Abstract:Experimental and theoretical approaches to verify the\ud
validity of the incremental theory of diffraction (ITD) are considered.\ud
After providing a simple recipe for the application of the ITD,\ud
three geometries are examined for its validation. First, the ITD formulation\ud
of the diffraction from a perfect electric conductor (PEC)\ud
straight wedge is compared with the uniform theory of diffraction\ud
(UTD) and with measurement results. Second, the ITD formulation\ud
of the diffraction from a PEC disc is … Show more
“…The asymptotic analysis performed here yields high‐frequency, closed form expressions which explicitly satisfy reciprocity, and are well behaved at any incident and observation aspects, including those close to and at the longitudinal coordinate axis of the cylindrical configuration. An analytical verification for the case of a disk is provided by Erricolo et al [2007]. It is also found that, for the scalar case, the same result was obtained by Rubinowicz [1965], by means of an entirely different method.…”
[1] A novel general procedure for defining incremental field contributions for double diffraction at a pair of perfectly conducting (PEC) wedges in an arbitrary configuration is presented. The new formulation provides an accurate first-order asymptotic description of the interaction between two edges, which is valid both for skewed separate wedges and for edges joined by a common PEC face. It also includes a double incremental slope diffraction augmentation, which provides the correct dominant high-frequency incremental contribution at grazing aspect of incidence and observation. This new formulation is obtained by applying to both edges, the wedge-shaped incremental dyadic diffraction coefficients for single edge diffraction. The total doubly diffracted field is obtained from a double spatial integration along each of the two edges on which consecutive diffractions occur. It is found that this distributed field representation precisely recovers the doubly diffracted field predicted by the uniform theory of diffraction (UTD) and that may be applied to complement ray field methods close to and at caustics. It can be applied as well in all those situations in which a stationary phase condition is not yet well established. Numerical examples are presented and compared with those calculated from both Method of Moment solution and second-order UTD ray techniques. Excellent agreement was found in all cases examined.
“…The asymptotic analysis performed here yields high‐frequency, closed form expressions which explicitly satisfy reciprocity, and are well behaved at any incident and observation aspects, including those close to and at the longitudinal coordinate axis of the cylindrical configuration. An analytical verification for the case of a disk is provided by Erricolo et al [2007]. It is also found that, for the scalar case, the same result was obtained by Rubinowicz [1965], by means of an entirely different method.…”
[1] A novel general procedure for defining incremental field contributions for double diffraction at a pair of perfectly conducting (PEC) wedges in an arbitrary configuration is presented. The new formulation provides an accurate first-order asymptotic description of the interaction between two edges, which is valid both for skewed separate wedges and for edges joined by a common PEC face. It also includes a double incremental slope diffraction augmentation, which provides the correct dominant high-frequency incremental contribution at grazing aspect of incidence and observation. This new formulation is obtained by applying to both edges, the wedge-shaped incremental dyadic diffraction coefficients for single edge diffraction. The total doubly diffracted field is obtained from a double spatial integration along each of the two edges on which consecutive diffractions occur. It is found that this distributed field representation precisely recovers the doubly diffracted field predicted by the uniform theory of diffraction (UTD) and that may be applied to complement ray field methods close to and at caustics. It can be applied as well in all those situations in which a stationary phase condition is not yet well established. Numerical examples are presented and compared with those calculated from both Method of Moment solution and second-order UTD ray techniques. Excellent agreement was found in all cases examined.
“…This behavior is due to the rapid spatial variation and to the non ray-optical behavior of the field diffracted by the first edge when it illuminates the second wedge. The same limitation is expected to affect the ITD representation [18], [19], [21], [35], thus preventing a simple cascaded application of the ITD coefficients for single diffraction. Therefore, it is necessary to develop an ITD double-diffraction coefficient that uniformly accounts for the different transitions that may occur.…”
A new high-frequency Incremental Theory of Diffraction (ITD) formulation for the double diffraction by metallic wedges when illuminated by Complex Source Points (CSP) is provided. The main motivation is the extension of the class of problems that can be studied using asymptotic (i.e. ray-based and incremental) methods by providing a double diffraction description for CSP, which are considered because they are efficient to analyze electrically large structures. The new formulation provides an accurate asymptotic description of the interaction between two edges in an arbitrary configuration, including slope diffraction contributions. Advantages of the ITD formulation for CSP illumination include avoiding the typical ray-caustic impairments of the GTD/UTD ray techniques and not requiring ray tracing in complex space. Numerical results are presented and compared to a Method-of-Moments analysis to demonstrate the accuracy of the solution.
“…Moreover, the scattering by wedges may also be computed with the Incremental Theory of Diffraction (ITD) [6]- [9] and the ITD was recently extended in [10] to compute CSP diffraction by metallic objects. The ITD is considered because, in many cases, it overcomes the typical impairments of the GTD/UTD ray techniques associated with possible ray caustics and with the difficulties of ray tracing in complex space.…”
An Incremental Fringe Formulation (IFF) for the scattering by large metallic objects illuminated by electromagnetic Complex Source Points (CSPs) is presented. This formulation has two main advantages. First, it improves the accuracy of Physical Optics (PO) computations by removing spurious scattered field contributions and, at the same time, substituting them with more accurate Incremental Theory of Diffraction field contributions. Second, it reduces the complexity of PO computations because it is applicable to arbitrary illuminating fields represented in terms of a CSP beam expansion. The advantage of using CSPs is mainly due to their beam-like properties: truncation of negligible beams lowers the computational burden in the determination of the solution. Explicit dyadic expressions of incremental fringe coefficients are derived for wedgeshaped configurations. Comparisons between the proposed method, PO and the Method of Moments (MoM) are provided.
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