Fresnel zone structure in planetary occultations


  • Thomas A. Croft


In many planetary and satellite occultations, both at light and at radio wavelengths, there may exist two propagation paths around an occulting body. The shorter of these two paths traverses the nearest portion of the limb, supports a stronger signal, and accounts for all radio occultation measurements to date. If the atmosphere of the occulting body is sufficiently deep and the path beyond the body is sufficiently long, a weaker signal will propagate via the far limb. Both paths satisfy Format's principle; the short path lies at a minimum of delay, and the long path is shown to be at a stationary point. Others have pointed out that the Fresnel zone for the near limb is a compressed circle much like an ellipse. I show here that the Fresnel zone at the far limb is shaped somewhat like the letter X. In the immediate vicinity of the zone, the phase path variation with respect to lateral and vertical displacement may be represented in the form of a hyperbolic paraboloid resembling a saddle. Farther away, at least in the lateral direction, the variation can be represented by a tilted torus for which the general formula is derived. By use of parameters representative of Venus and Jupiter, the formula is evaluated and the zones are drawn for circumstances of one special, limiting case. This peculiar X-shaped zone structure may influence the prediction and interpretation of farside occultation signal strength and scintillation.