Timothy Griesser

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.

Reflections, diffractions, and surface waves for an interior impedance wedge of arbitrary angle

The asymptotic-impedance wedge solution for plane-wave illumination at normal incidence is examined for interior wedge diffraction. An efficient method for calculating the diffraction coefficient for arbitrary wedge angle is presented, as previous calculations were very difficult except for three specific wedge angles for the uniform geometrical theory of diffraction (UTD) expansion. The asymptotic solution isolates the incident, singly reflected, multiply reflected, diffracted, surface wave, and associated surface wave transition fields. Multiply reflected fields of any order are considered. The multiply reflected fields from the exact solution arise as ratios of auxiliary Maliuzhinets functions; however, by using properties of the Maliuzhinets functions, this representation can be reduced to products of reflection coefficients which are much more efficient for calculation. A surface-wave transition field is added to the surface wave boundaries. Computations are presented for interior wedge diffractions although the formulation is equally valid for both exterior and interior wedges with uniform but different impedances on each face for both soft and hard polarizations. In addition, the accuracy of the high-frequency asymptotic expansion is examined for small diffraction distances by direct comparison of the exact and asymptotic solutions. >

RCS analysis and reduction for lossy dihedral corner reflectors

The radar cross-section patterns of lossy dihedral corner reflectors are calculated using a uniform geometrical theory of diffraction for impedance surfaces. All terms of up to third order reflections and diffractions are considered for patterns in the principal plane. The surface waves are included whenever they exist for reactive surface impedances. The dihedral corner reflectors examined have right, obtuse, and acute interior angles, and patterns over the entire 360 degrees azimuthal plane are calculated. The surface impedances can be different on the four faces of the dihedral corner reflector; however, the surface impedance must be uniform over each face. Computed cross sections are compared with a moment method technique for a dielectric/ferrite absorber coating on a metallic corner reflector. The analysis of the dihedral corner reflector is important because it demonstrates many of the important scattering contributors of complex targets including both interior and exterior wedge diffraction, half-plane diffraction, and dominant multiple reflections and diffractions. >

Oceanic low-angle monopulse radar tracking errors

Radar systems often experience difficulties when tracking low-altitude targets over the ocean because of multipath effects. Whenever the radar cannot resolve the target from its image, it will track a false target position which can move far above or below the actual position. In this paper, mathematical models are utilized to quantitatively determine the degradation in tracking ability of a monopulse radar due to multipath. The model incorporates provisions for the antenna sum and difference patterns, including sidelobes, and for the antenna polarization. Divergence factors are utilized to account for the curvature of the earths lossy surface. More accurate calculations of the phase length of the direct and reflected rays using the spherical earth model are included. Smooth and rough surface models are used to model the prevailing sea state. The smooth surface model determines both stable and unstable equilibrium directions toward which the target position is indicated. The rough surface model defines a band of maximum error in the indicated position, as a function of the surface waveheight, and it includes both the rough specular and the rough diffuse reflection term.

An integral equation solution for the RCS of large dihedral corner reflectors

An integral equation solution is obtained by careful application of the moment method and the utilization of the symmetric property. The authors present guidelines that make it possible to avoid redundant computations of the impedance elements and that reduce the computation time as well as the memory space through dedicated matrix computation routines. Computed RCS patterns for a 90 degrees C corner reflector for both vertical and horizontal polarizations are shown and found to compare well with high-frequency predictions and experimental data.<<ETX>>

Reflections, diffractions, and surface waves for an interior wedge with impedance surfaces

The exact solution for the interior impedance wedge was evaluation asymptotically to yield a geometrical theory of diffraction (GTD). The geometrical-optics terms correspond identically to simple ray-tracing results. The diffraction field is analogous to the perfectly conduction case with suitable multiplying factors to account for the lossy reflections. The surface-wave contribution and its associated transition field are included to account for complex poles of the auxiliary Maliuzhinets function. Numerical integration using an adaptive quadrature routine was used to verify the accuracy of the technique. The analysis of the interior wedge geometry extends the work of M.I. Herman and J.L. Volakis (1987) to allow the study of complex structures which may include many multiple reflections and diffractions within interior wedges.<<ETX>>

Diffractions from a lossy polygonal plate in the presence of an antenna

The coefficients are written in terms of the Maliuzhinets function of order n which has been approximated in terms of elementary functions [ 3 ] . The Maliuzhinets function arises from the solution of the boundary value problem of the canonical wedge with an impedance surface boundary condition. The validity of this boundary condition has been discussed in [ 4 ] . The edge is described by the relative surface impedance q and is considered to be opaque. The coefficients of the imperfect conductor UTD revert to the perfectly conducting UTD coefficients of [l] as q approaches zero for both normal and oblique incidences.

Double reflections in the physical theory of diffraction

integrations generally cannot be performed in closed form, and numerical integrations may be necessary. The analysis becomes nuch more difficult to formulate for general objects. The formulation for finding the double reflected field begins by first determining the physical optics current on the first surface due to the incident tangential magnetic field. The vector potential due to this current can be used to find the fields induced in all space. At another conducting surface, the reflected field is used to determine the physical optics current density due to the first reflection. The vector potential due to this second reflection can be found by a surface integration over the second conducting surface. The reflected fields, which contribute to the total backscatter cross section, can then be found using the far-field approximation. When adding higher order reflections, however, the surface