A uniform high-frequency description is presented for vertex (tip) diffraction at the tip of a pyramid, for source and observation points at finite distance from the tip. This provides an effective engineering tool able to describe the field scattered by a perfectly conducting faceted structure made by interconnected flat plates within a uniform theory of diffraction (UTD) framework. Despite the adopted approximation, the proposed closed form expression for the vertex diffracted ray is able to compensate for the discontinuities of the field predicted by standard UTD, i.e., geometrical optics combined with the UTD wedge diffracted rays. The present formulation leads to a uniform first order asymptotic field in all the transition regions of the tip diffracted field. The final analytical expression is cast in a UTD framework by introducing appropriate transition functions containing Generalized Fresnel Integrals. The effectiveness and accuracy of the solution is checked both through analytical limits and by comparison with numerical results provided by a full wave method of moments analysis. © 2009 IEEE.

We introduce our solution for the diffraction of a pulsed ray field, with spherical wavefront, by the vertex (tip) of a pyramid. Within the Uniform Geometrical Theory of Diffraction (UTD) we improve the time domain (TD) solutions available in the literature by introducing the field diffracted by a perfectly conducting faceted structure made by interconnected flat plates, for source and observation points at finite distance from the tip. The proposed closed form expression for an exciting impulsive source has been calculated by employing the one-sided inverse Fourier transform of the frequency domain solution. The solution obtained is able to compensate for the discontinuities of the field predicted by standard TD-UTD, i.e., time domain geometrical optics (TD-GO) combined with the TD-UTD wedge singly diffracted rays. © 2013 IEEE.