Diffraction by a quarter plane, the exact solution, and some numerical results

Satterwhite, R.

doi:10.1109/tap.1974.1140803

Cited by 47 publications

(19 citation statements)

References 3 publications

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“…In (7), the points and lie on face and , respectively, and both approach the integration point on edge (Fig. 2); such limit leads to a finite value despite the singular behavior of each of both terms in (7). The evaluation of implies the knowledge of the vector potential on the edges of the pyramid, which would require the knowledge of the unknown scattered field [see (3)].…”

Section: Scalar Formulationmentioning

confidence: 99%

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

Albani

Capolino

Carluccio

et al. 2009

IEEE Trans. Antennas Propagat.

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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.

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Section: Scalar Formulationmentioning

confidence: 99%

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

Albani

Capolino

Carluccio

et al. 2009

IEEE Trans. Antennas Propagat.

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“…The exact solution of the scalar problem for soft boundary conditions and 90 plane angular sector was obtained by Radlow [5], who used the Wiener-Hopf technique; his work was recently extended to the electromagnetic case by Albertsen [6]. For arbitrary corner angle, the exact electromagnetic solution was first found by Satterwhite and Kouyoumjian [7], [8]; however, the series expansion representation of the solution is slowly convergent when the distance from the tip increases and no practical asymptotic approximation has been found yet. An alternative derivation of the same solution was given in [9]; in the works by Smyshlyaev [10], [11] the exact solution was obtained as a particular case of an elliptical degenerated cone.…”

Section: Introductionmentioning

confidence: 99%

“…An alternative derivation of the same solution was given in [9]; in the works by Smyshlyaev [10], [11] the exact solution was obtained as a particular case of an elliptical degenerated cone. The solution in [7], [8] was used in [12] to obtain an interpolation of the fringe currents in a region close to the tip after extracting the UTD dominant terms. In [13], a hybrid method of moments (MoM)-UTD procedure was applied to a square plate in order to derive approximate analytical expressions for the currents on a right-angled plane angular sector.…”

Section: Introductionmentioning

confidence: 99%

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ITD formulation for the currents on a plane angular sector

Maci

Albani

Capolino

1998

IEEE Trans. Antennas Propagat.

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Abstract-Approximate high-frequency expressions for the currents induced on a perfectly conducting plane angular sector are derived on the basis of the incremental theory of diffraction (ITD). These currents are represented in terms of those predicted by physical optics (PO) plus fringe contributions excited by singly and doubly diffracted (DD) rays at the two edges of the angular sector. For each of these two contributions, additional currents associated to vertex diffracted rays are introduced that provide continuity at the relevant shadow boundary lines. The transition region of DD rays is described by a transition function involving cylinder parabolic functions. The asymptotic solution presented here is constructed in such a way to satisfy far from the vertex the expected edge singularities, which tend to be the same as those predicted by the exact solution of the half plane. Numerical results are compared with the exact solution of the same problem and with moments method results for scattering from polygonal plates.Index Terms-Geometrical theory of diffraction, high-frequency techniques, incremental theory of diffraction, physical optics.

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“…An even more serious impairment is encountered in applying GTD to RCS calculations, due to the fact that the leading edge contributions are restricted to lying on the pertinent diffraction cones. The canonical problem of the plane angular sector was solved by Satterwhite and Kouyoumjian [3,4], but the series expansion of the solution is hard to compute and not well-suited for a practical asymptotic evaluation. Most of the literature on this topic presents formulations based on numerical or hybrid techniques [5][6][7] or on approximate, high-frequency methods [8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%