Closed form expressions for integral ray geometric parameters for wave propagation on general quadric surfaces of revolution

The integral ray geometric parameters consisting of the relation between the geodesic coordinates v and u, the arc length, and the generalized Fock parameter are presented for the complete class of QUASORs (quadric surfaces of revolution). A geodesic constant method permits the derivation of these ray parameters in terms of the geodesic constant h alone. Since h can be expressed in terms of the source and observation point coordinates in the case of the sphere and cone, in these cases the ray parameters are in closed form. On the other hand, in the case of the ellipsoid of revolution and the general paraboloid and hyperboloid of revolution, h can be obtained using a simple univariate search. Hence in these cases, the ray parameters are in a one-parameter dependent form. Using this approach, it is possible to readily calculate the various radiation characteristics of the antenna in the vicinity of a general QUASOR.<>