# Uniform Geometrical Theory of Diffraction

15 Apr 2005-

TL;DR: In this paper, the authors discuss the application of the geometrical theory of diffraction (GTD) for solving problems of electromagnetic (EM) radiation and scattering at high frequencies.

Abstract: Keller's geometrical theory of diffraction (GTD) [1,2] constitutes a major breakthrough for solving problems of electromagnetic (EM) radiation and scattering at high frequencies. The GTD can also be applied to solving acoustic and elastic wave problems; however, only the EM case is discussed here.
Recently, the development of fast solvers for signifi-cantly increasing the efficiency of numerical methods in solving large problems has met with some success. However, for truly large problems, asymptotic high-frequency methods in general, and especially ray methods such as the GTD and its uniform version, still remain the most useful analysis tools.
Keywords:
Keller's geometrical theory of diffraction;
electromagnetic radiation;
geometrical optics;
uniform theory of diffraction;
diffracted ray field

##### Citations

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01 Dec 2016TL;DR: The KED model is shown to work well for indoor environments, and an empirical linear model with a fixed reference point is also presented and provides a better fit to the measured data around rounded corners in the outdoor environment.

Abstract: This paper presents diffraction measurements, analysis, and signal strength prediction models around objects such as corners, pillars, and irregular objects, at 10, 20, and 26 GHz. The diffraction measurements were conducted indoors and outdoors by using a continuous wave (CW) channel sounder with three pairs of identical directional horn antennas at the transmitter and receiver. The measurement results are compared with theoretical predictions based on the Knife Edge Diffraction (KED) in order to determine how well the theoretical model compares to real-world measurements. The KED model is shown to work well for indoor environments, and an empirical linear model with a fixed reference point is also presented and provides a better fit to the measured data around rounded corners in the outdoor environment. Diffraction loss is shown to increase with frequency in outdoor scenarios, but less so inside buildings due to reflection and transmission between walls. The model validation and new models will be useful for designing and calibrating ray-tracers and other wireless network simulators by simulating potential channel loss from diffraction around objects and understanding the impact of diffraction at centimeter-wave and millimeter-wave frequencies in indoor and outdoor environments.

55 citations

### Cites methods from "Uniform Geometrical Theory of Diffr..."

...The GTD diffraction coefficient for a right angle conducting wedge is found to be [48]:...

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...The GTD diffraction coefficient is given as [47, 48]:...

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...The UTD diffraction coefficient is given by multiplying each term in the above equation with a transition function [48]....

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16 Sep 2005

TL;DR: In this paper, different components of NLOS-multipath are studied in an urban canyon model and the probability to track a single reflected ray and the associated maximum pseudo-range (PR) bias error are computed.

Abstract: Different components of NLOS-Multipath are studied in an urban canyon model. First, in order to detect the single reflected ray case in our model, an original ray tracing method is presented. By using a power threshold, the probability to track a single reflected ray and the associated maximum Pseudo-Range (PR) bias error are computed. Extrapolations are carried out in order to study the influence of the distance from the receiver to the reflected wall on this probability and the associated error. Secondly, the diffraction effects are analyzed when no direct ray is present and no reflected rays are considered in this case. The Uniform Theory of Diffraction (UTD) is used in order to determine the diffracted rays which could be tracked by the receiver and the associated maximal PR bias error.

35 citations

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18 Sep 2018

TL;DR: This paper presents SecureScatter, a physical-layer solution that delegates the security of backscatter to an on- body smart device, and profiles the on-body propagation paths of back scatter links, and construct highly sensitive propagation signatures to identify on-Body backscattering links.

Abstract: The vision of battery-free communication has made backscatter a compelling technology for on-body wearable and implantable devices. Recent advances have facilitated the communication between backscatter tags and on-body smart devices. These studies have focused on the communication dimension, while the security dimension remains vulnerable. It has been demonstrated that wireless connectivity can be exploited to send unauthorized commands or fake messages that result in device malfunctioning. The key challenge in defending these attacks stems from the minimalist design in backscatter. Thus, in this paper, we explore the feasibility of authenticating an on-body backscatter tag without modifying its signal or protocol. We present SecureScatter, a physical-layer solution that delegates the security of backscatter to an on-body smart device. To this end, we profile the on-body propagation paths of backscatter links, and construct highly sensitive propagation signatures to identify on-body backscatter links. We implement our design in a software radio and evaluate it with different backscatter tags that work at 2.4 GHz and 900 MHz. Results show that our system can identify on-body devices at 93.23% average true positive rate and 3.18% average false positive rate.

29 citations

### Cites background from "Uniform Geometrical Theory of Diffr..."

..., creeping waves diffracted from human tissue and trapped along the body’s surface [20, 27, 29]....

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TL;DR: In this article, a beam tracing (BT) technique instead of the ray tracing (RT) is employed in the TD-SBR method, which provides much simpler procedure to avoid the divergence problem in the conventional SBR that happens when ray tubes intersecting discontinuous parts of the object.

Abstract: An efficient time-domain shooting and bouncing ray (TD-SBR) method is developed to analyze the transient scattering responses from large perfectly conducting objects illuminated by a pulsed plane wave. Differing from the conventional TD-SBR method, a beam tracing (BT) technique, instead of the ray tracing (RT), is first employed in the TD-SBR method, which provides much simpler procedure to avoid the divergence problem in the conventional SBR that happens when ray tubes intersecting discontinuous parts of the object. Applying a strategy of equivalent incident reference plane, alternative closed-form formulas are derived in the transient electromagnetic (EM) computations. Based on the closed-form representations, the characteristics of transition function and scattered fields are further investigated to show the physical phenomenon of scattering mechanisms. Due to the causality of transient fields, the proposed formulas are more efficient in EM calculations than the conventional frequency-domain formulas. Numerical examples illustrate that the BT technique can greatly improve the accuracy of the TD-SBR method, and the computational efficiency is enhanced significantly by using the direct TD formulas.

22 citations

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01 Sep 2011TL;DR: A statistical approach for modelling antennas behaviour in the vicinity of the human body, i.e., average and standard deviation, have been calculated for Uniform and Rayleigh antenna to body distance distributions.

Abstract: This paper introduces a statistical approach for modelling antennas behaviour in the vicinity of the human body. The statistics of radiation patterns, i.e., average and standard deviation, have been calculated for Uniform and Rayleigh antenna to body distance distributions. The coupling between the body and the antenna and reduction of antenna efficiency leads to the distortion of the antenna radiation pattern, which depends on the distance as well as on the location on the body. A patch antenna operating at 2.45 GHz was simulated in CST, near to regions of a voxel human model, i.e., Head, Chest, Arm and Leg. Results show that the relative change of the average radiation pattern for an antenna located on the Chest can reach 24%.

21 citations

##### References

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TL;DR: The mathematical justification of the theory on the basis of electromagnetic theory is described, and the applicability of this theory, or a modification of it, to other branches of physics is explained.

Abstract: The geometrical theory of diffraction is an extension of geometrical optics which accounts for diffraction. It introduces diffracted rays in addition to the usual rays of geometrical optics. These rays are produced by incident rays which hit edges, corners, or vertices of boundary surfaces, or which graze such surfaces. Various laws of diffraction, analogous to the laws of reflection and refraction, are employed to characterize the diffracted rays. A modified form of Fermat’s principle, equivalent to these laws, can also be used. Diffracted wave fronts are defined, which can be found by a Huygens wavelet construction. There is an associated phase or eikonal function which satisfies the eikonal equation. In addition complex or imaginary rays are introduced. A field is associated with each ray and the total field at a point is the sum of the fields on all rays through the point. The phase of the field on a ray is proportional to the optical length of the ray from some reference point. The amplitude varies in accordance with the principle of conservation of energy in a narrow tube of rays. The initial value of the field on a diffracted ray is determined from the incident field with the aid of an appropriate diffraction coefficient. These diffraction coefficients are determined from certain canonical problems. They all vanish as the wavelength tends to zero. The theory is applied to diffraction by an aperture in a thin screen diffraction by a disk, etc., to illustrate it. Agreement is shown between the predictions of the theory and various other theoretical analyses of some of these problems. Experimental confirmation of the theory is also presented. The mathematical justification of the theory on the basis of electromagnetic theory is described. Finally, the applicability of this theory, or a modification of it, to other branches of physics is explained.

3,032 citations

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01 Nov 1974TL;DR: In this article, a compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edse formed by perfectly conducting curved plane surfaces is obtained, which is based on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by cylindrical, conical, and spherical waves.

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.

2,582 citations

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TL;DR: In this article, a ray-shooting approach is presented for calculating the interior radar cross section (RCS) from a partially open cavity, where a dense grid of rays is launched into the cavity through the opening.

Abstract: A ray-shooting approach is presented for calculating the interior radar cross section (RCS) from a partially open cavity. In the problem considered, a dense grid of rays is launched into the cavity through the opening. The rays bounce from the cavity walls based on the laws of geometrical optics and eventually exit the cavity via the aperture. The ray-bouncing method is based on tracking a large number of rays launched into the cavity through the opening and determining the geometrical optics field associated with each ray by taking into consideration: (1) the geometrical divergence factor, (2) polarization, and (3) material loading of the cavity walls. A physical optics scheme is then applied to compute the backscattered field from the exit rays. This method is so simple in concept that there is virtually no restriction on the shape or material loading of the cavity. Numerical results obtained by this method are compared with those for the modal analysis for a circular cylinder terminated by a PEC plate. RCS results for an S-bend circular cylinder generated on the Cray X-MP supercomputer show significant RCS reduction. Some of the limitations and possible extensions of this technique are discussed. >

831 citations

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01 Sep 1972TL;DR: In this paper, a systematic use of matrix representation for the wavefront curvature and for its transformations simplify the handling of arbitrary pencils of rays and, consequently, the field computations.

Abstract: The principles of ray optics and, in more detail, some selected applications of ray techniques to electromagnetics are reviewed briefly. It is shown how a systematic use of matrix representation for the wavefront curvature and for its transformations simplify the handling of arbitrary pencils of rays and, consequently, the field computations. The same methods apply to complex rays which give a means of describing the effects of reflections and refractions on Gaussian beams. The relations of ray optics to other disciplines are also briefly discussed.

450 citations

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TL;DR: In this article, a high frequency solution for scattering from a thin dielectric slab is developed, based on a modification of the uniform geometrical theory of diffraction solution for a haft-plane, with the intention of developing a model for a windshield of a small private aircraft.

Abstract: A high frequency solution for scattering from a thin dielectric slab is developed, based on a modification of the uniform geometrical theory of diffraction solution for a haft-plane, with the intention of developing a model for a windshield of a small private aircraft. Results of the theory are compared with experimental measurements and moment method calculations showing good agreement. Application of the solution is also addressed.

279 citations