Bistatic Scattering Cross Section Research Articles

Solving Combined Field Integral Equation With Deep Neural Network for 2-D Conducting Object

Solving the combined field integral equation (CFIE) for the large-scale scattering problem is computationally expensive. In this letter, we investigate the feasibility of applying deep learning to solve the CFIE for 2-D perfect electrically conducting objects. Inspired by the conjugate gradient method, an iterative deep neural network is designed to learn the manner of solving the surface current density from the CFIE, with the input being the coefficient matrix of the equation. This process involves physics through surface integration and need less iterations than the conventional iterative equation solver. In numerical tests, we evaluate the network's performance by comparing the predicted surface current density and bistatic scattering cross section with the solutions rigorously computed. This method provides an insight into applying machine learning techniques together with electromagnetic (EM) physics to fast EM computation with the same level of accuracy as traditional method.

Spaceborne Demonstration of GNSS-R Scattering Cross Section Sensitivity to Wind Direction

This letter investigates the sensitivity of the ocean surface bistatic scattering cross section measured by the Cyclone Global Navigation Satellite System (CYGNSS) to wind direction using the kurtosis of the delay-Doppler map (DDM) samples within a given area. The azimuthal dependence of the kurtosis is modeled by a cosine expansion of the relative wind direction, as is done in scatterometry for the radar cross section. The harmonic coefficients of the model depend on wind speed and incidence angle. Results show a coefficient of determination ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R^{2}$ </tex-math></inline-formula> ) between 0.6 and 0.9 for wind speeds between 4 and 10 m/s and negligible sensitivity outside this range. This study opens the door to the potential of using CYGNSS data for wind direction estimation.

The Dependence of Resonance Frequency to Landing Angle in Reciprocal Scattering Phenomena of the Waves From an Elliptical Plasma Dielectric Antenna

Scattering of an electromagnetic plane wave in transverse electric mode which is obliquely incident to an elliptical plasma antenna with a dielectric rod is comprehensively investigated. The field solutions of the incident, transmitted, and the scattered waves will be derived in terms of Mathieu and modified Mathieu functions. Using asymptotic expansions of Mathieu functions, the scattering cross section per unit length is obtained. It will be shown that in such an elliptical plasma antenna, the backscattering cross section depends on the incident angle and the bistatic scattering cross section varies with scattering angle significantly. Such effects are not seen in antennas with circular cross section due to the circular symmetry in them. The validation of the presented formulations and numerical computation will be examined with the circular case that is an asymptotic well-known case. The graphs of backscattering cross section, scattering pattern, and their corresponding to the polarized charge densities are presented. The dependence of the backscattering cross section and the scattering pattern upon the density and geometrical dimension of the plasma and dielectric are investigated. In addition, it will be shown that the resonance frequencies, under which the plasma antenna response will be maximum, essentially depend on the incident angle of the incident wave.

Machine Learning-Assisted Analysis of Polarimetric Scattering From Cylindrical Components of Vegetation

Reliable and efficient analysis of electromagnetic scattering by cylindrical components of vegetation is important for microwave remote sensing of vegetated terrain. In this paper, we proposed a machine learning (ML) scheme for the analysis of polarimetric bistatic scattering from a finite dielectric cylinder. A deep neural network architecture is adopted in the hope that with increased depth of the neural network, hence increased abstraction capability, it may be able to handle the highly oscillatory scattering patterns to an adequately acceptable degree. The scheme has demonstrated the capability of modifying and adapting itself to capture the complicated polarimetric bistatic scattering patterns of a finite dielectric cylinder. The physical consideration of reciprocity relation is largely fulfilled except for the scattered directions close to the cylinder axis. Moreover and more importantly, for cases where interpolation is expected, the scheme has unambiguously demonstrated the capability of learning the bistatic scattering cross section and phase patterns. The performance is also robust against the number of parameters to be interpolated, be it single or multiple. In summary, the proposed ML scheme bodes well for the design of the future physically based algorithms where the conventional datacube was used as the base for interpolation.

The simulation of electromagnetic scattering from a cluster of needles based on filtered coupled-dipole approximation

ABSTRACTThe electromagnetic scattering of a cluster of needles based on filtered coupled-dipole approximation (FCD) is studied in this paper. This computational method is deriving from the Discrete Dipole Approximation (DDA) algorithm, which can improve the performance of standard DDA algorithm based on the sampling theory. In this study, the backscattering and bistatic scattering cross sections of a cluster of needles simulated by FCD algorithm are compared with the results obtained by standard DDA algorithm, and the accuracy of the new method is assessed by simulation results. In addition, we discuss the errors of the FCD and standard DDA algorithms generated in different relative permittivity. The simulations demonstrate that the FCD can achieve a higher accuracy than the standard DDA, even for high-permittivity scatterers.

음원과 수신기 사이에 교차 산란단면적을 이용한 양상태 잔향음 모의

소나 운용에서 잔향음은 수중 표적 탐지의 제한요소이기 때문에 정확한 예측이 중요하다. 최근에는 단상태소나 연구에서 공간적으로 송수신기의 위치가 다른 양상태 소나에 대한 연구로 확장되고 있는 추세이다. 양상태 잔향음을 모의하기 위해서는 양상태 음파전달, 양상태 산란강도 및 산란단면적 등에서 단상태와 다른 복잡한 계산이 요구된다. 전 세계적으로 양상태 잔향음에 대한 연구가 활발하게 진행되고 있지만 잔향음을 예측하는데 중요한 요소인 양상태 산란단면적을 정확하게 계산하는 방법에 대한 연구는 미비하다. 본 논문에서는 거리 독립 환경의 양상태 잔향음모의에서 두 원의 교차되는 면적을 응용하는 새로운 산란단면적 계산 방법을 제안한다. 최종적으로 본 논문의 양상태 산란단면적 계산 방법으로 모의된 잔향음 준위는 기존에 제안되었던 방법들의 예측값과 비교되며 2013년 5월에 수행된 해상 실험의 측정값과 비교를 수행하였다. It is important to predict accurately reverberation level, which is a limiting factor in underwater target detection. Recently, the studies have been expanded from monostatic sonar to bistatic sonar in which source and receivers are separated. To simulate the bistatic reverberation level, the computation processes for propagation, scattering strength, and scattering cross section are different from those in monostatic case and more complex computation processes are required. Although there have been many researches for bistatic reverberation, few studies have assessed the bistatic scattering cross section which is a key factor in simulate reverberation level. In this paper, a new method to estimate the bistatic scattering cross section is suggested, which uses the area of intersection between two circles. Finally, the reverberation levels simulated with the scattering cross section estimated using the method suggested in this paper are compared with those estimated using the methods previously suggested and those measured from an acoustic measurements conducted in May 2013.

Mono- and Bistatic Scattering Reduction by a Metamaterial Low Reflection Coating

Significant reduction of mono- and bistatic scattering cross sections of an electrically large metallic cube through the application of an electrically thin metamaterial low reflection coating operating in the Ka-band (30-40 GHz) is described. A coating composed of a metallic array of sub-wavelength sized capacitively loaded strip inclusions printed on top of a thin, slightly lossy and grounded substrate has been designed and fabricated to experimentally evaluate the performance of the coating in scattering reduction. The scattering reduction is estimated by comparing the mono- and bistatic scattering patterns of the coated and uncoated cube. The measurement results are compared with full wave and physical theory of diffraction simulations, and the possibility of accurately modeling the low reflection coatings with impedance boundary conditions is pointed out.

3-D Vector Electromagnetic Scattering From Arbitrary Random Rough Surfaces Using Stabilized Extended Boundary Condition Method for Remote Sensing of Soil Moisture

We develop the stabilized extended boundary condition method (SEBCM) based on the classical EBCM to solve the 3-D vector electromagnetic scattering problem from arbitrary random rough surfaces. Similar to the classical EBCM, we expand the fields in terms of Floquet modes and match the extended boundary conditions at test surfaces away from the actual rough surface to retrieve the surface currents and therefore the scattered fields. However, to solve long-standing stability problems of the classical EBCM, we introduce a z-coordinate transformation to restrict and control the test surface locations explicitly. We also introduce the concepts of moderated test surface locations and balanced k-charts for further stabilization and optimization of the solutions. The computational efficiency is optimized by judicious submatrix decomposition. The resulting bistatic scattering cross sections are validated by comparing with analytical and numerical solutions. Specifically, the solutions are compared with those from the small perturbation method and small-slope approximation within their validity region, and with those from the method of moments outside the validity domains of analytical solutions. It is shown that SEBCM gives accurate, numerically efficient, full-wave solutions over a large range of surface roughnesses and medium losses, which are far beyond the validity range of analytical methods. These properties are expected to make SEBCM a competitive forward solver for soil moisture retrieval from radar measurements.

A Systematic Study of the Lowest Order Small Slope Approximation for a Pierson–Moskowitz Spectrum

In an earlier work, a model for calculating scattering from rough surfaces at very low grazing angles was presented. The utility of this model depends on the lowest order small slope approximation (SSA1). In order to ascertain when this new model, called the SSA+, is applicable, we present a systematic study of the accuracy of the SSA1 bistatic scattering cross section for 1-D surfaces for a Pierson-Moskowitz roughness spectrum and the Dirichlet boundary condition. Different frequencies, angles of incidence, and wind speeds are combined to examine 112 different cases. The ranges of scattering angles for which the SSA1 is accurate are given, and an analysis of when the SSA+ can be used is presented. All data and plots are available online.

Hybrid method for investigation of electromagnetic scattering interaction between the conducting target and rough sea surface

A current based hybrid method combining the MOM with the Kirchhoff approximation for analysis of scattering interaction between a two-dimensional infinitely long conducting target with arbitrary cross section and a 1-D rough sea surface with PM spectrum is proposed. The electromagnetic scattering region in the hybrid method is split into KA region and MOM region，respectively. The computational time of the hybrid method mainly depends on the number of unknowns of the target due to the induced current on the rough sea surface does not need to be calculated. The composite bistatic scattering cross section for the infinitely long cylinder above the rough sea surface with PM spectrum is calculated，the numerical results are compared and verified with those obtained by the conventional MOM，which shows the high efficiency of the hybrid method. Finally，the influence of the windspeed，the size and location of the target on the bistatic scattering cross section with different polarizations is discussed in detail.

Scattering models for Reverberation Modeling Workshop I problems

For many of the problems posed for Reverberation Modeling Workshop I, the boundary roughness was presented in terms of roughness spectra. Models and/or tables were also supplied for the bistatic scattering cross section and for the coherent reflection loss. Integral equation simulations were used to verify the accuracy of the bistatic scattering cross sections, and rough boundary PE simulations were used to verify the accuracy of the coherent reflection losses. The results of this work will be briefly summarized. The issue also arises for reverberation simulations whether the coherent reflection loss is appropriate for the boundary loss, or whether some other loss model is more appropriate, or whether the loss due to roughness should be simply ignored. This issue will be discussed in light of rough boundary PE simulations. [Work supported by ONR.]

Hollow Cylinder Microwave Model for Stems

Present electromagnetic models represent crop stems as full homogeneous cylinders. However, several ground measurements indicate that mature stems are hollow. In this paper, a model is presented which describes stems as hollow dielectric cylinders. The field on the surface of a hollow infinite cylinder is found at first, then applying the equivalence theorem, the scattered field from a hollow cylinder offinite length and any radius is obtained, and it is applied to the typical dimensions and permittivities ofwheat stems. The effects ofstem hollowness on microwave attenuation are investigated for a case study. Then, the extinction and bistatic scattering cross sections ofthe cylinder are included in the model developed at Tor Vergata University in order to study the effects ofstem hollowness on crop backscattering.

Numerical analysis of electromagnetic wave diffraction on a three-dimensional magnetodielectric body

A variant of the method of discrete sources suitable for solving problems of electromagnetic wave scattering on three-dimensional magnetodielectric bodies having a smooth surface of arbitrary shape is suggested and realized. A computer program implementing the suggested variant is briefly described. Some results of numerical calculations that illustrate the opportunities of the method are presented. Special attention is given to a study of the influence of deviations of the body shape from axisymmetric one on the bistatic scattering cross sections.

Modelling microwave scattering from long curved leaves

This paper describes the theoretical simulations carried out with a model of the backscattering coefficient of crops, where the leaf geometry is represented by a curved rectangular dielectric sheet. A general formulation is introduced for the bistatic scattering cross section of the curved sheet, and numerical results based on this approach are compared with those obtained by considering disc shaped leaves.

Resolution of Maxwell's equations by spectral moments method. Local approach

In previous work, we have presented a computation method based on the determination of the Green functions of the electromagnetic field with the help of the spectral moments method (SMM). In this method, the Green functions are calculated in the form of continued fractions, and one determines the coefficients of their development. Two approaches have been presented: one, we call global approach, where all space is discretized in a box, the other, we call the local approach, where only the diffracting item is considered. In this work we present the results obtained for the one, two and three-dimensional cases by the local approach. We first develop the necessary tools for the computing. We establish the analytical form of the Green functions of the continuous vacuum and of the discretized vacuum, the dispersion curves and the selection rules which appear. We show that the real part of the diagonal Green functions is directly linked to the vibrational density of states and therefore perfectly determined whatever dimension the space is. Longitudinal, non physical modes are found to play a subsequent role. As regards scattering, we principally report a series of tests on some canonical systems, such as cylinders or spheres, showing that the backscattering cross- section and the impulsional response obtained with SMM are in very good agreement with the analytical results. Bi-static scattering cross section is also studied.

Study of the Electromagnetic Scattering from the Very Rough Fractal Sea Surface**The project supported by National Natural Science Foundation of China under Grant No. 60101001 and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of Ministry of Education of China

In this paper, based on the fundamental formulae of the first-order and second-order Kirchhoff approximation and with consideration of the shadowing effect, the backscattering enhancement of the one-dimensional very rough fractal sea surface with Pierson-Moskowitz spectrum is studied under the second-order Kirchhoff approximation at microwave frequency. The numerical results are compared with those of the first-order Kirchhoff approximation and integral equation method. The dependencies of the bistatic scattering cross section and the backscattering enhancement on the incident angle, fractal dimension, and windspeed over the sea surface are analyzed in detail.

IMAGING OF HELICAL SURFACE WAVE MODES IN THE NEAR FIELD

A K-space technique that has proven successful for analyzing acoustic fields is applied to electromagnetic fields in the very near reactive region. In cylindrical coordinates the K- space spectrum describes helical wave modes on a fixed radius cylindrical surface that represent either propagating and evanescent mode energy. When this surface encloses a radiating or scattering object the resulting K-space decomposition reveals information about the physics of the wave-object interaction. Originally applied to the scalar wave equations of acoustics this method has been adapted to the vector wave equations encountered in electromagnetics. Here, the K-space decomposition is applied to the near electric and magnetic fields generated by a plane wave scattered from a perfectly conducting, finite length cylinder. We numerically simulate electromagnetic fields scattered from cylinders with a smooth surface and a surface with periodic grooves to illustrate the ability of the K-space method to differentiate between propagating and evanescent modal energy. Features in the K-space spectrum that impact the far field bi-static scattering cross section are identified to provide the link between the near field analysis and far field cross section.

Electromagnetic scattering by partially buried PEC cylinder at the dielectric rough surface interface: TM case

The Gaussian rough surface with the Gaussian correlation function is used to represent the statistical rough surface. Electromagnetic scattering from a partially buried perfectly electrically conducting (PEC) cylinder at the rough surface interface between two dielectric media is solved for the case of TM wave incidence using the method of moments with point matching. The effects of surface roughness and moisture content of the soil on the bistatic scattering cross section of the partially buried PEC objects at the rough surface interface are investigated using the Monte Carlo procedure.

Numerical study of the extended Kirchhoff approach and the lowest order small slope approximation for scattering from ocean-like surfaces: Doppler analysis

The validity of the lowest order small slope approximation (SSA(1)) and the extended Kirchhoff approach (EKA) (Elfouhaily et al., 1999) has been studied by comparing the Doppler spectra of the backscattered signals predicted by these models to their counterparts from exact integral equation-based numerical simulations. The study is conducted at L and S bands (electromagnetic wavelengths 23 and 10 cm); the rough ocean-like surfaces correspond to the wind speed of 5 m/s and were generated using both linear and nonlinear (Creamer) models. The incidence angle varies from normal to low grazing. Expressions for the two analytical models possess many similarities but contain different incidence/scattering angle-dependent factors. The analysis of the bistatic scattering cross sections predicted by the two models reveals that SSA(1) follows the exact numerical results more closely than the EKA. Moreover, at horizontal polarization the extended Kirchhoff bistatic cross section displays certain anomalies (unlimited growth at grazing scattering angles) that are indicative of the problems with this model. However, in the backscattering direction, the expressions for the two models are identical. Doppler analysis of the backscattered signals shows that in general, the analytical models provide better agreement with the numerical results for smaller incident angles. In addition, the agreement between the models and the exact numerical simulations is always better in the case of vertical polarization for which the analytical models give a satisfactory prediction of the Doppler spectrum for incident angles as large as 85/spl deg/ from the normal for both linear and nonlinear surfaces. For horizontal polarization, the models give increasingly poor predictions of the shape, magnitude, and location of the Doppler spectrum for incident angles in the range from 60/spl deg/ to low grazing. Doppler analysis proves to be a much more precise and sensitive tool in assessing the scattering model's validity than the usual comparison of cross sections.

Small perturbation method of high-frequency bistatic volume scattering from marine sediments

The first-order small perturbation method (Born approximation), as frequently applied to high-frequency scattering from marine sediments, is critically reviewed, tested for accuracy and extended. The sediment is modeled as an acoustic-fluid half space with random fluctuations in density and compressibility. Several cases of volume scattering from typical marine sand and mud sediments are presented to illustrate the effects of two important assumptions: (1) the effects of assuming the density and compressibility fluctuations are proportional, and (2) half-space effects. By relaxing the assumption that the sediment density and compressibility are proportional, the bistatic scattering cross section is significantly altered. The effects of properly modeling the sediment as a random half space (as opposed to an infinite continuum) are also discussed. In the context of first-order perturbation theory, half-space effects manifest themselves as a "modified" spectra for density and compressibility fluctuations. It is shown that, for lossy sediments and for scattering near the specular direction, half-space effects are significant and cannot be neglected. This result is significant because current models of sediment volume scattering do not include half-space effects. In addition to the theoretical model, exact numerical simulations are used to evaluate the accuracy of the perturbation model for a limited number of cases.