Time-domain version of the physical theory of diffraction

A time-domain version of the equivalent edge current (EEC) formulation of the physical theory of diffraction is derived. The time-domain EECs (TD-EECs) apply to the far-field analysis of diffraction by edges of perfectly conducting three dimensional (3-D) structures with planar faces illuminated by a time-domain plane wave. By adding the field predicted by the TD-EECs to the time-domain physical optics (TD-PO) field, a significant improvement is obtained compared to what can be achieved by using TD-PO alone. The TD-EECs are expressed as the integral of the time-domain fringe wave current (the exact current minus the TD-PO current) on the canonical wedge along truncated incremental strips. Closed-form expressions for the TD-EECs are obtained in the half-plane case by analytically carrying out the integration along the truncated incremental strip directly in the time domain. In the general wedge case, closed-form expressions for the TD-EECs are obtained by transforming the corresponding frequency-domain EECs to the time-domain. The TD-EECs are tested numerically on the triangular cylinder and the results are compared with those obtained using the method of moments in combination with the inverse fast Fourier transform     

Backscatter analysis of dihedral corner reflectors using physical optics and the physical theory of diffraction

Physical optics (PO) and the physical theory of diffraction (PTD) are used to determine the backscatter cross sections of dihedral corner reflectors in the azimuthal plane for the vertical and horizontal polarizations. The analysis incorporates single, double, and triple reflections; single diffractions; and reflection-diffractions. Two techniques for analyzing these backscatter mechanisms are contrasted. In the first method, geometrical optics (GO) is used in place of physical optics at initial reflections to maintain the planar nature of the reflected wave and subsequently reduce the complexity of the analysis. The objective is to avoid any surface integrations which cannot be performed in closed form. This technique is popular because it is inherently simple and is readily amenable to computer solutions. In the second method, physical optics is used at nearly every reflection to maximize the accuracy of the PTD solution at the expense of a rapid increase in complexity. In this technique, many of the integrations cannot be easily performed, and numerical techniques must be utilized. However, this technique can yield significant improvements in accuracy. In this paper, the induced surface current densities and the resulting cross section patterns are illustrated for these two methods. Experimental measurements confirm the accuracy of the analytical calculations for dihedral corner reflectors with right, acute, and obtuse interior angles.     

On the role of the geometrical optics field in aperture diffraction

The asymptotic solution of a high-frequency electromagnetic field transmitted through a finite aperture is studied. In applying Keller's geometrical theory of diffraction (GTD), a basic yet unanswered question for an observation point in the lit region is: "Should the geometrical optics field on a direct incident ray be included in the total field solution?" By studying a test problem and utilizing the newly developed uniform asymptotic theory (UAT), we have deduced simple and explicit rules for the role of the geometrical optics field and the regions of validity for GTD in a general aperture diffraction. The rules reveal that the success of GTD in treating aperture problems in the literature depends critically on the assumption that both the source and the observation points are infinitely far away from the aperture. Had either point been a finite distance away, Keller's GTD, in general, would fail and UAT must be used. The paper also demonstrates a physical phenomenon: the diffusion of the incident field as the observation point moves away from the aperture.     

A technique to combine the geometrical theory of diffraction and the moment method

A technique is presented in which the moment method (MM) is combined with the geometrical theory of diffraction (GTD). Since diffraction solutions exist for only relatively few structures, it is very desirable to have a means of obtaining the diffracted field for additional structures. Solutions for many structures can be obtained from this combination of techniques, and thus one is able to handle a wide variety of new problems which could not have been solved previously. The approach is developed and applied to a variety of structures in order to illustrate the approach and its validity.     

A uniform geometrical theory of diffraction for an imperfectly conducting half-plane

Diffraction tensors are presented in the context of the uniform geometrical theory of diffraction (UTD) for the high frequency scattering by an impedance half-plane at normal and oblique (skew) incidence. These are based on the exact Wiener-Hopf solution and were derived according to the UTD ansatz. In addition, unlike previous uniform diffraction coefficients, the ones given here reduce to the known UTD diffraction coefficients for the perfectly conducting case. The coefficients are explicit and therefore appropriate for practical applications. Several scattering patterns are also presented and compared to a previous heuristic solution.     

A hybrid technique for combining moment methods with the geometrical theory of diffraction

A technique for combining moment methods with the geometrical theory of diffraction (GTD) is presented, which permits the application of the method of moments to a larger class of problems. The fundamental idea used to develop the hybrid technique is to modify the usual impedance matrix that characterizes, for example, a wire antenna such that a metallic body or discontinuity on that body is properly accounted for. It is shown in general that one can modify the impedance matrix for any basis and/or weighting functions if one can compute the correct modification to the impedance matrix element. The modification is readily accomplished using the geometrical theory of diffraction and/or geometrical optics. Several example problems are considered to illustrate the usefulness of the technique. First, the canonical problem of a monopole near a conducting wedge is investigated. Second, a monopole at the center of a four-sided and an eight-sided flat plate is considered. Impedance results for the latter case are in good agreement with measurements. Third, a monopole at the center of a circular disc is examined and compared with experimental measurements in the literature, and fourth, the problem of a monopole near a conducting step is solved and the dependence of the input impedance upon the step height shown.     

Time-domain uniform geometrical theory of diffraction for a curvedwedge

A time-domain version of the uniform geometrical theory of diffraction (TD-UTD) is developed to describe, in closed form, the transient electromagnetic scattering from a perfectly conducting, arbitrarily curved wedge excited by a general time impulsive astigmatic wavefront. This TD-UTD impulse response is obtained by a Fourier inversion of the corresponding frequency domain UTD solution. An analytic signal representation of the transient fields is used because it provides a very simple procedure to avoid the difficulties that result when inverting frequency domain UTD fields associated with rays that traverse line or smooth caustics. The TD-UTD response to a more general transient wave excitation of the wedge may be found via convolution. A very useful representation for modeling a general pulsed astigmatic wave excitation is also developed which, in particular, allows its convolution with the TD-UTD impulse response to be done in closed form. Some numerical examples illustrating the utility of these developments are presented     

The geometrical theory of diffraction for axially symmetric reflectors

The geometrical theory of diffraction (GTD) (cf. [1], for example) may be applied advantageously to many axially symmetric reflector antenna geometries. The material in this communication presents analytical, computational, and experimental results for commonly encountered reflector geometries, both to illustrate the general principles and to present a compact summary of generally applicable formulas.     

The physical theory of slope diffraction

The physical theory of diffraction (PTD) has been expanded for the case of slope diffraction, when an incident wave is zero but its derivative is not zero in the direction of a perfectly conducting scattering edge. High frequency asymptotics are found both for elementary edge waves and for the total edge waves scattered by arbitrary curved edges. Great attention is given to fields created by the nonuniform (diffraction) component of edge currents. These fields are usually called ptd corrections to the Physical Optics approach. These corrections are found for diffraction fields in ray regions and in diffraction regions such as the vicinities of shadow boundaries, smooth caustics, and foci.     

A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface

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.     

Treatment of singularities in the physical theory of diffraction

The diffraction coefficients describing scattering from an edged body in the physical theory of diffraction are reformulated so as to provide improved behavior in the neighborhood of singularities. Numerical results show that as singularities are approached, the reformulated coefficients are better behaved than the original by several orders of magnitude.     

Radar cross section of curved plates using geometrical and physical diffraction techniques

Geometrical and physical optics techniques, supplemented by their respective extensions, i.e., geometrical and physical diffraction, are applied to the problem of finite cylindrically curved plates. Numerical calculations of the radar backscattering cross sections were made, and a graphical comparison of these methods with experimental results is made. Keller's and Ufimtsev's theories axe discussed and compared as they apply to this problem.     

Application of the geometrical theory of diffraction to Cassegrain subreflectors with laterally defocused feeds

The geometrical theory of diffraction (GTD) as formulated by R. G. Kouyoumjian has been applied to predict the radiation characteristics of hyperboloidal subreflectors with laterally defocused feeds. In caustic or multicaustic directions the scattered fields are determined using an equivalent ring current placed along the edge of the subreflector. The theoretical results are compared to measured amplitude and phase data. In order to improve the agreement, the blocking effects of the feed horn have been accounted for using the geometrical theory of diffraction. The calculated subreflector fields have been used to illuminate a paraboloid from which the scattered field is determined by physical optics. The results are compared to those obtained using a laterally defocused equivalent paraboloid.     

The geometrical theory of diffraction applied to antenna pattern and impedance calculations

The geometrical theory of diffraction is applied to the calculation of the radiation pattern and impedance of a monopole antenna on a perfectly conducting circular ground plane of limited extent. In this calculation, the radiation problem is resolved into two components, one being the monopole contribution and one the edge contribution. The impedance problem is resolved into the components of a reflection from the monopole in an infinite ground plane and a reflection from the circular edge as seen through the antenna. The known solutions of these individual components then permit the calculation of the overall radiation pattern and impedance by superposition. The techniques described are general and are considered applicable to a large class of similar radiating structures.     

Physical optics inverse diffraction

A general method for solving the inverse diffraction problem is presented. It is based on an identity of Bojarski which states thatgamma(x)andGamma(p)are a Fourier transform pair. Heregamma(x)is the characteristic function of the target (gamma=1inside the target,gamma = 0outside),p = (2omega/c)J,omegais the frequency,Jis a unit vector specifying the aspect, andGamma(P)can be obtained by measurement of the backscattered electromagnetic far field at frequencyomega = (c/2)|P|and aspectJ=|p|^{-1}p. If data is obtained in any subsetDofpspace, the method yields partial or complete information about the target geometry. It is used to rederive earlier results very simply and to obtain a significant new solution, in which the target geometry is completely determined using frequencies only in a practical frequency band and aspects in a narrow cone.     

A modified geometrical optics method for scattering by dielectric bodies

A method based on ray optics is developed for calculating the scattering from dielectric bodies. The fields of geometrical optics are used except for two types of rays where the fields must be corrected from physical optics solutions. The customary advantages of ray techniques are realized, namely, a simplicity in the resulting formulas, a ready interpretation of the scattering mechanism and the possibility of extension to a wider class of problems through the inclusion of additional rays. The method has been applied to several lossless dielectric shapes: the circular cylinder, the sphere, the prolate spheroid and to a lossy dielectric shell. The relative dielectric constants considered range from 0.25 to 1.80, except in the case of the shell. The calculated results are compared with those obtained from boundary value solutions, with the exception of the spheroid where measured values are used. Good results are obtained for all sizes considered except those which are very small and behave as Rayleigh scatterers. The failure in the region of Rayleigh scattering is to be expected. Thus, for the class of dielectric scatterers treated here there is no region of scattering resonance corresponding to that of similar metallic shapes where the geometrical optics solution is no longer valid.     

An analysis of the radiation from apertures in curved surfaces by the geometrical theory of diffraction

In this paper the geometrical theory of diffraction is extended to treat the radiation from apertures or slots in convex perfectly conducting surfaces. It is assumed that the tangential electric field in the aperture is known so that an equivalent infinitesimal source can be defined at each point in the aperture. Surface rays emanate from this source which is a caustic of the ray system. A launching coefficient is introduced to describe the excitation of the surface ray modes. If the field radiated from the surface is desired, the ordinary diffraction coefficients are used to determine the field of the rays shed tangentially from the surface rays. The field of the surface ray modes is not the field on the surface; hence if the mutual coupling between slots is of interest, a second coefficient related to the launching coefficient must be employed. In the region adjacent to the shadow boundary, the component of the field directly radiated from the source is represented by Fock-type functions. In the illuminated region the incident radiation from the source (this does not include the diffracted field components) is treated by geometrical optics. This extension of the geometrical theory of diffraction is applied to calculate the radiation from slots on elliptic cylinders, spheres, and spheroids.     

Modified theory of physical optics solution of impedance half plane problem

The scattering of electric polarized plane waves from an impedance half plane problem is examined by the method of modified theory of physical optics (MTPO). Two integrals, consisting of incident and reflected scattered fields, are obtained. These integrals are evaluated asymptotically by the methods of stationary phase and edge point. The obtained scattered fields are compared with the exact solution numerically.