A Time Domain Point Source Method for Inverse Scattering by Rough Surfaces

In this paper we propose a new method to determine the location and shape of an unbounded rough surface from measurements of scattered electromagnetic waves. The proposed method is based on the point source method of Potthast (IMA J. Appl. Math. 61, 119–140, 1998) for inverse scattering by bounded obstacles. We propose a version for inverse rough surface scattering which can reconstruct the total field when the incident field is not necessarily time harmonic. We present numerical results for the case of a perfectly conducting surface in TE polarization, in which case a homogeneous Dirichlet condition applies on the boundary. The results show great accuracy of reconstruction of the total field and of the prediction of the surface location.     

A scattering model for perfectly conducting random surfaces I. Model development

Abstract

The standard integral equation for the surface current is solved iterativcly to obtain an estimate of the surface current on a perfectly conducting randomly rough surface. The far-zone scattered fields and the backscattering coefficients for vertical, horizontal and cross-polarizations are then computed using this current estimate. The polarized backscattering coefficients are explicit functions of the surface parameters and reduce to the Kirchhoff solution in the high-frequency region and to the first-order perturbation solution in the low-frequency region. The cross-polarized scattering coefficient reduces to the second-order perturbation result in the low-frequency region and to zero in the high-frequency limit. A comparison is made with scattering measurements taken under laboratory conditions on a random surface with ka equal to 0-44 and kl equal to 3-25 ( l is the correlation length) It is found that better agreement is obtained with the current model than with the first-order perturbation model in predicting polarized scattering. It is also shown that the separation between VV and HH polarizations decreases gradually with frequency and approaches zero in the high-frequency limit     

Comparison of unified full-wave solutions for normal incidence microwave backscatter from sea with physical optics and hybrid solutions

Abstract

The unified full-wave solution for electromagnetic wave scatter from a rough surface is expressed as an integral similar in form to physical optics solutions. However it correctly predicts return for small and intermediate roughness scales where the physical optics approach fails. This full-wave solution is used here to evaluate microwave sea surface backscatter at normal incidence for both the like-and cross-polarized linear components. Surface heights and slopes are assumed to be Gaussian, the sea is characterized by its surface height spectral density function and both perfectly and finitely conducting surfaces are considered. Results from this complete full-wave evaluation are compared with approximations, involving single-scale (specular point) and two-scale models. For both of these models, however, it is necessary to assume a spectral wavenumber, ν_d, where spectral splitting between the large and the small scales of the rough surface occurs. The full-wave solution is used as a guide in the selection of ν_d and to study the accuracy and sensitivity of the different approximations to ν_d. It is also shown that results for cross-polarized backscatter based on the physical optics or two-scale models are totally inadequate.     

分层粗糙面与上方目标的复合电磁散射研究

针对粗糙面与目标复合电磁散射特性的应用前景,采用空间域合成法生成Alpha-Stable分布分层粗糙面,运用矩量法研究了锥形波入射时分层粗糙面与上方圆柱体的复合电磁散射特性,通过数值计算得到了复合散射系数随散射角的变化曲线,分析了稳定性系数、归一化尺度参数、互相关长度、入射波频率、粗糙面间距、圆柱体横截面半径以及粗糙面下方介质介电常数对复合散射系数的影响.结果表明,稳定性系数、归一化尺度参数、互相关长度、入射波频率、粗糙面间距对复合散射系数影响较大,而圆柱体横截面半径、粗糙面下方介质的介电常数对散射系数影响较小.     

随机粗糙面的一种新双站散射模型

描述了一种对改进的IEM模型的扩展双站散射模型。我们发现在非相干功率的表达式中,交叉分量和补充分量都由两项组成:一项与误差函数无关,而另一项与误差函数有关。后一项可看成是由误差函数引起的修正项。模型预测值和测量数据的良好吻合显示了这种扩展双站散射模型的有效性。     

Computer simulation of wave scattering from three-dimensional conducting random surfaces

Numerical simulation studies had been carried out by the conjugate gradient method to compute the solutions of the field integral equation for three-dimensional, perfectly conducting, Gaussian, random rough surfaces. The rate of convergence of the conjugate gradient method was fundamentally controlled by the root mean square (rms.) surface slope. Solutions computed using this method result in a significant reduction in CPU running time compared to those using direct methods, such as the Gaussian Elimination method. The validity of the numerical results of backscattering coefficients is verified by comparing simulation results with Kirchhoff theory, small perturbation theory, and Integral Equation methods at their valid regions. The efficiency and versatility of the numerical simulation algorithm as a practical tool to study rough surface scattering is demonstrated.     

Scattering cross sections for composite surfaces with large mean square slopes—full wave analysis

Abstract

In this work the full wave approach to rough surface scattering is applied to composite models of rough surfaces with large mean square slopes. It is shown that both specular point scattering as well as Bragg scattering are accounted for in the analysis and the results are compared with earlier solutions based on a combination of physical optics and perturbation theories. Using the full wave approach it is not essential to decompose the rough surface into individual surfaces with different roughness scales unless it is desired to separate the specular point contribution from the Bragg contribution to the scattering cross sections. Shadowing is accounted for in the analysis.     

Electromagnetic scattering from finite conductivity wind-roughened water surfaces

Numerical moment-method calculations of the electromagnetic backscattering from experimentally measured wind-roughened water surfaces that were previously made assuming perfectly conducting surfaces have been repeated taking into account the finite conductivity of sea water. The finite conductivity of the scattering medium was treated using impedance boundary conditions. Comparison with the earlier calculations shows that the backscattering drops slightly at horizontal polarization and much more dramatically at vertical polarization when the finite conductivity is considered. At small and moderate incidence angles, the magnitudes of the scattering drops are consistent with that predicted by the two-scale scattering model. The asymmetry in the upwind and downwind looking scattering that results from the non-uniform distribution of the Braggresonant electromagnetically small-scale waves across the larger scale waves is unaffected by the reduced conductivity at horizontal polarization and reduced very slightly at vertical polarization. The limitations of the two-scale model are essentially the same whether the surface is treatedwith perfect or sea-water conductivity.     

Radar multipath scattering from the composite model: Specular image modified model and ISAR imaging analysis

The theoretical implementation aspect of high‐frequency electromagnetic scattering prediction from the composite model is proposed in this work. First, the composite model is described and the multipath scattering prediction method (physical optics + equivalent edge currents + four‐path model) is formulated. Then, by introducing the concept of the specular image facet, a modification, named specular image modified four‐path model (SIMFPM), is developed to calculate the coupling scattering field between the electrically large three‐dimensional perfect electric conducting target and the dielectric rough surface. The proposed procedure makes preparation for the analysis of the multipath scattering effects on inverse synthetic aperture radar (ISAR) imaging in the final part. Numerical examples demonstrate the accuracy of the SIMFPM and present the multipath effects on the ISAR image.     

A program to compute EM scattering of plane wave by a perfectly conducting half-plane in a finitely conducting layered half-space

A FORTRAN program utilizing an integral equation calculates 10 field quantities relating to the electromagnetic (EM) scattering of plane wave by a perfectly conducting half-plane buried in a finitely conducting layered half-space. The computing algorithm is executable on a computer of small storage capacity such as PDP 11/40 and as such is useful to many exploration scientists without the facility of a mainframe computer, for computing model curves to interpret field data.     

The numerical calculation of two-dimensional rough surface scattering by the conjugate gradient method

Numerical simulation studies have been carried out by the conjugate gradient method to compute the solutions of the field integral equation for two-dimensional, perfectly conducting, Gaussian (normal), randomly rough surfaces. The rate of convergence of the conjugate gradient method is fundamentally controlled by the root mean square (r.m.s.) surface slope (gradient). Solutions computed using this method result in a significant reduction in CPU running time compared to those by direct methods, for example Gaussian Elimination method. The backscattering coefficients were calculated and compared with the small perturbation method results and Kirchhoff method results, and a good approximation resulted.     

A hybrid message passing/shared memory parallelization of the adaptive integral method for multi-core clusters

A hybrid message passing and shared memory parallelization technique is presented for improving the scalability of the adaptive integral method (AIM), an FFT based algorithm, on clusters of identical multi-core processors. The proposed hybrid MPI/OpenMP parallelization scheme is based on a nested one-dimensional (1-D) slab decomposition of the 3-D auxiliary regular grid and the associated AIM calculations: If there are M processors and T cores per processor, the scheme (i) divides the regular grid into M slabs and MT sub-slabs, (ii) assigns each slab/sub-slab and the associated operations to one of the processors/cores, and (iii) uses MPI for inter-processor data communication and OpenMP for intra-processor data exchange. The MPI/OpenMP parallel AIM is used to accelerate the solution of the combined-field integral equation pertinent to the analysis of time-harmonic electromagnetic scattering from perfectly conducting surfaces. The scalability of the scheme is investigated theoretically and verified on a state-of-the-art multi-core cluster for benchmark scattering problems. Timing and speedup results on up to 1024 quad-core processors show that the hybrid MPI/OpenMP parallelization of AIM exhibits better strong scalability (fixed problem size speedup) than pure MPI parallelization of it when multiple cores are used on each processor.     

Radiation analysis of on‐platform antenna using MoM‐PO combined with surface–surface configuration

In this article, wire antennas installed on electrically large structures are modeled by surface–surface configuration. The surface–surface configuration is applied to the hybrid method of moments–physical optics (MoM‐PO) to solve electromagnetic radiation problem of wire antennas mounted on electrically large conducting platform. Numerical results for the arbitrary shaped perfectly electric conducting are considered. Compared with the wire–surface configuration, the surface–surface configuration is easy to ensure the current continuity at the junction and maintain the required good accuracy. Additional complex basis functions are not required in surface–surface junction model compared with wire–surface junction model. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2010.     

An approximate model for the microwave brightness temperature of the sea

Abstract

A modified two-scale model is proposed for scattering and emissivity calculations for certain classes of random rough surfaces. It is based on an approach by Burrows and by Brown, but it has been extended to bistatic scattering by lossy dielectric surfaces, and it incorporates modified Fresnel reflection coefficients and a simple correction for multiple-scattering effects. The method is shown to be applicable to the ocean surface for light and moderate winds. A contracted form of the radiative-transfer equation is proposed and the included Wentz correction for surface scattering is discussed. This could lead to a method that could be both simple and accurate enough for real-time inversion algorithms in microwave remote sensing.     

Multi-functional, optofluidic, in-plane, bi-concave lens: tuning light beam from focused to divergent

The miniaturization and integration of in-plane micro-lenses into microfluidic networks for improving fluorescence detection has been widely investigated recently. This article describes the design and demonstration of an optofluidic in-plane bi-concave lens to perform both light focusing and diverging. The concave lens is hydrodynamically formed in a rectangular chamber with a liquid core liquid cladding (L ²) configuration. In the focusing mode, an auxiliary cladding stream is introduced to sandwich the L ² configuration for protecting the light rays from scattering at the rough chamber wall. In the diverging mode, the auxiliary cladding liquid changes its role from avoiding light-scattering to being the low-refractive-index cladding of the lens. The focal length in the focusing mode and the divergent angle of light beam in the diverging mode can be tuned by adjusting the flow rate ratio between core and cladding streams.     

Electromagnetic scattering by an array of conducting strips by an integral equation technique

Scattering of electromagnetic waves by an array of perfectly conducting infinitesimally thin strips is analyzed by a numerical procedure based on an integral equation formulation. The solution of the integral equation gives the induced surface current from which the reflected and transmitted waves are conveniently computed. Results are compared against other numerical results available in the literature which demonstrate the accuracy of the proposed method Further results are presented which show interesting physical phenomena.     

The application of compact polarimetric decomposition algorithms to L-band PolSAR data in agricultural areas

ABSTRACT

In this paper, the applicability of the recently developed compact polarimetric decomposition and inversion algorithm to estimate soil moisture under low agricultural vegetation cover is investigated using simulated L-band compact polarimetric synthetic aperture radar (PolSAR) data. The surface scattering component is separated from the volume component of the vegetation through a model-based compact polarimetric decomposition (m-α) under the assumption of randomly orientated vegetation volume and reflection symmetry. The extracted surface scattering component is compared with two physics-based, low frequency surface scattering models such as extended Bragg (X-Bragg) and polarimetric two scale model (PTSM) in order to invert soil moisture for corresponding model- and data-derived surface scattering mechanism parameter α_s. In addition to the parameter α_s from m-α decomposition, the applicability of other scattering mechanism parameters, such as δ (relative phase) and χ (degree of circularity) from m-δ and m-χ decompositions are also investigated for their suitability to invert soil moisture. The algorithm is applied on a time series of simulated L-band compact polarimetric E-SAR data from the AgriSAR’2006 campaign over the Görmin test site in Northern Germany. The compact PolSAR-derived soil moisture is validated against in situ time-domain reflectometry (TDR) measurements. Including various growth stages of three different crop types, the estimated soil moisture values indicate an overall root mean square error (RMSE) of 9–12 and 9–15 vol.% using the X-Bragg model and the PTSM, respectively. The inversion rate for vegetation covered soils ranges from 5% to 40% including all phenological stages of the crops and different soil moisture conditions (range from 4 to 34 vol.%). The time series of soil moisture inversion results using compact polarimetry reveal that the developed algorithm is less sensitive to wet soils under growing agriculture crops due to less sensitivity of scattering mechanism parameters α_s and χ for ε_s > 20. Thus, further developments and investigations are needed to invert soil moisture for compact PolSAR data with high inversion rates and consistently less RMSE (<5 vol.%) over the various crop growing season.     

Electromagnetic wave scattering from the sea surface in the presence of wind wave patterns

The study is concerned with electromagnetic wave (EM) scattering by a random sea surface in the presence of coherent wave patterns. The coherent patterns are understood in a broad sense as the existence of certain dynamical coupling between linear Fourier components of the water wave field. We show that the presence of weakly nonlinear wave patterns can significantly change the EM scattering compared to the case of a completely random wave field. Generalizing the Random Phase Approximation (RPA) we suggest a new paradigm for EM scattering by a random sea surface.

The specific analysis carried out in the paper synthesizes the small perturbation method for EM scattering and a weakly nonlinear approach for wind wave dynamics. By investigating, in detail, two examples of a random sea surface composed of either Stokes waves or horse-shoe (‘crescent-shaped’) patterns the mechanism of the pattern effect on scattering is revealed. Each Fourier harmonic of the scattered EM field is found to be a sum of contributions due to different combinations of wave field harmonics. Among these ‘partial scatterings’ there are phase-dependent ones and, therefore, the intensity of the resulting EM harmonic is sensitive to the phase relations between the wind wave harmonics. The effect can be interpreted as interference of partial scatterings due to the co-existence of several phase-related periodic scattering grids. A straightforward generalization of these results enables us to obtain, for a given wind wave field and an incident EM field, an a priori estimate of whether the effects due to the patterns are significant and the commonly used RPA is inapplicable. When the RPA is inapplicable, we suggest its natural generalization by re-defining the statistical ensemble for water surface. First, EM scattering by an ‘elementary’ constituent pattern should be considered. Each such scattering is affected by the interference because the harmonics comprising the pattern are dynamically linked. Then, ensemble averaging, which takes into account the distribution of the pattern parameters (based on the assumption that the phases between the patterns are random), should be carried out. It is shown that, generally, this interference does not vanish for any statistical ensemble due to dynamical coupling between water wave harmonics. The suggested RPA generalization takes into account weak non-Gaussianity of water wave field m contrast to the traditional RPA which ignores it.     

Generalized system function analysis of resonant behavior of electromagnetic open systems

1 Introduction A severe challenge for the electromagnetic compatibility (EMC) of a complex elec-tromagnetic system has been given with the increasingly complicated electromagnetic environment and dense electric devices. In particular, there are a lot of various antennas and scattering bodies on the large electromagnetic objects, such as airplane, ship, car, etc., and the interaction and mutual coupling between antennas and scatterers become more and more severe, which sometimes gives rise to …