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     

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 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.     

Time-domain three-dimensional diffraction by the isorefractivewedge

The extension of the Biot-Tolstoy (1957) exact time domain solution to the electromagnetic isovelocity or isorefractive wedge is described. The TM field generated by a Hertzian electric dipole can be represented by a vector potential parallel to the apex of the wedge and a scalar potential necessitated by the three dimensionality of the magnetic field. The derivation of the former is exactly that of the pressure in the corresponding acoustic situation, and a more efficient version of the lengthy details is presented herein. A Lorentz gauge determines the scalar potential from the vector potential, and the diffracted field contains impulsive and “switch-on” terms that cannot be evaluated in closed form. The ratio of arrival times, at a given point, of the geometrical optics and diffracted fields provides a convenient parameter, in addition to the usual metric-related variable, for graphically displaying this scalar potential     

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.     

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.     

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     

Uniform physical theory of diffraction equivalent edge currents fortruncated wedge strips

New uniform closed-form expressions for physical theory of diffraction equivalent edge currents are derived for truncated incremental wedge strips. In contrast to previously reported expressions, the new expressions are well behaved for all directions of incidence and observation and take a finite value for zero strip length. This means that the expressions are well suited for implementation in general computer codes. The new expressions are expressed as the difference between two terms. The first term is obtained by integrating the exact fringe wave current on a wedge along an untruncated incremental strip extending from the leading edge of the structure under consideration. The second term is calculated from an integration of the asymptotic fringe wave (FW) current along another untruncated incremental strip extending from the trailing edge of the structure. The new expressions are tested numerically on a triangular cylinder and the results are compared with those obtained using the method of moments and the previously reported expressions     

Time-domain analysis of the Sommerfeld VMD problem based on theexact image theory

A novel time-domain solution of the Sommerfeld half-space problem is constructed through the exact image theory. The radiation from a vertical magnetic dipole (VMD) above the planar interface of two lossless and dispersionless dielectric media is analyzed. The reflection field is given as a Laplace transform when the refraction index of the lower medium is greater. The converse case of refraction indexes is also studied, and the reflection field is written as originating from an image source located in homogeneous space. The present theory is seen to lead to a numerically efficient result, which is demonstrated with examples     

Some problems in the asymptotic theory of diffraction

The paper is a review of asymptotic methods in the theory of diffraction and emphasizes Soviet contributions. Without going into mathematical details it presents a survey of a number of applications of ray techniques and their generalizations to problems of diffraction.     

标量衍射理论的非傍轴修正

当光束具有较大的发散角或光束束腰可与波长相比拟时,傍轴近似不再成立.用微扰级数法处理非傍轴光束的传播问题,数值计算发现,对受硬边光阑限制的光束,由于高频分量的贡献,当传输距离较大时,高阶级数解的修正效果不好,甚至失效,级数解的有效范围将受到很大限制.在标量衍射理论角谱表示的基础上,以平面波圆孔衍射为例,给出了衍射场的非傍轴修正解,得到的非傍轴修正解避免了级数解本身在数学上的发散性问题,并在一定条件下,可过渡到级数解,并且指出在近场或非傍轴区对傍轴解进行高阶修正的必要性和有效性.     

One hundred years of diffraction theory

The development of diffraction theory in the last 100 years is discussed from a personal viewpoint, with emphasis on the geometrical theory of diffraction. First some early work of Kirchhoff, Rayleigh, Sommerfeld, MacDonald and others is mentioned to indicate the state of the field in the 1940's. Next the author's work during World War II is described. Then the considerations that led him to the geometrical theory of diffraction are explained, and the defects of that theory are outlined. Finally the advances in the theory since its introduction, which have remedied many of these defects, are mentioned.     

Field correlation diffraction theory of the symmetrical cassegrainian antenna

The received field as focused by the parabolic main reflector of a Cassegrainian antenna at the surface of an arbitrary profile subreflector is calculated by a spherical wave expansion. This facilitates the application of the field correlation principle and leads to an expression for aperture efficiency taking into account diffraction effects. A comparison is made with numerical results previously published or obtained by other methods. The potential advantage of the technique is the speed of computation and the capability for synthesis as well as analysis of reflector shapes.     

Antenna installed performance using diffraction theory

It is the performance of an antenna when installed in a complete system that is important. In situ measurements and measurements on scale models can be impractical or too costly. Computation of the performance of antennas on aircraft or spacecraft has considerable advantages, and may use the method of moments or diffraction theory. The paper concentrates on discussing the use of diffraction theory to compute the radiation patterns of low-gain antennas installed on conducting structures     

光栅的标量衍射理论与耦合波理论的分析比较

光栅的标量衍射理论是计算衍射效率的一种近似方法 ;耦合波理论是分析光栅衍射的严格方法。本文详尽地分析了这两种方法在计算具体的光栅衍射问题时的异同 ,从中得出了有意义的结论 :光栅的标量衍射理论的近似是有条件的 ,光栅周期和光栅槽形就是影响这一近似条件的两大因素。     

The diffraction theory of large-aperture spherical reflector antennas

The field along the axis of a spherical reflector is determined from the geometry of the system rather than from each term of the aberration taken separately. The procedure shows how the field distribution changes from the case of small aberration, where there is a well-defined focus, to the geometric optics limit. A spherical reflector becomes an efficient antenna when a set of feed elements is located along the axis to reduce the effects of spherical aberration. The number and position of these elements is dictated by the size and curvature of the reflector and the allowable distortion of the wavefront.     

Solution of a difference equation in diffraction theory

A simple technique is described for solving a class of second-order functional difference equations that occur in diffraction problems involving edges and corners     

Incremental theory of diffraction: a new-improved formulation

In this paper, a general systematic procedure is presented for defining incremental field contributions. They may provide effective tools to describe a wide class of scattering and diffraction phenomena at any aspect, within a unitary, self-consistent framework. This procedure is based on a generalization of the incremental theory of diffraction (ITD) localization process for uniform cylindrical, local canonical problems with elementary source illumination and arbitrary observation aspects. In particular, it is shown that the spectral integral formulation of the exact solution for the local canonical problem may also be represented as a spatial integral convolution along the longitudinal coordinates of the cylindrical configuration. Its integrand is then directly used to define the relevant incremental field contribution. For the sake of convenience, but without loss of generality, this procedure is illustrated for the case of local wedge configurations. Also, a specific suitable asymptotic analysis is developed to derive new closed form high-frequency expressions from the spectral integral formulation. These expressions for the incremental field contributions explicitly satisfy reciprocity and are applicable at any incidence and observation aspect. This generalization of the ITD localization process together with its more accurate asymptotic analysis provides a definite improvement of the method.