A numerical method for extending ray trace calculations of radio fields into strong focusing regions


  • R. E. Warren,

  • R. N. DeWitt,

  • C. R. Warber


This paper presents a practical method for computing radio fields in regions of strong focusing, using ray intercept data provided by a standard ray-tracing program. The procedure extends the usefulness of the ray trace by allowing fields to be computed near caustics and cusps where ray density calculations fail. Using a plane wave decomposition of the field components, phase integrals are computed by curve-fitting intercepts of rays traced through ionospheric or tropospheric media whose refractive indices vary arbitrarily with altitude. A numerical algorithm is described for performing the plane wave angular spectral integrations. This procedure avoids the complications associated with higher-order asymptotic techniques, allowing a broad range of refractive-index profiles to be analyzed by a single method. It is applied to two sample profiles, and the results agree very closely with higher-order stationary-phase estimates in caustic regions. Moreover, the computer code runs efficiently, despite the presence of highly oscillatory integrands. The method is capable of including the effects of weak collisions, the spherical earth, and azimuthally dependent transmitter configurations.