An incremental theory of double edge diffraction

Abstract

[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.

Recent advances in the Incremental Theory of Diffraction for Complex Source Point illumination

“…To obtain a double diffraction description that provides the proper asymptotic order in all the different transitions that may occur, it is best to retain the product of both the even and the odd parts of each cotangent associated with the spectral Green's Function of a single wedge [10]. An example where the introduction of the double diffraction results in a better estimation of the radiated field is the problem of a circular metallic disc illuminated by a single CSP.…”

“…When the dominant field of a singly-diffracted ray is shadowed by a second edge, a discontinuity may occur in the field estimate mostly at grazing incidence and observation aspects. Thus, the introduction of a double diffraction field compensates for such a discontinuity [10]. In this framework, a formulation for the incremental double diffraction problem for the case of CSP illumination has been recently proposed [9].…”

ITD Double-Edge Diffraction for Complex Source Beam Illumination

“…where M β (γ 12 ) is the first row of the transformation matrix M (γ 12 ) between the two local spherical systems at Q l1 and Q l2 , and γ 12 is the rotation angle defined between the ray-fixed unit vectors (β 1 ,φ 1 ) and (β 2 ,φ 2 ), as illustrated in [26]. As a consequence, theẑ l2 -component of the incident field at Q l2 is then…”

“…As pointed out in other existing UTD formulations for real source illumination [23], [25], [26], [29], [33], [34], the cascaded application of ordinary UTD coefficients fails when the edge of the second wedge lies within the transition region of the field diffracted by the first wedge. 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.…”

Including high-frequency surface diffraction in a hybrid FEBI-MLFMM-UTD method

“…Problems arising from both memory and computation time efforts affecting the boundary integral method are solved by the introduction of fast integral equation solvers like the adaptive integral method (AIM) [2] and the fast multipole method (FMM) [3]. A significant gain in both memory and computation time can be achieved if one combines boundary integral method with asymptotic ray-methods like Uniform Theory of Diffraction (UTD) [4], or high-frequency incremental methods like Physical Theory of Diffraction (PTD) [5], or the Incremental Theory of Diffraction [6], [7]. In [8] method called FEBI-MLFMM-UTD was introduced which provides a technique for coupling the fields scattered by large planar objects computed by using UTD with radiating current sources located at various FMM levels.…”