Abstract

A formula to compute the index of stellar scintillation detected with a finite spectral bandpass and with arbitrary aperture is derived in the limit of weak perturbations. It also applies to differential scintillation (relative fluctuations of light intensity in a pair of apertures), where the effect of finite bandpass turns out to be significant. The new formula is used for measurements of free-atmosphere seeing and low-resolution turbulence profiles with concentric-ring apertures.

© 2003 Optical Society of America

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References

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  1. D. Dravins, L. Lindegren, E. Mezey, “Atmospheric intensity scintillation of stars. III. Effects for different telescope apertures,” Publ. Astron. Soc. Pac. 110, 610–633 (1998).
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    [CrossRef]
  4. A. Ziad, R. Conan, A. Tokovinin, F. Martin, J. Borgnino, “From the Grating Scale Monitor (GSM) to the Generalized Seeing Monitor (GSM),” Appl. Opt. 39, 5415–5425 (2000).
    [CrossRef]
  5. A. Rocca, F. Roddier, J. Vernin, “Detection of atmospheric turbulent layers by spatiotemporal and spatioangular correlation measurements of stellar-light scintillations,” J. Opt. Soc. Am. 64, 1000–1004 (1974).
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  6. G. R. Ochs, Ting-i Wang, R. S. Lawrence, S. F. Clifford, “Refractive-turbulence profiles measured by one-dimensional spatial filtering of scintillations,” Appl. Opt. 15, 2504–2510 (1976).
    [CrossRef] [PubMed]
  7. J. L. Caccia, M. Azouit, J. Vernin, “Wind and CN2 profiling by single-star scintillation analysis,” Appl. Opt. 26, 1288–1294 (1987).
    [CrossRef] [PubMed]
  8. V Kornilov, A Tokovinin, O Voziakova, A Zaitsev, N Shatsky, S Potanin, M Sarazin, “MASS:  a monitor of the vertical turbulence distribution,” in Adaptive Optical Systems Technologies II, P. L. Wizinovich, ed., Proc. SPIE4839, paper 102 (2002).
  9. V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961).
  10. F Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, Vol. XIX, E. Wolf, ed. (North-Holland, Amsterdam, 1981), pp. 281–376.
  11. A. A. Tokovinin, “A new method to measure the atmospheric seeing,” Astron. Lett. 24, 662–664 (1998).
  12. A. Tokovinin, “Measuring seeing and atmospheric time constant by differential scintillations,” Appl. Opt. 41, 957–964 (2002).
    [CrossRef] [PubMed]
  13. J. Vernin, M. Azouit, “Traitement d’image adapté au speckle atmospherique. I. Formation du speckle en atmosphère turbulente. Propriétés statistiques,” J. Opt. (Paris) 14, 5–9 (1983).
    [CrossRef]
  14. V. G. Kornilov, A. A. Tokovinin, “Measurement of the turbulence in the free atmosphere above Maidanak,” Astron. Rep. 45, 395–408 (2001).
    [CrossRef]

2002 (1)

2001 (1)

V. G. Kornilov, A. A. Tokovinin, “Measurement of the turbulence in the free atmosphere above Maidanak,” Astron. Rep. 45, 395–408 (2001).
[CrossRef]

2000 (1)

1998 (2)

D. Dravins, L. Lindegren, E. Mezey, “Atmospheric intensity scintillation of stars. III. Effects for different telescope apertures,” Publ. Astron. Soc. Pac. 110, 610–633 (1998).
[CrossRef]

A. A. Tokovinin, “A new method to measure the atmospheric seeing,” Astron. Lett. 24, 662–664 (1998).

1993 (1)

1987 (1)

1983 (1)

J. Vernin, M. Azouit, “Traitement d’image adapté au speckle atmospherique. I. Formation du speckle en atmosphère turbulente. Propriétés statistiques,” J. Opt. (Paris) 14, 5–9 (1983).
[CrossRef]

1979 (1)

1976 (1)

1974 (1)

Azouit, M.

J. L. Caccia, M. Azouit, J. Vernin, “Wind and CN2 profiling by single-star scintillation analysis,” Appl. Opt. 26, 1288–1294 (1987).
[CrossRef] [PubMed]

J. Vernin, M. Azouit, “Traitement d’image adapté au speckle atmospherique. I. Formation du speckle en atmosphère turbulente. Propriétés statistiques,” J. Opt. (Paris) 14, 5–9 (1983).
[CrossRef]

Borgnino, J.

Caccia, J. L.

Clifford, S. F.

Conan, R.

Dravins, D.

D. Dravins, L. Lindegren, E. Mezey, “Atmospheric intensity scintillation of stars. III. Effects for different telescope apertures,” Publ. Astron. Soc. Pac. 110, 610–633 (1998).
[CrossRef]

Hogge, C.

Kornilov, V

V Kornilov, A Tokovinin, O Voziakova, A Zaitsev, N Shatsky, S Potanin, M Sarazin, “MASS:  a monitor of the vertical turbulence distribution,” in Adaptive Optical Systems Technologies II, P. L. Wizinovich, ed., Proc. SPIE4839, paper 102 (2002).

Kornilov, V. G.

V. G. Kornilov, A. A. Tokovinin, “Measurement of the turbulence in the free atmosphere above Maidanak,” Astron. Rep. 45, 395–408 (2001).
[CrossRef]

Krause-Polstorf, J.

Lawrence, R. S.

Lindegren, L.

D. Dravins, L. Lindegren, E. Mezey, “Atmospheric intensity scintillation of stars. III. Effects for different telescope apertures,” Publ. Astron. Soc. Pac. 110, 610–633 (1998).
[CrossRef]

Loos, G.

Martin, F.

Mezey, E.

D. Dravins, L. Lindegren, E. Mezey, “Atmospheric intensity scintillation of stars. III. Effects for different telescope apertures,” Publ. Astron. Soc. Pac. 110, 610–633 (1998).
[CrossRef]

Murphy, E. A.

Ochs, G. R.

Potanin, S

V Kornilov, A Tokovinin, O Voziakova, A Zaitsev, N Shatsky, S Potanin, M Sarazin, “MASS:  a monitor of the vertical turbulence distribution,” in Adaptive Optical Systems Technologies II, P. L. Wizinovich, ed., Proc. SPIE4839, paper 102 (2002).

Rocca, A.

Roddier, F

F Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, Vol. XIX, E. Wolf, ed. (North-Holland, Amsterdam, 1981), pp. 281–376.

Roddier, F.

Sarazin, M

V Kornilov, A Tokovinin, O Voziakova, A Zaitsev, N Shatsky, S Potanin, M Sarazin, “MASS:  a monitor of the vertical turbulence distribution,” in Adaptive Optical Systems Technologies II, P. L. Wizinovich, ed., Proc. SPIE4839, paper 102 (2002).

Shatsky, N

V Kornilov, A Tokovinin, O Voziakova, A Zaitsev, N Shatsky, S Potanin, M Sarazin, “MASS:  a monitor of the vertical turbulence distribution,” in Adaptive Optical Systems Technologies II, P. L. Wizinovich, ed., Proc. SPIE4839, paper 102 (2002).

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961).

Tokovinin, A

V Kornilov, A Tokovinin, O Voziakova, A Zaitsev, N Shatsky, S Potanin, M Sarazin, “MASS:  a monitor of the vertical turbulence distribution,” in Adaptive Optical Systems Technologies II, P. L. Wizinovich, ed., Proc. SPIE4839, paper 102 (2002).

Tokovinin, A.

Tokovinin, A. A.

V. G. Kornilov, A. A. Tokovinin, “Measurement of the turbulence in the free atmosphere above Maidanak,” Astron. Rep. 45, 395–408 (2001).
[CrossRef]

A. A. Tokovinin, “A new method to measure the atmospheric seeing,” Astron. Lett. 24, 662–664 (1998).

Vernin, J.

Voziakova, O

V Kornilov, A Tokovinin, O Voziakova, A Zaitsev, N Shatsky, S Potanin, M Sarazin, “MASS:  a monitor of the vertical turbulence distribution,” in Adaptive Optical Systems Technologies II, P. L. Wizinovich, ed., Proc. SPIE4839, paper 102 (2002).

Walters, D. L.

Wang, Ting-i

Zaitsev, A

V Kornilov, A Tokovinin, O Voziakova, A Zaitsev, N Shatsky, S Potanin, M Sarazin, “MASS:  a monitor of the vertical turbulence distribution,” in Adaptive Optical Systems Technologies II, P. L. Wizinovich, ed., Proc. SPIE4839, paper 102 (2002).

Ziad, A.

Appl. Opt. (6)

Astron. Lett. (1)

A. A. Tokovinin, “A new method to measure the atmospheric seeing,” Astron. Lett. 24, 662–664 (1998).

Astron. Rep. (1)

V. G. Kornilov, A. A. Tokovinin, “Measurement of the turbulence in the free atmosphere above Maidanak,” Astron. Rep. 45, 395–408 (2001).
[CrossRef]

J. Opt. (Paris) (1)

J. Vernin, M. Azouit, “Traitement d’image adapté au speckle atmospherique. I. Formation du speckle en atmosphère turbulente. Propriétés statistiques,” J. Opt. (Paris) 14, 5–9 (1983).
[CrossRef]

J. Opt. Soc. Am. (1)

Publ. Astron. Soc. Pac. (1)

D. Dravins, L. Lindegren, E. Mezey, “Atmospheric intensity scintillation of stars. III. Effects for different telescope apertures,” Publ. Astron. Soc. Pac. 110, 610–633 (1998).
[CrossRef]

Other (3)

V Kornilov, A Tokovinin, O Voziakova, A Zaitsev, N Shatsky, S Potanin, M Sarazin, “MASS:  a monitor of the vertical turbulence distribution,” in Adaptive Optical Systems Technologies II, P. L. Wizinovich, ed., Proc. SPIE4839, paper 102 (2002).

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961).

F Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, Vol. XIX, E. Wolf, ed. (North-Holland, Amsterdam, 1981), pp. 281–376.

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Figures (1)

Fig. 1
Fig. 1

Weighting functions Q ( z ) of Eq. (21) in 10 10   m - 1 / 3 at 500-nm wavelength. (a) Differential scintillation WFs for a pair of 2-cm and 4-cm concentric apertures: solid curve, monochromatic; dashed curve, bandwidth 100 nm. The dotted curve is the sum of the differential WFs with 0.027 of the single 2-cm aperture WF for 100-nm bandwidth. (b) Normal scintillation WFs for a 2-cm diameter aperture: solid curve, monochromatic; dashed curve, bandwidth 300 nm.

Equations (21)

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F ( λ ) d λ = 1 .
W ( x ) d 2 x = 1 .
I = exp [ 2 χ ( x ,   λ ) ] F ( λ ) W ( x ) d λ d 2 x 1 + 2 χ ¯ ( λ ) F ( λ ) d λ ,
χ ¯ ( λ ) = χ ( x ,   λ ) W ( x ) d 2 x
s = I 2 - I 2 = 4 χ ¯ ( λ 1 ) χ ¯ ( λ 2 ) F ( λ 1 ) F ( λ 2 ) d λ 1 d λ 2 .
s d = ( I 1 - I 2 ) 2 ,
χ ¯ ( λ ) = ϕ ˜ ( f ,   λ ) sin ( π λ zf 2 ) W ˜ ( f ) d f .
Φ l ( f ) = 9.69 × 10 - 3 f - 11 / 3 C n 2 ( z ) d z .
B χ ( λ 1 ,   λ 2 ) = ϕ ˜ ( f ,   λ 1 ) ϕ ˜ * ( f ,   λ 2 ) × sin ( π λ 1 zf 2 ) sin ( π λ 2 zf 2 ) × W ˜ ( f ) W ˜ * ( f ) d f d f .
ϕ ˜ ( f ,   λ 1 ) ϕ ˜ * ( f ,   λ 2 ) = 4 π 2 λ 1 λ 2   Φ l ( f ) δ ( f - f ) .
B χ ( λ 1 ,   λ 2 ) = ( 9.69 × 10 - 3 ) C n 2 ( z ) d z   4 π 2 λ 1 λ 2 × f - 11 / 3 sin ( π λ 1 zf 2 ) × sin ( π λ 2 zf 2 ) A ( f ) d f ,
s = Q ( z ) C n 2 ( z ) d z ,
Q ( z ) = 32 π 3 ( 9.69 × 10 - 3 ) 0 f - 8 / 3 A ( f   ) S ( z ,   f   ) d f ,
S ( z ,   f   ) = ( λ 1 λ 2 ) - 1 sin ( π λ 1 zf 2 ) sin ( π λ 2 zf 2 ) × F ( λ 1 ) F ( λ 2 ) d λ 1 d λ 2 = λ - 1 F ( λ ) sin ( π λ zf 2 ) d λ 2 .
F ˜ ( k ) = d λ λ - 1 F ( λ ) exp ( 2 π ik λ ) ,
S ( z ,   f   ) = [ F ˜ i ( zf 2 / 2 ) ] 2 .
s = C n 2 ( z ) Q ( z ) d z .
F ( λ ) = λ λ 0 1 σ 2 π   exp - ( λ - λ 0 ) 2 2 σ 2 .
F ˜ i ( k ) = 1 λ 0 sin ( 2 π λ 0 k ) exp ( - 2 π 2 σ 2 k 2 ) ,
S ( z ,   f   ) = λ 0 - 2 sin 2 ( π λ 0 zf 2 ) exp ( - π 2 σ 2 z 2 f 4 ) .
Q ( z ) = 9.62 λ 0 - 2 0 d ff - 8 / 3 A ( f   ) × exp ( - 1.780 z 2 f 4 Λ 2 ) sin 2 ( π λ 0 zf 2 ) ,

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