Effects of turbulence in a planetary atmosphere on radio occultation

There has been considerable interest in the amplitude and phase fluctuations of the radio signal received from a flyby spacecraft during occultation by a planetary atmosphere. For planetary flyby missions, the Fresnel-zone size exceeds the outer scale size of turbulence, and existing formulations for the frequency spectra of the amplitude and phase fluctuations are inadequate because they do not account for the inhomogeneity of the turbulence in the direction transverse to the propagation path. In this paper, the formulation is given for the correlation functions for the log-amplitude and phase fluctuations of both spherical and plane waves propagating in a turbulent medium whose correlation function for refractive index fluctuations is described by the product of a function of the average coordinate and a function of the difference coordinate. The results are applied to radio occultation of a flyby space probe by the atmosphere of Venus, assuming that the turbulence in the atmosphere exists as a layer, that it is localized, isotropic, and smoothly varying, and that the localized turbulence is described by the Kolmogorov spectrum. Closed-form solutions for both variances and frequency spectra of the log-amplitude and phase fluctuations are obtained using Rytov's method, and it is seen that the shape of the frequency spectra depends a great deal on the characteristics and extent of the turbulence.