Electromagnetic Scattering

The following sections are included:

• PREFACE
• CONTENTS

This chapter deals with the modeling of bistatic scattering from a randomly rough surface. In particular, an advanced integral equation model (AIEM) is presented by giving its general framework of model developments, model expressions, and predictions of bistatic scattering under various surface conditions. Extension work to improve the model accuracy is also reported in more detail. Model performance is illustrated, demonstrated, and validated by extensive comparisons with numerical simulations and measurements. The updated AIEM remains a compact algebraic form for single scattering and substantially improves prediction accuracy in bistatic scattering that is attracting more applications in earth remote sensing.

This chapter mainly describes a framework for the simulations and analysis of electromagnetic (EM) characteristics of a maritime scene with a target, including its radar returns and Doppler spectra, which plays an important role in the field of ocean remote sensing, ocean early warning, and the detection and recognition of marine targets. First, for the scattering of sea surface, we propose the facet-based asymptotical model (FBAM) to give the scattering field, which includes both amplitude and phase information. So it could facilitate the postprocessing computation of the composite scene. From the good agreement between the mean levels normalized radar cross section (NRCS) calculated by FBAM and the first-order small-slope approximation (SSA), FBAM shows higher accuracy results and computing efficiency. In addition, the simulations of Doppler spectra from time-evolving sea surface under different marine conditions also prove that FBAM is superior to some available models. To further analyze the time-evolving scattering characteristics and Doppler spectra of the dynamic composite scene, the motion of the ship in six degrees of freedom in two-dimensional (2-D) sea surface is investigated to get the attitude change of the ship at any time instant. Together with the specular reflection weighted four-path model (SRWFPM) used to calculate the multiple scattering between the object and the sea surface, the total coupling field can be easily obtained by summing up all weighted contributions. All the numerical results show good tractability of the total simulation scheme for the dynamic composite ship–ocean scene, and the proposed simulation scheme in this work could enable us to provide a preliminary prediction on the radar cross section (RCS) mean levels for the electrically large object–sea model.

The finite element method (FEM) can easily be used to analyze complex dielectric problems because of its powerful ability to model inhomogeneous materials that may be difficult to solve by the classical boundary integral method (BIM) [1]. In traditional applications of FEM, approximate absorbing boundaries, such as ABC [2, 3] and PML [4, 5], were usually adopted to truncate the infinite domain when electromagnetic scattering problems were discussed with FEM. To maintain their precisions, approximate absorbing boundaries must often be set sufficiently far from the model surface. However, these boundaries suffer from a large number of unknowns and require vast computational memory, especially for the scattering problem of a large model. The FEM combined with the BIM [6–9] has recently been paid increased attention to its application in electromagnetic scattering problems. As the most accurate boundary, the application of the truncated boundary obtained by BIM in FEM can not only deal with the complex model easier than BIM, but also maintain high precision and be set near the model surface to reduce the computation region.

Electromagnetic (EM) scattering by penetrable objects represents an important category of scattering problems because such objects are popular in nature and they exist in many applications such as remote sensing, medical imaging, geophysical exploration, and so on. To understand the involved interacting mechanism of EM wave with the penetrable objects, it is essential to efficiently solve the governing equations describing the problem and accurately quantifying the parameters reflecting their characteristics. Though many numerical methods such as finite-difference time-domain (FDTD) and finite element method (FEM) can be used to solve the problem, we adopt the integral equation method (IEM) to develop volume integral equation (VIE) solvers for the problem. The IEM possesses several advantages compared with the differential equation method (DEM), which the FDTD and FEM belong to, including the smaller solution domain and removal of absorbing boundary condition (ABC), therefore they have received extensive studies and applications. In this chapter, we first present the VIEs to describe the scattering problem by penetrable objects and then introduce two primary numerical methods to solve them, that is, the method of moments (MoM) and the Nyström method. We show their basic principle and numerical implementation and then demonstrate their effectiveness by typical numerical examples.

In the areas of remote sensing, antenna, and microwave engineering, numerical modeling of electromagnetic scattering by single body of revolution (BoR) or multiple BoRs have received lots of attention. Because of the advantage of high accuracy, integral equation method (IEM) is often used in solving BoR problems. For single BoR, the 3-D problem can be reduced to 2.5-D problem by using of the modal Green’s function and BoR basis functions. This property leads to a great reduction of unknowns compared with traditional local basis function methods which that not consider the rotational symmetry of BoRs [1–5]. Unfortunately, it is difficult to extend the BoR basis functions to multiple BoRs, thus seeking some fast algorithms is inevitable. In this chapter, numerical solution of single/multiple BoRs by IEM and fast algorithms are introduced. The content include two parts: method of moment (MOM) for single BoR (BoR–MoM) is introduced in the first part, followed by two fast solvers for multiple BoRs in the second part, which are, respectively, fast direct solver based on characteristic basis functions method and fast iterative solver based on domain decomposition. Some useful investigation and discussions are also given.

The following sections are included:

• Introduction
• Finite Cylinder
• Thin Dielectric Disk
• References

The electromagnetic scattering by canonical physical objects is important in many applications. For the case of dielectric cylinder with finite length, an exact analytical solution is still elusive. The conventional T-matrix approach may fail for scatterers with extreme geometry, for instance, cylinders with large aspect ratios. To deal with such difficulty, recently we proposed a method based on an extension of the T-matrix approach, where a long cylinder is hypothetically divided into a cluster of identical subcylinders, for each the T-matrix can be numerically stably calculated. Special care was paid to fulfill the boundary conditions at the hypothetic surface of any two neighboring subcylinders. The resultant-coupled equations are different from that of multiscatterer theory. The model results were in good agreement with experiment data available in the literature. When compared to the results of a method of moments (MoM) code, the proposed method was found to be applicable to dielectric cylinders of arbitrary length as long as the T-matrix is attainable for the elementary subcylinder. The conditions for the T-matrix to be numerically stably calculated in terms of the equivalent volumetric radius and relative dielectric constant were also empirically obtained.

In this chapter, we discuss wave scattering in dense inhomogenous media, when the mean distance between discrete scatterers embedded in the medium is smaller than the wavelength. We describe a scattering model based on the iterative solutions to the equations of radiative transfer. This model incorporates the dense medium phase and amplitude correction theory (DM-PACT) to account for coherent effects between scatterers, along with Fresnel field amplitude and phase corrections, in the development of the phase matrices of the scatterers. We describe applications of this dense medium model in the remote sensing of sea ice and snow, as well as for vegetation canopies, that is, boreal forests, rice fields, and oil palm plantations. We demonstrate how the model can be used for retrieving sea ice thickness from remote sensing images through inversion algorithms. We also demonstrate how including the dense medium considerations improve estimates of the backscattering coefficient of vegetation in comparison to other models.

Feature extraction is the key step for target detection and target classification. Kennaugh studied the optimal polarization states for a given target scattering matrix. This can be regarded as one kind of target features. Huynen studied radar polarimetry for a long time and proposed a set of parameters for describing target surface features and geometric features based on the Mueller matrix with zero orientation angle. However, this set of parameters cannot be used for describing a complex target. Later, some researchers tried to decompose a target into several components. Up to now, many decomposition approaches have been proposed. From target decomposition, we can obtain many target features. In this chapter, we make an overview of feature extraction of a target. The objective of target decomposition is to extract physical information of scatterers from the observed microwaves backscattered from surface and volume structures. The polarimetric synthetic aperture radar (SAR) data can be expressed as a sum of independent elements such that different physical scattering mechanisms of targets can be interpreted. On the view point of representation of polarimetric SAR data, there are mainly two types of decomposition theorems: those based on the scattering matrix which represents a single scattering mechanism and those based on the second-order statistical observable which describes the average polarimetric scattering behavior of natural targets. In this chapter, first we present important polarimetric descriptors, and then we introduce target decomposition theorems.

The following section is included:

• INDEX