There are little research on the subject of probability density function of the phase fluctuations in turbulent atmosphere at
present. There is still no analytical model under the most general case. Based on Born perturbation theory, the exact
model of the phase fluctuation in Elliptical-Gaussian speckle filed was theoretically deduced. And then three
approximate models (Circular-Gaussian approximation, Strong-Turbulence approximation and Strong-Turbulence-
Circular-Gaussian approximation model) which are corresponding to the irradiance fluctuation models were deduced
through appropriate simplification. Finally, the correlations of the models proposed were simulated analysed, and the
results prove the accuracy of the exact model.