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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 70, Iss. 11 — Nov. 1, 1980
  • pp: 1354–1361

Space-time analysis of photon-limited stellar speckle interferometry

K. A. O’Donnell and J. C. Dainty  »View Author Affiliations

JOSA, Vol. 70, Issue 11, pp. 1354-1361 (1980)

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The standard method of stellar speckle interferometry, in which short exposure photographs are individually analyzed, is not the most general method of extracting object information from the time-varying image intensity. We introduce a space-time analysis in which both spatial and temporal fluctuations are taken into account; the aim is to measure the power spectrum of the image with an increased signal to noise ratio. Surprisingly, our more general space-time analysis does not yield an improved signal to noise ratio at very low light levels.

© 1980 Optical Society of America

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)

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  12. The quantity Α(0,t) does in fact fluctuate owing to scintillation and this effect is small if Dr0. Because of this (small) fluctuation ømeas (0) does not exactly equal the square of the power; this is discussed by Korff.5.
  13. Details of this transformation may be found in A. Papoulis, Probability, Random Variables and Stochastic Processes, (McGraw-Hill, New York, 1965), p. 325.
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  15. R. J. Scaddan and J. G. Walker, "Statistics of stellar speckle patterns," Appl. Opt. 17, 3779–3784 (1978).
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  17. J. G. Walker, "Optimum exposure time and filter bandwidth in speckle interferometry," IAU Colloquium No. 50, High Angular Resolution Stellar Interferometry, Maryland, Aug.–Sept. 1978 (unpublished).
  18. We are not aware of any rigorous proof that Λ(u,t) is a circular complex Gaussian random process; it can be shown to be a circular complex Gaussian random variable, for frequencies greater than the reciprocal of the width of the point-spread function, by the following heuristic argument. Using the autocorrelation theorem of Fourier transform theory, Λ(u,t) α ∫DA*(ξ) A (ξ + λƒu) d ξ where A(ξ) is the complex amplitude within the telescope pupil. For atmospheric turbulence, the phase of A*(ξ) is distributed uniformly between -π and π and so is that of the product A*(ξ)A(ξ + λƒu) for the case λƒu > r0. Provided that Dr0, we can thus invoke the central limit theorem to show that Λ(u,t) is a circular complex Gaussian random variable.
  19. L. Mertz, "Speckle imaging, photon by photon," Appl. Opt. 18, 611–614 (1979).
  20. L. Mandel, "Fluctuations of photon beams and their correlations," Proc. Phys. Soc. 72, 1037–1048 (1958).

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