Uniform Asymptotic Theory Of Diffraction Research Articles

Uniform asymptotic theory for the edge diffraction of cylindrical waves

The uniform asymptotic theory of diffraction is reintroduced in terms of the Fresnel cylinder function for the diffraction problems of cylindrical waves. The transition function of the above theory, which compensates the discontinuities of the diffracted wave, is constructed according to the new function. The scattering problem of waves by a resistive half-plane is studied by the aid of the improved method. The uniform wave expressions are compared with the ones, obtained by the Fresnel integral at the near and far fields of the edge.

A uniform function for the diffraction of spherical waves

A function which occurs in the scattering problem of the spherical waves by a perfectly conducting half-plane is introduced for constructing the transition functions of the uniform theory of diffraction and uniform asymptotic theory of diffraction. The important properties of the function, related with the geometrical optics and diffracted field components, are derived mathematically. A uniform asymptotic theory of wedge diffraction is introduced based on the new function. The resultant field expressions are investigated numerically.

Elastodynamic models for extending GTD to penumbra and finite size flaws

The scattering of elastic waves from an obstacle is of great interest in ultrasonic Non Destructive Evaluation (NDE). There exist two main scattering phenomena: specular reflection and diffraction. This paper is especially focused on possible improvements of the Geometrical Theory of Diffraction (GTD), one classical method used for modelling diffraction from scatterer edges. GTD notably presents two important drawbacks: it is theoretically valid for a canonical infinite edge and not for a finite one and presents discontinuities around the direction of specular reflection. In order to address the first drawback, a 3D hybrid method using both GTD and Huygens secondary sources has been developed to deal with finite flaws. ITD (Incremental Theory of Diffraction), a method developed in electromagnetism, has also been developed in elastodynamics to deal with small flaws. Experimental validation of these methods has been performed. As to the second drawback, a GTD uniform correction, the UTD (Uniform Theory of Diffraction) has been developed in the view of designing a generic model able to correctly simulate both specular reflection and diffraction. A comparison has been done between UTD numerical results and UAT (Uniform Asymptotic Theory of Diffraction) which is another uniform solution of GTD.

A Novel UTD-Type Diffraction Coefficient for a Straight Edge in a Curved Screen

A novel uniform theory of diffraction (UTD)-type diffraction coefficient for a straight edge in a cylindrically curved screen valid for both convex and concave side wave incidence is obtained via uniform asymptotic theory of diffraction (UAT) formulations. The proposed curved screen UTD-type coefficient (CSUTD) allows uniform description of the fields at all aspect angles including the grazing incidence case, where UTD coefficient-based predictions deviate sharply from available measurements, when it is applied to the problem of monostatic radar cross section (RCS) of cylindrically curved plate.

Electromagnetic Scattering of a Dipole-Field by an Impedance Wedge, Part I: Far-Field Space Waves

This paper consists of two parts and deals with the scattering of the wave-field generated by a Hertzian dipole placed over an impedance wedge. Expanding the dipole field into plane waves and extending to complex “angles of incidence” our recently obtained exact solution of the diffraction of a skew-incident plane wave by an impedance wedge enables us to give an integral representation for the total field. Then by means of asymptotic evaluation of the multiple integral far-field expressions are developed and interpreted. In the present first part (I) of the paper formulation and basic steps of analysis are presented. In particular, the far-field expressions for the reflected and edge waves, including the UAT (uniform asymptotic theory of diffraction) version of the far-field representation, are given. Both numerical computation and physical explanation of the analytic results have been performed. The forthcoming second part (II) of the work will be dedicated to the study of different surface waves excited, as well as to their physical interpretation and numerical calculation.

A Time-Domain Uniform Asymptotic Theory Applied to the Analysis of Pulse-Excited PEC Wedges

In this letter, a time-domain version of the uniform asymptotic theory of diffraction, henceforth named TD-UAT, is introduced and is employed to obtain the fields scattered by a perfectly electrically conducting wedge illuminated by an arbitrarily oriented electric dipole. The results of TD-UAT are compared to those obtained from an implementation of the time-domain uniform theory of diffraction (TD-UTD), and its applicability is demonstrated.

A UTD/FDTD investigation on procedures to assess compliance of cellular base-station antennas with human-exposure limits in a realistic urban environment

In this paper, different exposure situations for a subject standing inside a room of a building with a window facing a rooftop-mounted base-station antenna are analyzed. The study is accomplished by using a technique combining the uniform asymptotic theory of diffraction and the finite-difference time-domain method, suitable to characterize human exposure in realistic urban environments at a reasonable computational cost. The different exposure conditions examined are analyzed to highlight the problems related to compliance assessment procedures in complex exposure scenarios and to suggest some possible solutions. A comparison of the results obtained in these scenarios with those computed neglecting the presence of the room walls (free-space situations) evidences that, under certain conditions, average exposure field levels and specific absorption rates (SARs) in the realistic environments can be higher than in free space, thus demonstrating that compliance assessment carried out in free space can yield nonconservative results. As concerns implications of field nonuniformities, typical of realistic urban environments, on SAR values, the results show that the whole-body averaged SAR is related to the average field value, provided the averaging procedure is appropriately chosen to cover all the volume occupied by the subject (V/sub S/) and not only a vertical surface. Local SAR values, instead, show a more complex relation with the exposure field, such that considering only the V/sub S/-averaged field value for compliance assessment might lead to an underestimation of the real exposure level, while using the peak of the field in V/sub S/ leads to a remarkable overestimation.

Far-field analysis of the Malyuzhinets solution for plane and surface waves diffraction by an impedance wedge

The basic problem of determining the far-field scattered from the edge of a wedge of exterior angle 2 Φ with arbitrary impedance conditions on either face is considered. An accurate solution in the form of a Sommerfeld integral obtained by Malyuzhinets is evaluated for kr≫1. A fairly complete discussion of the far-field response is provided, including uniform and non-uniform asymptotic approximations. The far-field is split into edge-diffracted, surface, and geometrical optics waves, including multiply reflected components. The edge-diffracted field is defined by the diffraction coefficient, which we show has a simple factorisation: D= u 0( φ) u 0( φ 0) F Φ ( φ, φ 0), where φ and φ 0 are the source and observation directions, u 0( φ) is the value of the wave function at the edge for a plane wave of unit amplitude incident from the direction φ, and F Φ ( φ, φ 0) involves only trigonometric functions. We demonstrate that the monostatic tip diffraction from a wedge of arbitrary angle can be made to vanish by appropriate choice of the surface impedance. The unique value of impedance is always real, and an explicit formula is given for its evaluation. New results are presented for the reflection and transmission of surface waves on an impedance wedge, including simple approximations for an internal wedge with small Φ. Finally, a complete uniform description of the far-field is given in the format of the Uniform Asymptotic Theory of Diffraction.

Numerical study of diffraction and slope-diffraction at anisotropic impedance wedges by the method of parabolic equation: space waves

The method of parabolic equation (PE) has been successfully applied to the numerical determination of diffraction, slope-diffraction, and multiple-diffraction coefficients of scalar impedance wedges illuminated by a line source. As a continuation, this paper studies-for the first time to the authors' knowledge-another important canonical problem for the uniform geometrical theory of diffraction (UTD), namely, diffraction and slope-diffraction of an incident cylindrical wave at wedges with anisotropic impedance surfaces, by using the same method. For the diffracted fields, the exact Helmholtz equation is asymptotically approximated by the corresponding parabolic one. It is proved that the sufficient conditions for the unique solution of the Helmholtz equation also guarantee the uniqueness of the solution of the parabolic one. The latter is then efficiently solved by using Crank-Nicholson finite-difference (FD) scheme. Due to the lack of exact solutions, the PE results were compared to uniform asymptotic theory of diffraction (UAT) ones for weak anisotropy and, in this case, very good agreement has been achieved. The diffraction and slope-diffraction behavior dependent upon the measure of the weakness of the anisotropy has been demonstrated by several examples.

Radar cross section reduction of a flat plate by ram coating

AbstractThe problem of reduction of radar cross section (RCS) of a flat plate coated with a radar absorbing material has been examined using the uniform asymptotic theory of diffraction. The variation and reduction of RCS with different parameters have been studied and theoretical results have been compared with the experiment and the spectral Galerkin method.

Radiation pattern of an offset hyperbolic reflector

The radiation pattern of a focus-fed offset hyperbolic reflector is determined by using the uniform geometrical theory of diffraction (UTD) and the uniform asymptotic theory of diffraction (UAT). The patterns predicted by these two theories are observed to differ considerably around incident and reflection boundaries. The effects of the slope diffraction as well as those of additional terms in the improved UTD solution are ignored.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Electromagnetic scattering by a curved plate--Solution by uniform asymptotic theory of diffraction

The uniform asymptotic theory (UAT) of diffraction has been applied to find the monostatic scattered field by curved plate with a plane wave illumination with electric field parallel to the edge. The solution is valid for all positions of the receiver and is uniform around the reflection boundaries. The theoretical monostatic radar cross section (RCS) shows good agreement with experimental results. The formulation works very well for arbitrary radius of curvature of the plate down to a value of \lambda/2 .

Uniform asymptotic theory of diffraction by apertures

Simple and explicit formulas that represent uniform asymptotic approximations to double integrals are derived and applied to obtain a uniform asymptotic theory of diffraction by apertures. The formulas are used to evaluate the diffracted field or its angular spectrum in regions in which the results of ordinary asymptotic theories, such as the theory of the boundary diffracted wave and the geometrical theory of diffraction, break down. Thus our results remain valid in regions containing geometrical shadow boundaries or caustics of diffracted rays. To illustrate their general applicability, we apply them to two diffraction problems involving a circular aperture: For a diverging spherical incident wave we compute its diffracted field, and for a converging incident wave we compute both its angular spectrum and its diffracted field far from focus.

A simplified expression of the dyadic Green's function for a conducting half-sheet

Simple analytical expressions of the dyadic Green's function for a conducting half-sheet have been derived. These expressions involve some finite integrals which can be easily calculated by a digital computer and are much simpler than those involving the vector mode function expansion. Input impedances of monopole antennas on and near an edge of a conducting half-sheet and the impedance of a notch antenna have been obtained, and the usefulness of these simplified expressions has been proved. The present results can be applied to check the limits of the applicability of the asymptotic theories, e.g., the geometrical theory of diffraction (GTD) and the uniform asymptotic theory of diffraction (UAT).

Interference of corner reflected and edge diffracted signals for a surface-breaking crack

Backscatter of time-harmonic longitudinal waves from a surface-breaking crack is investigated in the high-frequency range. It is assumed that the distance of the transducer to the crack is large as compared to the crack depth, and that the incident rays are normal to the crack edge. The crack length is assumed much greater than its depth. A two-dimensional model for the transducer is considered. In the time domain, the first and second received signals are the edge-diffracted signal and the corner-reflected signal, respectively. These signals are analyzed in the frequency domain, by using the uniform asymptotic theory of diffraction. The response of the transducer due to the interference of the two signals is calculated. It is shown that the transducer’s response is a sensitive function of its position.

Uniform Asymptotic Theory of Diffraction by a Finite Cylinder

Uniform asymptotic expressions for the far field scattered by a finite solid cylinder are found by the method of edge waves. New results have been obtained for the field in the vicinity of the specular reflected ray. The role of the second term of the Luneburg–Kline’s expansion in forming the specular reflection is emphasized. Some computational errors in the Ahluwalia’s work (1970) are noted. After these errors are corrected, Ahluwalia’s theory gives exactly the same results as the method of edge waves.

Diffraction by an arbitrary subreflector: GTD solution

The high-frequency asymptotic solution of diffraction by a conducting subreflector is studied. By using Keller's geometrical theory of diffraction and the newly developed uniform asymptotic theory of diffraction, the scattered field is determined up to an including terms of order k^{-1/2} relative to the incident field. The key feature of the present work is that the surface of the subreflector is completely arbitrary. In fact, it is only necessary to specify the surface at a set of discrete points over a random net. Our computer program will fit those points by cubic spline functions and calculate the necessary geometrical parameters of the subreflector. In a companion paper by Y. Rahmat-Samii, R. Mittra, and V. Galindo-Israel, the scattered field from the submflector is used to calculate the secondary pattern of an arbitrarily shaped reflector by a series expansion method. Thus, in these two papers, it is hoped that we have developed a universal computer program that can analyze most dual-reflector antennas currently conceivable. It should also be added that our method of calculation is extremely numerically efficient. In many cases, it is one order of magnitude faster than the conventional integration method based on physical optics.

Addendum to: Diffraction of Plane Waves by a Strip; Exact and Asymptotic Solutions—the Solution in the General Case

Previous article Addendum to: Diffraction of Plane Waves by a Strip; Exact and Asymptotic Solutions—the Solution in the General CasePeter WolfePeter Wolfehttps://doi.org/10.1137/0124063PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[B1] D. S. Ahluwalia, , R. M. Lewis and , J. Boersma, Uniform asymptotic theory of diffraction by a plane screen, SIAM J. Appl. Math., 16 (1968), 783–807 10.1137/0116065 MR0241047 0189.40801 LinkISIGoogle Scholar[B2] R. M. Lewis and , J. B. Keller, Asymptotic methods for partial differential equations: The reduced wave equation and Maxwell's equation, Res. Rep., EM 194, New York University, New York, 1964 Google Scholar[B3] P. Wolfe, Diffraction by a strip; The solution in the general case, Tech. Rep., TR 71-56, Dept. of Mathematics, University of Maryland, College Park, 1971 Google Scholar Previous article FiguresRelatedReferencesCited ByDetails Diffraction of a plane wave by a circular diskJournal of Mathematical Analysis and Applications, Vol. 67, No. 1 | 1 Jan 1979 Cross Ref The decay of solutions of the two dimensional wave equation in the exterior of a straight stripTransactions of the American Mathematical Society, Vol. 231, No. 2 | 1 January 1977 Cross Ref Diffraction of a pulse by a stripJournal of Mathematical Analysis and Applications, Vol. 48, No. 1 | 1 Oct 1974 Cross Ref Volume 24, Issue 4| 1973SIAM Journal on Applied Mathematics425-618 History Submitted:21 December 1971Published online:17 February 2012 InformationCopyright © 1973 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0124063Article page range:pp. 613-618ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics

Uniform Asymptotic Theory of Diffraction by a Plane Screen by the Method of Boundary Layers

We discuss the diffraction of high frequency acoustic waves by a circular aperture in a plane screen. Our analysis shows that techniques based on boundary layers are as effective in diffraction theory as they are in fluid mechanics. By using these techniques we obtain a uniform asymptotic expansion of the diffracted field in all regions.

Uniform Asymptotic Theory of Diffraction by the Edge of a Three-Dimensional Body

Uniform Asymptotic Theory of Diffraction by the Edge of a Three-Dimensional Body