Abstract

Speckle masking is a speckle method that is capable of reconstructing true diffraction-limited images from astronomical speckle interferograms. Image degradation caused by the atmosphere and by telescope aberrations can be overcome completely. Speckle masking is a solution of the phase problem in speckle interferometry. We propose a new, modified version of speckle masking that is based on cross triple correlation processing (or cross bispectrum processing) instead of autotriple correlation processing. The advantage of cross triple correlation processing is the fact that undesired photon bias terms in the average bispectrum of the speckle interferograms are overcome completely. We show computer simulations (astronomical magnitude of ~16m) that illustrate the feasibility of the method.

© 1987 Optical Society of America

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References

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  1. J. C. Dainty, “Stellar Speckle Interferometry,” in Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, Berlin, 1975).
    [CrossRef]
  2. G. P. Weigelt, “Modified Speckle Interferometry: Speckle Masking,” Opt. Commun. 21, 55 (1977).
    [CrossRef]
  3. G. P. Weigelt, B. Wirnitzer, “Image Reconstruction by the Speckle-Masking Method,” Opt. Lett. 8, 389 (1983).
    [CrossRef] [PubMed]
  4. A. W. Lohmann, G. P. Weigelt, B. Wirnitzer, “Speckle Masking in Astronomy: Triple Correlation Theory and Applications,” Appl. Opt. 22, 4028 (1983).
    [CrossRef] [PubMed]
  5. G. P. Weigelt, G. Baier, J. Ebersberger, F. Fleischmann, K.-H. Hofmann, R. Ladebeck, “High Resolution Speckle Methods for Overcoming Image Degradation Caused by the Atmosphere and Telescope Aberrations,” Opt. Eng. 25, 706 (1986).
    [CrossRef]
  6. K.-H. Hofmann, G. P. Weigelt, “Imaging Speckle Interferometer (ISIS) in Space: Digital Simulations of Image Reconstruction and Photon Noise,” in Proceedings, Kilometric Optical Arrays in Space, Cargese (Corsica), 23–25 Oct. 1984, N. Longdon, O. Melita, Eds. (ESA, c/o ESTEC, Nordwijk, The Netherlands, 1984), pp. 145–151.
  7. K.-H. Hofmann, G. P. Weigelt, “Speckle Masking Observations of the Central Object in NGC 3603,” Astron. Astrophys. 167, L15 (1986).
  8. K.-H. Hofmann, G. Weigelt, “Imaging Speckle Interferometer in Space: Image Reconstruction by Speckle Masking,” J. Opt. Soc. Am. A 3, 1908 (1986).
    [CrossRef]
  9. A. Labeyrie, “Attainment of Diffraction-Limited Resolution in Large Telescopes by Fourier Analysing Speckle Patterns in Star Images,” Astron. Astrophys. 6, 85 (1970).
  10. C. Aime, R. G. Petrov, F. Martin, G. Ricort, J. Borgnino, “Speckle Interferometry and Differential Speckle Interferometry Using Cross-Spectrum Techniques,” Opt. Eng. 25, 716 (1986).
    [CrossRef]
  11. B. Wirtnitzer, “Bispectral Analysis at Low Light Levels and Astronomical Speckle Masking,” J. Opt. Soc. Am. A 2, 14 (1985).
    [CrossRef]
  12. J. W. Goodman, J. F. Belsher, “Fundamental Limitations in Linear-Invariant Restoration of Atmospherically Degraded Images,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 141 (1976).
  13. G. Weigelt, “Large Field Speckle Interferometry,” Optik 43, 111 (1974).

1986 (4)

G. P. Weigelt, G. Baier, J. Ebersberger, F. Fleischmann, K.-H. Hofmann, R. Ladebeck, “High Resolution Speckle Methods for Overcoming Image Degradation Caused by the Atmosphere and Telescope Aberrations,” Opt. Eng. 25, 706 (1986).
[CrossRef]

K.-H. Hofmann, G. P. Weigelt, “Speckle Masking Observations of the Central Object in NGC 3603,” Astron. Astrophys. 167, L15 (1986).

C. Aime, R. G. Petrov, F. Martin, G. Ricort, J. Borgnino, “Speckle Interferometry and Differential Speckle Interferometry Using Cross-Spectrum Techniques,” Opt. Eng. 25, 716 (1986).
[CrossRef]

K.-H. Hofmann, G. Weigelt, “Imaging Speckle Interferometer in Space: Image Reconstruction by Speckle Masking,” J. Opt. Soc. Am. A 3, 1908 (1986).
[CrossRef]

1985 (1)

1983 (2)

1977 (1)

G. P. Weigelt, “Modified Speckle Interferometry: Speckle Masking,” Opt. Commun. 21, 55 (1977).
[CrossRef]

1976 (1)

J. W. Goodman, J. F. Belsher, “Fundamental Limitations in Linear-Invariant Restoration of Atmospherically Degraded Images,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 141 (1976).

1974 (1)

G. Weigelt, “Large Field Speckle Interferometry,” Optik 43, 111 (1974).

1970 (1)

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

Aime, C.

C. Aime, R. G. Petrov, F. Martin, G. Ricort, J. Borgnino, “Speckle Interferometry and Differential Speckle Interferometry Using Cross-Spectrum Techniques,” Opt. Eng. 25, 716 (1986).
[CrossRef]

Baier, G.

G. P. Weigelt, G. Baier, J. Ebersberger, F. Fleischmann, K.-H. Hofmann, R. Ladebeck, “High Resolution Speckle Methods for Overcoming Image Degradation Caused by the Atmosphere and Telescope Aberrations,” Opt. Eng. 25, 706 (1986).
[CrossRef]

Belsher, J. F.

J. W. Goodman, J. F. Belsher, “Fundamental Limitations in Linear-Invariant Restoration of Atmospherically Degraded Images,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 141 (1976).

Borgnino, J.

C. Aime, R. G. Petrov, F. Martin, G. Ricort, J. Borgnino, “Speckle Interferometry and Differential Speckle Interferometry Using Cross-Spectrum Techniques,” Opt. Eng. 25, 716 (1986).
[CrossRef]

Dainty, J. C.

J. C. Dainty, “Stellar Speckle Interferometry,” in Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, Berlin, 1975).
[CrossRef]

Ebersberger, J.

G. P. Weigelt, G. Baier, J. Ebersberger, F. Fleischmann, K.-H. Hofmann, R. Ladebeck, “High Resolution Speckle Methods for Overcoming Image Degradation Caused by the Atmosphere and Telescope Aberrations,” Opt. Eng. 25, 706 (1986).
[CrossRef]

Fleischmann, F.

G. P. Weigelt, G. Baier, J. Ebersberger, F. Fleischmann, K.-H. Hofmann, R. Ladebeck, “High Resolution Speckle Methods for Overcoming Image Degradation Caused by the Atmosphere and Telescope Aberrations,” Opt. Eng. 25, 706 (1986).
[CrossRef]

Goodman, J. W.

J. W. Goodman, J. F. Belsher, “Fundamental Limitations in Linear-Invariant Restoration of Atmospherically Degraded Images,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 141 (1976).

Hofmann, K.-H.

G. P. Weigelt, G. Baier, J. Ebersberger, F. Fleischmann, K.-H. Hofmann, R. Ladebeck, “High Resolution Speckle Methods for Overcoming Image Degradation Caused by the Atmosphere and Telescope Aberrations,” Opt. Eng. 25, 706 (1986).
[CrossRef]

K.-H. Hofmann, G. P. Weigelt, “Speckle Masking Observations of the Central Object in NGC 3603,” Astron. Astrophys. 167, L15 (1986).

K.-H. Hofmann, G. Weigelt, “Imaging Speckle Interferometer in Space: Image Reconstruction by Speckle Masking,” J. Opt. Soc. Am. A 3, 1908 (1986).
[CrossRef]

K.-H. Hofmann, G. P. Weigelt, “Imaging Speckle Interferometer (ISIS) in Space: Digital Simulations of Image Reconstruction and Photon Noise,” in Proceedings, Kilometric Optical Arrays in Space, Cargese (Corsica), 23–25 Oct. 1984, N. Longdon, O. Melita, Eds. (ESA, c/o ESTEC, Nordwijk, The Netherlands, 1984), pp. 145–151.

Labeyrie, A.

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

Ladebeck, R.

G. P. Weigelt, G. Baier, J. Ebersberger, F. Fleischmann, K.-H. Hofmann, R. Ladebeck, “High Resolution Speckle Methods for Overcoming Image Degradation Caused by the Atmosphere and Telescope Aberrations,” Opt. Eng. 25, 706 (1986).
[CrossRef]

Lohmann, A. W.

Martin, F.

C. Aime, R. G. Petrov, F. Martin, G. Ricort, J. Borgnino, “Speckle Interferometry and Differential Speckle Interferometry Using Cross-Spectrum Techniques,” Opt. Eng. 25, 716 (1986).
[CrossRef]

Petrov, R. G.

C. Aime, R. G. Petrov, F. Martin, G. Ricort, J. Borgnino, “Speckle Interferometry and Differential Speckle Interferometry Using Cross-Spectrum Techniques,” Opt. Eng. 25, 716 (1986).
[CrossRef]

Ricort, G.

C. Aime, R. G. Petrov, F. Martin, G. Ricort, J. Borgnino, “Speckle Interferometry and Differential Speckle Interferometry Using Cross-Spectrum Techniques,” Opt. Eng. 25, 716 (1986).
[CrossRef]

Weigelt, G.

Weigelt, G. P.

G. P. Weigelt, G. Baier, J. Ebersberger, F. Fleischmann, K.-H. Hofmann, R. Ladebeck, “High Resolution Speckle Methods for Overcoming Image Degradation Caused by the Atmosphere and Telescope Aberrations,” Opt. Eng. 25, 706 (1986).
[CrossRef]

K.-H. Hofmann, G. P. Weigelt, “Speckle Masking Observations of the Central Object in NGC 3603,” Astron. Astrophys. 167, L15 (1986).

A. W. Lohmann, G. P. Weigelt, B. Wirnitzer, “Speckle Masking in Astronomy: Triple Correlation Theory and Applications,” Appl. Opt. 22, 4028 (1983).
[CrossRef] [PubMed]

G. P. Weigelt, B. Wirnitzer, “Image Reconstruction by the Speckle-Masking Method,” Opt. Lett. 8, 389 (1983).
[CrossRef] [PubMed]

G. P. Weigelt, “Modified Speckle Interferometry: Speckle Masking,” Opt. Commun. 21, 55 (1977).
[CrossRef]

K.-H. Hofmann, G. P. Weigelt, “Imaging Speckle Interferometer (ISIS) in Space: Digital Simulations of Image Reconstruction and Photon Noise,” in Proceedings, Kilometric Optical Arrays in Space, Cargese (Corsica), 23–25 Oct. 1984, N. Longdon, O. Melita, Eds. (ESA, c/o ESTEC, Nordwijk, The Netherlands, 1984), pp. 145–151.

Wirnitzer, B.

Wirtnitzer, B.

Appl. Opt. (1)

Astron. Astrophys. (2)

K.-H. Hofmann, G. P. Weigelt, “Speckle Masking Observations of the Central Object in NGC 3603,” Astron. Astrophys. 167, L15 (1986).

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

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

G. P. Weigelt, “Modified Speckle Interferometry: Speckle Masking,” Opt. Commun. 21, 55 (1977).
[CrossRef]

Opt. Eng. (2)

G. P. Weigelt, G. Baier, J. Ebersberger, F. Fleischmann, K.-H. Hofmann, R. Ladebeck, “High Resolution Speckle Methods for Overcoming Image Degradation Caused by the Atmosphere and Telescope Aberrations,” Opt. Eng. 25, 706 (1986).
[CrossRef]

C. Aime, R. G. Petrov, F. Martin, G. Ricort, J. Borgnino, “Speckle Interferometry and Differential Speckle Interferometry Using Cross-Spectrum Techniques,” Opt. Eng. 25, 716 (1986).
[CrossRef]

Opt. Lett. (1)

Optik (1)

G. Weigelt, “Large Field Speckle Interferometry,” Optik 43, 111 (1974).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

J. W. Goodman, J. F. Belsher, “Fundamental Limitations in Linear-Invariant Restoration of Atmospherically Degraded Images,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 141 (1976).

Other (2)

J. C. Dainty, “Stellar Speckle Interferometry,” in Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, Berlin, 1975).
[CrossRef]

K.-H. Hofmann, G. P. Weigelt, “Imaging Speckle Interferometer (ISIS) in Space: Digital Simulations of Image Reconstruction and Photon Noise,” in Proceedings, Kilometric Optical Arrays in Space, Cargese (Corsica), 23–25 Oct. 1984, N. Longdon, O. Melita, Eds. (ESA, c/o ESTEC, Nordwijk, The Netherlands, 1984), pp. 145–151.

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Figures (5)

Fig. 1
Fig. 1

Object.

Fig. 2
Fig. 2

One of the 2400 simulated object speckle interferograms: (a) no photon noise, and (b) with photon noise corresponding to a mean count number of twenty-five photon events per speckle interferogram.

Fig. 3
Fig. 3

Average bispectra of the 2400 simulated object speckle interferograms (object of Fig. 1): (a) average autobispectrum without photon noise, (b) average autobispectrum with photon noise corresponding to a mean count number of seventy-five photon events per interferogram, and (c) average cross bispectrum with photon noise corresponding to a mean count number of three times twenty-five photon events per triple of speckle interferograms.

Fig. 4
Fig. 4

Images reconstructed by speckle masking: (a) autobispectrum processing with photon noise corresponding to seventy-five photon events per speckle interferogram and 2400 interferograms, and (b) cross bispectrum processing with photon noise corresponding to three times twenty-five photon events per triplet of interferograms [same photon noise as in (a)] and 2400 interferograms.

Fig. 5
Fig. 5

Image reconstructed by speckle masking: cross bispectrum processing with photon noise corresponding to a mean count number of three times twenty-five photon events per interferogram, 2400 interferograms, and additive noise of three times five photon events per interferogram triplet.

Equations (13)

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I ( x ) = O ( x ) * P ( x ) ,
I ( 3 ) ( x , x ) = I ( x ) I ( x + x ) I ( x + x ) d x ,
I ( a b c ) ( x , x ) = I a ( x ) I b ( x + x ) I c ( x + x ) d x ,
I ˜ ( a b c ) ( u , v ) = I ˜ a ( u ) I ˜ b ( v ) I ˜ c ( - u - v ) ,
I ˜ ( a b c ) ( u , v ) = O ˜ ( u ) O ˜ ( v ) O ˜ ( - u - v ) × P ˜ a ( u ) P ˜ b ( v ) P ˜ c ( - u - v ) ,
D a ( x ) = j = 1 N a δ ( x - x j ) , D b ( x ) = k = 1 N b δ ( x - x k ) , D c ( x ) = l = 1 N c δ ( x - x l ) ,
E [ D ˜ ( a b c ) ( u , v ) ] = E [ D ˜ a ( u ) D ˜ b ( v ) D ˜ c ( - u - v ) ]
E j k l [ D ˜ ( a b c ) ( u , v ) ] = j , k , l E j k l ( exp { - 2 π i [ u ( x j - x l ) + v ( x k - x l ) ] } ) ,
j = k = l , j = k l , j l = k , j k = l , j k l ,
E [ D ˜ ( a b c ) ( u , v ) ] = const I ˜ ( 3 ) ( u , v ) ,
B ( x ) = j = 1 N δ ( x - x j ) * f ( x ) ,
E [ B ˜ ( 3 ) ( u , v ) ] = E [ D ˜ ( 3 ) ( u , v ) ] · f ˜ ( 3 ) ( u , v ) ,
E [ B ˜ ( a b c ) ( u , v ) ] = const I ˜ ( 3 ) ( u , v ) · f ˜ ( 3 ) ( u , v ) ,

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