions.

© 1976 Optical Society of America

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References

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  1. D. Y. Gezari, A. Labeyrie, and R. V. Stachnik, Astrophys. J. (Letters) 173, L1 (1972).
    [CrossRef]
  2. K. T. Knox and B. J. Thompson, Astrophys. J. (Letters) 193, L45 (1974).
    [CrossRef]
  3. D. P. Karo and A. M. Schneiderman, Technical Digest, in Imaging in Astronomy, OSA Topical Meeting (1975), paper ThC4.
  4. P. Nisenson, in Proceedings of the SPIE/SPSE Symposium, Imaging through the Atmosphere, 1976, Vol. 25.
  5. D. Korff, G. Dryden, and M. G. Miller, Opt. Commun. 5, 187 (1972).
    [CrossRef]
  6. D. Korff, J. Opt. Soc. Am. 63, 971 (1973).
    [CrossRef]
  7. J. C. Dainty, Opt. Commun. 7, 129 (1973).
    [CrossRef]
  8. A. M. Schneiderman, P. F. Kellen, and M. G. Miller, J. Opt. Soc. Am. 65, 1287 (1975).
    [CrossRef]
  9. K. T. Knox, in Proceeding of the International Optical Computing Conference, 1975, IEEE Catalog #75 CH0941-5C, 94.
  10. K. T. Knox, Ph. D. thesis, (Institute of Optics, University of Rochester, Rochester, New York, 1975).
  11. Sky and Telescope, p. 11, July1971.

1975 (2)

D. P. Karo and A. M. Schneiderman, Technical Digest, in Imaging in Astronomy, OSA Topical Meeting (1975), paper ThC4.

A. M. Schneiderman, P. F. Kellen, and M. G. Miller, J. Opt. Soc. Am. 65, 1287 (1975).
[CrossRef]

1974 (1)

K. T. Knox and B. J. Thompson, Astrophys. J. (Letters) 193, L45 (1974).
[CrossRef]

1973 (2)

D. Korff, J. Opt. Soc. Am. 63, 971 (1973).
[CrossRef]

J. C. Dainty, Opt. Commun. 7, 129 (1973).
[CrossRef]

1972 (2)

D. Y. Gezari, A. Labeyrie, and R. V. Stachnik, Astrophys. J. (Letters) 173, L1 (1972).
[CrossRef]

D. Korff, G. Dryden, and M. G. Miller, Opt. Commun. 5, 187 (1972).
[CrossRef]

1971 (1)

Sky and Telescope, p. 11, July1971.

Dainty, J. C.

J. C. Dainty, Opt. Commun. 7, 129 (1973).
[CrossRef]

Dryden, G.

D. Korff, G. Dryden, and M. G. Miller, Opt. Commun. 5, 187 (1972).
[CrossRef]

Gezari, D. Y.

D. Y. Gezari, A. Labeyrie, and R. V. Stachnik, Astrophys. J. (Letters) 173, L1 (1972).
[CrossRef]

Karo, D. P.

D. P. Karo and A. M. Schneiderman, Technical Digest, in Imaging in Astronomy, OSA Topical Meeting (1975), paper ThC4.

Kellen, P. F.

Knox, K. T.

K. T. Knox and B. J. Thompson, Astrophys. J. (Letters) 193, L45 (1974).
[CrossRef]

K. T. Knox, in Proceeding of the International Optical Computing Conference, 1975, IEEE Catalog #75 CH0941-5C, 94.

K. T. Knox, Ph. D. thesis, (Institute of Optics, University of Rochester, Rochester, New York, 1975).

Korff, D.

D. Korff, J. Opt. Soc. Am. 63, 971 (1973).
[CrossRef]

D. Korff, G. Dryden, and M. G. Miller, Opt. Commun. 5, 187 (1972).
[CrossRef]

Labeyrie, A.

D. Y. Gezari, A. Labeyrie, and R. V. Stachnik, Astrophys. J. (Letters) 173, L1 (1972).
[CrossRef]

Miller, M. G.

Nisenson, P.

P. Nisenson, in Proceedings of the SPIE/SPSE Symposium, Imaging through the Atmosphere, 1976, Vol. 25.

Schneiderman, A. M.

D. P. Karo and A. M. Schneiderman, Technical Digest, in Imaging in Astronomy, OSA Topical Meeting (1975), paper ThC4.

A. M. Schneiderman, P. F. Kellen, and M. G. Miller, J. Opt. Soc. Am. 65, 1287 (1975).
[CrossRef]

Stachnik, R. V.

D. Y. Gezari, A. Labeyrie, and R. V. Stachnik, Astrophys. J. (Letters) 173, L1 (1972).
[CrossRef]

Thompson, B. J.

K. T. Knox and B. J. Thompson, Astrophys. J. (Letters) 193, L45 (1974).
[CrossRef]

Astrophys. J. (Letters) (2)

D. Y. Gezari, A. Labeyrie, and R. V. Stachnik, Astrophys. J. (Letters) 173, L1 (1972).
[CrossRef]

K. T. Knox and B. J. Thompson, Astrophys. J. (Letters) 193, L45 (1974).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Commun. (2)

D. Korff, G. Dryden, and M. G. Miller, Opt. Commun. 5, 187 (1972).
[CrossRef]

J. C. Dainty, Opt. Commun. 7, 129 (1973).
[CrossRef]

Sky and Telescope (1)

Sky and Telescope, p. 11, July1971.

Technical Digest, in Imaging in Astronomy, OSA Topical Meeting (1)

D. P. Karo and A. M. Schneiderman, Technical Digest, in Imaging in Astronomy, OSA Topical Meeting (1975), paper ThC4.

Other (3)

P. Nisenson, in Proceedings of the SPIE/SPSE Symposium, Imaging through the Atmosphere, 1976, Vol. 25.

K. T. Knox, in Proceeding of the International Optical Computing Conference, 1975, IEEE Catalog #75 CH0941-5C, 94.

K. T. Knox, Ph. D. thesis, (Institute of Optics, University of Rochester, Rochester, New York, 1975).

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Figures (5)

FIG. 1
FIG. 1

The two independent paths of integration used to reconstruct the phase.

FIG. 2
FIG. 2

The function used to represent the object intensity distribution.

FIG. 3
FIG. 3

One of 80 point spread functions that were generated using a Gaussian random phase model for the atmospheric distortion.

FIG. 4
FIG. 4

One of 40 simulated short-exposure photographs of the object. This image is the convolution of the images in Figs. 2 and 3.

FIG. 5
FIG. 5

The four reconstructions that resulted from processing (a) 10 images, (b) 20 images, (c) 30 images, and (d) 40 images. The same number of additional point spread functions were used in each case for properly scaling the modulus.

Equations (10)

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

Ĩ ( u ) = Ĩ 0 * ( u ) S ˜ ( u ) ,
Ĩ ( u ) 2 = Ĩ 0 ( u ) 2 S ˜ ( u ) 2 .
Ĩ 0 ( u ) 2 = Ĩ ( u ) 2 / S ˜ ( u ) 2 .
Ĩ ( u ) Ĩ * ( u + Δ u ) = Ĩ 0 * ( u ) Ĩ 0 ( u + Δ u ) S ˜ ( u ) S ˜ * ( u + Δ u ) .
phase [ Ĩ ( u ) Ĩ * ( u + Δ u ) ] = θ ( u + Δ u ) - θ ( u ) + phase [ S ˜ ( u ) S ˜ * ( u + Δ u ) ] .
θ ( u + Δ u ) - θ ( u ) d θ ( u ) d u Δ u .
θ ( u ) = 0 u d θ ( u ) d u d u .
θ ( u + Δ u , v ) - θ ( u , v ) θ ( u , v ) u Δ u ,
θ ( u , v + Δ v ) - θ ( u , v ) θ ( u , v ) v Δ v .
θ ( u , v ) = C θ · d s .