A Time Domain Formulation of the Uniform Geometrical Theory of Diffraction for Scattering From a Smooth Convex Surface

A time-domain version of the uniform geometrical theory of diffraction (TD-UTD) is developed to describe, in closed form, the transient electromagnetic scattering from a smooth convex surface excited by a general time impulsive astigmatic ray field. This TD-UTD impulse response is obtained by employing an analytic time transform (ATT) for the inversion in time of an available and accurate corresponding frequency domain UTD (FD-UTD) solution. The ATT is employed because it overcomes the difficulties that occur when inverting FD-UTD fields associated with rays that traverse line or smooth caustics. Furthermore, the TD-UTD response to a general pulsed astigmatic wave excitation may be found by a convolution of the general excitation with the TD-UTD impulse response which can be performed in closed form. Some numerical examples illustrating the utility of this TD-UTD are presented.