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The Kolmogorov model of turbulence
junshan02 发表于 2012/7/14 10:54:00 |
A description of the nature of the wavefront perturbations introduced by the atmosphere is provided by the Kolmogorov model developed by Tatarski, based partly on the studies of turbulence by the Russian mathematician . This model is supported by a variety of experimental measurements and is widely used in simulations of astronomical imaging. The model assumes that the wavefront perturbations are brought about by variations in the refractive index of the atmosphere. These refractive index variations lead directly to phase fluctuations described by Moncler
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For simplicity, the phase fluctuations in Tatarski's model are often assumed to have a Gaussian random distribution with the following second order structure function: where is the atmospherically induced variance between the phase at two parts of the wavefront separated by a distance in the aperture plane, and represents the ensemble average.
For the Gaussian random approximation, the structure function of Tatarski (1961) can be described in terms of a single parameter : indicates the strength of the phase fluctuations as it corresponds to the diameter of a circular telescope aperture at which atmospheric phase perturbations begin to seriously limit the image resolution. Typical values for I band (900 nm wavelength) observations at good sites are 20---40 cm. It should be noted that also corresponds to the aperture diameter for which the variance of the wavefront phase averaged over the aperture comes approximately to unity: This equation represents a commonly used definition for Moncler
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