Abstract

We detail the theoretical description of a modern optical stellar interferometer by studying the addition of spectral capabilities in such instruments. We give what we believe is the first complete formalism to describe such an interferometer operating in the visible where the fringe signal from large telescope apertures is recorded at the output of a spectrograph. The dispersed-fringes mode and the multichromatic modes are detailed analytically in terms of spectral density and visibility analysis. All the theoretical results are validated through numerical simulation.

© 1999 Optical Society of America

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  1. A. H. Fizeau, “Bordin prize,” C. R. Hebd. Seances Acad. Sci. 66, 932–934 (1868).
  2. E. Stephan, “Extrait d’une lettre de M. Stéphan à M. Fizeau,” C. R. Hebd. Seances Acad. Sci. 76, 1008–1010 (1873).
  3. A. A. Michelson, “On the application of interference methods to astronomical measurements,” Astrophys. J. 51, 257–262 (1920).
    [CrossRef]
  4. A. Labeyrie, “Interference fringes obtained on Vega with two optical telescopes,” Astrophys. J. 196, 71–75 (1975).
    [CrossRef]
  5. G. P. DiBenedetto, R. Foy, “The angular diameter and the effective temperature of Acturus from Michelson interferometry,” Astron. Astrophys. 166, 204–210 (1986).
  6. 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, 705–715 (1994).
  7. D. Mourard, I. Bosc, A. Labeyrie, L. Koechlin, S. Saha, “The rotating envelope of the hot star gamma Cassiopeiae resolved by optical interferometry,” Nature (London) 342, 520–522 (1989).
    [CrossRef]
  8. J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).
  9. J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
    [CrossRef]
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  11. M. Tallon, I. Tallon-Bosc, “The object-image relationship in Michelson stellar interferometry,” Astron. Astrophys. 253, 641–645 (1992).
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  13. P. Berio, D. Mourard, F. Vakili, J. Borgnino, A. Ziad, “Effects of atmospheric spectral decorrelation on visibility measurements in Michelson interferometry,” J. Opt. Soc. Am. A 14, 114–121 (1997).
    [CrossRef]
  14. D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).
  15. F. Roddier, P. Léna, “Long-baseline Michelson interferometry with large ground-based telescopes operating at optical wavelengths,” J. Opt. 15, 171–182 (1984).
    [CrossRef]
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  17. P. Stee, F. X. de Araujo, F. Vakili, D. Mourard, L. Arnold, D. Bonneau, F. Morand, I. Tallon-Bosc, “γ Cassiopeiae revisited by spectrally resolved interferometry,” Astron. Astrophys. 300, 219–236 (1995).
  18. F. Vakili, D. Mourard, D. Bonneau, F. Morand, P. Stee, “Subtle structures in the wind of P Cygni,” Astron. Astrophys. 323, 183–188 (1997).
  19. N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. (Bellingham) 29, 1174–1180 (1990).
    [CrossRef]
  20. P. Harmanec, F. Morand, D. Bonneau, Y. Jiang, S. Yang, “Jet-like structures in beta Lyrae,” Astron. Astrophys. 312, 879–896 (1996).
  21. D. Mourard, D. Bonneau, L. Koechlin, A. Labeyrie, F. Morand, P. Stee, I. Tallon-Bosc, F. Vakili, “The mean angular diameter of δ Cephei measured by optical long-baseline interferometry,” Astron. Astrophys. 317, 789–792 (1997).
  22. C. Roddier, F. Roddier, “On the fringe visibility in a Michelson interferometer,” J. Opt. Soc. Am. 66, 580–584 (1976).
    [CrossRef]
  23. J. Borgnino, C. Aime, F. Martin, R. G. Petrov, G. Ricort, “Polychromatic transfer functions in stellar interferometry,” J. Opt. Soc. Am. A 6, 244–251 (1989).
    [CrossRef]
  24. A. W. Lohmann, G. Weigelt, B. Wirnitzer, “Speckle masking in astronomy: triple correlation theory and applications,” Appl. Opt. 22, 4028–4037 (1983).
    [CrossRef] [PubMed]

1998 (1)

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

1997 (3)

P. Berio, D. Mourard, F. Vakili, J. Borgnino, A. Ziad, “Effects of atmospheric spectral decorrelation on visibility measurements in Michelson interferometry,” J. Opt. Soc. Am. A 14, 114–121 (1997).
[CrossRef]

F. Vakili, D. Mourard, D. Bonneau, F. Morand, P. Stee, “Subtle structures in the wind of P Cygni,” Astron. Astrophys. 323, 183–188 (1997).

D. Mourard, D. Bonneau, L. Koechlin, A. Labeyrie, F. Morand, P. Stee, I. Tallon-Bosc, F. Vakili, “The mean angular diameter of δ Cephei measured by optical long-baseline interferometry,” Astron. Astrophys. 317, 789–792 (1997).

1996 (2)

P. Harmanec, F. Morand, D. Bonneau, Y. Jiang, S. Yang, “Jet-like structures in beta Lyrae,” Astron. Astrophys. 312, 879–896 (1996).

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

1995 (1)

P. Stee, F. X. de Araujo, F. Vakili, D. Mourard, L. Arnold, D. Bonneau, F. Morand, I. Tallon-Bosc, “γ Cassiopeiae revisited by spectrally resolved interferometry,” Astron. Astrophys. 300, 219–236 (1995).

1994 (2)

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

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, 705–715 (1994).

1992 (1)

M. Tallon, I. Tallon-Bosc, “The object-image relationship in Michelson stellar interferometry,” Astron. Astrophys. 253, 641–645 (1992).

1990 (1)

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. (Bellingham) 29, 1174–1180 (1990).
[CrossRef]

1989 (2)

D. Mourard, I. Bosc, A. Labeyrie, L. Koechlin, S. Saha, “The rotating envelope of the hot star gamma Cassiopeiae resolved by optical interferometry,” Nature (London) 342, 520–522 (1989).
[CrossRef]

J. Borgnino, C. Aime, F. Martin, R. G. Petrov, G. Ricort, “Polychromatic transfer functions in stellar interferometry,” J. Opt. Soc. Am. A 6, 244–251 (1989).
[CrossRef]

1986 (1)

G. P. DiBenedetto, R. Foy, “The angular diameter and the effective temperature of Acturus from Michelson interferometry,” Astron. Astrophys. 166, 204–210 (1986).

1984 (1)

F. Roddier, P. Léna, “Long-baseline Michelson interferometry with large ground-based telescopes operating at optical wavelengths,” J. Opt. 15, 171–182 (1984).
[CrossRef]

1983 (1)

1976 (1)

1975 (1)

A. Labeyrie, “Interference fringes obtained on Vega with two optical telescopes,” Astrophys. J. 196, 71–75 (1975).
[CrossRef]

1920 (1)

A. A. Michelson, “On the application of interference methods to astronomical measurements,” Astrophys. J. 51, 257–262 (1920).
[CrossRef]

1873 (1)

E. Stephan, “Extrait d’une lettre de M. Stéphan à M. Fizeau,” C. R. Hebd. Seances Acad. Sci. 76, 1008–1010 (1873).

1868 (1)

A. H. Fizeau, “Bordin prize,” C. R. Hebd. Seances Acad. Sci. 66, 932–934 (1868).

Aime, C.

Armstrong, J. T.

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

Arnold, L.

P. Stee, F. X. de Araujo, F. Vakili, D. Mourard, L. Arnold, D. Bonneau, F. Morand, I. Tallon-Bosc, “γ Cassiopeiae revisited by spectrally resolved interferometry,” Astron. Astrophys. 300, 219–236 (1995).

Baldwin, J. E.

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

Beckett, M. G.

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

Benson, J. A.

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

Berio, P.

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, 705–715 (1994).

Bonneau, D.

F. Vakili, D. Mourard, D. Bonneau, F. Morand, P. Stee, “Subtle structures in the wind of P Cygni,” Astron. Astrophys. 323, 183–188 (1997).

D. Mourard, D. Bonneau, L. Koechlin, A. Labeyrie, F. Morand, P. Stee, I. Tallon-Bosc, F. Vakili, “The mean angular diameter of δ Cephei measured by optical long-baseline interferometry,” Astron. Astrophys. 317, 789–792 (1997).

P. Harmanec, F. Morand, D. Bonneau, Y. Jiang, S. Yang, “Jet-like structures in beta Lyrae,” Astron. Astrophys. 312, 879–896 (1996).

P. Stee, F. X. de Araujo, F. Vakili, D. Mourard, L. Arnold, D. Bonneau, F. Morand, I. Tallon-Bosc, “γ Cassiopeiae revisited by spectrally resolved interferometry,” Astron. Astrophys. 300, 219–236 (1995).

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, 705–715 (1994).

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

Borgnino, J.

Bosc, I.

D. Mourard, I. Bosc, A. Labeyrie, L. Koechlin, S. Saha, “The rotating envelope of the hot star gamma Cassiopeiae resolved by optical interferometry,” Nature (London) 342, 520–522 (1989).
[CrossRef]

Bowers, P. F.

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

Boysen, R. C.

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

Burns, D.

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

Buscher, D. F.

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

Clark, J. H.

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

Cox, G. C.

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

de Araujo, F. X.

P. Stee, F. X. de Araujo, F. Vakili, D. Mourard, L. Arnold, D. Bonneau, F. Morand, I. Tallon-Bosc, “γ Cassiopeiae revisited by spectrally resolved interferometry,” Astron. Astrophys. 300, 219–236 (1995).

DiBenedetto, G. P.

G. P. DiBenedetto, R. Foy, “The angular diameter and the effective temperature of Acturus from Michelson interferometry,” Astron. Astrophys. 166, 204–210 (1986).

Elias, N. M.

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

Fizeau, A. H.

A. H. Fizeau, “Bordin prize,” C. R. Hebd. Seances Acad. Sci. 66, 932–934 (1868).

Foy, R.

G. P. DiBenedetto, R. Foy, “The angular diameter and the effective temperature of Acturus from Michelson interferometry,” Astron. Astrophys. 166, 204–210 (1986).

Ha, L.

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

Haniff, C. A.

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

Harmanec, P.

P. Harmanec, F. Morand, D. Bonneau, Y. Jiang, S. Yang, “Jet-like structures in beta Lyrae,” Astron. Astrophys. 312, 879–896 (1996).

Hummel, C. A.

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

Hutter, D. J.

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

Jiang, Y.

P. Harmanec, F. Morand, D. Bonneau, Y. Jiang, S. Yang, “Jet-like structures in beta Lyrae,” Astron. Astrophys. 312, 879–896 (1996).

Johnston, K. J.

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

Koechlin, L.

D. Mourard, D. Bonneau, L. Koechlin, A. Labeyrie, F. Morand, P. Stee, I. Tallon-Bosc, F. Vakili, “The mean angular diameter of δ Cephei measured by optical long-baseline interferometry,” Astron. Astrophys. 317, 789–792 (1997).

D. Mourard, I. Bosc, A. Labeyrie, L. Koechlin, S. Saha, “The rotating envelope of the hot star gamma Cassiopeiae resolved by optical interferometry,” Nature (London) 342, 520–522 (1989).
[CrossRef]

Labeyrie, A.

D. Mourard, D. Bonneau, L. Koechlin, A. Labeyrie, F. Morand, P. Stee, I. Tallon-Bosc, F. Vakili, “The mean angular diameter of δ Cephei measured by optical long-baseline interferometry,” Astron. Astrophys. 317, 789–792 (1997).

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, 705–715 (1994).

D. Mourard, I. Bosc, A. Labeyrie, L. Koechlin, S. Saha, “The rotating envelope of the hot star gamma Cassiopeiae resolved by optical interferometry,” Nature (London) 342, 520–522 (1989).
[CrossRef]

A. Labeyrie, “Interference fringes obtained on Vega with two optical telescopes,” Astrophys. J. 196, 71–75 (1975).
[CrossRef]

A. Labeyrie, “Interferometry with arrays of large aperture ground based telescopes,” in Proceedings of the Kitt Peak National Conference on Optical and Infrared Telescopes for the 1990’s, A. Hewitt, ed. (Kitt Peak National Observatory, Tucson, Arizona, 1980), Vol. 2, p. 786.

Léna, P.

F. Roddier, P. Léna, “Long-baseline Michelson interferometry with large ground-based telescopes operating at optical wavelengths,” J. Opt. 15, 171–182 (1984).
[CrossRef]

Ling, L. C.

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

Lohmann, A. W.

Mackay, C. D.

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

Martin, F.

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, 705–715 (1994).

Michelson, A. A.

A. A. Michelson, “On the application of interference methods to astronomical measurements,” Astrophys. J. 51, 257–262 (1920).
[CrossRef]

Morand, F.

D. Mourard, D. Bonneau, L. Koechlin, A. Labeyrie, F. Morand, P. Stee, I. Tallon-Bosc, F. Vakili, “The mean angular diameter of δ Cephei measured by optical long-baseline interferometry,” Astron. Astrophys. 317, 789–792 (1997).

F. Vakili, D. Mourard, D. Bonneau, F. Morand, P. Stee, “Subtle structures in the wind of P Cygni,” Astron. Astrophys. 323, 183–188 (1997).

P. Harmanec, F. Morand, D. Bonneau, Y. Jiang, S. Yang, “Jet-like structures in beta Lyrae,” Astron. Astrophys. 312, 879–896 (1996).

P. Stee, F. X. de Araujo, F. Vakili, D. Mourard, L. Arnold, D. Bonneau, F. Morand, I. Tallon-Bosc, “γ Cassiopeiae revisited by spectrally resolved interferometry,” Astron. Astrophys. 300, 219–236 (1995).

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, 705–715 (1994).

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

Mourard, D.

P. Berio, D. Mourard, F. Vakili, J. Borgnino, A. Ziad, “Effects of atmospheric spectral decorrelation on visibility measurements in Michelson interferometry,” J. Opt. Soc. Am. A 14, 114–121 (1997).
[CrossRef]

F. Vakili, D. Mourard, D. Bonneau, F. Morand, P. Stee, “Subtle structures in the wind of P Cygni,” Astron. Astrophys. 323, 183–188 (1997).

D. Mourard, D. Bonneau, L. Koechlin, A. Labeyrie, F. Morand, P. Stee, I. Tallon-Bosc, F. Vakili, “The mean angular diameter of δ Cephei measured by optical long-baseline interferometry,” Astron. Astrophys. 317, 789–792 (1997).

P. Stee, F. X. de Araujo, F. Vakili, D. Mourard, L. Arnold, D. Bonneau, F. Morand, I. Tallon-Bosc, “γ Cassiopeiae revisited by spectrally resolved interferometry,” Astron. Astrophys. 300, 219–236 (1995).

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

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, 705–715 (1994).

D. Mourard, I. Bosc, A. Labeyrie, L. Koechlin, S. Saha, “The rotating envelope of the hot star gamma Cassiopeiae resolved by optical interferometry,” Nature (London) 342, 520–522 (1989).
[CrossRef]

Mozurkewich, D.

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

Nightingale, N. S.

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

Petrov, R. G.

Richard, L. J.

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

Ricort, G.

Rigal, F.

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

Roddier, C.

Roddier, F.

F. Roddier, P. Léna, “Long-baseline Michelson interferometry with large ground-based telescopes operating at optical wavelengths,” J. Opt. 15, 171–182 (1984).
[CrossRef]

C. Roddier, F. Roddier, “On the fringe visibility in a Michelson interferometer,” J. Opt. Soc. Am. 66, 580–584 (1976).
[CrossRef]

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1981), Vol. XIX, p. 281.

Roddier, N.

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. (Bellingham) 29, 1174–1180 (1990).
[CrossRef]

Rogers, J.

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

Saha, S.

D. Mourard, I. Bosc, A. Labeyrie, L. Koechlin, S. Saha, “The rotating envelope of the hot star gamma Cassiopeiae resolved by optical interferometry,” Nature (London) 342, 520–522 (1989).
[CrossRef]

Scheuer, P. A. G.

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

Scott, T. R.

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

Simon, R. S.

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

Stee, P.

F. Vakili, D. Mourard, D. Bonneau, F. Morand, P. Stee, “Subtle structures in the wind of P Cygni,” Astron. Astrophys. 323, 183–188 (1997).

D. Mourard, D. Bonneau, L. Koechlin, A. Labeyrie, F. Morand, P. Stee, I. Tallon-Bosc, F. Vakili, “The mean angular diameter of δ Cephei measured by optical long-baseline interferometry,” Astron. Astrophys. 317, 789–792 (1997).

P. Stee, F. X. de Araujo, F. Vakili, D. Mourard, L. Arnold, D. Bonneau, F. Morand, I. Tallon-Bosc, “γ Cassiopeiae revisited by spectrally resolved interferometry,” Astron. Astrophys. 300, 219–236 (1995).

Stee, Ph.

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

Stephan, E.

E. Stephan, “Extrait d’une lettre de M. Stéphan à M. Fizeau,” C. R. Hebd. Seances Acad. Sci. 76, 1008–1010 (1873).

Tallon, M.

M. Tallon, I. Tallon-Bosc, “The object-image relationship in Michelson stellar interferometry,” Astron. Astrophys. 253, 641–645 (1992).

Tallon-Bosc, I.

D. Mourard, D. Bonneau, L. Koechlin, A. Labeyrie, F. Morand, P. Stee, I. Tallon-Bosc, F. Vakili, “The mean angular diameter of δ Cephei measured by optical long-baseline interferometry,” Astron. Astrophys. 317, 789–792 (1997).

P. Stee, F. X. de Araujo, F. Vakili, D. Mourard, L. Arnold, D. Bonneau, F. Morand, I. Tallon-Bosc, “γ Cassiopeiae revisited by spectrally resolved interferometry,” Astron. Astrophys. 300, 219–236 (1995).

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

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, 705–715 (1994).

M. Tallon, I. Tallon-Bosc, “The object-image relationship in Michelson stellar interferometry,” Astron. Astrophys. 253, 641–645 (1992).

Tuthill, P. G.

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

Vakili, F.

P. Berio, D. Mourard, F. Vakili, J. Borgnino, A. Ziad, “Effects of atmospheric spectral decorrelation on visibility measurements in Michelson interferometry,” J. Opt. Soc. Am. A 14, 114–121 (1997).
[CrossRef]

F. Vakili, D. Mourard, D. Bonneau, F. Morand, P. Stee, “Subtle structures in the wind of P Cygni,” Astron. Astrophys. 323, 183–188 (1997).

D. Mourard, D. Bonneau, L. Koechlin, A. Labeyrie, F. Morand, P. Stee, I. Tallon-Bosc, F. Vakili, “The mean angular diameter of δ Cephei measured by optical long-baseline interferometry,” Astron. Astrophys. 317, 789–792 (1997).

P. Stee, F. X. de Araujo, F. Vakili, D. Mourard, L. Arnold, D. Bonneau, F. Morand, I. Tallon-Bosc, “γ Cassiopeiae revisited by spectrally resolved interferometry,” Astron. Astrophys. 300, 219–236 (1995).

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

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, 705–715 (1994).

Von der Lühe, O.

O. Von der Lühe, “An introduction to interferometry with the ESO Very Large Telescope,” in Proceedings on Science with the VLT Interferometer, F. Paresce, ed. (European Southern Observatory, Garching, Germany, 1996), p. 13.

Warner, P. J.

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

Weigelt, G.

White, N. M.

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

Wilson, D. M. A.

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

Wilson, R. W.

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

Wirnitzer, B.

Yang, S.

P. Harmanec, F. Morand, D. Bonneau, Y. Jiang, S. Yang, “Jet-like structures in beta Lyrae,” Astron. Astrophys. 312, 879–896 (1996).

Ziad, A.

Appl. Opt. (1)

Astron. Astrophys. (9)

P. Stee, F. X. de Araujo, F. Vakili, D. Mourard, L. Arnold, D. Bonneau, F. Morand, I. Tallon-Bosc, “γ Cassiopeiae revisited by spectrally resolved interferometry,” Astron. Astrophys. 300, 219–236 (1995).

F. Vakili, D. Mourard, D. Bonneau, F. Morand, P. Stee, “Subtle structures in the wind of P Cygni,” Astron. Astrophys. 323, 183–188 (1997).

G. P. DiBenedetto, R. Foy, “The angular diameter and the effective temperature of Acturus from Michelson interferometry,” Astron. Astrophys. 166, 204–210 (1986).

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, 705–715 (1994).

J. E. Baldwin, M. G. Beckett, R. C. Boysen, D. Burns, D. F. Buscher, G. C. Cox, C. A. Haniff, C. D. Mackay, N. S. Nightingale, J. Rogers, P. A. G. Scheuer, T. R. Scott, P. G. Tuthill, P. J. Warner, D. M. A. Wilson, R. W. Wilson, “The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epoch,” Astron. Astrophys. 306, 13–16 (1996).

M. Tallon, I. Tallon-Bosc, “The object-image relationship in Michelson stellar interferometry,” Astron. Astrophys. 253, 641–645 (1992).

D. Mourard, I. Tallon-Bosc, F. Rigal, F. Vakili, D. Bonneau, F. Morand, Ph. Stee, “Estimation of visibility amplitude by optical long-baseline Michelson interferometry with large apertures,” Astron. Astrophys. 288, 675–682 (1994).

P. Harmanec, F. Morand, D. Bonneau, Y. Jiang, S. Yang, “Jet-like structures in beta Lyrae,” Astron. Astrophys. 312, 879–896 (1996).

D. Mourard, D. Bonneau, L. Koechlin, A. Labeyrie, F. Morand, P. Stee, I. Tallon-Bosc, F. Vakili, “The mean angular diameter of δ Cephei measured by optical long-baseline interferometry,” Astron. Astrophys. 317, 789–792 (1997).

Astrophys. J. (3)

J. T. Armstrong, D. Mozurkewich, L. J. Richard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L. C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer NPOI,” Astrophys. J. 496, 550–571 (1998).
[CrossRef]

A. A. Michelson, “On the application of interference methods to astronomical measurements,” Astrophys. J. 51, 257–262 (1920).
[CrossRef]

A. Labeyrie, “Interference fringes obtained on Vega with two optical telescopes,” Astrophys. J. 196, 71–75 (1975).
[CrossRef]

C. R. Hebd. Seances Acad. Sci. (2)

A. H. Fizeau, “Bordin prize,” C. R. Hebd. Seances Acad. Sci. 66, 932–934 (1868).

E. Stephan, “Extrait d’une lettre de M. Stéphan à M. Fizeau,” C. R. Hebd. Seances Acad. Sci. 76, 1008–1010 (1873).

J. Opt. (1)

F. Roddier, P. Léna, “Long-baseline Michelson interferometry with large ground-based telescopes operating at optical wavelengths,” J. Opt. 15, 171–182 (1984).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Nature (London) (1)

D. Mourard, I. Bosc, A. Labeyrie, L. Koechlin, S. Saha, “The rotating envelope of the hot star gamma Cassiopeiae resolved by optical interferometry,” Nature (London) 342, 520–522 (1989).
[CrossRef]

Opt. Eng. (Bellingham) (1)

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. (Bellingham) 29, 1174–1180 (1990).
[CrossRef]

Other (3)

O. Von der Lühe, “An introduction to interferometry with the ESO Very Large Telescope,” in Proceedings on Science with the VLT Interferometer, F. Paresce, ed. (European Southern Observatory, Garching, Germany, 1996), p. 13.

A. Labeyrie, “Interferometry with arrays of large aperture ground based telescopes,” in Proceedings of the Kitt Peak National Conference on Optical and Infrared Telescopes for the 1990’s, A. Hewitt, ed. (Kitt Peak National Observatory, Tucson, Arizona, 1980), Vol. 2, p. 786.

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1981), Vol. XIX, p. 281.

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Figures (4)

Fig. 1
Fig. 1

Top, numerically simulated GI2T interferogram in the multichromatic mode and bottom, the corresponding spectral density. The fringe peaks are centered at ±b/λ0 because of the pupil rearrangement. (Coordinates are in arbitrary units.)

Fig. 2
Fig. 2

Top, numerically simulated GI2T interferogram in the dispersed-fringes mode and bottom, the corresponding spectral density. The fringe peaks are centered at ±b/λ0 because of the pupil rearrangement. The spike is due to spectral windowing. (Coordinates are in arbitrary units.)

Fig. 3
Fig. 3

Visibility data obtained from the GI2T simulation in the dispersed-fringes mode. The angular diameter of the observed star is ϕtheo=5.6 mas; the spectral bandwidth is Δλ=5 nm (centered at λ0=650 nm). Solid curve, the uniform disk model that gives the best fit to the data on both base lengths.

Fig. 4
Fig. 4

Visibility data obtained from the GI2T simulation in the multichromatic mode. The angular diameter of the observed star is ϕtheo=5.6 mas; the spectral bandwidth is Δλ=0.5 nm (centered at λ0=650 nm). Solid curve, the uniform disk model that gives the best fit to the data on both base lengths.

Equations (95)

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

I(u)=O(u)S(u),
W(f)=|I˜(f)|2=|O˜(f)|2|S˜(f)|2,
WSMTF(f )=ΔλΔλW12(f)dλ1dλ2,
WSMTF(f)=[W12(1a)(f)+W12(2)(f )+W12(1b)(f)+W12(3a)(f)+W12(3b)(f)]dλ1dλ2.
WSMTF(f)=(F1+F2)2Wsee(f)+(F12+F22)Wspec(f)+F1F2[Wfringe+(f)+Wfringe-(f)],
WΔλ(f)=|O˜(f)|2WSMTF(f).
Wfringe+(f)=Wspec(f)δ(f-L/λ0),
Wfringe-(f)=Wspec(f)δ(f+L/λ0).
Wfringe+(f)=12βWspec(f)δ(f-L/λ0),
Wfringe-(f)=12βWspec(f)δ(f+L/λ0),
C1=|O˜(L/λ0)|2F1F2[Wfringe+(f)+Wfringe-(f)]df|O˜(0)|2(F12+F22)Wspec(f)df=2F1F2F12+F22β|O˜(L/λ0)|2|O˜(0)|2.
C2(f)=|O˜(f)|2F1F2[Wfringe+(f)+Wfringe-(f)]|O˜(0)|2(F12+F22)Wspec(f)=2F1F2F12+F22β|O˜(f)|2|O˜(0)|2.
Wspeckle(f)=W12(1b)(f, λ1, λ2)dλ1dλ2=(F12+F22)B12(ρ)B12*[ρ+(λ1-λ2)f ]
×A0(f, ρ, λ1, λ2)dρ dλ1dλ2.
Wspec(f)ΔλΔλT0,λ1(f)dλ1dλ2,
T0,λ1(f)=|P0(u)|2|P0(u+λ1f)|2du,
T0,λ1(f)=2πarccos|λ1f|D-|λ1f|D1-|λ1f|2D21/2.
WΔλ1Δλ2(f)=O˜Δλ1(f)O˜Δλ2*(f)Δλ1Δλ2W12(f)dλ1dλ2,
=|O˜Δλ1(f)||O˜Δλ2(f)|exp(iΔϕ)
×WSMTF,Δλ1Δλ2(f),
C1=2F1F2F12+F22β|O˜Δλ1(L/λ01)||O˜Δλ2(L/λ02)|exp(iΔϕ)|O˜Δλ1(0)||O˜Δλ2(0)|,
C2(f)=2F1F2F12+F22β|O˜Δλ1(f)||O˜Δλ2(f)|exp(iΔϕ)|O˜Δλ1(0)||O˜Δλ2(0)|,
Hλ(uy)=Iλ(ux, uy)U(ux, uy)dux,=[Iλ(ux, uy)U(ux, uy)][δ(uy)1ux],
IΔλ(ux, uy)=Δλ[Hλ1(uy)1ux][δ(ux-λ1)δ(uy)]dλ1ΠuxΔλ1uy,
I˜Δλ(k, fy)=ΔλH˜λ1(fy)δ(k)exp(-2iπλ1k)1fydλ1Δλ sinc(Δλk)δ(fy),
I˜Δλ(k, fy)=ΔλH˜λ1(fy)dλ1Δλ sinc(Δλk),
H˜λ(fy)=[I˜λ(k, fy)U˜(k, fy)]δ(k)1fy,
U˜(k, fy)=sin(πkl)πklδ(fy)=sinc(kl)δ(fy),
H˜λ(fy)=I˜λ(k, fy)sinc(kl)dk.
I˜λ(k, fy)=O˜(k, fy)S˜λ(k, fy).
H˜λ(fy)=O˜(0, fy)S˜λ(k, fy)sinc(kl)dk.
WΔλ(k, fy)=|I˜Δλ(k, fy)|2=ΔλΔλH˜λ1(fy)
×H˜λ2*(fy)dλ1dλ2Δλ2 sinc2(Δλk).
H˜λ1(fy)H˜λ2*(fy)=|O˜(0, fy)|2S˜λ1(k, fy)×S˜λ2*(k, fy)sinc(kl)sinc(kl)dkdk
=|O˜(0, fy)|2W12(fy).
WΔλ(f)=|O˜(0, fy)|2Δλ2 sinc2(Δλk)[W12(1a)(fy)+W12(2)(fy)+W12(1b)(fy)+W12(3a)(fy)+W12(3b)(fy)]dλ1dλ2.
WΔλ(f)=|O˜(0, fy)|2Δλ2 sinc2(Δλk){(F1+F2)2Wsee(fy)+(F12+F22)Wspec(fy)+F1F2[Wfringe+(fy)+Wfringe-(fy)]}.
Wspec(fy)ΔλΔλT0,λ1(f)×sinc(kl)sincλ1λ2kld kdλ1dλ2,
W12(f)=S˜λ1(f)S˜λ2*(f),
S˜λ1(f)=1sψ1(u)ψ1*(u+λ1f)P(u)P*(u+λ1f)du,
P(u)=F1P0(u)+F2P0(u+L).
W12(f)=M12(f, ρ)A12(f, ρ)d ρ,
M12(f, ρ)=ψ1(u)ψ1*(u+λ1f)ψ2*(u+ρ)
×ψ2(u+ρ+λ2f).
M12(f, ρ)=ψ1(u)ψ1*(u+λ1f)
×ψ2*(u+ρ)ψ2(u+ρ+λ2f)
+ψ1(u)ψ2*(u+ρ)
×ψ1*(u+λ1f)ψ2(u+ρ+λ2f),
M12(f, ρ)=B1(f)B2*(f)+B12(ρ)B12*[ρ+(λ1-λ2)f].
A12(f, ρ)=P(u)P*(u+λ1f)P*(u+ρ)×P(u+ρ+λ2f)du.
F12P0(u)P0*(u+λ1f)P0*(u+ρ)P0(u+ρ+λ2f)
+F22P0(u+L)P0*(u+L+λ1f)
×P0*(u+L+ρ)P0(u+ρ+L+λ2f).
A0(f, ρ, λ1, λ2)=P0(u)P0*(u+λ1f)P0*(u+ρ)×P0(u+ρ+λ2f)du.
W12(1)(f)=(F12+F22)M12(f, ρ)A0(f, ρ, λ1, λ2)dρ.
W12(1a)(f)=(F12+F22)B1(f)B2*(f)×A0(f, ρ, λ1, λ2)dρ,
W12(1b)(f)=(F12+F22)B12(ρ)B12*(ρ+(λ1-λ2)f)A0(f, ρ, λ1, λ2)dρ.
F1F2P0(u+L)P0*(u+L+λ1f)P0*(u+ρ)
×P0(u+ρ+λ2f)+F1F2P0(u)P0*(u
+λ1f)P0*(u+L+ρ)P0(u+ρ+L+λ2f).
W12(2)(f)=F1F2|ρ-L|<DM12(f, ρ)P0(u+L)×P0*(u+L+λ1f)×P0*(u+ρ)P0(u+ρ+λ2f)dudρ+F1F2|ρ+L|<DM12(f, ρ)×P0(u)P0*(u+λ1f)P0*(u+L+ρ)×P0(u+ρ+L+λ2f)dudρ.
W12(2)(f)=2F1F2B1(f)B2*(f)A0(f, ρ, λ1, λ2)dρ+F1F2B12(ρ+L)×B12*(ρ+L+(λ1-λ2)f )×A0(f, ρ, λ1, λ2)dρ+F1F2B12(ρ-L)×B12*(ρ-L+(λ1-λ2)f )×A0(f, ρ, λ1, λ2)dρ.
W12(2)(f)=2F1F2B1(f)B2*(f)A0(f, ρ, λ1, λ2)dρ.
F1F2P0(u+L)P0*(u+λ1f)P0*(u+L+ρ)
×P0(u+ρ+λ2f)+F1F2P0(u)P0*(u+L+λ1f)
×P0*(u+ρ)P0(u+ρ+L+λ2f).
W12(3a)(f)=F1F2M12(f, ρ)P0(u+L)×P0*(u+λ1f)P0*(u+L+ρ)×P0(u+ρ+λ2f)dudρ,
W12(3b)(f)=F1F2M12(f, ρ)P0(u)×P0*(u+L+λ1f)P0*(u+ρ)×P0(u+ρ+L+λ2f)dudρ,
W12(3a)(f)=F1F2B12(ρ)B12*(ρ+(λ1-λ2)f)×P0(u+L)P0*(u+λ1f)×P0*(u+L+ρ)P0(u+ρ+λ2f)dudρ,
W12(3b)(f)=F1F2B12(ρ)B12*(ρ+(λ1-λ2)f)×P0(u)P0*(u+L+λ1f)P0*(u+ρ)×P0(u+ρ+L+λ2f)dudρ.
W12(3a)g+Lλ0=F1F2B12(ρ)B12*ρ+(λ1-λ2)g+(λ1-λ2)λ0LP0(u+L)×P0*u+λ1g+λ1λ0L×P0*(u+L+ρ)×P0u+ρ+λ2g+λ2λ0Ldudρ,
W12(3b)g-Lλ0=F1F2B12(ρ)B12*ρ+(λ1-λ2)×g-(λ1-λ2)λ0L×P0(u)P0*(u+ρ)×P0*u+λ1g+1-λ1λ0L×P0u+ρ+λ2g+1-λ2λ0Ldudρ,
W12(fy)=S˜λ1(k, fy)S˜λ2*(k, fy)×sinc(kl)sinc(kl)dkdk.
W12(fy)=S˜λ1(k, fy)S˜λ2*(k+hx, fy)×sinc(kl)sinc[(k+hx)l]dkdhx,
W12(fy)=M12(f, h, ρ)A12(f, h, ρ)
×sinc(kl)sinc[(k+hx)l]dkdhxdρ,
M12(f, h, ρ)=ψ1(u)ψ1*(u+λ1f)ψ2*(u+ρ)×ψ2(u+ρ+λ2f+λ2h),
A12(f, h, ρ)=P(u)P*(u+λ1f)P*(u+ρ)×P(u+ρ+λ2f)du.
M12(f, h, ρ)=B1(f)B2*(f+h)+B12(ρ)
×B12*(ρ+(λ2-λ1)f+λ2h).
W12(fy)=W12(1a)(fy)+W12(1b)(fy)+W12(2)(fy)+W12(3a)(fy)+W12(3b)(fy).
W12(1a)(fy)=(F12+F22)B12(ρ)×B12*(ρ+(λ2-λ1)f+λ2h)×sinc(kl)sinc[(k+hx)l]×A0(f, h, ρ, λ1, λ2)dρdkdhx,
W12(1b)(fy)=(F12+F22)B12(ρ)×B12*(ρ+(λ2-λ1)f+λ2h)×sinc(kl)sinc[(k+hx)l]×A0(f, h, ρ, λ1, λ2)dρdkdhx,
W12(2)(fy)=2F1F2B1(f)B2*(f+h)
×sinc(kl)sinc[(k+hx)l]
×A0(f, h, ρ, λ1, λ2)dρdkdhx,
A0(f, h, ρ, λ1, λ2)=P0(u)P0*(u+λ1f)P0*(u+ρ)×P0(u+ρ+λ2(f+h))du.
W12(3a)(fy)=F1F2B12(ρ)B12*(ρ+(λ2-λ1)×f+λ2h)P0(u+L)P0*(u+λ1f)×P0*(u+L+ρ)P0(u+ρ+λ2(f+h))du×sinc(kl)sinc[(k+hx)l]dρdkdhx,
W12(3b)(fy)=F1F2B12(ρ)B12*(ρ+(λ2-λ1)×f+λ2h)P0(u)P0*(u+L+λ1f)×P0*(u+ρ)P0(u+ρ+L+λ2(f+h))du×sinc(kl)sinc[(k+hx)l]dρ dkdhx.
Bi(ρ)=exp[-12Di(ρ)],
Di(ρ)=6.88|ρ/r0i|5/3,
Bij(ρ)=ψi(u)ψj*(u+ρ).
Bij(ρ)=exp[-12|ϕi(u)-αϕi(u+ρ)|2],
Bij(ρ)=exp{-12[(1-α)2σϕi2+αDi(ρ)]},
Bi(ρ)=const δ(ρ),Bij(ρ)=const δ(ρ).

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