UTD Vertex Diffraction Coefficient for the Scattering by Perfectly Conducting Faceted Structures

Abstract

Abstract-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.Index Terms-Asymptotic diffraction theory, geometrical theory of diffraction, radar cross section (RCS), scattering, uniform theory of diffraction (UTD), vertex diffraction.

Analytic impulsive time-domain UTD coefficient for pyramid-vertex diffraction

“…In particular, we derived the TD-UTD vertex diffraction coefficient for a tip illuminated by an impulsive field. The diffraction coefficient presented here guarantees the compensation of the discontinuities at GO and UTD wedge diffracted field [3] planar and conical shadow boundaries (SBs), that are typical in vertex diffraction phenomena [10], and, thus, to uniformly describe the total field. Since the UTD is a high-frequency asymptotic theory, its results in the frequency domain remain accurate for moderate to high frequencies; the corresponding TD ray solution, therefore, is valid only for "early to intermediate times".…”

“…The term + d v is the dyadic TD-UTD analytic impulse response vertex diffraction coefficient. It can be conveniently calculated by using the rayfixed reference system defined in [10], and it is expressed as…”

“…This analytic TD transition functions is the one-side inverse Fourier transform of the frequency domain vertex transition function in [10]. During the conference, a detailed analysis of the dyadic diffraction coefficient will be provided along with various representative numerical results, which show the validity and the effectiveness of the proposed solution.…”

“…Such result is obtained by calculating the analytic time transform of the frequency domain (FD) UTD solution recently developed in [10]. As a consequence, the transient fields propagate along the ray paths of the UTD.…”

Vertex Diffracted Edge Waves on a Perfectly Conducting Plane Angular Sector

“…These end-point contributions are interpreted as corner diffracted fields. Based on this idea, uniform theory of diffraction (UTD) vertex diffraction coefficients describing the fields diffracted by the tip of a pyramidal structure when the source point is at a finite distance from the tip were derived in [12]. An approximate corner diffraction coefficient based on the geometrical theory of diffraction (GTD) was first 0018-926X/$26.00 © 2010 IEEE proposed by Burnside and Pathak [13].…”