Wenzhe Yan

EM Scattering from a Long Dielectric Circular Cylinder

A new iterative technique based on the T -matrix approach is proposed for the electromagnetic scattering by dielectric cylinders, in particular cylinders with large aspect ratios. For such cases the conventional T -matrix approach fails. We use hypothetic surfaces to divide a cylinder into a cluster of N identical sub-cylinder, for each the T matrix can be directly calculated. Since any two neighboring sub- cylinder are touching via the division interface, the conventional multi- scatterer equation method is not directly applicable. The coupling among sub-cylinder and boundary conditions at the interfaces are taken care of in our approach. The validity of the proposed method is demonstrated through agreement between theoretical predictions and numerical simulations as well as measurements for scattering from dielectric circular cylinders with finite length. The results clearly demonstrate that the new iterative technique can extend regular T - matrix approach to solve cylindrical cases with large aspect ratio.

Electromagnetic Scattering from a Corn Canopy at L and C Bands

The ability to retrieve and monitor soil moisture and vegetation water content (VWC) is of great importance. Yet accurate retrieval of such information from microwave observations presents a big challenge, which calls for the development of high fidelity scattering models. In the literature, a ”discrete scatter” approach was usually deployed, which attempted to determine first the scattering behavior of the individual constituent of the canopy, then that of canopy as a whole by summing up either incoherently [1] [?] or coherently [2]–[3]. To simplify the problem, constituents of the canopy are modeled as canonical geometrical objects. For corn canopy, the stalks are modeled as dielectric circular cylinders with finite length, and the leaves are represented as thin dielectric disks with elliptic cross section. Since scattering from each of the canonical object serves as the base for further ”assembling”, it is expected to be accurately determined. However, mush is still desired in this regard. For a dielectric cylinder of finite length, in studying its scattering behavior the generalized Rayleigh-Gans approximation (GRGA) [4] is usually applied, which approximates the induced current in a finite cylinder by assuming infinite length. This method is valid for a needle shaped scatterer with radius much smaller than the wavelength. Yet caution must be taken even at L band when EM scattering from the stalk of a corn plant is to be evaluated using GRGA. It is also well known that GRGA fails to satisfy the reciprocity theorem [2]. In the evaluation of scattering amplitude of leaves, the GRGA method is usually used. However, caution must be taken here. At C band the wavelength is 5.6 cm, which is comparable to the length of minor axis of corn leaves, which presents an unfavorable condition in applying GRGA and thus appreciable error is expected in the predicted scattering amplitude. When corn canopy is at its early stage of growth, or when the incidence angle is not large, contribution from the underlying ground is appreciable and thus its accurate prediction is important. Yet this roughness effect has not been adequately addressed in canopy scattering models, where what is typically applied is conventional analytical method such as Kirchhoff approximation (KA), or the small perturbation method (SPM) [5], or the more advanced yet still improvement-needed integral equation method (IEM) [6]. In this study, we choose to apply a more rigorous treatment of the rough surface contribution using the recently advanced EAIEM model by the authors [7]. With the advancement of several scattering models of dielectric cylinder and disks and of rough surfaces, it is the aim of this paper to investigate if a coherent combination of these constituent models can improve predictive power of the resultant canopy scattering model. To be more specific, in analyzing electromagnetic scattering from a dielectric cylinder of finite length, we use the new approach that we have recently proposed [8], where a long cylinder is divided into a cluster of N identical sub-cylinder by using N — 1 hypothetic surfaces, for each the T matrix can be calculated stably in the numerical sense. The boundary conditions at the hypothetic interface are treated carefully. A system of equations is set up for each sub-cylinder, and the overall system of equations is coupled and linear, thus can be solved by appropriate iterative method. Moreover, the VPM method is found to be applicable to dielectric cylindersof arbitrary length as long as the T matrix is attainable for the elementary sub-cylinder. The applicable relative dielectric constant can go up to 70 (real part), which is normally the upper bound for corn stalks at C band. The radius of the cylinder can be as high as 5 wavelengths, a feature of the model that is expected to be useful for forest applications [9]. Scattering from rough surface is treated using the EAIEM model [7], which is a unifing model recently developed by us for electromagnetic scattering from a Gaussian rough surface with small to moderate heights. It is based on the integral equation formulation where the spectral representations of the Greens function and its gradient are in complete forms, a general approach similar to those used in the advanced integral equation model (AIEM) [10]. Yet this new model can be regarded as an extension to these two models on two accounts: first it has made fewer and less restrictive assumptions in evaluating the complementary scattering coefficient for single scattering, and second it contains a more rigorous analysis by the inclusion of the error function related terms for the cross — and complementary scattering coefficients, which stems from the absolute phase term in the spectral representation of the Greens function. The proposed coherent scattering model will be validated at both L and C bands. At C band we acquired some RADARSAT-2 data of several test fields of corn canopy in Jiangsu province, China, in 2009, and carried out simultaneous measurement campaigns to collect the in situ ground truth. At L band high quality AIRSAR measurement data are available along with detailed ground truth in the literature [1] and will be used in the current work.

EM scattering from multiple cylinders

In this paper we propose to extend the recently proposed iterative technique with extension to the T-matrix approach to the problem of electromagnetic scattering from a cluster of parallel dielectric circular cylinders. The overall treatment is separated into two stages: at the first stage, scattering from a single cylinder is obtained as the first-order solution; and at the second stage, a recursive process that accounts for multiple scattering, where the scattered field from one cylinder is considered as the illuminating wave for the other cylinder and vice verse, is formed. The procedure is found to converge very fast except for the case when any pair of cylinders is very close to each other. It should be noted that since no approximation is introduced in the procedure, this approach is thus more rigorous. Moreover, the formalism is general and can be readily applied to cylinders with cross section other than circular so long as the T matrix of each sub-cylinder can be accurately obtained. The validity of the proposed method has been verified by good agreement between model results and numerical simulations.

A Two-scale Model for Composite Rough Surface Scattering

A new two-scale model is proposed for wave scattering from a composite surface. For each single scale surface roughness, we use a weighted sum of the newly developed statistical integral equation model and the second-order small slope approximation. With these two unifying models collaborating at each scale, this proposed compound model may capture the actual scattering mechanisms and lead to more accurate predictions. It holds the potential to bridge the gap between the regions of validity of the Kirchhoff approximation and the small perturbation model.The chosen simulation parameters suggest that the new two-scale model holds the potential to expand the validity regions of both its large scale and small scale components. The new model may have promising applications for electromagnetic scattering from the ocean surface, whose entire roughness spectrum can be discomposed into smalland large-scale components. DOI: 10.2529/PIERS061113040537 For electromagnetic scattering from a composite rough surface, different forms of two-scale model (TSM) are usually employed [1, 2]. The surface perturbation is typically divided into the large scale part and the small scale one, which are treated by using different analytical models in these TSM models. To calculate the scattering coefficient, in [1], the Kirchhoff approximation (KA) was used for the large scale and the small perturbation method (SPM) for the small scale, while in [2], the SPM was replaced by the first-order small slope approximation (SSA1) for the small scale calculation, leaving KA representation for the large scale untouched. However, the existence of a gap between the valid regions of the KA and the SPM models may render TSM modles of such combination inaccurate for configurations that are beyond the aforementioned valid regions. Meanwhile, in the literature, some researchers introduced a scaledividing parameter to distinguish large and small scales in the surface spectrum. Values of the cut-off were often chosen in an ad hoc manner. On the other hand, both the second order SSA (SSA2) [3] and the recently developed statistical integral equation model (SIEM) [4] hold the potential to bridge the gap between the valid regions of the KA and SPM models, with varying degree of success. This observation motivates the study in which we use the weighted sum of the SIEM and SSA2 for the single scale computation for our new TSM. We shall briefly review these two models, and then present the new compound model. Finally some numerical simulations will also be provided. Unlike the conventional integral equation model (IEM) and its various variations, the SIEM treats the local coordinates and related field terms statistically over the orientation distribution of the surface unit normal vector, which is characterized by joint probability distribution function. Furthermore, it incorporates rigorously the shadow function in the field calculation. The scattering coefficient of the SIEM model is σ qp = σ 0 qp1 − σ qp2 + σ qp3 (1)

Microwave scattering model for a corn canopy

Extraction of vegetation water content and soil moisture from microwave observations requires development of a high fidelity scattering model. A number of factors associated with the vegetation canopy and with the underlying bare soil should be taken into account. In this paper, we propose an electromagnetic scattering model for a corn canopy which includes the coherent effect due to the corn structure and takes advantage of recently advanced scattering models for dielectric cylinder of finite length and for rough surface.

EM Scattering from a Dielectric Circular Clinder of Finite Length

A new iterative technique based on the T-matrix approach for the electromagnetic scattering by dielectric cylindrical objects is proposed and the boundary conditions are also carefully treated in this paper. The validity of the proposed method is demonstrated through agreement between theoretical predictions and numerical simulations as well as measurements for scattering from circular cylinders with finite length. The results clearly demonstrate that the new iterative technique can extend regular T-matrix approach to solve rod cases with large aspect ratio.

A Two-Scale Model for Composite Rough Surface Bistatic Scattering

A new two-scale model is proposed for bistatic scattering from a composite surface. For the large scale surface roughness, we use the newly developed statistical integral equation model; for the small scale surface roughness, we adopt the second-order small slope approximation. It holds the potential to bridge the gap between the regions of validity of the Kirchhoff approximation and the small perturbation model. Keywords-two scale model; statistical integral equation mode;, small slope approximation; bistatic scattering