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Essam A. Marouf (San Jose State University)
We use the classical diffraction screen approach to develop a theoretical foundation for investigation of the intensity scintillations observed during stellar occultation of the Voyager spacecraft by Saturn’s rings (Showalter and Nicholson, {\em Icarus} {\bf 87}, 285-306, 1990). The formulation is guided by procedures developed for analysis of scintillations of stars observed through the turbulent Earth atmosphere and of natural radio sources observed through the interstellar medium. The steps are: i) propagate in free-space the source distribution to the plane of the screen to find the incident field (using, for example, the Fresnel-Huygens principle), ii) for an assumed random screen transmittance that models the cumulative effects of the random medium, calculate the statistical averages of the wavefront emerging from the screen, and iii) propagate in free-space the mean and mean-square wavefront intensity to determine their values at the detector in terms of statistical averages of the screen. Solution of the free-space parabolic wave equation for the second and fourth order moments of the diffracted field accomplishes this objective. Thus, the formulation effectively relates the intensity variance (or, equivalently, the scintillation index) at the detector to statistical averages of the screen, hence to physical media properties. In the interstellar scintillations case, the screen is a phase screen approximation (v., e.g., Rumsey, {\em Radio Science}, {\bf 10}, 107-114, 1975). In the rings scintillation case, the screen is a binary amplitude screen that models the random blocking of the incident radiation by ring particles (Marouf, {\em BAAS} {\bf 26}, 1150, 1994 and {\em BAAS} {\bf 29}, 1000, 1997). For an assumed physical ring model (particle sizes, ring thickness, packing fraction,\ldots etc), calculation of the second and fourth order moments of the random screen transmittance is a stochastic geometry problem for which closed form analytical solutions are not easy to obtain, in general. Work is in progress to adapt analytical results to numerical simulations and to investigate dependence of the scintillation index on physical ring properties, particularly particle sizes.
The author(s) of this abstract have provided an email address for comments about the abstract: emarouf@email.sjsu.edu