A phase matrix for a dense discrete random medium: evaluation ofvolume scattering coefficient

In the derivation of the conventional scattering phase matrix of a discrete random medium, the far-field approximation is usually assumed. In this paper, the phase matrix of a dense discrete random medium is developed by relaxing the far-field approximation and accounting for the effect of volume fraction and randomness properties characterized by the variance and correlation function of scatterer positions within the medium. The final expression for the phase matrix differs from the conventional one in two major aspects: there is an amplitude and a phase correction. The concept used in the derivation is analogous to the antenna array theory. The phase matrix for a collection of scatterers is found to be the Stokes matrix of the single scatterer multiplied by a dense medium phase correction factor. The close spacing amplitude correction appears inside the Stokes matrix. When the scatterers are uncorrelated, the phase correction factor approaches unity. The phase matrix is used to calculate the volume scattering coefficients for a unit volume of spherical scatterers, and the results are compared with calculations from other theories, numerical simulations, and laboratory measurements. Results indicate that there should be a distinction between physically dense medium and electrically dense medium     

EM propagation and backscattering discrete model for medium of sparsely distributed lossy random particles

Electromagnetic wave propagation and backscattering from a random medium are studied. The random medium is modeled by discrete lossy dielectric scatterers, for which the dyadic scattering amplitudes and orientation statistics are known. A method is developed to compute the propagation and backscattering coefficients. The technique is valid for scatterers having characteristic dimensions comparable to a wavelength. The procedure is valid when the albedo of individual scatterers is small, that is, when the scatterers are highly absorbing. Numerical calculations for the propagation and backscattering coefficients are presented, and compared with the literature.     

Polarimetric scattering from a layer of random clusters of smallspheroids

Employing the volume integral equation formulation with self-interaction term for internal fields, the Jones scattering matrix and phase matrix for random clusters of small spheroids are derived. The mutual coherent wave interactions among clustered spheroids are included. Clustering enhances the internal fields and the scattering amplitude function. Substituting the newly derived phase matrix into the Mueller matrix in the approach of vector radiative transfer for a layer of random clusters of small spheroids, fully polarimetric copolarized and cross-polarized backscattering are numerically calculated. Clustering effects of a layer of random spheroids are quantitatively illustrated, and the backscattering enhancement of several dB order and its functional dependence on parameters are discussed     

A Monte Carlo method for radar backscatter from a half-space randommedium

The problem of electromagnetic multiple scattering in a random medium is treated by a Monte Carlo method, in which an incident beam of photons is progressively scattered by scattering centers in the medium. The theory characterizes each scattering by functions describing the probability of the photon being scattered or absorbed, and the probability of its being scattered into certain directions. This process is tracked until the photon is finally absorbed or backscattered into the receiver. Variance reduction techniques are introduced to reduce the computation time required for acceptable ensemble averages of the backscattering cross sections. Ellipsoidal dielectric scatterers are used to model circular disk-shaped leaves, elliptical disk-shaped leaves, and needle-shaped leaves, which are randomly distributed in a half-space medium. The Monte Carlo simulations give good comparison with experimental data of backscattering cross sections from fields of wheat, corn, and milo     

Branching model for vegetation

A branching model is proposed for the remote sensing of vegetation. The frequency and angular responses of a two-scale cylinder cluster are calculated to demonstrate the significance of vegetation architecture. The results indicate that the architecture of vegetation plays an important role in determining the observed coherent effects. A two-scale branching model is implemented for soybean with its internal structure and the resulting clustering effects considered. At the scale of soybean fields, the relative location of soybean plants is described by a pair distribution function. The polarimetric backscattering coefficients are obtained in terms of the scattering properties of soybean plants and the pair distribution function. Theoretical backscattering coefficients evaluated using the hole-correction pair distribution are in good agreement with extensive data from soybean fields. The hole-correction approximation, which prevents two soybean plants from overlapping each other, is more realistic and improves the agreement between the model calculation and experimental data near normal incidence     

Propagation constant and the velocity of the coherent wave in adense strongly scattering medium

Frequency- and time-domain experiments are conducted to study the effective propagation constant of the coherent wave in a dense strongly scattering medium. A wide-band microwave signal (10-40 GHz) is propagated through randomly distributed glass spheres with a 5.73 mm average diameter and separated into incoherent and coherent fields. The real and imaginary parts of the propagation constant are obtained from the coherent field. The narrow size distribution of the particles enables the authors to study scattering from the Rayleigh region through the Mie resonance scattering region. The results of the experiments are compared to independent scattering, effective-field approximation (Foldy's), and the higher order quasi-crystalline approximation (QCA) using Mie scattering coefficients and the Percus-Yevick approximation for the pair-distribution function. The phase and group velocities of the coherent wave are obtained from the effective propagation constant and compared with theory. In addition, the velocity of the coherent wave in random media is measured using the time-domain technique. It is shown that the velocity of the coherent wave in random media is neither phase nor group velocity     

植被散射的蒙特卡罗模拟及其在低掠角散射中应用

本文提出利用蒙特卡罗算法研究植被散射及其低掠角散射特性.根据双层植被的散射模型,考虑到植被层内各散射体场的相干和多径效应,利用蒙特卡罗算法模拟随机分布和簇规则分布植被的低掠角散射系数,适当解释植被散射的后向增强和掠射特性.     

A combined method to model microwave scattering from a forest medium

A novel method, which employs both a matrix doubling algorithm and the first-order solution of a radiative transfer (RT) equation for modeling microwave backscattering from forest, is presented in the paper. The method is based on the assumption that a forest canopy can be divided into a number of distinct horizontal vegetation layers over a dielectric half-space rough surface. The scattering phase matrix of each layer is calculated by either matrix doubling to account for the multiple-scattering effect or first-order solution of an RT equation, depending on the scattering characteristics of the layer. The first-order solution of the RT equation is used for the trunk layer while the matrix doubling technique is applied to both the crown layer and understory. The advanced integral equation model and reflectivity matrix are used to calculate the noncoherent and coherent surface boundary conditions. Comparisons between model predictions and field measurements on radar backscattering coefficients for a walnut orchard showed a good agreement at both L-band and X-band and for all three polarizations. Comparative analyses of model predictions for backscattering from a forest medium calculated using the combined model, first-order RT model, and the standard matrix doubling model were also presented. Understory effects, that can significantly change the weight of each scattering mechanism, were also evaluated by using the combined method.     

一层非均匀随机取向非球形粒子的全极化散射

本文推导了非均匀随机取向非球形粒子散射矩阵的各个元素,得到了矢量辐射传输方程中非对角化的消光矩阵,以及相矩阵。用矢量辐射的积分方程和Mueller矩阵,计算一层非均匀随机取向非球形粒子的全极化散射,讨论了任一极化的同极化和去极化后向散射系数、极化度,VV和hh波之间的相位差,及其与各有关参数的定量的函数关系。     

Radar backscatter from a dense discrete random medium

A dense medium phase matrix developed based on the concept of random lattice perturbation is employed in the radiative transfer theory to calculate the coand cross-polarized backscatter from a layer of randomly distributed spherical scatterers. The position randomness properties are characterized by the variance and correlation function of scatterer positions within the medium. The dense medium phase matrix differs from the conventional one in two major aspects, i.e., there is an amplitude and a phase correction. These corrections account for the effects of close spacing and position correlation between scatterers in a dense discrete random medium. This study shows that phase coherency and close-spacing amplitude modifications are two separate corrections necessary for an electrically dense medium. Results indicate that there is a need to distinguish between spatially and electrically dense medium. The phase correction is found to have a greater impact on cross-polarized than like-polarized backscatter coefficients; the converse is true of the amplitude correction. Backscattering calculations from the theory are compared with measurements from controlled microwave experiments on random media consisting of closely packed spheres, and from field measurements of dry snowpack. Predictions from such a theory agree well with the measured data     

Simulating coherent backscattering from crops during the growingcycle

The backscattering coefficient and the position of interferometric phase center of wheat and sunflowers during the growing cycle have been computed by using a coherent electromagnetic model. In the model, the scattered fields are added coherently and the attenuation in the canopy is computed by means of Foldy's approximation. The comparison between model simulations and experimental data has shown that model results match reasonably well with the measured backscattering. As the plant grows, the backscattering of wheat ("narrow leaf" crop) decreases, whereas that of sunflowers ("broad leaf") increases. An analysis of the various terms that contribute to backscattering has indicated that the most significant contribution is given by the double scattering soil-stalk and that the position of the interferometric phase center is close to the soil. When the contribution of leaves is more significant, as in the case of sunflowers, the interferometric phase center goes up to about one quarter of the full plant height. This result demonstrates the potential of the interferometric observation in providing significant new information on crop classification algorithms based on scattering mechanisms     

A new numerical approach to the calculation of electromagnetic scattering properties of two-dimensional bodies of arbitrary cross section

A new method is introduced for formulating the scattering problem in which the scattered fields (and the interior fields in the case of a dielectric scatterer) are represented in an expansion in terms of free-space modal wave functions in cylindrical coordinates, the coefficients of which are the unknowns. The boundary conditions are satisfied using either an analytic continuation procedure, in which the far-field pattern (in Fourier series form) is continued into the near field and the boundary conditions are applied at the surface of the scatterer; or the completeness of the modal wave functions, to approximately represent the fields in the interior and exterior regions of the scatterer directly. The methods were applied to the scattering of two-dimensional cylindrical scatterers of arbitrary cross section and only the TM polarization of the excitation is considered. The solution for the coefficients of the modal wave functions are obtained by inversion of a matrix which depends only on the shape and material of the scatterer. The methods are illustrated using perfectly conducting square and elliptic cylinders and elliptic dielectric cylinders. A solution to the problem of multiple scattering by two conducting scatterers is also obtained using only the matrices characterizing each of the single scatterers. As an example, the method is illustrated by application to a two-body configuration.     

Mueller matrix elements that characterize scattering from coatedrandom rough surfaces

The Mueller matrix completely characterizes scattered electromagnetic waves. It relates the incident to the scattered Stokes vectors. The Mueller matrix, which contains intensity and relative phase data, is very useful for remote sensing. The Mueller matrix characterizing scattering from coated two-dimensional (2-D) random rough surfaces is obtained from full-wave solutions for the scattered fields considered in the companion paper. The general bistatic scattering case is considered in the analysis. However, for the numerical simulations presented here, the backscatter case is considered in particular, since backscatter is usually measured in remote sensing. The uniformly coated 2-D random rough surfaces are assumed here to be homogeneous and isotropic, with a Gaussian surface-height joint probability-density function. The diffuse incoherent and coherent contributions to the Mueller matrix elements are evaluated. The computer simulations of realistic models of relevant physical problems related to remote sensing of irregular stratified media can be used to determine the optimum modes of detection involving the selection of polarization, frequency, backscatter angle, and the specific Mueller matrix elements most sensitive to changes in medium parameters     

A Study of Backscattering and Emission from Closely Packed Inhomogeneous Media

The effects of close spacing between small scattering spheres were examined by keeping the distance-dependent terms in the expressions for the transverse scattered fields. The phase matrix was then derived from these fields and was used in the radiative transfer formulation to model scattering and emission from a densely populated, inhomogeneous layer. Computed results were compared with those obtained when the phase matrix was specialized to the far-field condition. It was found that the use of the far-zone condition tended to underestimate both the level of the copolarized backscattering and the cross-polarized backscattering. In emission computations, the use of the far-zone condition overestimated the level of the brightness temperature. hese effecit decreased with a decrease in the volume fraction or an increase in the exploring frequency, as expected. An improvement on the snow parameter (density and crystal size) estimation was shown to be possible when this new phase matrix was used.     

植被电磁散射中后向散射增强的研究

本文应用直接求散射体散射场的方法，运用Ｍｏｎｔｅ－Ｃａｒｌｏ模拟技术研究了植被电磁散射中由植被层的体散射和地面层的面散射相互作用引起的后向散射增强。计算得到了不同高度的植被层的散射特性，给出了人们感兴趣的后向增强角宽度的量级。结果表明，在植被层较矮即地面影响较强时后向散射增强较大，由体－面相互作用散射引起的后向散射增强的角宽度较宽，约在１０￣４０度之间。     

Multiple scattering and depolarization by a randomly rough Kirchhoff surface

A matrix approach has been developed to compute bistatic scattering coefficients which include shadowing and multiple scattering effects for a randomly rough Kirchhoff surface. The method permits the computation of these coefficients in terms of the existing single-scatter bistatic scattering coefficients. Thus the effects of multiple scattering are readily recognized from the expressions obtained. The bistatic scattering coefficients are shown to satisfy energy conservation to at least two significant figures. It is observed that while polarized backscattering is dominated by the single-scattering process, the depolarized backscattering is due to multiple scattering. Unlike depolarization by slightly rough surfaces or volume scattering, the angular behavior of the depolarized backscattering is similar to that of the polarized backscattering. The transitional behavior of the relative dominance between single and multiple scattering for the polarized and depolarized scattering coefficient as a function of the azimuth angle is illustrated.     

基于分形结构的植被高阶相干散射模型研究

电磁波低频入射情况下,植被中散射体独立不相关的假设无效,此时应考虑散射体之间的相干效应以及近场互作用。该文提出一种基于分形结构的植被高阶相干散射模型,该模型利用分形理论生成近乎真实植被的3维几何结构,根据每个散射体的空间位置信息考虑了相干效应,应用互易定理计算了相邻散射体间高阶互作用,结合非相干的分层模型中后向散射机制划分方式,给出了各项散射机制的表达式。与机载合成孔径雷达实验数据对比,验证了模型的准确性。在针叶林仿真参数下,分析了各项散射机制对总散射效应的贡献与入射频率、角度、植被结构的关系,结果表明,低频入射条件下,稀疏植被散射模型可进一步简化从而应用于参数反演中。     

Electromagnetic scattering from slightly rough surfaces withinhomogeneous dielectric profiles

Remote sensing of soil moisture using microwave sensors require accurate and realistic scattering models for rough soil surfaces. In the past, much effort has been devoted to the development of scattering models for either perfectly conducting or homogeneous rough surfaces. In practice, however, the permittivity of most soil surfaces is nonuniform, particularly in depth, for which analytical solution does not exist. The variations in the permittivity of a soil medium can easily be related to its soil moisture profile and soil type using the existing empirical models. In this paper, analytical expressions for the bistatic scattering coefficients of soil surfaces with slightly rough interface and stratified permittivity profile are derived. The scattering formulation is based on a new approach where the perturbation expansion of the volumetric polarization current instead of the tangential fields is used to obtain the scattered field. Basically, the top rough layer is replaced with an equivalent polarization current and, using the volumetric integral equation in conjunction with the dyadic Green's function of the remaining stratified half-space medium, the scattering problem is formulated. Closed-form analytical expressions for the induced polarization currents to any desired order are derived, which are then used to evaluate the bistatic scattered fields up to and including the third order. The analytical solutions for the scattered fields are used to derive the complete second-order expressions for the backscattering coefficients as well as the statistics of phase difference between the scattering matrix elements. The theoretical results are shown to agree well with the backscatter measurements of rough surfaces with known dielectric profiles and roughness statistics     

Synthetic imaging from coherent backscattering

Scattered fields from radar targets can be processed to construct target images. An analytical simulation of coherent backscattering and synthetic imaging is reviewed. Conducting objects with an axial symmetry are used as examples to demonstrate the results of analytical backscattering and synthesis procedure. An interrogating radar waveform is simulated using the Hamming weighting function. The pulse repetition frequency is selected so as to avoid slant-range image ambiguity. Backscatterings from axially symmetric targets are formulated by using the diffraction coefficients in the plane containing symmetry axis. Target-backscattered pulses are coherently processed along the aspect angles of interrogation. Coherent data are then synthesized using the Woodward method to construct target images. Four examples of synthesized images demonstrate that adequate shape and size estimates can be made even with partial backscatterings. The totally analytical simulations on scattering and imaging constitute an economical tool to visualize scattering mechanisms of complex targets and to more effectively utilize synthetic-imaging capability.