Abstract

Measurements of the space–time correlation function of images at the focus of a large telescope have been made. They indicate that the image boiling has a directional component that is parallel to the motion of the turbulence in the pupil plane.

© 1981 Optical Society of America

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References

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  1. L. Mertz, “Speckle imaging, photon by photon,” Appl. Opt. 18, 611–614 (1979).
    [Crossref] [PubMed]
  2. K. A. O’Donnell and J. C. Dainty, “Space–time analysis of photon limited stellar speckle interferometry,” J. Opt. Soc. Am. 70, 1354–1361 (1980).
    [Crossref]
  3. D. P. Karo and A. M. Scheiderman, “Speckle interferometry lens-atmosphere MTF measurements,” J. Opt. Soc. Am. 66, 1252–1256 (1976).
    [Crossref]
  4. C. Aime and et al., “Measurements of stellar speckle interferometry lens-atmosphere modulation transfer function,” Opt. Acta 26, 575–581 (1979).
    [Crossref]
  5. D. Korff, “Analysis of a method for obtaining near-diffraction-limited information in the presence of atmospheric turbulence,” J. Opt. Soc. Am. 63, 971–980 (1973).
    [Crossref]
  6. R. J. Scaddan and J. G. Walker, “Statistics of stellar speckle patterns,” Appl. Opt. 17, 3779–3784 (1978).
    [Crossref] [PubMed]
  7. G. Parry and et al., “On the statistics of stellar speckle patterns and pupil plane scintillation,” Opt. Acta 26, 563–574 (1979).
    [Crossref]
  8. C. Roddier and F. Roddier, “Influence of exposure time on spectral properties of turbulence-degraded astronomical images,” J. Opt. Soc. Am. 65, 664–667 (1975).
    [Crossref]
  9. In fact, Ref. 8 considers the effect of time integration on the spatial power spectrum rather than the spatial autocorrelation function.
  10. C. Aime and et al., “The influence of scanning rate in sequential analysis of a speckle pattern. Application to speckle boiling,” Opt. Commun. (to be published).
  11. H. Z. Cummins and E. R. Pike, eds., Photon Correlation and Light Beating Spectroscopy (Plenum, London, 1974), p. 75.
  12. A speckle size is taken to be equal to the angular Rayleigh resolution limit α associated with an unobstructed telescope aperture of diameter d: α= 1.22λ/d.
  13. V. V. Anisimov and et al., “Space–time statistical properties of coherent radiation scattered by a moving diffuser,” Opt. Spectrosc. 27, 258–262 (1969).
  14. E. Jakeman and P. N. Pusey, “Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen. I. Theory,” J. Phys. A. 8, 369–391 (1975).
    [Crossref]
  15. E. Jakeman, “The effect of wavefront curvature on the coherence properties of laser light scattered by target centres in uniform motion,” J. Phys. A. 8, L23–L28 (1975).
    [Crossref]

1980 (1)

1979 (3)

C. Aime and et al., “Measurements of stellar speckle interferometry lens-atmosphere modulation transfer function,” Opt. Acta 26, 575–581 (1979).
[Crossref]

G. Parry and et al., “On the statistics of stellar speckle patterns and pupil plane scintillation,” Opt. Acta 26, 563–574 (1979).
[Crossref]

L. Mertz, “Speckle imaging, photon by photon,” Appl. Opt. 18, 611–614 (1979).
[Crossref] [PubMed]

1978 (1)

1976 (1)

1975 (3)

E. Jakeman and P. N. Pusey, “Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen. I. Theory,” J. Phys. A. 8, 369–391 (1975).
[Crossref]

E. Jakeman, “The effect of wavefront curvature on the coherence properties of laser light scattered by target centres in uniform motion,” J. Phys. A. 8, L23–L28 (1975).
[Crossref]

C. Roddier and F. Roddier, “Influence of exposure time on spectral properties of turbulence-degraded astronomical images,” J. Opt. Soc. Am. 65, 664–667 (1975).
[Crossref]

1973 (1)

1969 (1)

V. V. Anisimov and et al., “Space–time statistical properties of coherent radiation scattered by a moving diffuser,” Opt. Spectrosc. 27, 258–262 (1969).

Aime, C.

C. Aime and et al., “Measurements of stellar speckle interferometry lens-atmosphere modulation transfer function,” Opt. Acta 26, 575–581 (1979).
[Crossref]

C. Aime and et al., “The influence of scanning rate in sequential analysis of a speckle pattern. Application to speckle boiling,” Opt. Commun. (to be published).

Anisimov, V. V.

V. V. Anisimov and et al., “Space–time statistical properties of coherent radiation scattered by a moving diffuser,” Opt. Spectrosc. 27, 258–262 (1969).

Dainty, J. C.

Jakeman, E.

E. Jakeman and P. N. Pusey, “Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen. I. Theory,” J. Phys. A. 8, 369–391 (1975).
[Crossref]

E. Jakeman, “The effect of wavefront curvature on the coherence properties of laser light scattered by target centres in uniform motion,” J. Phys. A. 8, L23–L28 (1975).
[Crossref]

Karo, D. P.

Korff, D.

Mertz, L.

O’Donnell, K. A.

Parry, G.

G. Parry and et al., “On the statistics of stellar speckle patterns and pupil plane scintillation,” Opt. Acta 26, 563–574 (1979).
[Crossref]

Pusey, P. N.

E. Jakeman and P. N. Pusey, “Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen. I. Theory,” J. Phys. A. 8, 369–391 (1975).
[Crossref]

Roddier, C.

Roddier, F.

Scaddan, R. J.

Scheiderman, A. M.

Walker, J. G.

Appl. Opt. (2)

J. Opt. Soc. Am. (4)

J. Phys. A. (2)

E. Jakeman and P. N. Pusey, “Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen. I. Theory,” J. Phys. A. 8, 369–391 (1975).
[Crossref]

E. Jakeman, “The effect of wavefront curvature on the coherence properties of laser light scattered by target centres in uniform motion,” J. Phys. A. 8, L23–L28 (1975).
[Crossref]

Opt. Acta (2)

G. Parry and et al., “On the statistics of stellar speckle patterns and pupil plane scintillation,” Opt. Acta 26, 563–574 (1979).
[Crossref]

C. Aime and et al., “Measurements of stellar speckle interferometry lens-atmosphere modulation transfer function,” Opt. Acta 26, 575–581 (1979).
[Crossref]

Opt. Spectrosc. (1)

V. V. Anisimov and et al., “Space–time statistical properties of coherent radiation scattered by a moving diffuser,” Opt. Spectrosc. 27, 258–262 (1969).

Other (4)

In fact, Ref. 8 considers the effect of time integration on the spatial power spectrum rather than the spatial autocorrelation function.

C. Aime and et al., “The influence of scanning rate in sequential analysis of a speckle pattern. Application to speckle boiling,” Opt. Commun. (to be published).

H. Z. Cummins and E. R. Pike, eds., Photon Correlation and Light Beating Spectroscopy (Plenum, London, 1974), p. 75.

A speckle size is taken to be equal to the angular Rayleigh resolution limit α associated with an unobstructed telescope aperture of diameter d: α= 1.22λ/d.

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Figures (5)

Fig. 1
Fig. 1

Diagram of the dual-channel photometer. The instrument is mounted at the Cassegrain focus.

Fig. 2
Fig. 2

Cross-correlation functions of the intensity in the image of an unresolved star for pinhole separations of 0, 0.5, 0.75 and 1.0 speckles.

Fig. 3
Fig. 3

Cross-correlation functions for positive and negative time lags. The broken curve for Δx = 0 is simply a mirror image of the positive lag curve.

Fig. 4
Fig. 4

Cross-correlation functions for pinhole separations (Δx = 1) parallel and perpendicular to the turbulence in the pupil plane.

Fig. 5
Fig. 5

Cross-correlation functions of the image intensity for uniform translation of turbulence across an abberation-free square [calculated by using Eq. (3)].

Equations (4)

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C ( x 1 , x 2 , τ ) Δ I ( x 1 , t ) Δ I ( x 2 , t + τ ) I ( x 1 , t ) I ( x 2 , t ) ,
Δ I ( x , t ) = I ( x , t ) - I ( x , t ) ,
C ( Δ x , τ ) = Δ I ( x , t ) Δ I ( x + Δ x , t + τ ) I ( x , t ) 2 .
C ( Δ x , Δ y , τ ) | - A ( ξ , η ) A * ( ξ + u τ , η ) × exp [ - 2 π i λ f ( ξ Δ x + η Δ y ) ] d ξ d η | 2 ,