Abstract

In a recent paper [ J. Opt. Soc. Am. A 9, 203 ( 1992)] the benefits of pupil apodization were examined for the near-infrared imaging of bright sources. In the current paper we extend these considerations to optical speckle imaging, in which photon noise rather than detector readout noise is important. We demonstrate that a one-dimensional pupil geometry (i.e., a thin slit) has several advantages over an unapodized aperture when faint sources are being observed through atmospheric turbulence. The use of a slit aperture does not decrease the signal-to-noise ratios of the power-spectrum and bispectrum measurements, and in many cases it increases them, despite the large reduction in signal level. The disadvantage of this apodization is a reduction in Fourier-plane coverage, which must be compensated for by observations with the slit aligned at several position angles. The performance of many of the current generation of photon-counting imaging detectors deteriorates at the high counting rates that can be experienced even when one is observing sources that are approaching the limiting magnitude of the speckle imaging technique. Under such conditions, we recommend the use of an apodized pupil, in contrast to the current preference for employing a neutral-density filter to reduce the detector count rate.

© 1993 Optical Society of America

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  1. See, e.g., D. M. Alloin, J.-M. Mariotti, Diffraction-Limited Imaging with Very Large Telescopes (Kluwer, Dordrecht, The Netherlands, 1989), pp. 157–169 and 191–200.
  2. G. R. Ayers, M. J. Northcott, J. C. Dainty, “Knox–Thompson and triple correlation imaging through atmospheric turbulence,” J. Opt. Soc. Am. A 5, 963–985 (1988).
    [CrossRef]
  3. C. A. Haniff, C. D. Mackay, D. J. Titterington, D. Sivia, J. E. Baldwin, P. J. Warner, “The first images from optical aperture synthesis,” Nature (London) 328, 694–696 (1988).
    [CrossRef]
  4. T. Nakajima, S. R. Kulkarni, P. W. Gorham, A. M. Ghez, G. Neugebauer, J. B. Oke, T. A. Prince, A. C. S. Readhead, “Diffraction-limited imaging. II. Optical aperture synthesis imaging of two binary stars,” Astron. J. 97, 1510–1521 (1989).
    [CrossRef]
  5. J. G. Robertson, T. R. Bedding, R. G. Marson, P. R. Gillingham, R. H. Frater, J. D. O’Sullivan, R. P. Norris, “High-resolution imaging by optical aperture synthesis: first results from the MAPPIT project,” Proc. Astron. Soc. Aust. 9, 162–163 (1991).
  6. D. F. Buscher, C. A. Haniff, J. E. Baldwin, P. J. Warner, “Detection of a bright feature on the surface of Betelgeuse,”M. Not. R. Astron. Soc. 245, 7P–11P (1990).
  7. C. A. Haniff, A. M. Ghez, P. W. Gorham, S. R. Kulkarni, K. Matthews, G. Neugebauer, “Optical aperture synthetic imaging of the photosphere and molecular atmosphere of Mira,” Astron. J. 103, 1662–1667 (1992).
    [CrossRef]
  8. R. W. Wilson, J. E. Baldwin, D. F. Buscher, P. J. Warner, “High-resolution imaging of Betelgeuse and Mira,”M. Not. R. Astron. Soc. 257, 369–376 (1992).
  9. C. A. Haniff, D. F. Buscher, “Diffraction-limited imaging with partially redundant masks. I. Infrared imaging of bright objects,” J. Opt. Soc. Am. A 9, 203–218 (1992). (Paper 1).
    [CrossRef]
  10. C. Aime, F. Roddier, “One-dimensional stellar and solar speckle interferometry,” Opt. Commun. 21, 435–438 (1977).
    [CrossRef]
  11. S. Kadiri, C. Aime, G. Ricort, “Speckle interférométrie à une dimension en astronomie: étude des fonctions de transfert instrument–atmosphère obtenues par analyze statistique de speckles stellaires fournis par un objectif rectangulaire,”J. Opt. (Paris) 12, 143–151 (1981).
    [CrossRef]
  12. C. Papalolios, P. Nisenson, S. Ebstein, “Speckle imaging with the PAPA camera,” Appl. Opt. 24, 287–292 (1985).
    [CrossRef]
  13. P. R. Lawson, School of Physics, University of Sydney, Sydney, NSW 2006, Australia (personal communication, January1993).
  14. A. C. S. Readhead, T. Nakajima, T. J. Pearson, G. Neugebauer, J. B. Oke, W. L. W. Sargent, “Diffraction-limited imaging with ground-based optical telescopes,” Astron. J. 95, 1278–1296 (1988).
    [CrossRef]
  15. F. Roddier, “Redundant versus nonredundant beam recombination in an aperture synthesis with coherent optical arrays,” J. Opt. Soc. Am. A 4, 1396–1401 (1987).
    [CrossRef]
  16. D. F. Buscher, “Getting the most out of C.O.A.S.T.,” Ph.D. dissertation (Cambridge University, Cambridge, 1988).
  17. J. W. Goodman, J. F. Belsher, “Fundamental limitations in linear invariant restoration of atmospherically degraded images,” in Imaging through the Atmosphere, J. C. Wyant, ed., Proc. Soc. Photo-Opt. Instrum. Eng.75, 141–154 (1976).
    [CrossRef]
  18. J. C. Dainty, A. H. Greenaway, “Estimation of spatial power spectra in speckle interferometry,”J. Opt. Soc. Am. 69, 786–790 (1979).
    [CrossRef]
  19. S. N. Karbelkar, “Optimum weighting function in bispectral analysis in speckle interferometry: binary star parity detection,” Astron. Astrophys. 238, 485–493 (1990).
  20. H. Bartelt, A. W. Lohmann, B. Wirnitzer, “Phase and amplitude recovery from the bispectrum,” Appl. Opt. 23, 3121–3129 (1984).
    [CrossRef] [PubMed]
  21. R. G. Petrov, C. Aime, J. Borgnino, F. Martin, G. Ricort, “16-m large slit aperture telescope for very high angular resolution astronomy,” Proc. IAU Colloq. 79, 295–308 (1984).
  22. See, e.g., G. Weigelt, “Speckle interferometry, speckle holography, speckle spectroscopy and reconstruction of high-resolution images from ST data,” in Proceedings of the ESO Conference on the Scientific Importance of High Angular Resolution at Infrared and Optical Wavelengths, M.-H. Ulrich, K. Kjär, eds. (European Southern Observatory, Garching, Germany, 1981), pp. 95–114.
  23. See, e.g., E. K. Hege, A. Eckart, J. C. Christou, “The noise bias problem in optical speckle imaging: experience with a real detector,” in Instrumentation in Astronomy VI, P. L. Crawford, ed., Proc. Soc. Photo-Opt. Instrum. Eng.627, 772–779 (1986).
    [CrossRef]
  24. K.-H. Hofmann, “Photon-counting speckle imaging: the photon-counting hole in triple correlation,” J. Opt. Soc. Am. A 10, 329–335 (1993).
    [CrossRef]
  25. P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. Prince, “Diffraction-limited imaging. III. 30mas closure phase imaging of six binary stars with the Hale 5 m telescope,” Astron. J. 98, 1783–1799 (1989).
    [CrossRef]
  26. F. Martin, A. Bijaoui, H. Touma, C. Aime, “Astronomical image reconstruction via space slit aperture telescope,” in Infrared, Adaptive and Synthetic Aperture Optical Systems, R. B. Johnson, W. L. Wolfe, J. S. Fender, eds., Proc. Soc. Photo-Opt. Instrum. Eng.643, 189–193 (1986).
    [CrossRef]
  27. F. Martin, “Imagery in astronomy by inverse Radon transformation, using a rotating slit aperture telescope (SAT),” in Inverse Problems in Optics, E. R. Pike, ed., Proc. Soc. Photo-Opt. Instrum. Eng.808, 206–208 (1987).
    [CrossRef]
  28. F. Martin, H. Touma, A. Bijaoui, C. Aime, “Reconstruction d’images en astronomie par utilisation d’un télescope à pupile fente,”J. Opt. (Paris) 18, 133–138 (1987).
    [CrossRef]
  29. T. J. Pearson, A. C. S. Readhead, “Image formation by self-calibration in radio astronomy,” Ann. Rev. Astron. Astrophys. 22, 97–130 (1984).
    [CrossRef]
  30. C. A. Haniff, D. F.Buscher, J. C. Christou, S. T. Ridgway, “Synthetic aperture imaging at infrared wavelengths,”M. Not. R. Astron. Soc. 241, 51P–56P (1989).
  31. C. A. Haniff, D. F. Buscher, J. C. Christou, S. T. Ridgway, “Diffraction-limited imaging at IR wavelengths using aperture masks and fully-filled apertures,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng1237, 259–271 (1990).
    [CrossRef]

1993

1992

C. A. Haniff, A. M. Ghez, P. W. Gorham, S. R. Kulkarni, K. Matthews, G. Neugebauer, “Optical aperture synthetic imaging of the photosphere and molecular atmosphere of Mira,” Astron. J. 103, 1662–1667 (1992).
[CrossRef]

R. W. Wilson, J. E. Baldwin, D. F. Buscher, P. J. Warner, “High-resolution imaging of Betelgeuse and Mira,”M. Not. R. Astron. Soc. 257, 369–376 (1992).

C. A. Haniff, D. F. Buscher, “Diffraction-limited imaging with partially redundant masks. I. Infrared imaging of bright objects,” J. Opt. Soc. Am. A 9, 203–218 (1992). (Paper 1).
[CrossRef]

1991

J. G. Robertson, T. R. Bedding, R. G. Marson, P. R. Gillingham, R. H. Frater, J. D. O’Sullivan, R. P. Norris, “High-resolution imaging by optical aperture synthesis: first results from the MAPPIT project,” Proc. Astron. Soc. Aust. 9, 162–163 (1991).

1990

D. F. Buscher, C. A. Haniff, J. E. Baldwin, P. J. Warner, “Detection of a bright feature on the surface of Betelgeuse,”M. Not. R. Astron. Soc. 245, 7P–11P (1990).

S. N. Karbelkar, “Optimum weighting function in bispectral analysis in speckle interferometry: binary star parity detection,” Astron. Astrophys. 238, 485–493 (1990).

1989

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. Prince, “Diffraction-limited imaging. III. 30mas closure phase imaging of six binary stars with the Hale 5 m telescope,” Astron. J. 98, 1783–1799 (1989).
[CrossRef]

C. A. Haniff, D. F.Buscher, J. C. Christou, S. T. Ridgway, “Synthetic aperture imaging at infrared wavelengths,”M. Not. R. Astron. Soc. 241, 51P–56P (1989).

T. Nakajima, S. R. Kulkarni, P. W. Gorham, A. M. Ghez, G. Neugebauer, J. B. Oke, T. A. Prince, A. C. S. Readhead, “Diffraction-limited imaging. II. Optical aperture synthesis imaging of two binary stars,” Astron. J. 97, 1510–1521 (1989).
[CrossRef]

1988

C. A. Haniff, C. D. Mackay, D. J. Titterington, D. Sivia, J. E. Baldwin, P. J. Warner, “The first images from optical aperture synthesis,” Nature (London) 328, 694–696 (1988).
[CrossRef]

A. C. S. Readhead, T. Nakajima, T. J. Pearson, G. Neugebauer, J. B. Oke, W. L. W. Sargent, “Diffraction-limited imaging with ground-based optical telescopes,” Astron. J. 95, 1278–1296 (1988).
[CrossRef]

G. R. Ayers, M. J. Northcott, J. C. Dainty, “Knox–Thompson and triple correlation imaging through atmospheric turbulence,” J. Opt. Soc. Am. A 5, 963–985 (1988).
[CrossRef]

1987

F. Roddier, “Redundant versus nonredundant beam recombination in an aperture synthesis with coherent optical arrays,” J. Opt. Soc. Am. A 4, 1396–1401 (1987).
[CrossRef]

F. Martin, H. Touma, A. Bijaoui, C. Aime, “Reconstruction d’images en astronomie par utilisation d’un télescope à pupile fente,”J. Opt. (Paris) 18, 133–138 (1987).
[CrossRef]

1985

1984

H. Bartelt, A. W. Lohmann, B. Wirnitzer, “Phase and amplitude recovery from the bispectrum,” Appl. Opt. 23, 3121–3129 (1984).
[CrossRef] [PubMed]

T. J. Pearson, A. C. S. Readhead, “Image formation by self-calibration in radio astronomy,” Ann. Rev. Astron. Astrophys. 22, 97–130 (1984).
[CrossRef]

R. G. Petrov, C. Aime, J. Borgnino, F. Martin, G. Ricort, “16-m large slit aperture telescope for very high angular resolution astronomy,” Proc. IAU Colloq. 79, 295–308 (1984).

1981

S. Kadiri, C. Aime, G. Ricort, “Speckle interférométrie à une dimension en astronomie: étude des fonctions de transfert instrument–atmosphère obtenues par analyze statistique de speckles stellaires fournis par un objectif rectangulaire,”J. Opt. (Paris) 12, 143–151 (1981).
[CrossRef]

1979

1977

C. Aime, F. Roddier, “One-dimensional stellar and solar speckle interferometry,” Opt. Commun. 21, 435–438 (1977).
[CrossRef]

Aime, C.

F. Martin, H. Touma, A. Bijaoui, C. Aime, “Reconstruction d’images en astronomie par utilisation d’un télescope à pupile fente,”J. Opt. (Paris) 18, 133–138 (1987).
[CrossRef]

R. G. Petrov, C. Aime, J. Borgnino, F. Martin, G. Ricort, “16-m large slit aperture telescope for very high angular resolution astronomy,” Proc. IAU Colloq. 79, 295–308 (1984).

S. Kadiri, C. Aime, G. Ricort, “Speckle interférométrie à une dimension en astronomie: étude des fonctions de transfert instrument–atmosphère obtenues par analyze statistique de speckles stellaires fournis par un objectif rectangulaire,”J. Opt. (Paris) 12, 143–151 (1981).
[CrossRef]

C. Aime, F. Roddier, “One-dimensional stellar and solar speckle interferometry,” Opt. Commun. 21, 435–438 (1977).
[CrossRef]

F. Martin, A. Bijaoui, H. Touma, C. Aime, “Astronomical image reconstruction via space slit aperture telescope,” in Infrared, Adaptive and Synthetic Aperture Optical Systems, R. B. Johnson, W. L. Wolfe, J. S. Fender, eds., Proc. Soc. Photo-Opt. Instrum. Eng.643, 189–193 (1986).
[CrossRef]

Alloin, D. M.

See, e.g., D. M. Alloin, J.-M. Mariotti, Diffraction-Limited Imaging with Very Large Telescopes (Kluwer, Dordrecht, The Netherlands, 1989), pp. 157–169 and 191–200.

Ayers, G. R.

Baldwin, J. E.

R. W. Wilson, J. E. Baldwin, D. F. Buscher, P. J. Warner, “High-resolution imaging of Betelgeuse and Mira,”M. Not. R. Astron. Soc. 257, 369–376 (1992).

D. F. Buscher, C. A. Haniff, J. E. Baldwin, P. J. Warner, “Detection of a bright feature on the surface of Betelgeuse,”M. Not. R. Astron. Soc. 245, 7P–11P (1990).

C. A. Haniff, C. D. Mackay, D. J. Titterington, D. Sivia, J. E. Baldwin, P. J. Warner, “The first images from optical aperture synthesis,” Nature (London) 328, 694–696 (1988).
[CrossRef]

Bartelt, H.

Bedding, T. R.

J. G. Robertson, T. R. Bedding, R. G. Marson, P. R. Gillingham, R. H. Frater, J. D. O’Sullivan, R. P. Norris, “High-resolution imaging by optical aperture synthesis: first results from the MAPPIT project,” Proc. Astron. Soc. Aust. 9, 162–163 (1991).

Belsher, J. F.

J. W. Goodman, J. F. Belsher, “Fundamental limitations in linear invariant restoration of atmospherically degraded images,” in Imaging through the Atmosphere, J. C. Wyant, ed., Proc. Soc. Photo-Opt. Instrum. Eng.75, 141–154 (1976).
[CrossRef]

Bijaoui, A.

F. Martin, H. Touma, A. Bijaoui, C. Aime, “Reconstruction d’images en astronomie par utilisation d’un télescope à pupile fente,”J. Opt. (Paris) 18, 133–138 (1987).
[CrossRef]

F. Martin, A. Bijaoui, H. Touma, C. Aime, “Astronomical image reconstruction via space slit aperture telescope,” in Infrared, Adaptive and Synthetic Aperture Optical Systems, R. B. Johnson, W. L. Wolfe, J. S. Fender, eds., Proc. Soc. Photo-Opt. Instrum. Eng.643, 189–193 (1986).
[CrossRef]

Borgnino, J.

R. G. Petrov, C. Aime, J. Borgnino, F. Martin, G. Ricort, “16-m large slit aperture telescope for very high angular resolution astronomy,” Proc. IAU Colloq. 79, 295–308 (1984).

Buscher, D. F.

C. A. Haniff, D. F. Buscher, “Diffraction-limited imaging with partially redundant masks. I. Infrared imaging of bright objects,” J. Opt. Soc. Am. A 9, 203–218 (1992). (Paper 1).
[CrossRef]

R. W. Wilson, J. E. Baldwin, D. F. Buscher, P. J. Warner, “High-resolution imaging of Betelgeuse and Mira,”M. Not. R. Astron. Soc. 257, 369–376 (1992).

D. F. Buscher, C. A. Haniff, J. E. Baldwin, P. J. Warner, “Detection of a bright feature on the surface of Betelgeuse,”M. Not. R. Astron. Soc. 245, 7P–11P (1990).

D. F. Buscher, “Getting the most out of C.O.A.S.T.,” Ph.D. dissertation (Cambridge University, Cambridge, 1988).

C. A. Haniff, D. F. Buscher, J. C. Christou, S. T. Ridgway, “Diffraction-limited imaging at IR wavelengths using aperture masks and fully-filled apertures,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng1237, 259–271 (1990).
[CrossRef]

Christou, J. C.

C. A. Haniff, D. F.Buscher, J. C. Christou, S. T. Ridgway, “Synthetic aperture imaging at infrared wavelengths,”M. Not. R. Astron. Soc. 241, 51P–56P (1989).

C. A. Haniff, D. F. Buscher, J. C. Christou, S. T. Ridgway, “Diffraction-limited imaging at IR wavelengths using aperture masks and fully-filled apertures,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng1237, 259–271 (1990).
[CrossRef]

See, e.g., E. K. Hege, A. Eckart, J. C. Christou, “The noise bias problem in optical speckle imaging: experience with a real detector,” in Instrumentation in Astronomy VI, P. L. Crawford, ed., Proc. Soc. Photo-Opt. Instrum. Eng.627, 772–779 (1986).
[CrossRef]

Dainty, J. C.

Ebstein, S.

Eckart, A.

See, e.g., E. K. Hege, A. Eckart, J. C. Christou, “The noise bias problem in optical speckle imaging: experience with a real detector,” in Instrumentation in Astronomy VI, P. L. Crawford, ed., Proc. Soc. Photo-Opt. Instrum. Eng.627, 772–779 (1986).
[CrossRef]

F.Buscher, D.

C. A. Haniff, D. F.Buscher, J. C. Christou, S. T. Ridgway, “Synthetic aperture imaging at infrared wavelengths,”M. Not. R. Astron. Soc. 241, 51P–56P (1989).

Frater, R. H.

J. G. Robertson, T. R. Bedding, R. G. Marson, P. R. Gillingham, R. H. Frater, J. D. O’Sullivan, R. P. Norris, “High-resolution imaging by optical aperture synthesis: first results from the MAPPIT project,” Proc. Astron. Soc. Aust. 9, 162–163 (1991).

Ghez, A. M.

C. A. Haniff, A. M. Ghez, P. W. Gorham, S. R. Kulkarni, K. Matthews, G. Neugebauer, “Optical aperture synthetic imaging of the photosphere and molecular atmosphere of Mira,” Astron. J. 103, 1662–1667 (1992).
[CrossRef]

T. Nakajima, S. R. Kulkarni, P. W. Gorham, A. M. Ghez, G. Neugebauer, J. B. Oke, T. A. Prince, A. C. S. Readhead, “Diffraction-limited imaging. II. Optical aperture synthesis imaging of two binary stars,” Astron. J. 97, 1510–1521 (1989).
[CrossRef]

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. Prince, “Diffraction-limited imaging. III. 30mas closure phase imaging of six binary stars with the Hale 5 m telescope,” Astron. J. 98, 1783–1799 (1989).
[CrossRef]

Gillingham, P. R.

J. G. Robertson, T. R. Bedding, R. G. Marson, P. R. Gillingham, R. H. Frater, J. D. O’Sullivan, R. P. Norris, “High-resolution imaging by optical aperture synthesis: first results from the MAPPIT project,” Proc. Astron. Soc. Aust. 9, 162–163 (1991).

Goodman, J. W.

J. W. Goodman, J. F. Belsher, “Fundamental limitations in linear invariant restoration of atmospherically degraded images,” in Imaging through the Atmosphere, J. C. Wyant, ed., Proc. Soc. Photo-Opt. Instrum. Eng.75, 141–154 (1976).
[CrossRef]

Gorham, P. W.

C. A. Haniff, A. M. Ghez, P. W. Gorham, S. R. Kulkarni, K. Matthews, G. Neugebauer, “Optical aperture synthetic imaging of the photosphere and molecular atmosphere of Mira,” Astron. J. 103, 1662–1667 (1992).
[CrossRef]

T. Nakajima, S. R. Kulkarni, P. W. Gorham, A. M. Ghez, G. Neugebauer, J. B. Oke, T. A. Prince, A. C. S. Readhead, “Diffraction-limited imaging. II. Optical aperture synthesis imaging of two binary stars,” Astron. J. 97, 1510–1521 (1989).
[CrossRef]

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. Prince, “Diffraction-limited imaging. III. 30mas closure phase imaging of six binary stars with the Hale 5 m telescope,” Astron. J. 98, 1783–1799 (1989).
[CrossRef]

Greenaway, A. H.

Haniff, C. A.

C. A. Haniff, A. M. Ghez, P. W. Gorham, S. R. Kulkarni, K. Matthews, G. Neugebauer, “Optical aperture synthetic imaging of the photosphere and molecular atmosphere of Mira,” Astron. J. 103, 1662–1667 (1992).
[CrossRef]

C. A. Haniff, D. F. Buscher, “Diffraction-limited imaging with partially redundant masks. I. Infrared imaging of bright objects,” J. Opt. Soc. Am. A 9, 203–218 (1992). (Paper 1).
[CrossRef]

D. F. Buscher, C. A. Haniff, J. E. Baldwin, P. J. Warner, “Detection of a bright feature on the surface of Betelgeuse,”M. Not. R. Astron. Soc. 245, 7P–11P (1990).

C. A. Haniff, D. F.Buscher, J. C. Christou, S. T. Ridgway, “Synthetic aperture imaging at infrared wavelengths,”M. Not. R. Astron. Soc. 241, 51P–56P (1989).

C. A. Haniff, C. D. Mackay, D. J. Titterington, D. Sivia, J. E. Baldwin, P. J. Warner, “The first images from optical aperture synthesis,” Nature (London) 328, 694–696 (1988).
[CrossRef]

C. A. Haniff, D. F. Buscher, J. C. Christou, S. T. Ridgway, “Diffraction-limited imaging at IR wavelengths using aperture masks and fully-filled apertures,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng1237, 259–271 (1990).
[CrossRef]

Hege, E. K.

See, e.g., E. K. Hege, A. Eckart, J. C. Christou, “The noise bias problem in optical speckle imaging: experience with a real detector,” in Instrumentation in Astronomy VI, P. L. Crawford, ed., Proc. Soc. Photo-Opt. Instrum. Eng.627, 772–779 (1986).
[CrossRef]

Hofmann, K.-H.

Kadiri, S.

S. Kadiri, C. Aime, G. Ricort, “Speckle interférométrie à une dimension en astronomie: étude des fonctions de transfert instrument–atmosphère obtenues par analyze statistique de speckles stellaires fournis par un objectif rectangulaire,”J. Opt. (Paris) 12, 143–151 (1981).
[CrossRef]

Karbelkar, S. N.

S. N. Karbelkar, “Optimum weighting function in bispectral analysis in speckle interferometry: binary star parity detection,” Astron. Astrophys. 238, 485–493 (1990).

Kulkarni, S. R.

C. A. Haniff, A. M. Ghez, P. W. Gorham, S. R. Kulkarni, K. Matthews, G. Neugebauer, “Optical aperture synthetic imaging of the photosphere and molecular atmosphere of Mira,” Astron. J. 103, 1662–1667 (1992).
[CrossRef]

T. Nakajima, S. R. Kulkarni, P. W. Gorham, A. M. Ghez, G. Neugebauer, J. B. Oke, T. A. Prince, A. C. S. Readhead, “Diffraction-limited imaging. II. Optical aperture synthesis imaging of two binary stars,” Astron. J. 97, 1510–1521 (1989).
[CrossRef]

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. Prince, “Diffraction-limited imaging. III. 30mas closure phase imaging of six binary stars with the Hale 5 m telescope,” Astron. J. 98, 1783–1799 (1989).
[CrossRef]

Lawson, P. R.

P. R. Lawson, School of Physics, University of Sydney, Sydney, NSW 2006, Australia (personal communication, January1993).

Lohmann, A. W.

Mackay, C. D.

C. A. Haniff, C. D. Mackay, D. J. Titterington, D. Sivia, J. E. Baldwin, P. J. Warner, “The first images from optical aperture synthesis,” Nature (London) 328, 694–696 (1988).
[CrossRef]

Mariotti, J.-M.

See, e.g., D. M. Alloin, J.-M. Mariotti, Diffraction-Limited Imaging with Very Large Telescopes (Kluwer, Dordrecht, The Netherlands, 1989), pp. 157–169 and 191–200.

Marson, R. G.

J. G. Robertson, T. R. Bedding, R. G. Marson, P. R. Gillingham, R. H. Frater, J. D. O’Sullivan, R. P. Norris, “High-resolution imaging by optical aperture synthesis: first results from the MAPPIT project,” Proc. Astron. Soc. Aust. 9, 162–163 (1991).

Martin, F.

F. Martin, H. Touma, A. Bijaoui, C. Aime, “Reconstruction d’images en astronomie par utilisation d’un télescope à pupile fente,”J. Opt. (Paris) 18, 133–138 (1987).
[CrossRef]

R. G. Petrov, C. Aime, J. Borgnino, F. Martin, G. Ricort, “16-m large slit aperture telescope for very high angular resolution astronomy,” Proc. IAU Colloq. 79, 295–308 (1984).

F. Martin, A. Bijaoui, H. Touma, C. Aime, “Astronomical image reconstruction via space slit aperture telescope,” in Infrared, Adaptive and Synthetic Aperture Optical Systems, R. B. Johnson, W. L. Wolfe, J. S. Fender, eds., Proc. Soc. Photo-Opt. Instrum. Eng.643, 189–193 (1986).
[CrossRef]

F. Martin, “Imagery in astronomy by inverse Radon transformation, using a rotating slit aperture telescope (SAT),” in Inverse Problems in Optics, E. R. Pike, ed., Proc. Soc. Photo-Opt. Instrum. Eng.808, 206–208 (1987).
[CrossRef]

Matthews, K.

C. A. Haniff, A. M. Ghez, P. W. Gorham, S. R. Kulkarni, K. Matthews, G. Neugebauer, “Optical aperture synthetic imaging of the photosphere and molecular atmosphere of Mira,” Astron. J. 103, 1662–1667 (1992).
[CrossRef]

Nakajima, T.

T. Nakajima, S. R. Kulkarni, P. W. Gorham, A. M. Ghez, G. Neugebauer, J. B. Oke, T. A. Prince, A. C. S. Readhead, “Diffraction-limited imaging. II. Optical aperture synthesis imaging of two binary stars,” Astron. J. 97, 1510–1521 (1989).
[CrossRef]

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. Prince, “Diffraction-limited imaging. III. 30mas closure phase imaging of six binary stars with the Hale 5 m telescope,” Astron. J. 98, 1783–1799 (1989).
[CrossRef]

A. C. S. Readhead, T. Nakajima, T. J. Pearson, G. Neugebauer, J. B. Oke, W. L. W. Sargent, “Diffraction-limited imaging with ground-based optical telescopes,” Astron. J. 95, 1278–1296 (1988).
[CrossRef]

Neugebauer, G.

C. A. Haniff, A. M. Ghez, P. W. Gorham, S. R. Kulkarni, K. Matthews, G. Neugebauer, “Optical aperture synthetic imaging of the photosphere and molecular atmosphere of Mira,” Astron. J. 103, 1662–1667 (1992).
[CrossRef]

T. Nakajima, S. R. Kulkarni, P. W. Gorham, A. M. Ghez, G. Neugebauer, J. B. Oke, T. A. Prince, A. C. S. Readhead, “Diffraction-limited imaging. II. Optical aperture synthesis imaging of two binary stars,” Astron. J. 97, 1510–1521 (1989).
[CrossRef]

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. Prince, “Diffraction-limited imaging. III. 30mas closure phase imaging of six binary stars with the Hale 5 m telescope,” Astron. J. 98, 1783–1799 (1989).
[CrossRef]

A. C. S. Readhead, T. Nakajima, T. J. Pearson, G. Neugebauer, J. B. Oke, W. L. W. Sargent, “Diffraction-limited imaging with ground-based optical telescopes,” Astron. J. 95, 1278–1296 (1988).
[CrossRef]

Nisenson, P.

Norris, R. P.

J. G. Robertson, T. R. Bedding, R. G. Marson, P. R. Gillingham, R. H. Frater, J. D. O’Sullivan, R. P. Norris, “High-resolution imaging by optical aperture synthesis: first results from the MAPPIT project,” Proc. Astron. Soc. Aust. 9, 162–163 (1991).

Northcott, M. J.

O’Sullivan, J. D.

J. G. Robertson, T. R. Bedding, R. G. Marson, P. R. Gillingham, R. H. Frater, J. D. O’Sullivan, R. P. Norris, “High-resolution imaging by optical aperture synthesis: first results from the MAPPIT project,” Proc. Astron. Soc. Aust. 9, 162–163 (1991).

Oke, J. B.

T. Nakajima, S. R. Kulkarni, P. W. Gorham, A. M. Ghez, G. Neugebauer, J. B. Oke, T. A. Prince, A. C. S. Readhead, “Diffraction-limited imaging. II. Optical aperture synthesis imaging of two binary stars,” Astron. J. 97, 1510–1521 (1989).
[CrossRef]

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. Prince, “Diffraction-limited imaging. III. 30mas closure phase imaging of six binary stars with the Hale 5 m telescope,” Astron. J. 98, 1783–1799 (1989).
[CrossRef]

A. C. S. Readhead, T. Nakajima, T. J. Pearson, G. Neugebauer, J. B. Oke, W. L. W. Sargent, “Diffraction-limited imaging with ground-based optical telescopes,” Astron. J. 95, 1278–1296 (1988).
[CrossRef]

Papalolios, C.

Pearson, T. J.

A. C. S. Readhead, T. Nakajima, T. J. Pearson, G. Neugebauer, J. B. Oke, W. L. W. Sargent, “Diffraction-limited imaging with ground-based optical telescopes,” Astron. J. 95, 1278–1296 (1988).
[CrossRef]

T. J. Pearson, A. C. S. Readhead, “Image formation by self-calibration in radio astronomy,” Ann. Rev. Astron. Astrophys. 22, 97–130 (1984).
[CrossRef]

Petrov, R. G.

R. G. Petrov, C. Aime, J. Borgnino, F. Martin, G. Ricort, “16-m large slit aperture telescope for very high angular resolution astronomy,” Proc. IAU Colloq. 79, 295–308 (1984).

Prince, T. A.

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. Prince, “Diffraction-limited imaging. III. 30mas closure phase imaging of six binary stars with the Hale 5 m telescope,” Astron. J. 98, 1783–1799 (1989).
[CrossRef]

T. Nakajima, S. R. Kulkarni, P. W. Gorham, A. M. Ghez, G. Neugebauer, J. B. Oke, T. A. Prince, A. C. S. Readhead, “Diffraction-limited imaging. II. Optical aperture synthesis imaging of two binary stars,” Astron. J. 97, 1510–1521 (1989).
[CrossRef]

Readhead, A. C. S.

T. Nakajima, S. R. Kulkarni, P. W. Gorham, A. M. Ghez, G. Neugebauer, J. B. Oke, T. A. Prince, A. C. S. Readhead, “Diffraction-limited imaging. II. Optical aperture synthesis imaging of two binary stars,” Astron. J. 97, 1510–1521 (1989).
[CrossRef]

A. C. S. Readhead, T. Nakajima, T. J. Pearson, G. Neugebauer, J. B. Oke, W. L. W. Sargent, “Diffraction-limited imaging with ground-based optical telescopes,” Astron. J. 95, 1278–1296 (1988).
[CrossRef]

T. J. Pearson, A. C. S. Readhead, “Image formation by self-calibration in radio astronomy,” Ann. Rev. Astron. Astrophys. 22, 97–130 (1984).
[CrossRef]

Ricort, G.

R. G. Petrov, C. Aime, J. Borgnino, F. Martin, G. Ricort, “16-m large slit aperture telescope for very high angular resolution astronomy,” Proc. IAU Colloq. 79, 295–308 (1984).

S. Kadiri, C. Aime, G. Ricort, “Speckle interférométrie à une dimension en astronomie: étude des fonctions de transfert instrument–atmosphère obtenues par analyze statistique de speckles stellaires fournis par un objectif rectangulaire,”J. Opt. (Paris) 12, 143–151 (1981).
[CrossRef]

Ridgway, S. T.

C. A. Haniff, D. F.Buscher, J. C. Christou, S. T. Ridgway, “Synthetic aperture imaging at infrared wavelengths,”M. Not. R. Astron. Soc. 241, 51P–56P (1989).

C. A. Haniff, D. F. Buscher, J. C. Christou, S. T. Ridgway, “Diffraction-limited imaging at IR wavelengths using aperture masks and fully-filled apertures,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng1237, 259–271 (1990).
[CrossRef]

Robertson, J. G.

J. G. Robertson, T. R. Bedding, R. G. Marson, P. R. Gillingham, R. H. Frater, J. D. O’Sullivan, R. P. Norris, “High-resolution imaging by optical aperture synthesis: first results from the MAPPIT project,” Proc. Astron. Soc. Aust. 9, 162–163 (1991).

Roddier, F.

Sargent, W. L. W.

A. C. S. Readhead, T. Nakajima, T. J. Pearson, G. Neugebauer, J. B. Oke, W. L. W. Sargent, “Diffraction-limited imaging with ground-based optical telescopes,” Astron. J. 95, 1278–1296 (1988).
[CrossRef]

Sivia, D.

C. A. Haniff, C. D. Mackay, D. J. Titterington, D. Sivia, J. E. Baldwin, P. J. Warner, “The first images from optical aperture synthesis,” Nature (London) 328, 694–696 (1988).
[CrossRef]

Titterington, D. J.

C. A. Haniff, C. D. Mackay, D. J. Titterington, D. Sivia, J. E. Baldwin, P. J. Warner, “The first images from optical aperture synthesis,” Nature (London) 328, 694–696 (1988).
[CrossRef]

Touma, H.

F. Martin, H. Touma, A. Bijaoui, C. Aime, “Reconstruction d’images en astronomie par utilisation d’un télescope à pupile fente,”J. Opt. (Paris) 18, 133–138 (1987).
[CrossRef]

F. Martin, A. Bijaoui, H. Touma, C. Aime, “Astronomical image reconstruction via space slit aperture telescope,” in Infrared, Adaptive and Synthetic Aperture Optical Systems, R. B. Johnson, W. L. Wolfe, J. S. Fender, eds., Proc. Soc. Photo-Opt. Instrum. Eng.643, 189–193 (1986).
[CrossRef]

Warner, P. J.

R. W. Wilson, J. E. Baldwin, D. F. Buscher, P. J. Warner, “High-resolution imaging of Betelgeuse and Mira,”M. Not. R. Astron. Soc. 257, 369–376 (1992).

D. F. Buscher, C. A. Haniff, J. E. Baldwin, P. J. Warner, “Detection of a bright feature on the surface of Betelgeuse,”M. Not. R. Astron. Soc. 245, 7P–11P (1990).

C. A. Haniff, C. D. Mackay, D. J. Titterington, D. Sivia, J. E. Baldwin, P. J. Warner, “The first images from optical aperture synthesis,” Nature (London) 328, 694–696 (1988).
[CrossRef]

Weigelt, G.

See, e.g., G. Weigelt, “Speckle interferometry, speckle holography, speckle spectroscopy and reconstruction of high-resolution images from ST data,” in Proceedings of the ESO Conference on the Scientific Importance of High Angular Resolution at Infrared and Optical Wavelengths, M.-H. Ulrich, K. Kjär, eds. (European Southern Observatory, Garching, Germany, 1981), pp. 95–114.

Wilson, R. W.

R. W. Wilson, J. E. Baldwin, D. F. Buscher, P. J. Warner, “High-resolution imaging of Betelgeuse and Mira,”M. Not. R. Astron. Soc. 257, 369–376 (1992).

Wirnitzer, B.

Ann. Rev. Astron. Astrophys.

T. J. Pearson, A. C. S. Readhead, “Image formation by self-calibration in radio astronomy,” Ann. Rev. Astron. Astrophys. 22, 97–130 (1984).
[CrossRef]

Appl. Opt.

Astron. Astrophys.

S. N. Karbelkar, “Optimum weighting function in bispectral analysis in speckle interferometry: binary star parity detection,” Astron. Astrophys. 238, 485–493 (1990).

Astron. J.

A. C. S. Readhead, T. Nakajima, T. J. Pearson, G. Neugebauer, J. B. Oke, W. L. W. Sargent, “Diffraction-limited imaging with ground-based optical telescopes,” Astron. J. 95, 1278–1296 (1988).
[CrossRef]

T. Nakajima, S. R. Kulkarni, P. W. Gorham, A. M. Ghez, G. Neugebauer, J. B. Oke, T. A. Prince, A. C. S. Readhead, “Diffraction-limited imaging. II. Optical aperture synthesis imaging of two binary stars,” Astron. J. 97, 1510–1521 (1989).
[CrossRef]

C. A. Haniff, A. M. Ghez, P. W. Gorham, S. R. Kulkarni, K. Matthews, G. Neugebauer, “Optical aperture synthetic imaging of the photosphere and molecular atmosphere of Mira,” Astron. J. 103, 1662–1667 (1992).
[CrossRef]

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. Prince, “Diffraction-limited imaging. III. 30mas closure phase imaging of six binary stars with the Hale 5 m telescope,” Astron. J. 98, 1783–1799 (1989).
[CrossRef]

J. Opt. (Paris)

F. Martin, H. Touma, A. Bijaoui, C. Aime, “Reconstruction d’images en astronomie par utilisation d’un télescope à pupile fente,”J. Opt. (Paris) 18, 133–138 (1987).
[CrossRef]

S. Kadiri, C. Aime, G. Ricort, “Speckle interférométrie à une dimension en astronomie: étude des fonctions de transfert instrument–atmosphère obtenues par analyze statistique de speckles stellaires fournis par un objectif rectangulaire,”J. Opt. (Paris) 12, 143–151 (1981).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

M. Not. R. Astron. Soc.

R. W. Wilson, J. E. Baldwin, D. F. Buscher, P. J. Warner, “High-resolution imaging of Betelgeuse and Mira,”M. Not. R. Astron. Soc. 257, 369–376 (1992).

D. F. Buscher, C. A. Haniff, J. E. Baldwin, P. J. Warner, “Detection of a bright feature on the surface of Betelgeuse,”M. Not. R. Astron. Soc. 245, 7P–11P (1990).

C. A. Haniff, D. F.Buscher, J. C. Christou, S. T. Ridgway, “Synthetic aperture imaging at infrared wavelengths,”M. Not. R. Astron. Soc. 241, 51P–56P (1989).

Nature (London)

C. A. Haniff, C. D. Mackay, D. J. Titterington, D. Sivia, J. E. Baldwin, P. J. Warner, “The first images from optical aperture synthesis,” Nature (London) 328, 694–696 (1988).
[CrossRef]

Opt. Commun.

C. Aime, F. Roddier, “One-dimensional stellar and solar speckle interferometry,” Opt. Commun. 21, 435–438 (1977).
[CrossRef]

Proc. Astron. Soc. Aust.

J. G. Robertson, T. R. Bedding, R. G. Marson, P. R. Gillingham, R. H. Frater, J. D. O’Sullivan, R. P. Norris, “High-resolution imaging by optical aperture synthesis: first results from the MAPPIT project,” Proc. Astron. Soc. Aust. 9, 162–163 (1991).

Proc. IAU Colloq.

R. G. Petrov, C. Aime, J. Borgnino, F. Martin, G. Ricort, “16-m large slit aperture telescope for very high angular resolution astronomy,” Proc. IAU Colloq. 79, 295–308 (1984).

Other

See, e.g., G. Weigelt, “Speckle interferometry, speckle holography, speckle spectroscopy and reconstruction of high-resolution images from ST data,” in Proceedings of the ESO Conference on the Scientific Importance of High Angular Resolution at Infrared and Optical Wavelengths, M.-H. Ulrich, K. Kjär, eds. (European Southern Observatory, Garching, Germany, 1981), pp. 95–114.

See, e.g., E. K. Hege, A. Eckart, J. C. Christou, “The noise bias problem in optical speckle imaging: experience with a real detector,” in Instrumentation in Astronomy VI, P. L. Crawford, ed., Proc. Soc. Photo-Opt. Instrum. Eng.627, 772–779 (1986).
[CrossRef]

See, e.g., D. M. Alloin, J.-M. Mariotti, Diffraction-Limited Imaging with Very Large Telescopes (Kluwer, Dordrecht, The Netherlands, 1989), pp. 157–169 and 191–200.

P. R. Lawson, School of Physics, University of Sydney, Sydney, NSW 2006, Australia (personal communication, January1993).

D. F. Buscher, “Getting the most out of C.O.A.S.T.,” Ph.D. dissertation (Cambridge University, Cambridge, 1988).

J. W. Goodman, J. F. Belsher, “Fundamental limitations in linear invariant restoration of atmospherically degraded images,” in Imaging through the Atmosphere, J. C. Wyant, ed., Proc. Soc. Photo-Opt. Instrum. Eng.75, 141–154 (1976).
[CrossRef]

C. A. Haniff, D. F. Buscher, J. C. Christou, S. T. Ridgway, “Diffraction-limited imaging at IR wavelengths using aperture masks and fully-filled apertures,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng1237, 259–271 (1990).
[CrossRef]

F. Martin, A. Bijaoui, H. Touma, C. Aime, “Astronomical image reconstruction via space slit aperture telescope,” in Infrared, Adaptive and Synthetic Aperture Optical Systems, R. B. Johnson, W. L. Wolfe, J. S. Fender, eds., Proc. Soc. Photo-Opt. Instrum. Eng.643, 189–193 (1986).
[CrossRef]

F. Martin, “Imagery in astronomy by inverse Radon transformation, using a rotating slit aperture telescope (SAT),” in Inverse Problems in Optics, E. R. Pike, ed., Proc. Soc. Photo-Opt. Instrum. Eng.808, 206–208 (1987).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Schematic diagrams of various pupil geometries. The redundant copies of a given baseline are represented by the dumbell-shaped diagrams. The values of the baseline redundancy R and the pupil area A are given beside each pupil.

Fig. 2
Fig. 2

Schematic diagrams of various pupil geometries. The redundant copies of a given pupil triplet are represented by the triple-dumbell diagrams. The values of the triplet redundancy Rt and the pupil area A are given beside each pupil.

Fig. 3
Fig. 3

Power-spectrum SNR as a function of spatial frequency for a variety of pupil geometries. The curves in (a) have been evaluated for a photon rate of 0.1 photon per r0-sized patch per coherent integration time, while those in (b) have been computed for a photon rate ten times higher. The SNR is relatively Independent of the total number of photons detected for the slit and for the fully filled pupil, and at high spatial frequencies the pupils with smaller area give the best SNR’s. The seeing limit (r0/λ) corresponds to a spatial frequency of 5 units, and the diffraction limit to 128 units.

Fig. 4
Fig. 4

Fractional miscalibration of the mean power spectrum when the Fried parameter r0 rises by 20% between the observations of source and calibrator. Curves are plotted for the filled aperture, a thin annular pupil, and three of the slit-type pupils discussed in the text.

Fig. 5
Fig. 5

Three-dimensional surface plot of the bispectrum-phase SNR for the filled pupil, evaluated for a photon rate of 0.1 detected photon per coherence patch per coherence time. Only the nondegenerate portion of the bispectrum, which has a triangular support in the (u1, u2) plane, is plotted. The vertical height of the surface at any point is proportional to the logarithm of the phase SNR at that point.

Fig. 6
Fig. 6

Contour plots of the bispectrum-phase SNR for five slit pupils and a filled aperture. All the slits have a long dimension equal to the diameter of the filled aperture (25.6r0) and that is short dimensions of r0, 2r0, 4r0, 8r0, and 16r0. The simulated photon rate is 0.1 photon per coherence patch per coherence time, i.e., the mean photon rates per interferogram are 3, 7, 13, 26, 49, and 66 for (a), (b), (c), (d), (e), and (f), respectively. The contour levels are plotted at values of 10−9, 10−5, 10−4, 10−3, 10−2, 10−1, and 100. For clarity the 10−3 levels are shown as dotted curves. The seeing limit corresponds to a spatial frequency of 5 units.

Fig. 7
Fig. 7

Contour plots of the bispectrum-phase SNR for (a) the 4r0-wide slit and (b) the filled aperture. The simulated photon rate is 0.3 photon per r0-sized patch per coherent integration time, i.e., 3 times the rate used to generate Fig. 6. The contour levels are the same as for Fig. 6.

Fig. 8
Fig. 8

Contour plots of the bispectrum-phase SNR for (a) the 4r0-wide slit and (b) the filled aperture. The simulated photon rate is 1.0 photon per r0-sized patch per coherent integration time, i.e., 10 times the rate used to generate Fig. 6. The contour levels are the same as for Figs. 6 and 7.

Fig. 9
Fig. 9

Observed power-spectrum SNR per frame measured at the Hale 5-m telescope. The effective photon rates were 10, 20, and 265 per interferogram for the three pupil geometries investigated. A spatial frequency of 80 corresponds to the maximum observed baseline of 4.5 m. Note the better SNR characteristics of the pupils with smaller effective area.

Fig. 10
Fig. 10

Observed bispectrum-phase SNR measured at the Hale 5-m telescope. The effective photon rates were 10, 20, and 256 per interferogram for the three pupil geometries investigated. The gray scale runs logarithmically from −0.1 to 7.9, i.e., white regions of the plot contain no useful signal because the SNR after averaging 15,500 frames is less than 2 [ log ( 15 , 500 ) = 2.1 ]. The triangular contour defines the support of the nondegenerate portion of the bispectrum sampled by the telescope. The regions beyond this that appear to contain signal correspond to spatial frequencies sampled by the detector but not by the telescope. As in Fig. 9, a spatial frequency of 80 corresponds to a baseline of 4.5 m.

Fig. 11
Fig. 11

Self-calibration images of the binary star ϕ Andromedae obtained with a 4 m × 10 cm pupil mask. Contours are plotted at −2, 2, 4, 8, 16, 32, 64, and 99% of the peak intensity. The effective photon rates were (a) 50 and (b) 25 per interferogram. The restoring beam for each image is shown in the lower left-hand corner. North is up, and East is to the left.

Equations (5)

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

SNR ps = N 0 R / A 1 + N 0 R / A ,
SNR ps N 0 ( R / A ) ,
SNR bs S σ ,
SNR bs = N 0 3 R t ( N 0 A ) 3 / 2 / 2 = 2 N 0 3 / 2 ( R t A 3 / 2 ) ,
SNR ps = N ¯ I ( 2 ) ( u ) [ 1 + 2 N ¯ I ( 2 ) ( u ) + N ¯ 2 var { I ( 2 ) ( u ) } + I ( 2 ) ( 2 u ) ] 1 / 2 ,

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