Fresnel zone structure in planetary occultations

The structures of the Fresnel zones of an occulting body with a substantial atmosphere are analyzed. The first Fresnel zone is defined as the set of all contiguous points connected to the transmitter and receiver via paths with a combined length within one half wavelength of the stationary value, and calculated by the application of the Huygens-Fresnel principle to a wave front frozen in time as it traverses the region of interest, taking into account wave front curvature of waves undergoing refraction. Calculations of the Fresnel zones of a planet determined by the meeting of wave fronts represented as tori reveal that the zone along the propagation path traversing the nearest portion of the limb to the transmitter has a shape similar to an ellipse, while that of the far zone resembles the letter X. The phase delay along the farside path is found to be a stationary point rather than a minimum, since delay is distributed in the form of a hyperbolic paraboloid near the ray and in the form of a torus intersection for greater separations. Examples are presented for S band propagation deep in the atmospheres of Venus and Jupiter.