Experimental modeling the millimeter wave scattering from vegetation canopy

In the paper we present the results of experimental modeling the millimeter wave scattering from elements and fragments of a vegetation canopy. The dependence of amplitude and phase distributions of scattered field in near zone, of back-scattering cross section, and of scattered field distribution in Frenel zone for a fragment of wheat shoots upon the moisture and shape of an individual element is determined.     

Electromagnetic wave scattering from some vegetation samples

For an incident plane wave, the field inside a thin scatterer (disk and needle) is estimated by the generalized Rayleigh-Gans (GRG) approximation. This leads to a scattering amplitude tensor equal to that obtained via the Rayleigh approximation (dipole term) with a modifying function. For a finite-length cylinder the inner field is estimated by the corresponding field for the same cylinder of infinite length. The effects of different approaches in estimating the field inside the scatterer on the backscattering cross section are illustrated numerically for a circular disk, a needle and a finite-length cylinder as a function of the wave number and the incidence angle. Finally, the modeling predictions are compared with measurements     

Electromagnetic scattering from perfectly conducting rough surfaces(a new full wave method)

A method that does not make use of the telegraphist's equations and takes into account the two-dimensional roughness of the surface from the start is developed. It is shown that the scattering coefficients obtained agree with those given in earlier work by E. Bahar (1973, 1987). The method is based on reducing the three-dimensional scattering problem to a two-dimensional problem by expanding each rectangular component of Maxwell's equations in terms of local basis functions along the perpendicular direction to the mean surface. The transformed two-dimensional field equations are solved using Fourier transforms. The full wave solutions are also compared with the first-order perturbation solutions, the Kirchhoff-type solutions, and integral equation results     

Electromagnetic wave scattering by a system of two spheroids ofarbitrary orientation

An exact solution to the problem of the scattering of a plane electromagnetic wave by two perfectly conducting arbitrarily oriented prolate spheroids is obtained by expanding the incident and scattered electric fields in terms of an appropriate set of vector spheroidal eigenfunctions. The incident wave is considered to be a monochromatic, uniform plane electromagnetic wave of arbitrary polarization and angle of incidence. To impose the boundary conditions, the field scattered by one spheroid is expressed in terms of its spheroidal coordinates, using rotational-translational addition theorems for vector spheroidal wave functions. The column matrix of the scattered field expansion coefficients is equal to the product of a square matrix which is independent of the direction and polarization of the incident wave, and the column matrix of the known incident-field expansion coefficients. The unknown scattered-field expansion coefficients are obtained by solving the associated set of simultaneous linear equations. Numerical results for the bistatic and backscattering cross sections for prolate spheroids with various axial ratios and orientations are presented     

Modeling the gap probability of a discontinuous vegetation canopy

A model is presented for the gap probability of a discontinuous vegetation canopy, such as forest, savanna, or shrubland. The case in which the distribution of individual canopy sizes and shapes is known and individual canopies are randomly distributed but do not overlap, and the case in which the canopies to intersect and/or overlap such that foliage density remains constant with the overlap area are both considered, although an exact solution is provided only for the latter. A comparison of modeled gap probabilities with observed gap probabilities for a Maryland (US) pine stand (as taken from the literature) shows good agreement for zenith angles of illumination up to about 45°. Above 45°, the fit worsens, presumably because the horizontal branch structure of the pine canopy is less attenuating as the illumination angle approaches the horizon     

Electromagnetic scattering from a dielectric cylinder of finitelength

The dyadic scattering amplitude is determined for a planar electromagnetic wave incident on a dielectric cylinder of finite length and circular cross section under the assumption that the internal fields induced within the finite-length cylinder can be approximated by those within an infinite-length cylinder. These internal fields are then used to calculate the dyadic scattering amplitude in terms of the cylinder's physical dimensions, orientation, and dielectric properties. The theoretical development is complemented by numerical calculations, and its validity assessed by comparison with experiment     

Hybrid FDTD and single-scattering theory for simulation of scattering from hard targets camouflaged under forest canopy

A hybrid target-foliage model is developed to investigate the scattering behavior of hard targets embedded inside a forest canopy. The proposed model is composed of two existing electromagnetic-scattering models, one for the foliage and the other for the hard targets that are coupled in a computationally efficient manner. The connection between these two models, which accounts for the interaction between the foliage scatterers and the target, is accomplished through the application of Huygens' principle. Wave penetration through the forest canopy and near-field and far-field scattering from its constituents is calculated using a coherent single-scattering theory, which makes use of realistic tree structures. Defining a Huygens' surface enclosing the hard target and calculating the illuminating field (the scattered fields from the nearby vegetation scatterers and reduced incident field), the interaction between the foliage and the hard target is accounted for. Computing the scattered field from target on the Huygens' surface and using a reciprocity theorem target-foliage interaction is captured very efficiently. Calculation of scattering from a hard target is carried out using a finite-difference time-domain (FDTD) technique. For a typical vehicle dimensions, the required time and memory for the FDTD computation and exact field calculation inside the foliage limits the simulation frequency to upper very high frequency (VHF) band.     

Electromagnetic plane wave scattering by a system of two parallel conducting prolate spheroids

By means of modal series expansions of electromagnetic fields in terms of prolate spheroidal vector wave functions, as exact solution is obtained for the scattering by two perfectly conducting prolate spheroids in parallel configuration, the excitation being a monochromatic plane electromagnetic wave of arbitrary polarization and angle of incidence. Using the spheroidal translational addition theorems recently presented by the authors which are necessary for the two-body (or multibody) scattering solution, an efficient computational algorithm of the translational coefficients is given in terms of spherical translational coefficients. The field solution gives the column vector of the series coefficients of the scattered field in terms of the column vector of the series coefficients of the incident field by means of a matrix transformation in which the system matrix depends only on the scatterer ensemble. This eliminates the need for repeatedly solving a new set of simultaneous equations in order to obtain the scattered field for a new direction of incidence. Numerical results in the form of curves for the bistatic and monostatic radar cross sections are given for a variety of prolate spheroid pairs having resonant or near resonant lengths.     

Electromagnetic scattering from a spherical nonuniform medium-part I: General theory

The scattering of electromagnetic waves by a spherically symmetric continuous dielectric is examined. Two distinct methods for calculating the scattering amplitude are derived. It is shown that the scalar approximation is, in general, extremely poor. The radar cross section is discussed in some detail.     

Electromagnetic scattering from a chiral cylinder of arbitrarycross section

A simple moment solution is presented to the problem of electromagnetic scattering from a homogeneous chiral cylinder of arbitrary cross-section. The cylinder is assumed to be illuminated by either a TE or a TM wave. The surface equivalence principle is used to replace the cylinder by equivalent and magnetic-surface currents. These currents radiating in unbounded external medium produce the correct scattered field outside. When radiating in an unbounded chiral medium, they produce the correct total internal field. By enforcing the continuity of the tangential components of the total electric field on the surface of the cylinder, a set of coupled integral equations is obtained for the equivalent surface currents. Unlike a regular dielectric, the chiral scatterer produces both copolarized and cross-polarized scattered fields. Hence, both the electric and magnetic current each have a longitudinal and a circumferential component. These four components of the currents are obtained by using the method of moments (MoM) to solve the coupled set of integral equations. Pulses are used as expansion functions and point matching is used. The Green's dyads are used to develop explicit expressions for the electric field produced by two-dimensional surface currents radiating in an unbounded chiral medium. Some of the advantages and limitations of the method are discussed. The computed results include the internal field and the bistatic and monostatic echo widths. The results for a circular cylinder are in very good agreement with the exact eigenfunction solution     

Electromagnetic scattering from a dielectric wedge and the singlehypersingular integral equation

Electromagnetic fields scattered by a finite dielectric wedge are computed using a hypersingular integral equation (HIE). The results are compared with those obtained previously using a singular integral equation (SIE) and with the theory that predicts that the fields near the edge of the wedge behave like static fields. The HIE produces more consistent results than the SIE, probably because the unknown boundary function tends to a constant near the edge instead of diverging. The two numerical methods agree reasonably well, and these results agree only in part with the static field behavior     

Full-wave analysis of microwave scattering from short vegetation: an investigation on the effect of multiple scattering

A full-wave solution for polarimetric scattering from a cluster of randomly oriented three-dimensional lossy dielectric structures above an impedance surface is presented to investigate the importance of multiple scattering. The problem is formulated using an integral equation in conjunction with the exact image representation of dyadic Green's function for the half-space problem. Then, the integral equation is solved for the induced equivalent polarization currents using the method of moments. The accuracy of the numerical code is verified using other existing numerical results and experimental observations. The model is then used to examine the effect of multiple scattering among a cluster of relatively short stems and is shown that multiple scattering significantly affects the cross-polarized backscatter whereas it has a moderate effect on the copolarized backscattering depending on the stem density.     

Surface wave scattering from a notch in a dielectric-covered groundplane: TE-mode analysis

026The problem of TE mode surface wave scattering from a rectangular notch in a dielectric-covered ground plane is considered. A Fourier-transform technique is used to express the scattered field in the spectral domain in terms of parallel-plate waveguide modes. The boundary conditions are enforced on the ground plane and the notch aperture to obtain simultaneous equations for the transmitted field inside the notch. The simultaneous equations are solved to obtain a solution in a fast convergent series, thus facilitating the numerical computation. The transmission, reflection, and scattering coefficients are found to oscillate as the notch width increases especially when the notch depth is comparable to and larger than one wavelength. A limited number of computations show that the reflected power loss is less than 2% when the notch width is less than one wavelength     

Electromagnetic plane wave scattering by a system of two uniformlylossy dielectric prolate spheroids in arbitrary orientation

By means of modal series expansions of electromagnetic fields in terms of prolate spheroidal vector wave functions, an exact solution is obtained for the scattering by two uniformly lossy dielectric prolate spheroids in arbitrary orientation embedded in free space, the excitation being a monochromatic plane electromagnetic wave of arbitrary polarization and angle of incidence. Rotational-translational addition theorems for spheroidal vector wave functions are employed to transform the outgoing wave from one spheroid into the incoming wave at the other spheroid. The field solution gives the column vector of the unknown coefficients of the series expansions of the scattered and transmitted fields expressed in terms of the column vector of the known coefficients of the series expansions of the incident field and the system matrix which is independent of the direction and polarization of the incident wave. Numerical results in the form of curves for normalized bistatic and monostatic radar cross sections are given for a variety of two-body system of uniformly lossy dielectric prolate spheroids in arbitrary orientation having resonant or near resonant lengths and different distances of separation     

Coherent scattering of a spherical wave from an irregular surface

The scattering of a spherical wave from a rough surface using the Kirchhoff approximation is considered. An expression representing the measured coherent scattering coefficient is derived. It is shown that the sphericity of the wavefront and the antenna pattern can become an important factor in the interpretation of ground-based measurements. The condition under which the coherent scattering-coefficient expression reduces to that corresponding to a plane wave incidence is given. The condition under which the result reduces to the standard image solution is also derived. In general, the consideration of antenna pattern and sphericity is unimportant unless the surface-height standard deviation is small, i.e., unless the coherent scattering component is significant. An application of the derived coherent backscattering coefficient together with the existing incoherent scattering coefficient to interpret measurements from concrete and asphalt surfaces is shown.     

Ray analysis of low-grazing scattering from a breaking water wave

Low-grazing-angle backscattering from a modeled breaking-wave surface profile has been calculated using a ray-optical approach and compared with reference scattering found using an extended moment method. The calculations show that interference between the direct backscatter from the breaking plume and multipath scattering between the plume and wave face can lead to the HH-to-VV polarization-backscattering ratios of greater than 9 dB that characterize sea-spike events. The multipath effects can be accurately predicted from simple reflection from the front face at the smallest grazing angles. At higher angles, diffraction from rapid changes in the surface curvature must also be considered     

Electromagnetic spherical wave reflection from a perfectly conducting surface of revolution

The problem of electromagnetic spherical wave reflection from a perfectly conducting surface of revolution is considered. The expressions for the first two terms of the high frequency asymptotic expansion for the reflected field are found. The analysis is based on Lee's theory of electromagnetic reflection from a conducting surface.     

Measuring the propagation properties of a forest canopy using apolarimetric scatterometer

A truck-mounted 1.6-GHz polarimetric scatterometer was used from a 19-m high platform to measure the backscattering from a dense canopy of pine trees at an incidence angle of 40°. Two sets of measurements were made at each of many spatial locations, one set with and the other without a trihedral corner reflector present on the ground surface underneath the canopy. From the two sets of polarimetric measurements, it was possible to determine the mean values and the statistical distributions of the canopy attenuation factors for horizontal and vertical polarizations. The mean values of the one-way attenuation factors were found to be 9.31 dB for horizontal polarization and 9.16 dB for vertical polarization. The precision associated with the values of the canopy loss factor measured using the polarimetric technique is estimated to be on the order of ±0.3 dB     

Electromagnetic scattering from a spherical nonuniform medium-part II: The radar cross section of a flare

The radar cross section for scattering of electromagnetic waves by a plasma having an electron concentration proportional tor^{-2}is calculated. The exact solution is compared with the scalar approximation. It is found that the exact solution can be orders of magnitude smaller than any of the usual approximations.