Profiling Saturn's rings by radio occultation

The development of reconstruction algorithms that correct for diffraction effects in radio occultation measurements is described. The reciprocal Fresnel transform relationship between the complex amplitude of the observed coherent signal and the complex microwave transmittance of the rings is derived using the Huygens-Fresnel formulation of the diffraction problem. The effects of the finite data segment width, the uncertainties in the Fresnel scale, systematic phase errors in the kernel of the inverse transform, reference oscillator instabilities, and random noise measurements on the resolution of the reconstructed transmittance are analyzed. Examples of reconstructed opacity profiles for some regions of Saturn's rings derived by applying the reconstruction theory to Voyager 1 at Saturn data are presented.