Phase and angle fluctuations in radiowave scattering from an ionospheric layer

We investigate the scattering of radio waves in reflection from an ionospheric layer with random inhomogeneities of the electron concentration. It is assumed that the average shape of the layer is described by a parabolic model, and that the inhomogeneities have a Gaussian correlation function. The problem is solved by approximation of geometrical optics. It is well known that, within the framework of this approximation, the amplitude modulations of the field are negligibly small compared to those of the phase. Thus the fluctuations of the phase and its spatial derivatives (the direction cosines of the beam) are the fundamental characteristics of an ionospherically scattered field. In this paper we obtain analytical expressions for the dispersion of these quantities for both normal and oblique reflections. These expressions go over at low frequencies to the well known formulas for a linear layer, while differing appreciably from them at frequencies close to the maximum usable frequency.