Space-time analysis of photon-limited stellar speckle interferometry
JOSA, Vol. 70, Issue 11, pp. 1354-1361 (1980)
http://dx.doi.org/10.1364/JOSA.70.001354
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Abstract
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
Citation
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)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-70-11-1354
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References
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- The quantity Α(0,t) does in fact fluctuate owing to scintillation and this effect is small if D ≫ r_{0}. Because of this (small) fluctuation ø_{meas} (0) does not exactly equal the square of the power; this is discussed by Korff.^{5}.
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- 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 > r_{0}. Provided that D ≫ r_{0}, we can thus invoke the central limit theorem to show that Λ(u,t) is a circular complex Gaussian random variable.
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