Tapered Wave Incidence Research Articles

Electromagnetic Scattering and Doppler Spectrum Simulation of Land–Sea Junction Composite Rough Surface

In this paper, a weighted arctangent function is used in conjunction with the spectral method to generate a land–sea junction composite rough surface under the spatially homogeneous and time-stationary hypotheses. The exponential correlation function and the Joint North Sea Wave Project (JONSWAP) spectrum, combined with an experiment-verified shoaling coefficient, are applied to model the land surfaces and the time-varying sea surfaces separately. The second-order small slope approximation (SSA-II) with tapered wave incidence is utilized for evaluating the electromagnetic scattering characteristics and Doppler characteristics of the generated composite rough surface. The influence of land–sea interface factors on radar cross-section (RCS) and Doppler shift of radar echoes is investigated in detail by comparing the RCS and Doppler spectra of the land–sea junction composite rough surfaces with those of finite-depth sea surfaces. It can be found that the Doppler spectra of the land–sea junction composite rough surface is narrower than that of the finite-depth sea surface under upwind directions and wider than that of the finite-depth sea surface under crosswind directions.

Coherent Spatially Varying Bidirectional Scattering Distribution Function of Rough Surface

High-resolution synthetic aperture radar (SAR) as an imaging device becomes more and more like a “camera” at the microwave frequency band. How different objects or object surfaces may visually appear in SAR images becomes an interesting research topic. Inspired by the bidirectional reflectance distribution function (BRDF) models employed in computer graphics (CGs), this article proposes the coherent spatially varying bidirectional scattering distribution function (CSVBSDF) for characterizing the electromagnetic scattering and SAR imaging behavior of surfaces. The CSVBSDF establishes a mapping function from observation parameters and surface local parameters to multidimensional measurements. In this article, CSVBSDF of the randomly rough surface is derived via adapting the integral equation method (IEM) to finite-size pixel cells under the plane wave and tapered wave incidence, respectively. It is then validated against the numerical beam simulation method (BSM) in the SAR image domain. A ground-based rail SAR and a 3-D laser scanner are used to measure the SAR image and the corresponding 3-D geometry of a real ground surface. Surface-local parameters, such as the local slope and roughness, are estimated from the measured 3-D geometry and then fed into the CSVBSDF model to produce a synthetic SAR image. Comparison against the real SAR image preliminarily demonstrates the efficacy of the proposed CSVBSDF model.

Efficient and Accurate Electromagnetic Angular Sweeping of Rough Surfaces by MPI Parallel Randomized Low-Rank Decomposition

A message passing interface (MPI) parallel scheme on distributed memory platforms is developed for the low-rank decomposition to accommodate the memory requirement during angular sweeping of a rough surface in terms of tapered wave incidence. Numerical examples, including that conducted on a $160\times 160$ square wavelength rough surface, are carried out to demonstrate the performance of the proposed MPI angular sweeping with respect to accuracy, efficiency, scalability, and the peak memory requirement.

Reliable approach for bistatic scattering of three-dimensional targets from underlying rough surface based on parabolic equation**Project supported by the National Natural Science Foundation of China (Grant No. 61771407).

A parabolic equation (PE) based method for analyzing composite scattering under an electromagnetic wave incidence at low grazing angle, which composes of three-dimensional (3-D) electrically large targets and rough surface, is presented and discussed. A superior high-order PE version is used to improve the accuracy at wider paraxial angles, and along with the alternating direction implicit (ADI) differential technique, the computational efficiency is further improved. The formula of bistatic normalized radar cross section is derived by definition and near-far field transformation. Numerical examples are given to show the validity and accuracy of the proposed approach, in which the results are compared with those of Kirchhoff approximation (KA) and moment of method (MoM). Furthermore, the bistatic scattering properties of composite model in which the 3-D PEC targets on or above the two-dimensional Gaussian rough surfaces under the tapered wave incidence are analyzed.

Uniqueness Results for Scattering and Inverse Scattering by Infinite Rough Surfaces with Tapered Wave Incidence

The scattering by a bounded or periodic rough surface is often modeled by assuming the plane wave incidence. However, when the rough surface is unbounded and nonperiodic, a tapered incident wave may be more appropriate to realize asymptotic truncation for the unbounded rough surface. Despite this extensive practical interest, little mathematical analysis of these problems has been carried out. This paper is concerned with the scattering and inverse scattering problem of the infinite impedance rough surfaces with tapered wave incidence. A boundary integral equation formulation is derived by using a half-plane impedance Green's function. It is shown that the integral equation is uniquely solvable in the space of bounded and continuous functions. Further, the impedance boundary value problem for the scattered field is proved to have a unique solution under certain constraints on the boundary impedance. It is also proved that a class of rough surfaces can be uniquely determined by the measurements of the scattered field generated by the tapered incident waves.

The PML method to solve a class of potential scattering problem with tapered wave incidence

This paper concerns about the two-dimensional direct scattering problem for Schrödinger equation with a class of decaying potential under the tapered wave incidence. We focus on the numerical solution of the problem by using the perfectly matched layer (PML) method. Based on the idea of complex coordinate stretching, the boundary value problem for the PML equation is formulated. Then the variational equation to the boundary value problem is proved to exist a unique solution except possibly for a set of values of wavenumber. The numerical experiments illustrate the influence of the thickness of PML layer, the absorption parameter, the wavenumber, the control bandwidth and even the incidence angle of the tapered wave on the effectiveness of this method.

Polarimetric Doppler spectrum of backscattered echoes from nonlinear sea surface damped by natural slicks

Based on the Lombardini et al. model that can predict the hydrodynamic damping of rough sea surfaces in the presence of monomolecular slicks and the “choppy wave” model (CWM) that can describe the nonlinear interactions between ocean waves, the modeling of time-varying nonlinear sea surfaces damped by natural or organic sea slicks is presented in this paper. The polarimetric scattering model of second-order small-slope approximation (SSA-II) with tapered wave incidence is utilized for evaluating co- and cross-polarized backscattered echoes from clean and contaminated CWM nonlinear sea surfaces. The influence of natural sea slicks on Doppler shift and spectral bandwidth of radar sea echoes is investigated in detail by comparing the polarimetric Doppler spectra of contaminated sea surfaces with those of clean sea surfaces. A narrowing of Doppler spectra in the presence of oil slicks is observed for both co- and cross-polarization, which is qualitatively consistent with wave-tank measurements. Simulation results also show that the Doppler shifts in slicks can increase or decrease, depending on incidence angles and polarizations.

Multi-parameter identification and shape reconstruction for unbounded fractal rough surfaces with tapered wave incidence

In this paper, we study the inverse scattering of tapered waves from sound soft surfaces or horizontally polarized electromagnetic waves from perfectly conducting surfaces. By the related Fréchet derivative with respect to a given surface of the solution of direct scattering problems, an efficient algorithm is proposed to reconstruct the parameters of unbounded rough surfaces from a set of scattered field measurements. Tapered wave is introduced to realize the asymptotic truncation for unbounded fractal rough surface. In order to improve the results of reconstruction, multi-angle and multi-frequency incidence strategy has been used. The numerical results show that the method yields satisfactory reconstructions for some rough surface profiles.

Polarimetric Scattering from Two-Dimensional Dielectric Rough Sea Surface with a Ship-Induced Kelvin Wake

Based on the polarimetric scattering model of second-order small-slope approximation (SSA-II) with tapered wave incidence for reducing the edge effect caused by limited surface size, monostatic and bistatic polarimetric scattering signatures of two-dimensional dielectric rough sea surface with a ship-induced Kelvin wake is investigated in detail by comparison with those of sea surface without ship wake. The emphasis of this paper is on an investigation of depolarized scattering and enhanced backscattering of sea surface with a ship wake that changes the sea surface geometric structure especially for low wind conditions. Numerical simulations show that in the plane of incidence rough sea surface scattering is dominated by copolarized scattering rather than cross-polarized scattering and that under low wind conditions a larger ship speed gives rise to stronger enhanced backscattering and enhanced depolarized scattering. For both monostatic and bistatic configuration, simulation results indicate that electromagnetic scattering signatures in the presence of a ship wake dramatically differ from those without ship wake, which may serve as a basis for the detection of ships in marine environment.

CIRCULARLY POLARIZED WAVE SCATTERING FROM TWO-DIMENSIONAL DIELECTRIC ROUGH SEA SURFACE

Based on the polarimetric scattering model of second-order small-slope approximation (SSA-II) with tapered wave incidence under linear and circular polarization, monostatic and bistatic scattering from two-dimensional dielectric rough sea surface is investigated. The emphasis of the present study is on the polarization signature of the scattered wave under circularly polarized wave incidence, which is related to the Brewster angle. Numerical simulations show that for bistatic configuration under circularly polarized wave incidence, the polarization state of scattering wave strongly depends on incident angle, scattering angle, as well as their relation to the Brewster angle associated with medium permittivity.

Boundary integral equation methods for the scattering problem by an unbounded sound soft rough surface with tapered wave incidence

In this paper, we consider the scattering problem of tapered acoustic wave by an unbounded sound soft surface. The scattering problem is modeled as a boundary value problem governed by the Helmholtz equation with Dirichlet boundary condition. Although the tapered wave is often introduced to realize asymptotic truncation for unbounded rough surface, the standard Helmholtz integral equations which derive for the scattering of plane waves by an arbitrary bounded obstacle are often used to generate benchmark numerical solutions. Different from the scattering of plane waves by an arbitrary bounded obstacle, we use the angular spectrum representation radiation condition to replace the Sommerfeld radiation condition, and derive a boundary integral equation for studying the scattering problem. Then we study the integral equation by the truncation method, whereby the integral equation posed on an unbounded region is approximated by an integral equation on a bounded region. Some properties of the integral equation in an energy space with weights are proved. Then the collocation method is used to solve the integral equation on a bounded region, and its convergence is also obtained.

Hybrid method of scattering from a dielectric target above a rough surface: TM case

A hybrid method, combining analytic Kirchhoff approximation (KA) and numerical method of moment (MoM), is developed to solve the 2D scattering problem of a dielectric target with arbitrary cross section above a moderate perfect electric conductor (PEC) rough surface under TM-polarized tapered wave incidence. Consider the target as the MoM region and the rough surface as the KA region, the induced current on the rough surface is obtained through the KA method, which depends on the incident tapered wave and the field illuminating by current distribution on the target, leaving only unknowns on the target region. In order to reduce the computational costs further, the rough surface is truncated to speed up computation of the scattering contribution from the rough surface to the target. Compared with the conventional MoM, the hybrid method is very efficient to solve the composite scattering problem of target above rough surface, especially for long underlying rough surface. Simulation results validate the effectiveness and accuracy of the hybrid method.

Regularized conjugate gradient method with fast multipole acceleration for wave scattering from 1D fractal rough surface

Based on the integral equation method and regularization theory, the regularized conjugate gradient method (RCGM) is presented for studying wave scattering from a one-dimensional rough surface with tapered wave incidence. This study is limited to scattering of acoustic waves from sound soft surfaces or horizontally polarized electromagnetic waves from perfectly conducting surfaces. The problem is formulated by using the integral equation approach. Compared with plane wave incidence, there is a remainder on the right side of the integral equation. To solve the surface integral equation, especially when the rough surface is very large in terms of the wavelength, we treat the large-scale matrix computation problem which is generated by the fast multipole algorithm using the RCGM. A strategy for the selection of the regularization parameter is obtained by estimating the double integral as a perturbed right-hand side of the integral equation. Energy conservation is considered simultaneously in the process of designing stopping criteria of the RCGM. By comparison of the numerical results of bistatic scattering coefficient (BSC) between RCGM and method of moments (MOM), the validity and accuracy of RCGM is verified. Numerical examples are also given to show the relationship between the scattering characteristic and surface roughness of the one-dimensional fractal rough surfaces.

Electromagnetic Scattering from Randomly Rough Surfaces with Hybrid FEM/BIE

The hybrid finite element method (FEM) together with the boundary integral equation (BIE) is firstly applied to scattering from a conducting rough surface. The BIE is used as the truncation boundary condition for the special unbounded half space, whereas the FEM is used to solve the governing equation in the region surrounded by a rough surface and artificial boundary. Tapered wave incidence is employed to cancel the so-called “edge effect". A hybrid FEM/BIE formulation for generalized one-dimensional conducting rough surface scattering is presented, as well as examples that evaluate its validity compared to the method of moments. The bistatic scattering coefficients of a Gaussian rough surface are calculated for transverse-magnetic wave incidence. Conclusions are reached after analyzing the scattering patterns of rough surfaces with different rms heights and correlation lengths

BISTATIC SCATTERING FROM ROUGH DIELECTRIC SOIL SURFACE WITH A CONDUCTING OBJECT WITH ARBITRARY CLOSED CONTOUR PARTIALLY BURIED BY USING THE FBM/SAA METHOD

A hybrid approach of the forward-backward method (FBM) with spectral accelerate algorithm (SAA) and Monte Carlo method is developed in this paper. It is applied to numerical simulation of bistatic scattering from one-dimensional arbitrary dielectric constant soil surface with a conducting object with arbitrary closed contour partially buried under both the horizontal and vertical polarization tapered wave incidence at low grazing angle. The energy conservation has been checked for the FBM/SAA. Numerical simulations of bistatic scattering at low grazing angle have been discussed in this paper.

Fast iterative approach to difference scattering from the target above a rough surface

The difference field radar cross section (d-RCS) has been defined to analyze the scattering from the target above a rough surface, which takes account of scattering from the target and multiinteractions of the target and underlying rough surface. The d-RCS removes the effect of the finite illuminated surface length under the tapered wave incidence. In this paper, the electric field integral equations (EFIEs) of the difference-induced current J/sub sd/ on the rough surface and the induced current J/sub o/ on the target are derived. A small section of rough surface toward the target in the specular direction is taken to speed up computation of the scattering contribution E/sub s0/ from the moderate rough surface to the target. Then, an iterative approach is developed to solve the EFIEs of the induced currents, directly, and yields the bistatic d-RCS. A finite rough surface length for numerical iteration is taken, corresponding to the dependence on the maximum scattering angle. Using the Monte Carlo method to generate rough surface, the bistatic d-RCS of the target, e.g., a cylinder or a square column, above a Pierson-Morkowitz rough surface is numerically simulated. The induced currents on the target and the d-RCS are discussed, and compared with the case of the target in free-space.

Bistatic scattering and transmitting through a fractal rough surface with high permittivity using the physics-based two-grid method in conjunction with the forward-backward method and spectrum acceleration algorithm

To numerically calculate bistatic scattering from a fractal rough surface with high permittivity, a comprehensive approach of the forward-backward method (FBM) with spectral acceleration algorithm (SAA) combined with the physics-based two-grid (PBTG) method is developed. Bistatic scattering from and transmitting through one-dimensional (1-D) fractal rough surface with high permittivity, under TE and TM tapered wave incidence, are numerically simulated. Angular reflectivity and transmittivity demonstrate the energy conservation and the functional dependences upon the surface parameters.

Bistatic scattering from a fractal dynamic rough sea surface with a ship presence at low grazing‐angle incidence using the GFBM/SAA

AbstractA generalized forward–backward method (GFBM) with the spectral accelerated algorithm (SAA) to solve the magnetic‐field integral equation (MFIE) is developed. It is applied to the numerical simulation of bistatic scattering from a one‐dimensional (1‐D) fractal dynamic sea surface with a ship presence under TE tapered wave incidence at a low grazing angle (LGA). Numerical simulations of bistatic scattering at an LGA show the functional dependence upon the fractal dimension of the conducting rough surface, ship location, and other parameters. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 31: 146–151, 2001.