Where r is the classical radius of the electron, 2. 818 x 10 m, and n is the electron density. Phase fluctuations (in radians) along a path length are given by: A 1 percent fluctuation in total content along the propagation path causes a phase fluctuation of: where N is the mean total content. For example if cm and electron/cm radians. Now consider a sinusoidal phase fluctuation with amplitude and wavelength . Let be the field incident on the ionosphere. The coordinates and are in a plane perpendicular to the boresight direction. After propagating through the ionosphere the field distribution will take the form: where is a phase modulation due to scattering (diffraction) by the density irregularities. A simple sinusoidal irregularity gives rise to a phase modulation The latter Bessel function expansion is the Fourier series representation of the modulation. Fresnel diffraction theory shows that the field at some distant plane is given by:
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