Profiling Saturn's rings by radio occultation

Diffraction of radio waves is a prominent phenomenon in Voyager 1 radio occultation measurements of Saturn's rings. It limits the effective radial resolution of observed signal intensity and phase to the characteristic Fresnel scale F, which is set by the geometry and wavelength, Λ. For the two Voyager wavelengths at Saturn, F ≅ 9–15 km at 3.6 cm Λ, and F ≅ 17–29 km at 13 cm Λ. This limitation can be largely removed by inverse-Fresnel filtering of the complex (i.e., amplitude and phase) observed signals. An Huygens-Fresnel formulation of the diffracted signal in terms of a circularly symmetric, complex gray-screen model of the rings, valid to second order in phase, leads to an exact Fresnel transform solution for the complex transmittance of the screen, which is useful for analysis. Extension of the formulation to fourth order in the phase of the transform kernel provides a practical implementation where the final resolution is limited by uncertainties in system parameters and noise. Consideration of the effects of uncertainties in the geometry, finite width of the data window employed, analytical approximations used, profile reconstruction fidelity required, system thermal noise, and system phase stability shows the phase stability and thermal noise to be the most critical factors for realistic systems. For Voyager at Saturn, phase instability limits radial resolution to values of the order of F/90, or about 200 m for optically thin rings. For more opaque rings, useful signal-to-noise ratios are the limiting factor: the resolution achieved at 3.6 cm Λ is typically 200–400 m over Ring C and the Cassini Division, 1–4 km over Ring A, and is greater than about 4 km over Ring B. For Voyager 2 at Uranus, the achievable resolution at 3.6 cm Λ is set by system phase stability and should approach 30 m as long as the normal opacity does not exceed ∼2. Reconstructed profiles of limited regions of Saturn's rings illustrate the technique. These reveal a remarkable array of small-scale (∼1 km) ring structures, including very sharp edges, narrow ringlets, gaps with distinctive edge profiles, wakes of embedded satellites, bending waves, density waves, and many unidentified wave-like phenomena. Profiles reconstructed over the full extent of the rings are available currently at 4.2 km and 900 m resolutions, and will be available presently at 400 m resolution.