Uniform diffraction coefficients for an impedance wedge

Uniform diffraction coefficients for an astigmatic electromagnetic wave normally incident on a wedge having curved faces with given surface impedances are derived from the earlier work of Maliuzhinets. These coefficients are to be used with standard formulas in the geometrical theory of diffraction to predict diffraction effects from structures having impedance surfaces terminating in an edge.     

Time-domain equivalent edge currents for transient scattering

Time-domain equivalent edge currents (TD-EEC) are developed for the transient scattering analysis. The development is based an the Fourier inversion of frequency domain equivalent edge current expressions. The time-domain diffracted fields are expressed in terms of a contour integral along the diffracting edges for any arbitrary input pulse shape, thereby yielding finite results at the caustics of diffracted rays. The approach also eliminates the need for the evaluation of a convolution integral in the time domain geometrical theory of diffraction (GTD) analysis. The results are compared with the first order GTD results for the transient scattering analysis for a circular disk     

Reflector antenna radiation pattern analysis by equivalent edge currents

Equivalent edge currents, derived from the edge diffraction theory for a half-plane, are used to obtain the radiation patterns of a parabeloidal reflector antenna when illuminated by a source at the focus. Cylindrical wave diffraction coefficients are used. The method avoids infinities at caustics and shadow boundaries thus giving solutions which are finite everywhere. A slope-wave equivalent current correction term is applied when the illumination is tapered towards the edge of the reflector. Comparisons are given with the physical optics approach and experimental results.     

THE EVIDENCE OF LOSSY WEDGE DIFFRACTION COEFFICIENT IN THEORY

Formulas of diffraction field of lossy wedges with less than 180?wedge angle are derived on the basis of the Fresnel-Kirchhoff wave theory and their numerical results are compared with those of the heuristic lossy wedge diffraction coefficient given by Luebbers (1984), showing good agreement between the two types of numerical results which have different bases in theory. The agreement shows that the lossy wedge diffraction coefficient as an extension of UTD is quite reasonable.     

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 asymptotic theory of electromagnetic diffraction by a curved wedge

Diffraction of an arbitrary electromagnetic optical field by a conducting curved wedge is considered. The diffracted field according to Keller's geometrical theory of diffraction (GTD) can be expressed in a particularly simple form by making use of rotations of the incident and reflected fields about the edge. In this manner only a single scalar diffraction coefficient is involved. Near to shadow boundaries where the GTD solution is not valid, a uniform theory based on the Ansatz of Lewis, Boersma, and Ahluwalia is described. The dominant terms, to the order ofk^{-1/2}included, are used to compute the field exactly on the shadow boundaries. In contrast with the uniform theory of Kouyoumjian and Pathak, some extra terms occur: one depends on the edge curvature and wedge angle; another on the angular rate of change of the incident or reflected field at the point of observation.     

MM—PO混合法中一致性劈面绕射电流研究

研究了MM-PO混合算法中的劈面绕射电流基函数.基于一致性绕射理论,导出了不分区域的统一的一致性劈面绕射电流表达式,提出了UTD修正的MM-PO混合算法.理论分析和仿真计算表明,一致性MM-PO混合算法克服了当劈面从过渡区外向过渡区逐步逼近时分区域表达式的不连续性的困难,消除了相应的模型误差.研究还表明,所得到的修正混合算法也适用于阻抗劈包括各向异性阻抗劈情形.     

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     

Elimination of infinities in equivalent edge currents, Part II: Physical optics components

A solution finite for all directions of illumination and observation is derived for the physical optics (PO) components of equivalent edge currents. The solution is based on the uniform asymptotic theory of endpoint evaluation of integrals. An extension taking into account the variation of the surface metric with the distance from the edge is presented, and a similar extension for including slope diffraction is indicated. The expressions derived complement the results of our previous work on elimination of infinities from the fringe components of equivalent currents.     

Elimination of infinities in equivalent edge currents, part I: Fringe current components

New expressions are derived for the fringe current components of the equivalent edge currents. They are obtained by asymptotic endpoint evaluation of the fringe current radiation integral over the "ray coordinate" measured along the diffracted ray grazing the surface of the local wedge. The resulting expressions, unlike the previous ones, are finite for all aspects of illumination and observation, except for the special case where the direction of observation is the continuation of a glancing incident ray propagating "inwards" with respect to the wedge surface (the Ufimtsev singularity).     

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.     

Higher order equivalent edge currents for fringe wave radarscattering by perfectly conducting polygonal plates

An approach for including higher order edge diffraction in the equivalent edge current (EEC) method is proposed. This approach, which applies to monostatic as well as bistatic radar configurations with perfectly conducting polygonal plates, involves three distinct sets of EECs. All of these sets of EECs contain very few singularity problems. In order to obtain an approximation to the scattered field, the three sets are added and integrated along the circumference of the scatterer. This procedure is straightfoward, and since most singularity problems have been eliminated, it is numerically well behaved. The approach is applied to a configuration involving a square plate. Substantial improvements were achieved. The calculations also illustrate that the edge interaction can be significant, although the direction of incidence is far from the plane of the scatterer     

Comprehensive analysis for E-plane of horn antennas by edge diffraction theory

Edge diffraction theory is used in analyzing the radiation characteristics of typical horn antennas. The far-sidelobe and backlobe radiation has been solved without employing field equivalence principles which are impractical in the problem. A corner reflector with a magnetic line source located at the vertex is proposed as a model for the principalE-plane radiation of horn antennas. A complete pattern, including multiple interactions and images of induced line sources, is obtained in infinite series form. Diffraction mechanisms are used for appropriate approximations in the computations. The computed patterns are in excellent agreement with measured patterns of typical horn antennas. Radiation intensity of the backlobe relative to mainlobe intensity is obtained as a back-to-front ratio and plotted as a function of antenna dimensions.     

新型等效斜楔设计

针对现有的静态斜楔干涉具无法实现零光程差,并且对被测光的空间相干性要求较高,进而影响光谱反演的准确性和复杂性问题,提出了一种新型等效斜楔干涉具,该等效斜楔由两种折射率不同的材料构成,两个反射面完全垂直,干涉的两束光是由同一束光分开而得,因此对光的空间相干性无太高要求,并且可以实现零光程差。理论推导了该斜楔不同位置的光程差公式和光谱反演公式,并且设计了该等效斜楔,其最大光程差可达168.3 m,对光谱测量过程进行了仿真分析,结合最大光程差和所测光谱波段分析了线阵CCD的像元数要求。采用532 nm单纵模激光器和632.8 nm氦氖激光器进行了实验分析,实验结果得到中心波长误差小于0.2%。     

Application of wedge diffraction theory to estimating power density at airport humped runways

Shadowing caused by humped runways at some airports significantly attenuates the guidance signals of the microwave landing system as the aircraft approaches the touchdown point. Application of wedge diffraction theory provides an estimate of this effect. A wedge diffraction factor is presented which relates the signal strength in the shadow to that for line-of-sight on a flat runway. Computations are confirmed by measurements at two airports.     

A physical optics version of the geometrical theory of diffraction

The authors derive a diffraction coefficient which is suitable for calculating the filed diffracted by the vertices of perfectly conducting objects. This diffraction coefficient is used to calculate the field scattered by the corner of a metallic sheet. Two diffraction coefficients, one for edges and one for vertices, are derived by solving the appropriate canonical problems using the physical optics (PO) approximation. The diffraction coefficients are calculated by first using the PO approximation which consists of calculating the total field on the surface of an object from the incident field according to the laws of geometrical optics, and then calculating the scattered field by employing this total surface field in a vector diffraction integral. The validity of the diffraction coefficients has been investigated by comparing their predictions with experimental measurements of the scattered field from a single corner of a rectangular metal sheet, and good agreement was found     

Pulsed field diffraction by a perfectly conducting wedge: aspectral theory of transients analysis

The canonical problem of pulsed field diffraction by a perfectly conducting wedge is analyzed via the spectral theory of transients (STT). In this approach the field is expressed directly in the time domain as a spectral integral of pulsed plane waves. Closed-form expressions are obtained by analytic evaluation of this integral, thereby explaining explicitly in the time domain how spectral contributions add up to construct the field. For impulsive excitation the final results are identical with those obtained previously via time-harmonic spectral integral techniques. Via the STT, the authors also derive new solutions for a finite (i.e., nonimpulsive) incident pulse. Approximate uniform diffraction functions are derived to explain the field structure near the wavefront and in various transition zones. They are the time-domain counterparts of the diffraction coefficients of the geometrical theory of diffraction (GTD) and the uniform theory of diffraction (UTD). An important feature of the STT technique is that it can-be extended to solve the problem of wedge diffraction of pulsed beam fields (i.e., space-time wavepackets)     

Asymptotic transition region theory for edge diffraction. II.Calculation of diffraction losses in multireflector antennas

For pt.I see ibid., vol.38, no.9, p.1350-8 (1990). Asymptotic formulas that can be used to calculate diffraction losses in a multireflector antenna without having to integrate rapidly varying fields over the reflector surfaces and the aperture are presented. Two kinds of losses caused by edge diffraction are considered: the reduction in antenna efficiency and the increase in spillover. The asymptotic formulas are obtained from the standard transition region field introduced in part I and are expressed in terms at the Δρ defined there     

Near-field scattering by physical theory of diffraction andshooting and bouncing rays

This paper proposes a method to compute the near-field RCS and Doppler spectrum of a target when the distances to the antennas are comparable to the target size. By dealing with a small piece of the target surface at a time, the transmitting antenna, and the receiving antenna are in the far-field zone of the small piece of the induced currents. The electromagnetic field produced by this small piece of induced currents can be written as a spherical wave. Sum up all spherical waves produced by every small piece of induced currents and we can obtain the total scattered field at the receiving antenna. The physical theory of diffraction (PTD) and the method of shooting and bouncing rays (SBR) are modified to evaluate the received signals. Numerical results based on these techniques are obtained and discussed. The formulation applies the simple concepts of “equivalent” image and vector effective height, which are believed to be novel     

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.