Iterative Extended Boundary Condition Method Research Articles

Coherent Microwave Scattering Model of Marsh Grass

AbstractIn this work, we developed an electromagnetic scattering model to analyze radar scattering from tall‐grass‐covered lands such as wetlands and marshes. The model adopts the generalized iterative extended boundary condition method (GIEBCM) algorithm, previously developed for buried cylindrical media such as vegetation roots, to simulate the scattering from the grass layer. The major challenge of applying GIEBCM to tall grass is the extremely time‐consuming iteration among the large number of short subcylinders building up the grass. To overcome this issue, we extended the GIEBCM to multilevel GIEBCM, or M‐GIEBCM, in which we first use GIEBCM to calculate a T matrix (transition matrix) database of “straws” with various lengths, thicknesses, orientations, curvatures, and dielectric properties; we then construct the grass with a group of straws from the database and apply GIEBCM again to calculate the T matrix of the overall grass scene. The grass T matrix is transferred to S matrix (scattering matrix) and combined with the ground S matrix, which is computed using the stabilized extended boundary condition method, to obtain the total scattering. In this article, we will demonstrate the capability of the model by simulating scattering from scenes with different grass densities, different grass structures, different grass water contents, and different ground moisture contents. This model will help with radar experiment design and image interpretation for marshland and wetland observations.

Full-Wave Electromagnetic Scattering From Rough Surfaces With Buried Inhomogeneities

We develop a methodology for modeling coherent electromagnetic scattering from rough surfaces with buried inhomogeneities in three dimensions. The inhomogeneities considered in this paper include random spherical media, random cylindrical media, and root-like cylindrical clusters. They are used to simulate rocks, ice particles, and vegetation roots buried beneath the ground surface that can be seen by the low-frequency radars in Earth remote sensing applications. The approach we develop first calculates volumetric scattering from the media using coherent approaches, including both the conventional recursive transition matrix (T-matrix) method as well as a new generalized iterative extended boundary condition method we developed for tilted finite cylinders, and then transforms the T-matrix to the scattering matrix, which is then used to form the full scattered field of layered structures with rough surface and subsurfaces. We validate the methodology by comparing with other numerical solutions for special cases, and show sensitivity results for scattering from rough surface with buried random spherical media and random cylindrical media of different densities. We also construct a basic root model and calculate the scattering cross sections from single and multiple root clusters with or without a subsurface interface underneath. With the approach developed in this paper, we are able to study the sensitivity of radar signals to subsurface scatterers. For example, our simulations show that, depending on their density and water content, buried roots could enhance the backscatter from a single rough surface by as much as 5 dB in co-pol components, and substantially more in cross-pol components. The results of this model are expected to enable more accurate geophysical retrievals of soil moisture as well as soil organic content.

Optical scattering and absorption by branched chains of aerosols

We utilize the Volume Integral Equation Formulation (VIEF) and the method of moments to calculate the electromagnetic scattering and absorption of aerosol particles with branched-chain structures. Two kinds of polarization of the incident electromagnetic wave were considered: the cross- and end-fire polarizations. The numerical results of internal electric field distribution, absorbed power, and extinction and scattering cross sections, obtained from the VIEF, show excellent agreement with the Mie theory for the special case of spherical particles. Comparison between the results of the VIEF and Iterative Extended Boundary Condition Method for very long oriented (elongated) chains of particles also showed good agreement. After validating the accuracy of the VIEF, the absorption characteristics of three branched-chain structuressimulated from microscopic pictures of coagulated smoke aerosol particles were calculated. Results showed that the ratio of absorption in the two polarization cases, P(cross-fire)/P(end-fire), for very long oriented chain structures is as high as a factor of 4 at lower frequencies (lambda =10microm). While in the higher frequency (lambda = 0.5-microm) case, the ratio Of P(cross-fire)/P(end-fire) is reduced to 2.0. For branched-chain structures, the ratio Of P(cross-fire)/P(end-fire) decreased with the increase in the number of the side branches. These observations show that the frequency, polarization, and structure factors play important roles in determining the optical characteristics of branched chains of aerosol particles.

A new sectioning procedure for calculating scattering and absorption by elongated dielectric objects

The iterative extended boundary condition method (IEBCM) has recently been developed to calculate scattering and absorption by elongated dielectric objects. The authors present a new sectioning procedure to improve the computational efficiency of the IEBCM. In this technique, the total geometry of the object is divided into overlapping sections, each of which includes only 3-5 spherical expansions to describe the internal fields. The total number of expansions required to describe the internal fields in the overall object may be as large as 15. Results illustrating the improvement in the computational efficiency of the IEBCM, as well as the dependence of the minimum number of expansions that should be included in each section on the dielectric properties of the scatter and on the frequency, are presented. It is shown that the sectioning procedure is particularly useful at frequencies below (ka >

Scattering and Absorption by Elongated Aerosol Particles

Recently we developed a new technique, the iterative extended boundary condition method, which is suitable for calculating the scattering and absorption by elongated particles in a broad frequency range, including at resonance. This paper briefly describes this technique, illustrates its capabilities, and presents the results of its most recent extensions. This includes the implementation of a sectioning procedure and the use of a new segmentation method for calculating scattering by very long oriented chains of aerosols. Results of absorption cross sections in two different frequency ranges, visible and infrared, and for two different polarizations, parallel and end-fire polarizations, will be presented. The range of validity of some reported relationships between scattering from a single particle and from coagulated particles are discussed. It is shown that in the end-fire polarization case the sum of the absorption by separate n particles (P sum) is more than the absorption by a chain of n coagulated p...

Near-Field Absorption Characteristics of Biological Models in the Resonance Frequency Range (Short Paper)

In this paper, we utilized the new iterative extended boundary condition method (IEBCM) to calculate the near-field absorption characteristics of a spheroidal model of man in the resonance frequency range. These calculations complement our previous near-field results in the preresonance frequency range. Calculations were made for simple sources such as an electric dipole and a small current loop antenna. The near fields of these sources are known exactly and hence helped in explaining the absorption results in terms of the field components of the incident radiation. Numerical results for the normalized average SAR values are presented as a function of frequency for different near-field separation distances from the sources. It is generally observed that while the far-field results converge to the plane wave values, different near-field absorption characteristics occur for the two different sources. It was possible in both cases to explain the differences in the near-field average SAR values in terms of the incident near fields from the sources.

Optical scattering by metallic and carbon aerosols of high aspect ratio

The iterative extended boundary condition method (IEBCM) is utilized to calculate scattering and absorption by metallic colloids and carbon aerosols in the 0.4-μm < λ < 10-μm optical wavelength range. The colloids and aerosols were modeled by dielectric spheroids of high aspect ratio. The new IEBCM method is found to be suitable for making calculations for particles with aspect ratios as high as 12. Results are presented for silver and aluminum metallic aerosols as well as for atmospheric aerosols such as soot and iron oxides (magnetite). The various parameters used to examine the convergence of the IEBCM solution, such as the number of subdomain expansions and the size of the incremental change in intermediate object sizes used in the iterative process, are discussed. Using the internal field distribution to test the convergence of the results is also found to be more accurate than the traditional procedure which utilizes extinction and scattering cross-section data.

Accuracy of Block Models for Evaluation of the Deposition of Energy by Electromagnetic Fields

Numerical solutions were made for block models using as many as 3048 cubes to approximate a prolate spheroidal model of man at 100 and 225 MHz. A high-frequency modification of Hohmann's formulation (HFH) gave values of mean absorption within five to seven percent of those with the Iterative Extended Boundary Condition Method (IEBCM). Arrangement of the cells for a best-fit approximation of the spheroid is essential for such high accuracy. Numerical quadratures using the cubical shape of the cells verified the high accuracy of the closed-form expressions used for HFH matrix elements. Quadrature over spheres having the same volume as the cells gave inaccurate values for the matrix elements. Values of average absorption calculated with 296, 560, 1376, and 1944 cell models of the prolate spheroidal model of man differed from each other by no more than 17 percent at frequencies of 10 to 400 MHz, and by 5.0 percent at the resonant frequency of 75 MHz.

Scattering by lossy dielectric nonspherical objects with nonvanishing magnetic susceptibility

Using the recently formulated iterative extended boundary condition method (IEBCM) it is shown that the absorption mechanisms in a lossy dielectric object are enhanced by the presence of a nonvanishing magnetic susceptibility. In addition, there is a corresponding reduction in the backscattering cross section. The conditional convergence of the IEBCM algorithm is also proved.

Iterative extended boundary condition method for scattering by objects of high aspect ratios

The limitations of the T-matrix procedure or the extended boundary condition method (EBCM) for wave scattering problems, when used for long slender objects, are due to the shrinking volume over which the incident field is extinguished. The resulting ill-conditioning of the matrices involved makes it impossible to invert them. For nondissipative objects only, we observe that the Reinforced Modified Gram–Schmidt (RMGS) orthogonalization procedure works best of all such unitary approaches investigated, but information about the surface and the internal fields is lost in the process. An alternate approach, called the iterative EBCM (IEBCM) is more general in its scope since it provides convergent surface and internal field values and can also work for dissipative targets. This success of the IEBCM results because it extends the interior volume over which the incident field is extinguished.

Extension of the iterative EBCM to calculate scattering by low-loss or lossless elongated dielectric objects

The newly developed iterative extended boundary condition method (IEBCM) is extended to calculate the scattering by low-loss or lossless elongated dielectric objects. Specifically the iterative procedure is modified so as to utilize an initial assumption of the surface fields obtained from the Mie solution of a spherical object of the same dielectric properties. The solution for the elongated object is obtained by iteratively utilizing the regular EBCM technique to solve for objects of intermediate geometries between the substitute sphere and the object of interest. The other feature of the IEBCM which is related to subdividing the internal volume of the object into several overlapping subregions in each of which a separate field expansion is used is also utilized in the present extension. Results illustrating the adequacy of the IEBCM procedure to calculate the scattering by spheroids of an aspect ratio of more than 7:1 are presented.

Theoretical and Experimental Evaluation of Power Absorption in Elongated Biological Objects at and Beyond Resonance

The recently developed iterative extended boundary condition method (IEBCM) is used to calculate the average specific absorption rates (SAR's) in biological models of an average man and a sitting rhesus monkey at and beyond their resonance frequencies. The average SAR's for these objects are also experimentally determined in scaled saline phantoms. Close agreement thus found between the calculated and the measured SAR values validates the postresonance absorption calculations made using the novel IEBCM. Also, in order to check the adequacy of using the mixed basis functions in the IEBCM procedure, the SAR in a capped cylindrical model of an average man is calculated and the result verified experimentally. It is, therefore, concluded that to achieve an improved computational efficiency in the IEBCM, the choice of the basis functions for a particular lar subregion should be based on the geometry of that subregion.

An Iterative Extended Boundary Condition Method for Solving the Absorption Characteristics of Lossy Dielectric Objects of Large Aspect Ratios

The recently developed iterative extended boundary condition method (IEBCM) has been used to compute the internal fields induced in homogeneous, axisymmetric, lossy dielectric objects of large aspect ratios when exposed to incident planewave radiation. Calculations were made for both the E- and k-polarization cases. The computed results for a prolate spheroidal model of an average man are found to be accurate for frequencies up to 300 MHz, while the use of the popular EBCM [1] was found to be essentially restricted to frequencies less than 70 MHz for these models and exposure conditions. The applicability of the IEBCM to composite bodies has also been examined by studying the irradiation of a capped cylindrical object. This composite object was first partitioned into several overlapping spherical subregions, and, alternatively, into two spherical subregions overlapping with a central cylindrical subregion. Spherical harmonics were used to represent the internal fields in the spherical subregions, while cylindrical expansions were utilized in the cylindrical subregions. It is shown that the second partitioning scheme is more computationally efficient and thereby suggests that the basis functions used to represent the subregional fields should be compatible with the subregional geometry. The new IEBCM, therefore, is a very valuable procedure which provides the opportunity of using the mixed basis functions in the solution.

A new procedure for improving the solution stability and extending the frequency range of the EBCM

The extended boundary condition method (EBCM) has been frequently used to obtain the absorption and scattering characteristics of axisymmetric dielectric objects. For applications involving relatively high-loss dielectric objects, however, the method was usable only at frequencies below resonance. In this paper a new procedure for improving the stability and extending the frequency range of the EBCM is presented. This new procedure has two main features: 1) it is iterative, since it starts with a known solution that approximates the scattering problem, and 2) it involves separate field expansions in each of the overlapping subregions which describe the total interior volume of the object. For example, for high-loss dielectric objects, such as the biological models of humans and animals, the first step in the procedure is to replace the lossy dielectric object with a perfectly conducting one of the same shape and solving the scattering problem to determine the current density on the surface of the conductor. This surface current is then used to calculate the induced field expansions inside the dielectric object. It is shown that the numerical stability of the solution is further improved by dividing the interior region of the object into overlapping subregions, in each of which a separate field expansion is assumed. The electric and magnetic surface currents so obtained from the solution of the internal problem are then used to improve the initial estimate of the current density on the surface of the object. The iterative procedure continues until convergent values of the surface currents and the fields are obtained. Numerical results illustrating the improved stability of the iterative EBCM (IEBCM) solution at higher frequencies as well as its accuracy in calculating the absorption characteristics of a spheroidal model of man in the resonance and the postresonance frequency range are presented.

A new iterative procedure to solve for scattering and absorption by dielectric objects

We have devised a new iterative technique to improve the Extended Boundary Condition Method (EBCM) frequently used to solve for the scattering and absorption by lossy dielectric objects. This technique has two main features: 1) it requires an initial assumption of the external surface fields, and 2) it partitions the interior of the object into a number of overlapping subregions, thus assuring a more efficient numerical convergence. Preliminary results indicating the enhanced stability of the new iterative EBCM technique are presented.