Abstract

Numerical simulations of atmospheric turbulence and adaptive optics (AO) wavefront correction are performed to investigate the time scale for fringe motion in optical interferometers with spatial filters. These simulations focus especially on partial AO correction, where only a finite number of Zernike modes are compensated. The fringe motion is found to depend strongly on both the aperture diameter and the level of AO correction used. In all the simulations the coherence time scale for interference fringes is found to decrease dramatically when the Strehl ratio provided by the AO correction is ≲30%. For AO systems that give perfect compensation of a limited number of Zernike modes, the aperture size that gives the optimum signal for fringe phase tracking is calculated. For AO systems that provide noisy compensation of Zernike modes (but are perfectly piston neutral), the noise properties of the AO system determine the coherence time scale of the fringes when the Strehl ratio is ≲30%.

© 2005 Optical Society of America

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    [CrossRef]
  2. J. W. Keen, D. F. Buscher, P. J. Warner, “Numerical simulations of pinhole and single-mode fibre spatial filters for optical interferometers,” Mon. Not. R. Astron. Soc. 326, 1381–1386 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. R. N. Tubbs, “Seeing timescales for large-aperture optical/infrared interferometers from simulations,” in New Frontiers in Stellar Interferometry, W. Traub, ed., Proc. SPIE5491, 1240–1248 (2004).
    [CrossRef]
  14. 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 epochs,” Astron. Astrophys. 306, L13–L16 (1996).

2004

2003

J. D. Monnier, “Optical interferometry in astronomy,” in Rep. Prog. Phys. 66, 789–857 (2003).
[CrossRef]

2001

J. W. Keen, D. F. Buscher, P. J. Warner, “Numerical simulations of pinhole and single-mode fibre spatial filters for optical interferometers,” Mon. Not. R. Astron. Soc. 326, 1381–1386 (2001).
[CrossRef]

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 epochs,” Astron. Astrophys. 306, L13–L16 (1996).

1995

1982

F. Roddier, J. M. Gilli, G. Lund, “On the origin of speckle boiling and its effects in stellar speckle interferometry,” J. Opt. 13, 263–271 (1982).
[CrossRef]

1976

1941

A. N. Kolmogorov, “Dissipation of energy in the locally isotropic turbulence,” C. R. (Dok.) Acad. Sci. URSS 32, 16–18 (1941).

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynold’s numbers,” C. R. (Dok.) Acad. Sci. URSS 30, 301–305 (1941).

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 epochs,” Astron. Astrophys. 306, L13–L16 (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 epochs,” Astron. Astrophys. 306, L13–L16 (1996).

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 epochs,” Astron. Astrophys. 306, L13–L16 (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 epochs,” Astron. Astrophys. 306, L13–L16 (1996).

Buscher, D. F.

J. W. Keen, D. F. Buscher, P. J. Warner, “Numerical simulations of pinhole and single-mode fibre spatial filters for optical interferometers,” Mon. Not. R. Astron. Soc. 326, 1381–1386 (2001).
[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 epochs,” Astron. Astrophys. 306, L13–L16 (1996).

Conan, J.

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 epochs,” Astron. Astrophys. 306, L13–L16 (1996).

D’Arcio, L. A.

L. A. D’Arcio, “Selected aspects of wide-field stellar interferometry,” Ph.D. dissertation (Technische Universiteit Delft, 1999).

Fusco, T.

Gilli, J. M.

F. Roddier, J. M. Gilli, G. Lund, “On the origin of speckle boiling and its effects in stellar speckle interferometry,” J. Opt. 13, 263–271 (1982).
[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 epochs,” Astron. Astrophys. 306, L13–L16 (1996).

Keen, J. W.

J. W. Keen, D. F. Buscher, P. J. Warner, “Numerical simulations of pinhole and single-mode fibre spatial filters for optical interferometers,” Mon. Not. R. Astron. Soc. 326, 1381–1386 (2001).
[CrossRef]

Kolmogorov, A. N.

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynold’s numbers,” C. R. (Dok.) Acad. Sci. URSS 30, 301–305 (1941).

A. N. Kolmogorov, “Dissipation of energy in the locally isotropic turbulence,” C. R. (Dok.) Acad. Sci. URSS 32, 16–18 (1941).

Lund, G.

F. Roddier, J. M. Gilli, G. Lund, “On the origin of speckle boiling and its effects in stellar speckle interferometry,” J. Opt. 13, 263–271 (1982).
[CrossRef]

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 epochs,” Astron. Astrophys. 306, L13–L16 (1996).

Madec, P.

Monnier, J. D.

J. D. Monnier, “Optical interferometry in astronomy,” in Rep. Prog. Phys. 66, 789–857 (2003).
[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 epochs,” Astron. Astrophys. 306, L13–L16 (1996).

Noll, R. J.

Roddier, F.

F. Roddier, J. M. Gilli, G. Lund, “On the origin of speckle boiling and its effects in stellar speckle interferometry,” J. Opt. 13, 263–271 (1982).
[CrossRef]

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics (North-Holland, 1981), Vol. 19, pp. 281–376.
[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 epochs,” Astron. Astrophys. 306, L13–L16 (1996).

Rousset, G.

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 epochs,” Astron. Astrophys. 306, L13–L16 (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 epochs,” Astron. Astrophys. 306, L13–L16 (1996).

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

Tubbs, R. N.

R. N. Tubbs, “Seeing timescales for large-aperture optical/infrared interferometers from simulations,” in New Frontiers in Stellar Interferometry, W. Traub, ed., Proc. SPIE5491, 1240–1248 (2004).
[CrossRef]

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 epochs,” Astron. Astrophys. 306, L13–L16 (1996).

Warner, P. J.

J. W. Keen, D. F. Buscher, P. J. Warner, “Numerical simulations of pinhole and single-mode fibre spatial filters for optical interferometers,” Mon. Not. R. Astron. Soc. 326, 1381–1386 (2001).
[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 epochs,” Astron. Astrophys. 306, L13–L16 (1996).

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 epochs,” Astron. Astrophys. 306, L13–L16 (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 epochs,” Astron. Astrophys. 306, L13–L16 (1996).

Astron. Astrophys.

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 epochs,” Astron. Astrophys. 306, L13–L16 (1996).

C. R. (Dok.) Acad. Sci. URSS

A. N. Kolmogorov, “Dissipation of energy in the locally isotropic turbulence,” C. R. (Dok.) Acad. Sci. URSS 32, 16–18 (1941).

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynold’s numbers,” C. R. (Dok.) Acad. Sci. URSS 30, 301–305 (1941).

J. Opt.

F. Roddier, J. M. Gilli, G. Lund, “On the origin of speckle boiling and its effects in stellar speckle interferometry,” J. Opt. 13, 263–271 (1982).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Mon. Not. R. Astron. Soc.

J. W. Keen, D. F. Buscher, P. J. Warner, “Numerical simulations of pinhole and single-mode fibre spatial filters for optical interferometers,” Mon. Not. R. Astron. Soc. 326, 1381–1386 (2001).
[CrossRef]

Rep. Prog. Phys.

J. D. Monnier, “Optical interferometry in astronomy,” in Rep. Prog. Phys. 66, 789–857 (2003).
[CrossRef]

Other

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics (North-Holland, 1981), Vol. 19, pp. 281–376.
[CrossRef]

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

R. N. Tubbs, “Seeing timescales for large-aperture optical/infrared interferometers from simulations,” in New Frontiers in Stellar Interferometry, W. Traub, ed., Proc. SPIE5491, 1240–1248 (2004).
[CrossRef]

D. F. Buscher, “Getting the most out of C.O.A.S.T.,” Ph.D. dissertation (Cambridge University, 1988), http://www.mrao.cam.ac.uk/~dfb/publications/dfbphd.pdf .

L. A. D’Arcio, “Selected aspects of wide-field stellar interferometry,” Ph.D. dissertation (Technische Universiteit Delft, 1999).

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Figures (3)

Fig. 1
Fig. 1

Shown is the rms jitter in the optical phase in an interferometer with spatial filters, plotted against aperture diameter. The jitter results from wavefront corrugations in the telescope aperture plane. Each line connects models with a given level of AO correction and is labeled with the number of Zernike modes that have been suppressed. The phase jitter plotted represents the rms difference between the optical phase calculated for that model and the phase delay after ideal AO correction.

Fig. 2
Fig. 2

Coherence time scale for the optical phase for a range of aperture diameters and different levels of AO correction. The labels on the lines indicate the number of Zernike modes corrected from tip and tilt upwards. The curve labeled P corresponds to the coherence time scale of the piston mode, indicating the result expected for ideal AO correction. The end point of each curve is determined by the time resolution of the simulations performed.

Fig. 3
Fig. 3

Photon count through the spatial filter per coherence time scale normalized so that a diffraction-limited aperture of diameter r0 would give unity. The labels on the lines indicate the number of Zernike modes corrected from tip and tilt upwards. The curve labeled P corresponds to the coherence time scale of the piston mode, indicating the result expected for ideal AO correction.

Tables (1)

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Table 1 Models for AO Wavefront Correction

Equations (2)

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R exp ( - σ 2 ) ,
D j / r 0 = ( a j ) - 3 / 5 ,

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