Physical Theory of 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 MATLAB-based virtual diffraction tool, using analytical exact as well as well-known high-frequency asymptotic (HFA) techniques, is introduced. Electromagnetic wave scattering from a wedge-shaped object with perfect electrical conductor (PEC) boundaries, under both line-source and plane-wave illuminations, can be automatically analyzed. Effects of various parameters on the reflection, refraction, and diffraction can be investigated. Comparisons among Geometrical Optics (GO), Uniform Theory of Diffraction (UTD), Physical Optics (PO), Physical Theory of Diffraction (PTD), and Parabolic Equation (PE) models are possible through many scenarios and illustrations.

For the electromagnetic modeling of scattered fields from large and complex objects, a very efficient simulation tool based on the well-known Shooting-and-Bouncing-Rays (SBR) technique has been developed [1]. This algorithm uses field-based high-frequency approaches for finding the relevant propagation paths, i.e. rays are traced through the scenario according to the laws of Geometrical Optics (GO) and diffracted rays are generated according to the laws of the Uniform Theory of Diffraction (UTD). This GO/UTD part is combined with a source-based approach, where each ray generates an equivalent surface current at each interaction with the object. These currents are calculated using Physical Optics (PO) and Physical Theory of Diffraction (PTD), and the superposition of all these contributions leads to the total scattered field strengths. Further technical details about the ray tracing approach can be found in [1, 2, 4]. With this simulation tool, large and complex objects can be modeled, which are still too costly for numerically exact methods. Generally, both metallic and dielectric objects [2], and also combined metallic-dielectric objects, can be modeled.

The physical optics (PO) and the physical theory of diffraction (PTD) are in extensive use in the antenna design and RCS calculation. The specific feature of these approximations is the phenomenon of polarization coupling. This phenomenon has been known since 1975, but its physical nature is still not explained in the literature. In the present communication, it is shown that this phenomenon is caused by the charges at the edge of a scattering structure, which are accumulated there due to the discontinuity of the PO current component normal to the edge.

The accurate prediction of the far field radiated or scattered by large structures, such as large reflector antennas, requires efficient techniques for representing the illuminating field. Complex Source Points (CSP) inherently contain information about the source directivity, hence they can be used as the basis function to expand a given, but arbitrary, radiating wave field [1-3], such as the field incident on an antenna or a more general complex structure. As a consequence, a CSP field representation, when combined with the analytic continuation in complex space of typical ray-techniques such as the Geometrical and the Uniform Geometrical Theory of Diffraction (GTD/UTD), may provide a very efficient tool to estimate the fields radiated by large objects [4]. In this framework, an extension of the Incremental Theory of Diffraction (ITD) formulation for the scattering by wedges illuminated by CSP has been introduced [5], which essentially overcomes the typical impairments of the GTD/UTD ray techniques associated with possible ray caustics and with the difficulties of ray tracing in complex space. On the other hand, when dealing with the description of the field radiated by large structures, many of the existing electromagnetic codes resort to a Physical Optics (PO) representation also with an arbitrary incident field. It is however well known that the PO approach does not always produce accurate field predictions [6]. A significative augmentation of the PO field estimate can be achieved by including along the structure's edges a line integration of an incremental fringe field, that acts as a correction term for the field estimate. Several techniques have been published to derive these elementary contributions, leading to Physical Theory of Diffraction (PTD), Elementary Edge Waves/Incremental Length Diffraction Coefficient (EEW/ILDC), and ITD. In this work we discuss some recent advances in the incremental formulation for the field diffracted by edges in perfect electric conductor (PEC) objects when illuminated by a CSP beam expansion, with application to the analysis of large reflector antennas. A fringe formulation of the field diffracted by wedges with PEC faces when illuminated by a single CSP has been recently presented [7]. At each point on the edge the incremental fringe correction term is deduced from tangential canonical problems as the difference between the local ITD diffracted field [5] and an appropriate incremental end-point PO field (IEPO) scattered by the half-lit plane tangent to the edge [8]. The total spurious effects due to the presence of the edge are corrected by adiabatically distributing and integrating the local incremental fringe field coefficients along the line of the edges. This formulation yields more accurate predictions of the radiated field. For configurations in which several metallic edges are present and for grazing aspects of incidence and observation, the correct interactions between the edges in the problem need to be properly accounted for. Hence we introduce correct incremental double-diffraction coefficients for CSP illumination in the first-order fringe formulation [9]. These incremental coefficients have been derived by a proper analytical continuation of their real counterparts [10]. The formulation provides an accurate first-order asymptotic description of the interaction between two edges, which is valid both for skewed separate wedges and for edges joined by a common PEC face. It also includes a double incremental slope diffraction augmentation, which provides the correct dominant high-frequency incremental contribution at grazing aspects of incidence and observation. The total doubly-diffracted field is obtained from a double spatial integration along each of the two edges on which consecutive diffractions occur. In the application to the analysis of large reflector antennas the first-order fringe correction to the PO scattered fields tends to fail in those directions parallel to the aperture plane. Here, the addition of the incremental double diffracted field provides the correct estimation of the radiated field.

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.

In two-dimensional problems, the physical theory of diffraction (PTD) is valid for both electromagnetic and acoustic waves. This chapter presents the theoretical fundamentals for acoustic and electromagnetic waves. To complete formulation of the diffraction problem and ensure the uniqueness of its solution, the wave equation and boundary conditions are supplemented by the Sommerfeld radiation condition for the scattered field. The high-frequency physical optics (PO) approach is widely used in acoustic and electromagnetic diffraction problems. Among the properties of the shadow radiation, the most significant are the shadow contour theorem and the total power of shadow radiation, which are verified for acoustic and electromagnetic waves, in the chapter. Taking into account the diffraction and nonuniform components of surface fields, PTD overcomes the PO shortcomings and provides more accurate asymptotic results for high-frequency scattered fields.

In this paper the 3-D mathematical formulation and study for the simulation of the radio-propagation mechanisms in urban cellular environments are presented. The proposed methods and techniques are applicable to the 3-D radiocoverage prediction model, currently being developed by the authors' research group. In the far field area, the proposed analysis is based on the well-known deterministic methods of Physical Optics (PO) and Physical Theory of Diffraction (PTD). In the near field and Fresnel zone, a novel and time-efficient technique for the computation of the scattered and diffracted field is applied. Emphasis is also given to the time efficiency of the proposed approach since the high simulation time is one of the most important drawbacks of such radio-propagation prediction codes.

Due to simplicity, hybridization of geometrical optics (GO) and physical optics (PO) based on ray tracing has been widely used for fast scattering analyses. However, when targets of curved concavities are discretized by flat facets, the loss of divergence factor (DF) will degrade the simulation accuracy. To remedy this loss, a simple and efficient factor, entitled virtual divergence factor (VDF), is proposed to play the role of DF. To prove the validity of VDF and simulate the scattering of concave complex targets, a hybrid method of GO/PO and physical theory of diffraction (PTD) is elucidated. With VDF correction, several typical targets, including a S-shape cavity, are simulated by this hybrid method. In comparison to multilevel fast multipole algorithm (MLFMA) or measurements, the validaty of VDF is fully demonstrated by good agreements and the excellent performance relative to DF on canonical surfaces, where the great efficiency and flexibility of this hybrid method are also shown. Moreover, one interesting and important issue, the dependance of field convergence on the maximum number of ray reflections, is also investigated for the first time.

The maximum angle at which the physical optics (PO) formulation for offset reflector antenna problems is derived. Obliquely incident plane-wave diffraction by a flat plate is first discussed to demonstrate the accuracy of physical theory of diffraction (PTD) and to establish the method predicting the PO error in the offset plane. Then it is applied to the reflector antennas, and the PO error is expressed as functions of only the offset angle and observation angle. A variety of numerical results for actual offset reflectors shows the validity of these expressions. >

The authors apply the method of moments to analyse the surface currents and radiation patterns of offset-reflector antennas. For a small disk, the convergence of the techniques is compared with an exact solution. The results presented for an offset reflector are compared with the physical theory of diffraction, and the discrepancies explained.

A more general and rigorous form of the physical theory of diffraction (PTD) is presented. This theory is concerned with the field scattered by perfectly conducting bodies whose surfaces have sharp edges and whose linear dimensions and curvature radii are large in comparison with a wavelength. The PTD proposed here is based on the conception of elementary edge waves (EEWs). These are the waves scattered by the vicinity of an edge infinitesimal element. Their high-frequency asymptotics are given. Various definitions of EEWs (Maggi, Bateman, Rubinowicz, Mitzner, Michaeli) are discussed. Total edge waves (TEWs) scattered by the whole edge are found to be a linear superposition of all EEWs. PTD enables one to determine correctly the first (leading) term in the high-frequency asymptotic expansions for primary and multiple TEWs both in ray regions and diffraction regions such as caustics, shadow boundaries, and focal lines. Some examples of these asymptotics are given. The connection of PTD with other ...

In this paper, shooting and bouncing ray — physical optics / physical theory of diffraction (SBR-PO/PTD) hybrid method is studied to investigate the backward scattering from three-dimensional (3D) electrically large target. Shadowing effects, multiple bounce, and diffraction by edges are considered in this scattering model. Time-consuming is greatly reduces compared with the numerical methods such as MoM at high frequencies. The accuracy and performance of this method are validated and evaluated by comparing with the FEKO-MLFMM for electrically small targets. What's more, this method is used to generate inverse synthetic aperture radar (ISAR) raw data for imaging applications. The process from raw RCS data to ISAR image is explained in detail. Finally, ISAR imaging of an electrically large airplane model is provided.

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.

Noise control engineering and architectural acoustics practice have widely applied diffusing elements and devices to create surface scattering and diffuse reflections. An acoustical goniometer in the form of a circular microphone array has been used to characterize scattered responses for various types of diffusing elements/devices. This research is also intended for experimental validation of diffraction simulations of diffusing devices based on the physical theory of diffraction (PTD). To cope with experimental challenges, particularly for the research in the physical theory of diffraction, an acoustic goniometer must achieve a high enough angular resolution in addition to fulfilling far-field requirements. This paper discusses practical implementations and experimental results of portable goniometers with a radius of up to five meters and an angular resolution of 1.25 degrees. The practical implementation is intended to be easily deployable in empty, indoor spaces of sufficiently large dimensions for scattered reflection characterization. This paper discusses an effort of increasing experimental efficiency of characterization procedures for oblique incidences.