Geometrical Theory Of Diffraction Research Articles

The Uniform Geometrical Theory of Diffraction and Some of Its Applications

Keller introduced his Geometrical Theory of Diffraction (GTD) in the 1950s. The Geometrical Theory of Diffraction development was revolutionary, in that it explained the phenomena of wave diffraction entirely in terms of rays for the first time, via a systematic generalization of Fermat's principle. In its original form, the Geometrical Theory of Diffraction exhibited singularities at and near ray-shadow boundaries and caustics. For practical applications, it is necessary to patch up the Geometrical Theory of Diffraction in such regions. Uniform asymptotic high-frequency methods overcome the failure of the Geometrical Theory of Diffraction inside those regions, and outside those regions they generally reduce to the Geometrical Theory of Diffraction. One such highly developed approach happens to be the Uniform Geometrical Theory of Diffraction (UTD). The present article focuses on some key Uniform Geometrical Theory of Diffraction developments in a semi-historical fashion, with a few typical applications to illustrate the power and utility of the Geometrical Theory of Diffraction/Uniform Geometrical Theory of Diffraction concept to solve practical problems.

Diffraction by Canonical Metallic and Material-Coated Structures: A Review

Keller's landmark paper in 1962 formulated the Geometrical Theory of Diffraction (GTD). This was the beginning of a long process that brought the Geometrical Theory of Diffraction into practice, making it one of the most ubiquitous analysis methods in electromagnetics. This paper provides a personal historical trace of the Geometrical Theory of Diffraction: in particular, its further development in the 1970s and 1980s, and its realization into computer codes. The latter provided the first step for the analysis of complex realistic structures. The second half of the paper discusses the historical development of diffraction coefficients for impedance wedges using first- and higher-order generalized impedance boundary conditions.

50 years with J. B. Keller's Geometrical Theory of Diffraction in Denmark - Revisiting the Theory: Impedance Half-Plane Diffraction Coefficients

In the introduction, Danish contributions to J. B. Keller's Geometrical Theory of Diffraction are surveyed. The edge diffraction coefficient in the case of scattering by a half-plane with an impedance surface is then analyzed. In short-wavelength scattering theory, the amplitudes of the incident and the reflected rays are of the same order of magnitude. The consequence of this point of view for the structure of the diffraction coefficient is investigated.

Parametric Study and Validation of a UTD-PO Multiple-Cylinder Diffraction Solution Through Measurements at 60 GHz

A uniform theory of diffraction (UTD)-physical optics (PO) formulation for multiple-cylinder diffraction analysis is compared with measurements performed at 60 GHz. Thus, the influence of the variation of parameters, such as: the number of cylinders considered, the radius of curvature, the distance from the transmitter to the array of rounded obstacles, and the polarization is analyzed both theoretically and experimentally. The good agreement shown between the predicted and measured results validates such a theoretical solution for the analysis of radiowave propagation when multiple-diffraction over cylindrical surfaces has to be considered.

High-Frequency Techniques in Diffraction Theory: 50 Years of Achievements in GTD, PTD, and Related Approaches (Second Part)

This is the second part of a special section of the IEEE Antennas and Propagation Magazine that - as stated in the title - was conceived to celebrate 50 years since the publications of two fundamental scientific works: the paper by J. B. Keller, ?Geometrical Theory of Diffraction,? Journal of the Optical Society of America, 52, 1962, pp. 116?130; and the book by P. Ya. Ufimtsev, Method of Edge Waves in the Physical Theory of Diffraction, Moscow, Soviet Radio, 1962 (in Russian).

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

The purpose of this work is the description of the diffraction of a pulsed ray field, with spherical wavefront, by the vertex (tip) of a pyramid. In the framework of the uniform geometrical theory of diffraction (UTD), we augment the existing time-domain (TD) solutions available in the literature by introducing the field diffracted by a perfectly conducting faceted structure made by interconnected flat plates, for source and observation points at finite distance from the tip. The proposed closed-form expression for an exciting impulsive source has been obtained by employing the analytic time transform of the frequency-domain solution. The solution obtained is able to compensate for the discontinuities of the field predicted by standard TD-UTD, i.e., time-domain geometrical optics (TD-GO) combined with the TD-UTD wedge singly diffracted rays. The proposed result is valid only for early times, at and close to (behind) the vertex diffracted ray wavefront. The TD-UTD response to a more general pulsed excitation can be found via an efficient convolution of the TD-UTD solution for an impulsive (delta) excitation, and the general pulsed excitation itself. In particular, this convolution integral is evaluated in closed form, after expressing the analytic time transform of the general pulsed excitation as a sum of simple signals. The proposed TD-UTD vertex diffracted field is therefore suitable for analyzing the dispersion of a pulsed field due to diffraction from the tip and provides a new effective engineering tool within the UTD framework, as required in modern ray-based codes.

Efficient three-dimensional ray-tracing model for electromagnetic propagation prediction in complex indoor environments

A three-dimensional ray-tracing model for the use of the uniform theory of diffraction and geometrical optics in radio channel characterizations of indoor environments is presented in this paper. Based on the environment information chosen by the proposed modeling approach, the model is effectively applied by utilizing a technique in which multiple reflections, transmissions, and diffractions are considered via the ray-path classification into four different categories. Ray paths belonging to each ray category are determined by using different methods. Our theoretical results are compared with narrowband and wideband measurements. The good agreement with these measurements indicates that our prediction model works well for such indoor communication applications.

Conical Horn: Gain and Amplitude Patterns

The conical horn radiation characteristics (gain, aperture phase distributions, loss factors, and amplitude patterns) are revisited based on the spherical and quadratic aperture phase distributions. Calculations of the conical horn gain, using over the aperture either the dominant -mode of a circular waveguide or the modal variations of a conical waveguide, are calculated using the aperture phase distribution represented by spherical and quadratic wavefronts. The gains are compared with the classical data by Gray and Schelkunoff, in an attempt to confirm their validity and accuracy and to determine whether they were derived based on spherical or quadratic phase distribution. In addition, more accurate loss factors, to account for amplitude and phase tapering over the conical horn aperture, are derived which improve the conical horn gain. New formulas for the design of optimum gain conical horns, based on the more accurate spherical aperture phase distribution, are derived and reported, and guidelines are provided for their utility. This paper also introduces a method to calculate accurately the far-zone amplitude patterns in the E and H planes, including those in the far side and back lobe regions, of a conical horn by utilizing geometrical optics and diffraction theory.

High-Frequency Techniques in Diffraction Theory: 50 Years of Achievements in GTD, PTD, and Related Approaches [Special section introduction

As stated in the title, this special section of the IEEE Antennas and Propagation Magazine was conceived to celebrate 50 years since the publications of two fundamental scientific works: the paper by J. B. Keller, “Geometrical Theory of Diffraction,” Journal of the Optical Society of America, 52, 1962, pp. 116–130; and the book by P. Ya. Ufimtsev, Method of Edge Waves in the Physical Theory of Diffraction, Moscow, Soviet Radio, 1962 (in Russian).

GTD, UTD, UAT, and STD: A Historical Revisit and Personal Observations

In his landmark paper, dated February 1962, Prof. Joseph Keller detailed the notion of Keller's cone. He stated, “Geometrical optics, the oldest and most widely used theory of light propagation, fails to account for certain optical phenomena called diffraction....” I had a personal encounter with Keller's cone at a hotel in Florida! In the early morning on October 14, 2007, I witnessed Keller's cone on the door of my hotel room, resulting from edge diffraction from a TV stand due to the sun's rays coming through an opening of a window curtain. By now we know how to construct the local plane-wave behavior of the diffracted field along the diffracted rays, by invoking the fact that an edge forms one of the caustics of the diffracted wavefront. We also know that the diffracted field is of the order of k-1/2, in comparison to the geometrical-optics field, which is of the order of k0. In many antenna and scattering problems, this added diffracted term immensely enhances the accuracy of the total field. Due to the boundary-layer properties of the diffracted ray field along the incident and reflected shadow boundaries and also caustics, the original form of Keller's construction fails. These shadow-boundary shortcomings have been overcome through construction of the Uniform Theory of Diffraction (UTD, by Kouyoumjian and Pathak), the Uniform Asymptotic Theory (UAT, by Ahluwalia, Boersma, Lewis, Lee, and Deschamps), and the Spectral Theory of Diffraction (STD, by Rahmat-Samii, Ko, and Mittra). An overview and the salient features of these theories are revisited in a novel and unified manner, and a representative reflector-antenna example is highlighted.

A Comparative Study of Localization Methods in Indoor Environments

A comparative study, based on three different measurements (direction of ray arrival, time difference of arrival and received signal strength), to compute the unknown position of mobile stations in indoor environments is presented in this paper. The comparison is carried out considering the results of analyses in a real building in Madrid. To overcome the problems that arise in indoor areas due to the presence of non line of sight conditions, the fingerprinting technique is applied in each of the cases. Data for computations are provided by a simulation tool based on the uniform theory of diffraction and ray-tracing techniques. This information is stored in the fingerprinting database and contains information related to every mobile station, every reference node and every access point located inside the environment under analysis. Experimental results compare the mean error when localizing several mobile stations by using the three different approaches. The goal is to obtain high precision in the localization by means of alternative methods to the received signal strength classical measurement. These techniques will be useful in critical environments where high operational security requirement are demanded.

The impact of including diffraction when predicting the effect of listener environment on the perceived loudness of outdoor sonic booms

The human impact of sonic booms varies with listening environment. Given the incident sonic boom waveform, the specular field around a realistic geometry has been predicted via a C++ implementation of image source method (ISM) tailored to outdoor applications. This work explores the necessity of including the diffracted field when predicting time series and PLdB, both in and out of shadow zones. The impulsive nature of the excitation, and the sensitivity of the PLdB to temporal details, constrains appropriate diffraction modeling techniques to those capable of time domain accuracy. Uniform Theory of Diffraction (UTD) and Biot Tolstoy Medwin (BTM) approaches are considered. The benefits and challenges of each approach are explored, particularly with regards to scalability and bandwidth. The importance of accurately predicting diffraction in this application is evaluated through comparison with booms recorded around a building corresponding to the simulated geometry. [Work supported by the FAA/NASA/Transport Canada PARTNER Center Excellence and the Applied Research Laboratory. Experimental data courtesy of NASA.]

Reflection of ${\rm TE}_{0{n}}$ Modes at Open-Ended Oversized Circular Waveguide

Reflection of circular symmetric TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> modes ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> = 1-6) at an oversized, open-ended circular waveguide (C76-waveguide, inner diameter=27.79 mm, 70 GHz) radiating into free space has been investigated theoretically employing two scattering matrix codes (SMCs), the finite-difference time-domain code EMPIRE and the uniform geometrical theory of diffraction (UTD) as well as the first time experimentally. The measurements utilized mode converters for generation of pure TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> modes and a wavenumber spectrometer for mode analysis in the oversized waveguide. The total power reflection computed by EMPIRE is 4.1 to 13.4 dB lower than calculated from free-space wave and waveguide mode impedances. In all cases, most of the reflected power is carried by the backward traveling TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">06</sub> mode, which is the mode closest to cutoff. Experiments are in very good agreement with theoretical results.

An Improved UTD Based Model for the Multiple Building Diffraction of Plane Waves in Urban Environments by Using Higher Order Diffraction Coefficients

This paper describes an improved model for multiple building diffraction modeling based on the uniform theory of diffraction. A well-known problem in conventional uniform theory of diffraction (CUTD) is multiple edge transition zone diffraction. Here, higher order diffracted fields are used in order to improve the result. Hence, we use higher order diffraction coefficients to improve a hybrid physical optics (PO)-CUTD model, the results show that the new model can correct errors of the PO-CUTD model. Therefore, the proposed model can find application in the development of theoretical models to predict more realistic path loss in urban environments, when multiple building diffraction is considered.

Fifty years of high frequency diffraction

The study of high frequency diffraction phenomena mostly associated with geometrical theory of diffraction, uniform theory of diffraction, physical theory of diffraction, and their alternatives is reviewed. Several examples illustrate these theories and their applications in antennas and scattering problems. © 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.

Simplified analytical propagation model for railway environments based on uniform theory of diffraction

Proposed is a simplified analytical propagation model in railway environments. A heuristic ray tracing with geometrical optics and uniform theory of diffraction are adopted. Four typical and dominating ray paths that undergo reflections from ground and train roof and diffraction from the corner of the train are considered. The measurements verify that the analytical propagation model works very well in typical railway environments.

Analytic transient analysis of radiation from hyperboloid reflector antennas via surface curvature continuation of ellipsoidal surfaces

A transient analysis of a hyperbolic reflector antenna is performed based on a mathematic continuation of surface curvatures of an ellipsoidal reflector antenna with the analysis previously performed. This work makes the time-domain analysis useful for the design of reflector antennas since both ellipsoidal and hyperbolic reflectors are widely used as sub-reflectors for dual-reflector antenna system. In particular, this work interprets the scattering phenomena in terms of reflected and diffracted fields with respect to the frameworks of geometrical theories of diffraction, and allows one to analyse the reflector based on the local scattering mechanism.

Wedge diffraction of a critically incident Gaussian beam

A large embedded or surface-breaking crack in an otherwise isotropic and homogeneous solid is modeled as an infinite planar wedge with zero-traction faces. A Gaussian beam of transverse elastic waves is assumed to be incident on one of these faces with its axis at a near critical angle. It is assumed that the beam hits the face away from the crack corner. The rays impinging on the face at supercritical angles give rise to reflected transverse waves only, while those impinging on it at subcritical angles generate the reflected field, which contains both transverse and longitudinal modes. It is shown that when the beam hits relatively close to the wedge corner the incident field near the irradiated face can be approximated as a near grazing longitudinal wave of the Goodier–Bishop type. A recipe is offered for utilizing GTD (Geometrical Theory of Diffraction) to simulate the resulting transverse and longitudinal waves. The two-dimensional version of the above configuration is of interest in modeling ultrasonic Non-Destructive Testing and Evaluation.

Analysis of Arbitrary Reflector Antennas Applying the Geometrical Theory of Diffraction Together with the Master Points Technique

An efficient approach for the analysis of surface conformed reflector antennas fed arbitrarily is presented. The near field in a large number of sampling points in the aperture of the reflector is obtained applying the Geometrical Theory of Diffraction (GTD). A new technique named Master Points has been developed to reduce the complexity of the ray-tracing computations. The combination of both GTD and Master Points reduces the time requirements of this kind of analysis. To validate the new approach, several reflectors and the effects on the radiation pattern caused by shifting the feed and introducing different obstacles have been considered concerning both simple and complex geometries. The results of these analyses have been compared with the Method of Moments (MoM) results.

Application of S-UTD-CH Model into Multiple Diffraction Scenarios

Propagation prediction models based on ray tracing in coverage estimation for digital broadcasting systems are compared. Geometrical Theory of Diffraction (GTD), Slope Uniform Theory of Diffraction (S-UTD), and Slope UTD with Convex Hull (S-UTD-CH) models are compared for computation time and propagation path loss. S-UTD-CH model is optimum model with respect to computation time and relative path loss.