Abstract

Group-delay tracking is a method of fringe tracking used for optical stellar interferometry. It employs a photon-counting spectrometer to record short-exposure frames of channeled spectra. In each frame the number of fringes is proportional to the path difference, which can be extracted by power spectrum analysis. In this study the low-light-level limitations of the method are examined when the fast Fourier transform is used for data processing. Frame times are limited by the coherence time of the atmosphere, and for active tracking the sensitivity depends on the largest number of power spectra that can be integrated usefully. Rayleigh and Rician statistics are used to model the visibility amplitudes determined from the power spectra, and the probability of tracking loss is examined as a function of fringe visibility, the number of photons per frame, and the number of integrated frames. The effect of bracketing the fringe peak with a filter is also examined, and simulations are used to verify the predictions.

© 1995 Optical Society of America

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  1. K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1988).
    [CrossRef]
  2. A. A. Michelson, F. G. Pease, “Measurement of the diameter of αOrionis with the interferometer,” Astrophys. J. 53, 249–259 (1921).
    [CrossRef]
  3. A. Labeyrie, “Interference fringes obtained on Vega with two optical telescopes,” Astrophys. J. 196, L71–L75 (1975).
    [CrossRef]
  4. D. Bonneau, L. Koechlin, J. L. Onéto, F. Vakili, “Stellar diameter measurements by two telescope interferometry in optical wavelengths,” Astron. Astrophys. 103, 28–34 (1981).
  5. D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).
  6. L. Koechlin, “Interférométrie stellaire dans l’espace: détection des franges,”J. Opt. (Paris) 16, 269–276 (1985).
    [CrossRef]
  7. E. J. Kim, “Dispersed fringe group delay astrometry using the Mark III stellar interferometer,” M.S.E.E. thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1989).
  8. J. Davis, P. R. Lawson, A. J. Booth, W. J. Tango, E. Thorvaldson, “Atmospheric path variations for baselines up to 80 m measured with the Sydney University Stellar Interferometer,” Mon. Not. R. Astron. Soc. (to be published).
  9. P. Nisenson, W. Traub, “Magnitude limit of the group delay tracking method for long baseline interferometry,” in Interferometric Imaging in Astronomy, J. Goad, ed. (National Optical Astronomy Observatories, Tucson, Ariz., 1987), pp. 129–133.
  10. D. Buscher, “Low light level limits to tracking atmospheric fringe wander,” in Quantum Limited Imaging and Information Processing, Vol. 13 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 67–69.
  11. M. M. Colavita, M. Shao, “Photon-starved astrometric measurements with a large-aperture interferometer,” in High Resolution Imaging by Interferometry, F. Merkle, ed. (European Southern Observatory, Garching bei München, Germany, 1988), pp. 833–839.
  12. M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. L. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).
  13. J. C. Dainty, “Detection of images immersed in speckle noise,” Opt. Acta 18, 327–339 (1971).
    [CrossRef]
  14. J. F. Walkup, J. W. Goodman, “Limitations of fringe-parameter estimation at low light levels,”J. Opt. Soc. Am. 63, 399–407 (1973).
    [CrossRef]
  15. A. R. Thompson, J. M. Moran, G. W. Swenson, Interferometry and Synthesis in Radio Astronomy (Wiley, New York, 1986), pp. 165–167, 259–269.
  16. P. R. Lawson, “Group delay tracking with the Sydney University Stellar Interferometer,” Publ. Astron. Soc. Pac. 106, 917 (1994).
    [CrossRef]
  17. W. H. Steel, Interferometry (Cambridge U. Press, Cambridge, U.K., 1987), pp. 101–102.
  18. W. J. Tango, R. Q. Twiss, “Michelson stellar interferometry,” Prog. Opt. 17, 239–277 (1980).
    [CrossRef]
  19. S. M. Kay, S. L. Marple, “Spectrum analysis—a modern perspective,” Proc. IEEE 69, 1380–1418 (1981).
    [CrossRef]
  20. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 581–584.
  21. G. D. Bergland, “A guided tour of the fast Fourier transform,” IEEE Spectrum 6, 41–45 (1969).
    [CrossRef]
  22. J. W. Beletic, R. M. Goody, “Recovery of planetary images by speckle imaging,” Appl. Opt. 31, 6909–6921 (1992).
    [CrossRef] [PubMed]
  23. S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. 23, 282–332 (1944).
  24. S. O. Rice, “Mathematical analysis of random noise. Part II,” Bell Syst. Tech. J. 24, 46–156 (1945).
  25. S. O. Rice, “Statistical properties of a sine wave plus random noise,” Bell Syst. Tech. J. 27, 109–157 (1948).
  26. W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), pp. 54–55.
  27. M. Bester, W. C. Danchi, C. G. Degiacomi, L. J. Greenhill, C. H. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. 392, 357–374 (1992).
    [CrossRef]
  28. D. Buscher, “Optimizing a ground-based optical interferometer for sensitivity at low light levels,” Mon. Not. R. Astron. Soc. 235, 1203–1226 (1988).
  29. J. Davis, W. J. Tango, A. J. Booth, R. A. Minard, S. M. Owens, R. R. Shobbrook, “Progress in commissioning the Sydney University Stellar Interferometer (SUSI),” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2200231–241 (1994).
    [CrossRef]
  30. N. S. Nightingale, D. F. Buscher, “Interferometric seeing measurements at the La Palma Observatory,” Mon. Not. R. Astron. Soc. 251, 155–166 (1991).
  31. C. Masson, “Seeing,” in IAU Symposium 158 on Very High Angular Resolution Imaging, J. G. Robertson, W. J. Tango, eds. (Kluwer, Dordrecht, The Netherlands, 1994), pp. 1–9.
    [CrossRef]
  32. M. Shao, D. H. Staelin, “First fringe measurements with a phase tracking stellar interferometer,” Appl. Opt. 19, 1519–1522 (1980).
    [CrossRef] [PubMed]
  33. D. Mozurkewich, K. J. Johnston, R. S. Simon, P. F. Bowers, R. Gaume, D. J. Hutter, M. M. Colavita, M. Shao, X. P. Pan, “Angular diameter measurements of stars,” Astron. J. 101, 2207–2219 (1991).
    [CrossRef]
  34. W. J. Tango, “Dispersion in stellar interferometry,” Appl. Opt. 29, 516–521 (1990).
    [CrossRef] [PubMed]
  35. W. A. Traub, “Constant-dispersion grism spectrometer for channeled spectra,” J. Opt. Soc. Am. A 7, 1779–1791 (1990).
    [CrossRef]
  36. L. Koechlin, “Active fringe tracking,” in High Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching bei München, Germany, 1992), pp. 1239–1246.

1994 (2)

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

P. R. Lawson, “Group delay tracking with the Sydney University Stellar Interferometer,” Publ. Astron. Soc. Pac. 106, 917 (1994).
[CrossRef]

1992 (2)

J. W. Beletic, R. M. Goody, “Recovery of planetary images by speckle imaging,” Appl. Opt. 31, 6909–6921 (1992).
[CrossRef] [PubMed]

M. Bester, W. C. Danchi, C. G. Degiacomi, L. J. Greenhill, C. H. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. 392, 357–374 (1992).
[CrossRef]

1991 (2)

N. S. Nightingale, D. F. Buscher, “Interferometric seeing measurements at the La Palma Observatory,” Mon. Not. R. Astron. Soc. 251, 155–166 (1991).

D. Mozurkewich, K. J. Johnston, R. S. Simon, P. F. Bowers, R. Gaume, D. J. Hutter, M. M. Colavita, M. Shao, X. P. Pan, “Angular diameter measurements of stars,” Astron. J. 101, 2207–2219 (1991).
[CrossRef]

1990 (2)

1988 (3)

D. Buscher, “Optimizing a ground-based optical interferometer for sensitivity at low light levels,” Mon. Not. R. Astron. Soc. 235, 1203–1226 (1988).

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. L. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1988).
[CrossRef]

1985 (1)

L. Koechlin, “Interférométrie stellaire dans l’espace: détection des franges,”J. Opt. (Paris) 16, 269–276 (1985).
[CrossRef]

1981 (2)

D. Bonneau, L. Koechlin, J. L. Onéto, F. Vakili, “Stellar diameter measurements by two telescope interferometry in optical wavelengths,” Astron. Astrophys. 103, 28–34 (1981).

S. M. Kay, S. L. Marple, “Spectrum analysis—a modern perspective,” Proc. IEEE 69, 1380–1418 (1981).
[CrossRef]

1980 (2)

1975 (1)

A. Labeyrie, “Interference fringes obtained on Vega with two optical telescopes,” Astrophys. J. 196, L71–L75 (1975).
[CrossRef]

1973 (1)

1971 (1)

J. C. Dainty, “Detection of images immersed in speckle noise,” Opt. Acta 18, 327–339 (1971).
[CrossRef]

1969 (1)

G. D. Bergland, “A guided tour of the fast Fourier transform,” IEEE Spectrum 6, 41–45 (1969).
[CrossRef]

1948 (1)

S. O. Rice, “Statistical properties of a sine wave plus random noise,” Bell Syst. Tech. J. 27, 109–157 (1948).

1945 (1)

S. O. Rice, “Mathematical analysis of random noise. Part II,” Bell Syst. Tech. J. 24, 46–156 (1945).

1944 (1)

S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. 23, 282–332 (1944).

1921 (1)

A. A. Michelson, F. G. Pease, “Measurement of the diameter of αOrionis with the interferometer,” Astrophys. J. 53, 249–259 (1921).
[CrossRef]

Beletic, J. W.

Bergland, G. D.

G. D. Bergland, “A guided tour of the fast Fourier transform,” IEEE Spectrum 6, 41–45 (1969).
[CrossRef]

Bester, M.

M. Bester, W. C. Danchi, C. G. Degiacomi, L. J. Greenhill, C. H. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. 392, 357–374 (1992).
[CrossRef]

Blazit, A.

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

Bonneau, D.

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

D. Bonneau, L. Koechlin, J. L. Onéto, F. Vakili, “Stellar diameter measurements by two telescope interferometry in optical wavelengths,” Astron. Astrophys. 103, 28–34 (1981).

Booth, A. J.

J. Davis, P. R. Lawson, A. J. Booth, W. J. Tango, E. Thorvaldson, “Atmospheric path variations for baselines up to 80 m measured with the Sydney University Stellar Interferometer,” Mon. Not. R. Astron. Soc. (to be published).

J. Davis, W. J. Tango, A. J. Booth, R. A. Minard, S. M. Owens, R. R. Shobbrook, “Progress in commissioning the Sydney University Stellar Interferometer (SUSI),” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2200231–241 (1994).
[CrossRef]

Bowers, P. F.

D. Mozurkewich, K. J. Johnston, R. S. Simon, P. F. Bowers, R. Gaume, D. J. Hutter, M. M. Colavita, M. Shao, X. P. Pan, “Angular diameter measurements of stars,” Astron. J. 101, 2207–2219 (1991).
[CrossRef]

Buscher, D.

D. Buscher, “Optimizing a ground-based optical interferometer for sensitivity at low light levels,” Mon. Not. R. Astron. Soc. 235, 1203–1226 (1988).

D. Buscher, “Low light level limits to tracking atmospheric fringe wander,” in Quantum Limited Imaging and Information Processing, Vol. 13 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 67–69.

Buscher, D. F.

N. S. Nightingale, D. F. Buscher, “Interferometric seeing measurements at the La Palma Observatory,” Mon. Not. R. Astron. Soc. 251, 155–166 (1991).

Colavita, M. M.

D. Mozurkewich, K. J. Johnston, R. S. Simon, P. F. Bowers, R. Gaume, D. J. Hutter, M. M. Colavita, M. Shao, X. P. Pan, “Angular diameter measurements of stars,” Astron. J. 101, 2207–2219 (1991).
[CrossRef]

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. L. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

M. M. Colavita, M. Shao, “Photon-starved astrometric measurements with a large-aperture interferometer,” in High Resolution Imaging by Interferometry, F. Merkle, ed. (European Southern Observatory, Garching bei München, Germany, 1988), pp. 833–839.

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1988).
[CrossRef]

Dainty, J. C.

J. C. Dainty, “Detection of images immersed in speckle noise,” Opt. Acta 18, 327–339 (1971).
[CrossRef]

Danchi, W. C.

M. Bester, W. C. Danchi, C. G. Degiacomi, L. J. Greenhill, C. H. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. 392, 357–374 (1992).
[CrossRef]

Davenport, W. B.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), pp. 54–55.

Davis, J.

J. Davis, W. J. Tango, A. J. Booth, R. A. Minard, S. M. Owens, R. R. Shobbrook, “Progress in commissioning the Sydney University Stellar Interferometer (SUSI),” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2200231–241 (1994).
[CrossRef]

J. Davis, P. R. Lawson, A. J. Booth, W. J. Tango, E. Thorvaldson, “Atmospheric path variations for baselines up to 80 m measured with the Sydney University Stellar Interferometer,” Mon. Not. R. Astron. Soc. (to be published).

Degiacomi, C. G.

M. Bester, W. C. Danchi, C. G. Degiacomi, L. J. Greenhill, C. H. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. 392, 357–374 (1992).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 581–584.

Gaume, R.

D. Mozurkewich, K. J. Johnston, R. S. Simon, P. F. Bowers, R. Gaume, D. J. Hutter, M. M. Colavita, M. Shao, X. P. Pan, “Angular diameter measurements of stars,” Astron. J. 101, 2207–2219 (1991).
[CrossRef]

Goodman, J. W.

Goody, R. M.

Greenhill, L. J.

M. Bester, W. C. Danchi, C. G. Degiacomi, L. J. Greenhill, C. H. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. 392, 357–374 (1992).
[CrossRef]

Hershey, J. L.

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. L. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Hines, B. E.

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. L. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Hughes, J. A.

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. L. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Hutter, D. J.

D. Mozurkewich, K. J. Johnston, R. S. Simon, P. F. Bowers, R. Gaume, D. J. Hutter, M. M. Colavita, M. Shao, X. P. Pan, “Angular diameter measurements of stars,” Astron. J. 101, 2207–2219 (1991).
[CrossRef]

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. L. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Johnston, K. J.

D. Mozurkewich, K. J. Johnston, R. S. Simon, P. F. Bowers, R. Gaume, D. J. Hutter, M. M. Colavita, M. Shao, X. P. Pan, “Angular diameter measurements of stars,” Astron. J. 101, 2207–2219 (1991).
[CrossRef]

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. L. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Kaplan, G. H.

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. L. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Kay, S. M.

S. M. Kay, S. L. Marple, “Spectrum analysis—a modern perspective,” Proc. IEEE 69, 1380–1418 (1981).
[CrossRef]

Kim, E. J.

E. J. Kim, “Dispersed fringe group delay astrometry using the Mark III stellar interferometer,” M.S.E.E. thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1989).

Koechlin, L.

L. Koechlin, “Interférométrie stellaire dans l’espace: détection des franges,”J. Opt. (Paris) 16, 269–276 (1985).
[CrossRef]

D. Bonneau, L. Koechlin, J. L. Onéto, F. Vakili, “Stellar diameter measurements by two telescope interferometry in optical wavelengths,” Astron. Astrophys. 103, 28–34 (1981).

L. Koechlin, “Active fringe tracking,” in High Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching bei München, Germany, 1992), pp. 1239–1246.

Labeyrie, A.

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

A. Labeyrie, “Interference fringes obtained on Vega with two optical telescopes,” Astrophys. J. 196, L71–L75 (1975).
[CrossRef]

Lawson, P. R.

P. R. Lawson, “Group delay tracking with the Sydney University Stellar Interferometer,” Publ. Astron. Soc. Pac. 106, 917 (1994).
[CrossRef]

J. Davis, P. R. Lawson, A. J. Booth, W. J. Tango, E. Thorvaldson, “Atmospheric path variations for baselines up to 80 m measured with the Sydney University Stellar Interferometer,” Mon. Not. R. Astron. Soc. (to be published).

Marple, S. L.

S. M. Kay, S. L. Marple, “Spectrum analysis—a modern perspective,” Proc. IEEE 69, 1380–1418 (1981).
[CrossRef]

Masson, C.

C. Masson, “Seeing,” in IAU Symposium 158 on Very High Angular Resolution Imaging, J. G. Robertson, W. J. Tango, eds. (Kluwer, Dordrecht, The Netherlands, 1994), pp. 1–9.
[CrossRef]

Merlin, G.

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

Michelson, A. A.

A. A. Michelson, F. G. Pease, “Measurement of the diameter of αOrionis with the interferometer,” Astrophys. J. 53, 249–259 (1921).
[CrossRef]

Minard, R. A.

J. Davis, W. J. Tango, A. J. Booth, R. A. Minard, S. M. Owens, R. R. Shobbrook, “Progress in commissioning the Sydney University Stellar Interferometer (SUSI),” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2200231–241 (1994).
[CrossRef]

Moran, J. M.

A. R. Thompson, J. M. Moran, G. W. Swenson, Interferometry and Synthesis in Radio Astronomy (Wiley, New York, 1986), pp. 165–167, 259–269.

Morand, F.

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

Mourard, D.

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

Mozurkewich, D.

D. Mozurkewich, K. J. Johnston, R. S. Simon, P. F. Bowers, R. Gaume, D. J. Hutter, M. M. Colavita, M. Shao, X. P. Pan, “Angular diameter measurements of stars,” Astron. J. 101, 2207–2219 (1991).
[CrossRef]

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. L. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Nightingale, N. S.

N. S. Nightingale, D. F. Buscher, “Interferometric seeing measurements at the La Palma Observatory,” Mon. Not. R. Astron. Soc. 251, 155–166 (1991).

Nisenson, P.

P. Nisenson, W. Traub, “Magnitude limit of the group delay tracking method for long baseline interferometry,” in Interferometric Imaging in Astronomy, J. Goad, ed. (National Optical Astronomy Observatories, Tucson, Ariz., 1987), pp. 129–133.

Onéto, J. L.

D. Bonneau, L. Koechlin, J. L. Onéto, F. Vakili, “Stellar diameter measurements by two telescope interferometry in optical wavelengths,” Astron. Astrophys. 103, 28–34 (1981).

Owens, S. M.

J. Davis, W. J. Tango, A. J. Booth, R. A. Minard, S. M. Owens, R. R. Shobbrook, “Progress in commissioning the Sydney University Stellar Interferometer (SUSI),” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2200231–241 (1994).
[CrossRef]

Pan, X. P.

D. Mozurkewich, K. J. Johnston, R. S. Simon, P. F. Bowers, R. Gaume, D. J. Hutter, M. M. Colavita, M. Shao, X. P. Pan, “Angular diameter measurements of stars,” Astron. J. 101, 2207–2219 (1991).
[CrossRef]

Pease, F. G.

A. A. Michelson, F. G. Pease, “Measurement of the diameter of αOrionis with the interferometer,” Astrophys. J. 53, 249–259 (1921).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 581–584.

Rice, S. O.

S. O. Rice, “Statistical properties of a sine wave plus random noise,” Bell Syst. Tech. J. 27, 109–157 (1948).

S. O. Rice, “Mathematical analysis of random noise. Part II,” Bell Syst. Tech. J. 24, 46–156 (1945).

S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. 23, 282–332 (1944).

Root, W. L.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), pp. 54–55.

Shao, M.

D. Mozurkewich, K. J. Johnston, R. S. Simon, P. F. Bowers, R. Gaume, D. J. Hutter, M. M. Colavita, M. Shao, X. P. Pan, “Angular diameter measurements of stars,” Astron. J. 101, 2207–2219 (1991).
[CrossRef]

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. L. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

M. Shao, D. H. Staelin, “First fringe measurements with a phase tracking stellar interferometer,” Appl. Opt. 19, 1519–1522 (1980).
[CrossRef] [PubMed]

M. M. Colavita, M. Shao, “Photon-starved astrometric measurements with a large-aperture interferometer,” in High Resolution Imaging by Interferometry, F. Merkle, ed. (European Southern Observatory, Garching bei München, Germany, 1988), pp. 833–839.

Shobbrook, R. R.

J. Davis, W. J. Tango, A. J. Booth, R. A. Minard, S. M. Owens, R. R. Shobbrook, “Progress in commissioning the Sydney University Stellar Interferometer (SUSI),” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2200231–241 (1994).
[CrossRef]

Simon, R. S.

D. Mozurkewich, K. J. Johnston, R. S. Simon, P. F. Bowers, R. Gaume, D. J. Hutter, M. M. Colavita, M. Shao, X. P. Pan, “Angular diameter measurements of stars,” Astron. J. 101, 2207–2219 (1991).
[CrossRef]

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. L. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Staelin, D. H.

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. L. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

M. Shao, D. H. Staelin, “First fringe measurements with a phase tracking stellar interferometer,” Appl. Opt. 19, 1519–1522 (1980).
[CrossRef] [PubMed]

Steel, W. H.

W. H. Steel, Interferometry (Cambridge U. Press, Cambridge, U.K., 1987), pp. 101–102.

Swenson, G. W.

A. R. Thompson, J. M. Moran, G. W. Swenson, Interferometry and Synthesis in Radio Astronomy (Wiley, New York, 1986), pp. 165–167, 259–269.

Tallon-Bosc, I.

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

Tango, W. J.

W. J. Tango, “Dispersion in stellar interferometry,” Appl. Opt. 29, 516–521 (1990).
[CrossRef] [PubMed]

W. J. Tango, R. Q. Twiss, “Michelson stellar interferometry,” Prog. Opt. 17, 239–277 (1980).
[CrossRef]

J. Davis, W. J. Tango, A. J. Booth, R. A. Minard, S. M. Owens, R. R. Shobbrook, “Progress in commissioning the Sydney University Stellar Interferometer (SUSI),” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2200231–241 (1994).
[CrossRef]

J. Davis, P. R. Lawson, A. J. Booth, W. J. Tango, E. Thorvaldson, “Atmospheric path variations for baselines up to 80 m measured with the Sydney University Stellar Interferometer,” Mon. Not. R. Astron. Soc. (to be published).

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 581–584.

Thompson, A. R.

A. R. Thompson, J. M. Moran, G. W. Swenson, Interferometry and Synthesis in Radio Astronomy (Wiley, New York, 1986), pp. 165–167, 259–269.

Thorvaldson, E.

J. Davis, P. R. Lawson, A. J. Booth, W. J. Tango, E. Thorvaldson, “Atmospheric path variations for baselines up to 80 m measured with the Sydney University Stellar Interferometer,” Mon. Not. R. Astron. Soc. (to be published).

Townes, C. H.

M. Bester, W. C. Danchi, C. G. Degiacomi, L. J. Greenhill, C. H. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. 392, 357–374 (1992).
[CrossRef]

Traub, W.

P. Nisenson, W. Traub, “Magnitude limit of the group delay tracking method for long baseline interferometry,” in Interferometric Imaging in Astronomy, J. Goad, ed. (National Optical Astronomy Observatories, Tucson, Ariz., 1987), pp. 129–133.

Traub, W. A.

Twiss, R. Q.

W. J. Tango, R. Q. Twiss, “Michelson stellar interferometry,” Prog. Opt. 17, 239–277 (1980).
[CrossRef]

Vakili, F.

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

D. Bonneau, L. Koechlin, J. L. Onéto, F. Vakili, “Stellar diameter measurements by two telescope interferometry in optical wavelengths,” Astron. Astrophys. 103, 28–34 (1981).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 581–584.

Walkup, J. F.

Appl. Opt. (3)

Astron. Astrophys. (3)

D. Bonneau, L. Koechlin, J. L. Onéto, F. Vakili, “Stellar diameter measurements by two telescope interferometry in optical wavelengths,” Astron. Astrophys. 103, 28–34 (1981).

D. Mourard, I. Tallon-Bosc, A. Blazit, D. Bonneau, G. Merlin, F. Morand, F. Vakili, A. Labeyrie, “The GI2T interferometer on Plateau de Calern,” Astron. Astrophys. 283, 705–713 (1994).

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. L. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Astron. J. (1)

D. Mozurkewich, K. J. Johnston, R. S. Simon, P. F. Bowers, R. Gaume, D. J. Hutter, M. M. Colavita, M. Shao, X. P. Pan, “Angular diameter measurements of stars,” Astron. J. 101, 2207–2219 (1991).
[CrossRef]

Astrophys. J. (3)

M. Bester, W. C. Danchi, C. G. Degiacomi, L. J. Greenhill, C. H. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. 392, 357–374 (1992).
[CrossRef]

A. A. Michelson, F. G. Pease, “Measurement of the diameter of αOrionis with the interferometer,” Astrophys. J. 53, 249–259 (1921).
[CrossRef]

A. Labeyrie, “Interference fringes obtained on Vega with two optical telescopes,” Astrophys. J. 196, L71–L75 (1975).
[CrossRef]

Bell Syst. Tech. J. (3)

S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. 23, 282–332 (1944).

S. O. Rice, “Mathematical analysis of random noise. Part II,” Bell Syst. Tech. J. 24, 46–156 (1945).

S. O. Rice, “Statistical properties of a sine wave plus random noise,” Bell Syst. Tech. J. 27, 109–157 (1948).

IEEE Spectrum (1)

G. D. Bergland, “A guided tour of the fast Fourier transform,” IEEE Spectrum 6, 41–45 (1969).
[CrossRef]

J. Opt. (Paris) (1)

L. Koechlin, “Interférométrie stellaire dans l’espace: détection des franges,”J. Opt. (Paris) 16, 269–276 (1985).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Mon. Not. R. Astron. Soc. (2)

D. Buscher, “Optimizing a ground-based optical interferometer for sensitivity at low light levels,” Mon. Not. R. Astron. Soc. 235, 1203–1226 (1988).

N. S. Nightingale, D. F. Buscher, “Interferometric seeing measurements at the La Palma Observatory,” Mon. Not. R. Astron. Soc. 251, 155–166 (1991).

Opt. Acta (1)

J. C. Dainty, “Detection of images immersed in speckle noise,” Opt. Acta 18, 327–339 (1971).
[CrossRef]

Proc. IEEE (1)

S. M. Kay, S. L. Marple, “Spectrum analysis—a modern perspective,” Proc. IEEE 69, 1380–1418 (1981).
[CrossRef]

Prog. Opt. (2)

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1988).
[CrossRef]

W. J. Tango, R. Q. Twiss, “Michelson stellar interferometry,” Prog. Opt. 17, 239–277 (1980).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

P. R. Lawson, “Group delay tracking with the Sydney University Stellar Interferometer,” Publ. Astron. Soc. Pac. 106, 917 (1994).
[CrossRef]

Other (12)

W. H. Steel, Interferometry (Cambridge U. Press, Cambridge, U.K., 1987), pp. 101–102.

A. R. Thompson, J. M. Moran, G. W. Swenson, Interferometry and Synthesis in Radio Astronomy (Wiley, New York, 1986), pp. 165–167, 259–269.

E. J. Kim, “Dispersed fringe group delay astrometry using the Mark III stellar interferometer,” M.S.E.E. thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1989).

J. Davis, P. R. Lawson, A. J. Booth, W. J. Tango, E. Thorvaldson, “Atmospheric path variations for baselines up to 80 m measured with the Sydney University Stellar Interferometer,” Mon. Not. R. Astron. Soc. (to be published).

P. Nisenson, W. Traub, “Magnitude limit of the group delay tracking method for long baseline interferometry,” in Interferometric Imaging in Astronomy, J. Goad, ed. (National Optical Astronomy Observatories, Tucson, Ariz., 1987), pp. 129–133.

D. Buscher, “Low light level limits to tracking atmospheric fringe wander,” in Quantum Limited Imaging and Information Processing, Vol. 13 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 67–69.

M. M. Colavita, M. Shao, “Photon-starved astrometric measurements with a large-aperture interferometer,” in High Resolution Imaging by Interferometry, F. Merkle, ed. (European Southern Observatory, Garching bei München, Germany, 1988), pp. 833–839.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 581–584.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), pp. 54–55.

C. Masson, “Seeing,” in IAU Symposium 158 on Very High Angular Resolution Imaging, J. G. Robertson, W. J. Tango, eds. (Kluwer, Dordrecht, The Netherlands, 1994), pp. 1–9.
[CrossRef]

J. Davis, W. J. Tango, A. J. Booth, R. A. Minard, S. M. Owens, R. R. Shobbrook, “Progress in commissioning the Sydney University Stellar Interferometer (SUSI),” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2200231–241 (1994).
[CrossRef]

L. Koechlin, “Active fringe tracking,” in High Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching bei München, Germany, 1992), pp. 1239–1246.

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Figures (6)

Fig. 1
Fig. 1

One simulated frame of photon data from a detector with 256 pixels. The data is modeled to be Poisson distributed with a mean count rate of 10 detected photons/frame, representing a channeled spectrum with a visibility of 0.5 and 20 fringes across the detector. In this frame there are nine photons.

Fig. 2
Fig. 2

Integrating frames of transformed simulated data. (a) Modulus of the DFT of the frame shown in Fig. 1. (b) Result of the sum of 100 such frames. In (c) the number of frames has been increased to 1000. With 100 frames the peak has been correctly located at a spatial frequency of 20, and with 1000 frames it is easily distinguished above the noise.

Fig. 3
Fig. 3

Probability-density functions of signal plus noise and noise modeled for a single frame and for 100 integrated frames of DFT modulus estimates. The integrated frames are represented by the joint-probability distributions from Rayleigh and Rician distributions, as described in the text. The distributions shown here correspond with the example simulations of Figs. 2(a) and 2(b), respectively. A visibility of 0.5 is used with a mean photon count of 10 photons/frame. When 100 frames are integrated, as shown in (b), the distributions have little overlap, and the probability of tracking loss is low.

Fig. 4
Fig. 4

Probability-density functions of noise and signal plus noise are modeled for a single frame of data and for 10 integrated frames, with the Rayleigh and the Rician distributions. The probability of tracking loss depends on the extent of the overlap of the two distributions. Distributions for a flux of 20 photons/frame over 256 pixels are represented with a fringe visibility of 1.0, for (a) a single frame and (b) 10 integrated frames. In (b) the distributions are farther apart, and the probability of tracking loss is therefore smaller.

Fig. 5
Fig. 5

Probability of tracking error at three different fringe visibilities [(a)–(c)] as a function of light level and of the number of integrated frames. Both the results of calculation of Eq. (15), indicated by the curves, and simulations, indicated by the points, are shown. Detected light levels between 1 and 100 photons/frame are illustrated for a detector of 256 pixels. It is assumed that a DFT would be used to calculate 128 spatial-frequency components, one of which locates the fringe frequency.

Fig. 6
Fig. 6

Probability of tracking loss for a restricted search in spatial frequency. In this example the search is over 10 neighboring spatial frequencies rather than the 126 that are modeled in Fig. 5. The calculations are for a visibility of 0.5.

Equations (28)

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I ( λ ) = I s [ 1 + γ 12 cos ( 2 π x λ + ϕ 12 ) ] + I b ,
x = p Δ κ ,
Δ κ = 1 λ min - 1 λ max .
1 λ n = 1 λ max + n Δ κ N .
x = s 0 Δ κ .
k ¯ ( n ) = k s [ 1 + γ cos ( 2 π n s 0 N + ϕ ) ] + k b ,
N t = N ( k s + k b ) ,
γ = γ 12 sin ( π s 0 / N ) π s 0 / N ,
Λ ( s ) = { N t s = 0 N γ k s / 2 s = ± s 0 0 otherwise ,
SNR ( s ) = Λ ( s ) 2 [ N t 2 + 2 N t Λ ( s ) 2 ] 1 / 2 ,
SNR ( s 0 ) = 1 4 M 1 / 2 N t γ 2 [ 1 + 1 2 N t γ 2 ] 1 / 2 .
P ( Z ) = Z σ 2 exp [ - 1 2 σ 2 ( Z 2 + Λ 2 ) ] I 0 ( Λ Z σ 2 ) ,
Z 2 = Λ 2 + 2 σ 2 .
σ 2 = N t / 2.
p e = 1 - 0 P s ( Z ) [ 0 Z P n ( z ) d z ] b d Z ,
D ϕ ( t ) = ϕ ( t + t ) - ϕ ( t ) 2 = ( t / t 0 ) 5 / 3 ,
σ x = λ ¯ 2 π 2 ( t t 0 ) 5 / 6 ,
T t 0 ( π 2 1 λ ¯ Δ κ ) 6 / 5 ,
η = 1 2 π - exp ( - y 2 2 ) d y ,
= 1 2 σ x Δ κ .
r ( t ) = Λ cos ( ω c t + θ ) + n ( t ) ,
P ( Z ) = Z σ 2 exp [ - 1 2 σ 2 ( Z 2 + Λ 2 ) ] I 0 ( Λ Z σ 2 ) ,
P ( Z ) Λ = 0 = Z σ 2 exp ( - Z 2 2 σ 2 ) .
Z m = ( 2 σ 2 ) m / 2 Γ ( m 2 + 1 ) F 1 1 ( - m 2 ; 1 ; - ρ ) ,
F 1 1 ( a ; b ; x ) = 1 + a b x 1 ! + a b ( a + 1 ) ( b + 1 ) x 2 2 ! + a b ( a + 1 ) ( b + 1 ) ( a + 2 ) ( b + 2 ) x 3 3 ! + .
Z = e - ρ / 2 ( π σ 2 2 ) 1 / 2 [ ( 1 + ρ ) I 0 ( ρ 2 ) + ρ I 1 ( ρ 2 ) ] ,
Z 2 = Λ 2 + 2 σ 2 ,
Z 4 = Λ 4 + 8 σ 2 Λ 2 + 8 σ 4 .

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