Abstract

We discuss a recently developed technique to recover nearly diffraction-limited images of supergiant stars such as α Orionis (Betelgeuse) from speckle interferometry data. This method relies on the digital identification and coaddition of the brightest individual speckles within a large number of short-exposure speckle photographs. The resulting average speckle may be thought of as the convolution of a point source speckle profile with the actual object intensity pattern. By making use of this point we have derived angular diameters and limb darkening coefficients in addition to finding evidence of possible surface structure on the star. The limitations of this technique have been determined empirically and they are discussed in this paper.

© 1976 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Labeyrie, “Attainment of Diffraction Limited Resolution in Large Telescopes by Fourier Analyzing Speckle Patterns in Star Images,” Astron. Astrophys. 6, 85–87 (1970).
  2. D. Y. Gezari, A. Labeyrie, and R. V. Stachnik, “Speckle Interferometry: Diffraction-Limited Measurements of Nine Stars with the 200 inch Telescope,” Astrophys. Lett. 173, L1–L5 (1972).
    [Crossref]
  3. D. Korff, G. Dryden, and M. G. Miller, “Information Retrieval from Atmospheric Induced Speckle Patterns,” Opt. Commun. 5, 187–192 (1972).
    [Crossref]
  4. D. Korff, “Analysis of a Method for Obtaining Near-diffraction Limited Information in the Presence of Atmospheric Turbulance,” J. Opt. Soc. Am. 63, 971–980 (1973).
    [Crossref]
  5. J. C. Dainty, “Diffraction Limited Imaging of Stellar Objects Using Telescopes of Low Optical Quality,” Opt. Commun. 7, 129–134 (1973).
    [Crossref]
  6. F. Roddier, “Speckle Interferometry Through Small Multiple Apertures: Michelson Stellar Interferometry and Aperture Synthesis in Optics,” Opt. Commun. 10, 103–105 (1974).
    [Crossref]
  7. C. Aime, “Measurement of averaged squared modulus of atmospheric-lens modulation transfer function,” J. Opt. Soc. Am. 64, 1129–1132 (1974).
    [Crossref]
  8. J. C. Dainty, “The Transfer Function, Signal to Noise Ratio, and Limiting Magnitude in Stellar Speckle Interferometry,” Mon. Not. R. Astron. Soc. 169, 631–642 (1974).
  9. R. H. T. Bates and P. T. Gough, “Finding Picture Edges Through Collinearity of Feature Points,” IEEE Trans. Comput. G-25, 449–456 (1975).
    [Crossref]
  10. K. T. Knox and B. J. Thompson, “Recovery of Images from Atmospherically Degraded Short-exposure Photographs,” Astrophys. Lett. 193, L45–L48 (1974).
    [Crossref]
  11. C. R. Lynds, S. P. Worden, and J. W. Harvey, “Digital Image Reconstruction Applied to Alpha Orionis,” Astrophys. J. 207, 174–180 (1976).
    [Crossref]
  12. C. Y. C. Liu and A. W. Lohman, “High Resolution Image Formation Through the Turbulent Atmosphere,” Opt. Commun. 8, 372–377 (1973).
    [Crossref]
  13. A. Title, T. Pope, and S. Schoolman, “The Temporal and Spectral Extent of the Isoplanatic Patch,” Bull. Am. Astr. Soc. 7, 462 (1975).
  14. J. B. Breckinridge, “Measurement of the Amplitude of Phase Excursions in the Earth’s Atmosphere,” J. Opt. Soc. Am. 66, 143–144 (1976).
    [Crossref]

1976 (2)

C. R. Lynds, S. P. Worden, and J. W. Harvey, “Digital Image Reconstruction Applied to Alpha Orionis,” Astrophys. J. 207, 174–180 (1976).
[Crossref]

J. B. Breckinridge, “Measurement of the Amplitude of Phase Excursions in the Earth’s Atmosphere,” J. Opt. Soc. Am. 66, 143–144 (1976).
[Crossref]

1975 (2)

A. Title, T. Pope, and S. Schoolman, “The Temporal and Spectral Extent of the Isoplanatic Patch,” Bull. Am. Astr. Soc. 7, 462 (1975).

R. H. T. Bates and P. T. Gough, “Finding Picture Edges Through Collinearity of Feature Points,” IEEE Trans. Comput. G-25, 449–456 (1975).
[Crossref]

1974 (4)

K. T. Knox and B. J. Thompson, “Recovery of Images from Atmospherically Degraded Short-exposure Photographs,” Astrophys. Lett. 193, L45–L48 (1974).
[Crossref]

F. Roddier, “Speckle Interferometry Through Small Multiple Apertures: Michelson Stellar Interferometry and Aperture Synthesis in Optics,” Opt. Commun. 10, 103–105 (1974).
[Crossref]

C. Aime, “Measurement of averaged squared modulus of atmospheric-lens modulation transfer function,” J. Opt. Soc. Am. 64, 1129–1132 (1974).
[Crossref]

J. C. Dainty, “The Transfer Function, Signal to Noise Ratio, and Limiting Magnitude in Stellar Speckle Interferometry,” Mon. Not. R. Astron. Soc. 169, 631–642 (1974).

1973 (3)

D. Korff, “Analysis of a Method for Obtaining Near-diffraction Limited Information in the Presence of Atmospheric Turbulance,” J. Opt. Soc. Am. 63, 971–980 (1973).
[Crossref]

J. C. Dainty, “Diffraction Limited Imaging of Stellar Objects Using Telescopes of Low Optical Quality,” Opt. Commun. 7, 129–134 (1973).
[Crossref]

C. Y. C. Liu and A. W. Lohman, “High Resolution Image Formation Through the Turbulent Atmosphere,” Opt. Commun. 8, 372–377 (1973).
[Crossref]

1972 (2)

D. Y. Gezari, A. Labeyrie, and R. V. Stachnik, “Speckle Interferometry: Diffraction-Limited Measurements of Nine Stars with the 200 inch Telescope,” Astrophys. Lett. 173, L1–L5 (1972).
[Crossref]

D. Korff, G. Dryden, and M. G. Miller, “Information Retrieval from Atmospheric Induced Speckle Patterns,” Opt. Commun. 5, 187–192 (1972).
[Crossref]

1970 (1)

A. Labeyrie, “Attainment of Diffraction Limited Resolution in Large Telescopes by Fourier Analyzing Speckle Patterns in Star Images,” Astron. Astrophys. 6, 85–87 (1970).

Aime, C.

Bates, R. H. T.

R. H. T. Bates and P. T. Gough, “Finding Picture Edges Through Collinearity of Feature Points,” IEEE Trans. Comput. G-25, 449–456 (1975).
[Crossref]

Breckinridge, J. B.

Dainty, J. C.

J. C. Dainty, “The Transfer Function, Signal to Noise Ratio, and Limiting Magnitude in Stellar Speckle Interferometry,” Mon. Not. R. Astron. Soc. 169, 631–642 (1974).

J. C. Dainty, “Diffraction Limited Imaging of Stellar Objects Using Telescopes of Low Optical Quality,” Opt. Commun. 7, 129–134 (1973).
[Crossref]

Dryden, G.

D. Korff, G. Dryden, and M. G. Miller, “Information Retrieval from Atmospheric Induced Speckle Patterns,” Opt. Commun. 5, 187–192 (1972).
[Crossref]

Gezari, D. Y.

D. Y. Gezari, A. Labeyrie, and R. V. Stachnik, “Speckle Interferometry: Diffraction-Limited Measurements of Nine Stars with the 200 inch Telescope,” Astrophys. Lett. 173, L1–L5 (1972).
[Crossref]

Gough, P. T.

R. H. T. Bates and P. T. Gough, “Finding Picture Edges Through Collinearity of Feature Points,” IEEE Trans. Comput. G-25, 449–456 (1975).
[Crossref]

Harvey, J. W.

C. R. Lynds, S. P. Worden, and J. W. Harvey, “Digital Image Reconstruction Applied to Alpha Orionis,” Astrophys. J. 207, 174–180 (1976).
[Crossref]

Knox, K. T.

K. T. Knox and B. J. Thompson, “Recovery of Images from Atmospherically Degraded Short-exposure Photographs,” Astrophys. Lett. 193, L45–L48 (1974).
[Crossref]

Korff, D.

D. Korff, “Analysis of a Method for Obtaining Near-diffraction Limited Information in the Presence of Atmospheric Turbulance,” J. Opt. Soc. Am. 63, 971–980 (1973).
[Crossref]

D. Korff, G. Dryden, and M. G. Miller, “Information Retrieval from Atmospheric Induced Speckle Patterns,” Opt. Commun. 5, 187–192 (1972).
[Crossref]

Labeyrie, A.

D. Y. Gezari, A. Labeyrie, and R. V. Stachnik, “Speckle Interferometry: Diffraction-Limited Measurements of Nine Stars with the 200 inch Telescope,” Astrophys. Lett. 173, L1–L5 (1972).
[Crossref]

A. Labeyrie, “Attainment of Diffraction Limited Resolution in Large Telescopes by Fourier Analyzing Speckle Patterns in Star Images,” Astron. Astrophys. 6, 85–87 (1970).

Liu, C. Y. C.

C. Y. C. Liu and A. W. Lohman, “High Resolution Image Formation Through the Turbulent Atmosphere,” Opt. Commun. 8, 372–377 (1973).
[Crossref]

Lohman, A. W.

C. Y. C. Liu and A. W. Lohman, “High Resolution Image Formation Through the Turbulent Atmosphere,” Opt. Commun. 8, 372–377 (1973).
[Crossref]

Lynds, C. R.

C. R. Lynds, S. P. Worden, and J. W. Harvey, “Digital Image Reconstruction Applied to Alpha Orionis,” Astrophys. J. 207, 174–180 (1976).
[Crossref]

Miller, M. G.

D. Korff, G. Dryden, and M. G. Miller, “Information Retrieval from Atmospheric Induced Speckle Patterns,” Opt. Commun. 5, 187–192 (1972).
[Crossref]

Pope, T.

A. Title, T. Pope, and S. Schoolman, “The Temporal and Spectral Extent of the Isoplanatic Patch,” Bull. Am. Astr. Soc. 7, 462 (1975).

Roddier, F.

F. Roddier, “Speckle Interferometry Through Small Multiple Apertures: Michelson Stellar Interferometry and Aperture Synthesis in Optics,” Opt. Commun. 10, 103–105 (1974).
[Crossref]

Schoolman, S.

A. Title, T. Pope, and S. Schoolman, “The Temporal and Spectral Extent of the Isoplanatic Patch,” Bull. Am. Astr. Soc. 7, 462 (1975).

Stachnik, R. V.

D. Y. Gezari, A. Labeyrie, and R. V. Stachnik, “Speckle Interferometry: Diffraction-Limited Measurements of Nine Stars with the 200 inch Telescope,” Astrophys. Lett. 173, L1–L5 (1972).
[Crossref]

Thompson, B. J.

K. T. Knox and B. J. Thompson, “Recovery of Images from Atmospherically Degraded Short-exposure Photographs,” Astrophys. Lett. 193, L45–L48 (1974).
[Crossref]

Title, A.

A. Title, T. Pope, and S. Schoolman, “The Temporal and Spectral Extent of the Isoplanatic Patch,” Bull. Am. Astr. Soc. 7, 462 (1975).

Worden, S. P.

C. R. Lynds, S. P. Worden, and J. W. Harvey, “Digital Image Reconstruction Applied to Alpha Orionis,” Astrophys. J. 207, 174–180 (1976).
[Crossref]

Astron. Astrophys. (1)

A. Labeyrie, “Attainment of Diffraction Limited Resolution in Large Telescopes by Fourier Analyzing Speckle Patterns in Star Images,” Astron. Astrophys. 6, 85–87 (1970).

Astrophys. J. (1)

C. R. Lynds, S. P. Worden, and J. W. Harvey, “Digital Image Reconstruction Applied to Alpha Orionis,” Astrophys. J. 207, 174–180 (1976).
[Crossref]

Astrophys. Lett. (2)

D. Y. Gezari, A. Labeyrie, and R. V. Stachnik, “Speckle Interferometry: Diffraction-Limited Measurements of Nine Stars with the 200 inch Telescope,” Astrophys. Lett. 173, L1–L5 (1972).
[Crossref]

K. T. Knox and B. J. Thompson, “Recovery of Images from Atmospherically Degraded Short-exposure Photographs,” Astrophys. Lett. 193, L45–L48 (1974).
[Crossref]

Bull. Am. Astr. Soc. (1)

A. Title, T. Pope, and S. Schoolman, “The Temporal and Spectral Extent of the Isoplanatic Patch,” Bull. Am. Astr. Soc. 7, 462 (1975).

IEEE Trans. Comput. (1)

R. H. T. Bates and P. T. Gough, “Finding Picture Edges Through Collinearity of Feature Points,” IEEE Trans. Comput. G-25, 449–456 (1975).
[Crossref]

J. Opt. Soc. Am. (3)

Mon. Not. R. Astron. Soc. (1)

J. C. Dainty, “The Transfer Function, Signal to Noise Ratio, and Limiting Magnitude in Stellar Speckle Interferometry,” Mon. Not. R. Astron. Soc. 169, 631–642 (1974).

Opt. Commun. (4)

D. Korff, G. Dryden, and M. G. Miller, “Information Retrieval from Atmospheric Induced Speckle Patterns,” Opt. Commun. 5, 187–192 (1972).
[Crossref]

J. C. Dainty, “Diffraction Limited Imaging of Stellar Objects Using Telescopes of Low Optical Quality,” Opt. Commun. 7, 129–134 (1973).
[Crossref]

F. Roddier, “Speckle Interferometry Through Small Multiple Apertures: Michelson Stellar Interferometry and Aperture Synthesis in Optics,” Opt. Commun. 10, 103–105 (1974).
[Crossref]

C. Y. C. Liu and A. W. Lohman, “High Resolution Image Formation Through the Turbulent Atmosphere,” Opt. Commun. 8, 372–377 (1973).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

FIG. 1
FIG. 1

Speckle exposures taken on the Kitt Peak National Observatory 4 m telescope. Each photograph covers a 3 arc sec square area. (a) Alpha Orionis (Betelgeuse), a resolved supergiant star with an angular diameter of ~0.05 arc sec; (b) Gamma Orionis (Bellatrix), a point source star; (c) Alpha Auriga (Capella), a binary star with an angular separation of ~0.06 arc sec.

FIG. 2
FIG. 2

Reconstructed mean speckles for Alpha Orionis and Gamma Orionis along with one-dimensional radial profiles of these results.

Tables (1)

Tables Icon

TABLE I Derived angular diameters (uniform disk) for Alpha Orionis obtained using differing reduction parameters.

Equations (4)

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

o ( x , y ) = p ( x , y ) * I ( x , y ) .
0 ( x , y ) = o ( x , y ) = p ( x , y ) * I ( x , y ) ;
0 ( x , y ) = [ δ ( x , y ) * p ( x , y ) ] * I ( x , y ) .
I ( r ) = I c [ 1 - x ( 1 - cos θ ) ] ,