# Evaluation of edge-diffracted fields including equivalent currents for the caustic regions

Abstract: The fields diffracted by a body made up of finite axially symmetric cone frustums are obtained using the concepts of the geometrical theory of diffraction. The backscattered field for plane-wave incidence on such a target is obtained with particular emphasis on those regions that are usually avoided, namely, the caustic region and its immediate vicinity. The method makes use of equivalent electric and magnetic current sources which are incorporated in the geometrical theory of diffraction. This solution is such that it is readily incorporated in a general computer program, rather than requiring that a new program be written for each shape. Several results, such as the cone, the cylinder and the conically capped cylinder, are given. In addition, the method is readily applied to antenna problems. An example which is reported consists of the radiation by a stub over a circular ground plane. This present theory yields quite good agreement with experimental results reported by Lopez, whereas the original theory given by Lopez is in error by as much as 10 dB.

Topics: Uniform theory of diffraction (55%), Diffraction (51%)

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01 Nov 1974

Abstract: A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edse formed by perfectly conducting curved ot plane surfaces is obtained. This diffraction coefficient remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. Our method is based on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray-fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresenel integrals, which ensure that the total field is continuous at shadow and reflection boundaries. The diffraction coefficients have the same form for the different types of edge illumination; only the arguments of the Fresnel integrals are different. Since diffraction is a local phenomenon, and locally the curved edge structure is wedge shaped, this result is readily extended to the curved wedge. It is interesting that even though the polarizations and the wavefront curvatures of the incident, reflected, and diffracted waves are markedly different, the total field calculated from this high-frequency solution for the curved wedge is continuous at shadow and reflection boundaries.

2,478 citations

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Abstract: Explicit expressions for equivalent edge currents are derived for an arbitrary local wedge angle and arbitrary directions of illumination and observation. Thereby the method of equivalent currents (MEC) is completed as a practically applicable theory of the electromagnetic high-frequency diffraction by edges. The derivation is based on an asymptotic relationship between the surface radiation integral of the physical theory of diffraction (PTD) and the line radiation integral of MEC, and the resulting expressions are deduced from the exact solutions of the canonical wedge problem.

269 citations

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Abstract: The uniform geometrical theory of diffraction (GTD) is employed for calculating the edge diffracted fields from the finite ground plane of a microstrip antenna. The source field from the radiating patch is calculated by two different methods: the slot theory and the modal expansion theory. Many numerical and measured results are presented to demonstrate the accuracy of the calculations and the finite ground plane edge effect.

254 citations

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01 May 1989Abstract: A summary of the development and verifications of a computer code, RECOTA (return from complex target), developed at Boeing Aerospace for calculating the radar cross section of complex targets is presented. The code utilizes a computer-aided design package for modeling target geometry in terms of facets and wedges. It is based on physical optics, physical theory of diffraction, ray tracing, and semiempirical formulations, and it accounts for shadowing, multiple scattering and discontinuities for monostatic calculations. >

183 citations

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Abstract: New expressions are derived for the fringe current components of the equivalent edge currents. They are obtained by asymptotic endpoint evaluation of the fringe current radiation integral over the "ray coordinate" measured along the diffracted ray grazing the surface of the local wedge. The resulting expressions, unlike the previous ones, are finite for all aspects of illumination and observation, except for the special case where the direction of observation is the continuation of a glancing incident ray propagating "inwards" with respect to the wedge surface (the Ufimtsev singularity).

178 citations

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Abstract: Diffraction of a wave by an aperture of any shape in a thin screen is treated by a new method—``the geometrical theory of diffraction.'' This is an extension of geometrical optics which accounts for diffraction by introducing new rays called diffracted rays. They are produced when incident rays hit the aperture edge and they satisfy the ``law of diffraction.'' A field is associated with each ray in a quantitative way, by means of the optical principles of phase variation and energy conservation. In addition ``diffraction coefficients'' are introduced to relate the field on a diffracted ray to that on the corresponding incident ray.By this method a simple formula is obtained for the field diffracted by any aperture. It yields the field in the aperture, the diffraction pattern and the transmission cross section. Explicit formulas and numerical results are given for slits and circular apertures. The accuracy of the results increases as the wavelength decreases, but they are useful for wavelengths even as lar...

387 citations

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Abstract: By use of approximations based on physical reasoning radar cross-section results for bodies of revolution are found. In the Rayleigh region (wavelength large with respect to object dimensions) approximate solutions are found. Examples given include a finite cone, a lens, an elliptic ogive, a spindle and a finite cylinder. In the physical optics region (wavelength very small with respect to all radii of curvature) Kirchhoff theory and also geometric optics can be used. When the body dimensions are only moderately large with respect to the wavelength, Fock or Franz theory can be applied, and examples of the circular and elliptic cylinder are presented. In the region where some dimensions of the body are large with respect to the wavelength and other dimensions are small with respect to the wavelength, special techniques are used. One example, the finite cone, is solved by appropriate use of the wedge-like fields locally at the base. Another example is the use of traveling wave theory for obtaining approximate solutions for the prolate spheroid and the ogive. Other results are obtained for cones the base perimeter of which is of the order of a wavelength by using known results for rings of the same perimeter.

80 citations

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01 Aug 1965

Abstract: The ability of the geometrical theory of diffraction to predict the radar cross section (RCS) of a perfectly conducting, right circular cone as a function of viewing angle is evaluated by comparison of computed and measured values of RCS. Both vertical and horizontal polarization have been considered for cones ranging from 0.98 to 2.87 wavelengths in diameter at the base and having half angles of 4°, 15°, and 90°; the latter case corresponds to a disk. It is shown that for cones having normalized base circumference (ka) of 8 or 9 the predicted and measured RCS agree very well except when the cone is observed within about 30° of nose-on with vertical polarization, in which case large errors occur for some as yet unknown reason. For smaller cones having diameters about equal to the wavelength (ka around 3), the computed RCS is generally predicted within 5 dB, but the form of the RCS pattern is not predicted very accurately. Backscattering from the base of the cone is very nearly the same as backscattering from a disk of the same diameter for viewing angles within 60° of the normal to the base.

49 citations