The generalized forward-backward method for analyzing the scattering from targets on ocean-like rough surfaces

The Forward-Backward (FB) method and its accelerated version (SA-FB, Spectral Accelerated Forward-Backward) were developed to compute the electromagnetic scattering from ocean-like rough surfaces. The FB algorithm provides very accurate scattering results and a very fast convergence, but its computational cost is still O(N2) per iteration, being N the number of unknowns used to discretize the surface. The Spectral Acceleration Algorithm proposed later reduces this cost to O(N). Nevertheless, the SA-FB can only be applied to quasi-planar structures or slightly rough surfaces (such as the sea surface), but it cannot be used to solve problems involving very undulating surfaces such as terrain profiles. In this paper the SA-FB method is modified to enhance its scope of application to considerable undulating surfaces. It will be seen that significant changes with respect to the original formulation as well as modifications of the integration path are necessary to get accurate results when dealing with terrain profiles. The proposed method is presented for vertical and horizontal polarizations and for PEC and non-PEC surfaces.

To analyze EM scattering of a dielectric Target above the dielectric Gauss rough surface, a fast Cross Coupling iterative Approach is present in this paper. This algorithm combines the merit of both the bi-conjugate gradient method (Bi-CG) and forward backward method (FBM). At first, the electric field integral equations (EFIE) of the induced currents on the rough surface and the target are derived. An iterative approach was developed to solve the two EFIEs and scattering from both the target and underlying surface. The EFIE of the rough surface and the target are solved by using FBM and bi-conjugate gradient method (Bi-CG), respectively. The mutual effect between the rough surface and the target are implemented by iterative Calculation. The results of EM scattering form a dielectric cylinder above the dielectric Gauss rough surface showed that CCIA was well agreement with MOM. The accuracy, efficiency, and convergence of the method are then studied for rough surfaces with various parameters. The effect of these parameters for the scattering pattern was also discussed.

A robust and accurate iterative algorithm is proposed for the solution of electromagnetic wave scattering from 1-D layered rough surfaces. The forward–backward method (FBM) has been applied extensively for solving electromagnetic scattering from single-layer rough surfaces due to its rapid convergence rate. Nevertheless, the performance of the FBM deteriorates, as it is applied to layered random rough surface problems. The proposed method greatly improves the convergence rate of the FBM by applying a residual minimization step. The computational cost of the minimization step and the forward–backward sweeps is expedited by using the spectral acceleration. In this communication, the proposed algorithm is applied as a solution to the problem of electromagnetic wave scattering from layered rough surfaces. Numerical results are presented to demonstrate the better convergence properties of the proposed method as compared with the standard FBM. In addition, the proposed method is shown to be more robust than the FBM, especially as the distance between interfaces decreases. The computational complexity of the proposed algorithm is also presented and discussed.

In this paper the forward-backward (FB) method is used to solve the problem of scattering on a very rough surface for practical application to radio planning and site optimization for mobile radio systems. Novel spectral acceleration was developed for this method to reduce its computational cost to O(N), but the original implementation cannot be applied to solve the scattering on very rough surfaces. In this paper the spectral acceleration for the FB method is adapted to apply it on the calculation of scattering on considerable undulating surfaces.

In this paper the convergence properties of the buffered block forward Backward (BBFB) method are investigated and shown to be independent of source position. The BBFB method is applied to the electric field integral equation (EFIE) for the case of a three-dimensional flat plate and wedge scatterer, at varying source locations. The convergence of the solution for the two problems, at each source location, is obtained and the corresponding iteration matrices for each scatterer computed. The numerical data provided in this paper illustrates and supports the conclusion that the source position does not affect the ability of the BBFB method to converge. Rather the convergence of the method is based on the geometry of the problem itself and the specific application of the BBFB algorithm to the problem.

The buffered block forward backward method is described and applied to the problem of scattering from dielectric cylinders. Numerical results suggest that the method converges in the case of scattering from bodies closed at infinity while it produces divergent results in the case of scattering from closed bodies.

In this paper, a fast Cross Coupling iterative Approach (CCIA) is proposed for studying the composite scattering of the layered rough surfaces with buried target, which uses forward backward method (FBM) to solve the electric field integral equations (EFIE) of the layered rough surface and bi-conjugate gradient method (BI-CG) to solve the EFIE of the target, and the interaction between the rough surface and the target is achieved by updating the excitation term. The algorithm is applied to calculate the composite scattering coefficients of the rough surface with a buried target, the results match with those of the traditional numerical algorithm MOM while the error can be reduced to 10−3 by 6 iterations, and the convergence speed and calculation accuracy meet the requirements. The composite scattering coefficients and Angular Correlation Function (ACF) amplitudes of layered rough surface and dielectric targets with different conditions are calculated, and the effects of various factors such as target size and burial depth on the composite scattering characteristics are discussed. It is found that the buried targets will have a great influence on the scattering characteristics, weakening or neglecting the coupling between them will lead to larger errors. Moreover, the results show that ACF can suppress scattering from rough surfaces well, making the scattering characteristics of the target more obvious, which is important for detecting underground targets.

A discrete‐Fourier‐transform (DFT) based forward‐backward (FB) algorithm has been developed for the fast and accurate analysis of electrically large freestanding dipole arrays [1]. In this paper, an extension of the FB method (FBM) with a DFT‐based acceleration approach is presented to provide a relatively efficient analysis of EM radiation/scattering from an electrically large, planar, periodic, finite dipole array printed on a grounded dielectric substrate. Computational complexity of this new approach is O(Ntot), where Ntot is the number of unknowns. Numerical results are presented to validate the efficiency and accuracy of the method. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 37: 20–26, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10813

A computationally efficient algorithm, which combines the characteristic basis function method (CBFM), the physical optics (PO) approach (when applicable) with the forward backward method (FBM), is applied for the investigation of electromagnetic scattering fromand propagation overlarge-scale rough terrain problems. The algorithm utilizes high-level basis functions defined on macro-domains (blocks), called the characteristic basis functions (CBFs) that are constructed by aggregating low-level basis functions (i.e., conventional sub-domain basis functions). The FBM as well as the PO approach (when applicable) are used to construct the aforementioned CBFs. The conventional CBFM is slightly modified to handle large-terrain problems, and is further embellished by accelerating it, as well as reducing its storage requirements, via the use of an extrapolation procedure. Numerical results for the total fields, as well as for the path loss are presented and compared with either measured or previously published reference solutions to assess the efficiency and accuracy of the algorithm.

Wide-band electromagnetic scattering from multiple objects shallowly buried beneath rough earth soil surfaces has been an important research topic in recent years because of its extensive applications in detecting the buried objects such as mines, pipes, and tunnels. Due to the advantages of finite-difference time-domain (FDTD) method in simulating wide-band electromagnetic scattering from rough surface in the presence of multiple objects, the FDTD method under Gaussian differential pulse wave incidence is utilized in the present study to analyze the frequency response of rough soil surfaces with shallowly buried objects, which serves as a basis for the detection and discrimination of objects buried below rough soil surfaces. The Topp equation model that can predict the dielectric constant of soil-water mixture is adopted in the present study to properly describe the dielectric property of earth soil with water. The actual rough land surface is modeled as the realization of a Gaussian random process with exponential spectrum by using Monte Carlo method. Simulation results show that the variation of composite scattering coefficient with frequency is oscillatory. It is also shown that the composite scattering coefficient versus frequency increases with the increase of root-mean-square of soil surface, water ratio of soil, the target section height, and the separation distance of target. However, simulation results indicate that the composite scattering coefficient versus frequency decreases with the increase of target section width. In summary, the variation of wide-band scattering coefficient is very complicated and is very sensitive to the incidence angle of electromagnetic wave. However, the wide-band scattering coefficient under Gaussian differential pulse wave incidence is less sensitive to the correlation length of rough soil surface, the depth of buried objects, and the dielectric constant of target. These qualitative results relating to the frequency response of rough soil surfaces in the presence of multiple objects are potentially valuable for detecting and discriminating the objects buried below rough soil surfaces by utilizing a wide-band ground penetrating radar system, although the present study is limited to one-dimensional rough soil surface due to the severe computational burden encountered in the large-scale Monte Carlo simulations. In addition, compared with frequency-domain numerical methods, the FDTD method has significant advantages in calculating wide-band composite scattering from rough surfaces in the presence of multiple objects, and thus has extensive applications in radar imaging simulation of multiple objects below or above rough surfaces, which goes beyond the scope of this paper.

In this paper, a novel formulation for scattering from one-dimensional (1D) rough surface problem has been presented. The formulation is based on the representation of the scattering field in spectral domain with an unknown spectral coefficient which is solved by applying Taylor series and Fourier Transforms techniques. It is also shown that forward–backward (FB) acceleration technique can be adapted to the spectral formulation to improve the effectiveness in a limited region of convergence. The obtained results are compared with the conventional method of moments (MoM) and the limitations of the formulation are analyzed in detail.

Based on the Propagation-Inside-Layer Expansion (PILE) and Forward-Backward method (FBM), the composite scattering from the target below a dielectric rough soil surface using the extended PILE (EPILE) combined with the Forward-Backward method (FBM) is studied. The accuracy and e-ciency of the EPILE + FBM for this speciflc type of composite scattering is researched by comparing with the method of moments (MOM), the in∞uences of the target size, target depth, target horizontal distance, the rms height, the correlation length, the incident angle and the soil moisture content, etc., to the bistatic scattering coe-cient (BSC) are also investigated.

As robotic technologies advance and robots move out of factories and labs into the real world, grip on a variety of surfaces (e.g. smooth or rough) in a variety of conditions (e.g. dry or wet) becomes increasingly important. Bioinspired "microspines" have been previously explored, but primarily for vertical climbing applications or for small-scale robots applying low forces (less than 1 N). Further, these works primarily focused on rough surfaces. To advance this area of research, we present a composite material comprising high- friction rubber and compliant nitinol microspines which can passively retract below the surface of the rubber. We show that the composite can support large loads (greater than 75 N) with a high coefficient of friction on both smooth and rough surfaces (p > 1.1), outperforming microspines alone on smooth surfaces and rubber alone on rough surfaces, especially when wet and oily. Further, due to the retraction of the microspines, the composite does not damage relatively soft, smooth surfaces, like wood flooring. We also test durability, and show that it is improved by microspine compliance, and test the effects of varying microspine diameter, angle, and tip shape. Finally, we demonstrate that a small RC car can climb steeper slopes and stop more quickly in wet conditions with microspines.

Different types of plant leaves exhibit a broad spectrum of wetting behaviour because of their different pubescence, wax layer, scales, veins, etc. The wetting tension is used to express the wetting of a leaf with βsf = σf. cos θ (σf = the surface tension of a liquid and θ= the contact angle of a liquid to the surface of a leaf). Three different methods are used for measuring contact angles: the contact angle goniometer method, the meniscus rise method and the Wilhelmy plate method. All three methods are based on completely independent theories and produce absolutely uniform contact angles on smooth paraffin surfaces. Closed cup systems which could be thermostatted were used for making the measurements. Substantial differences in the contact angles become apparent when contact angle measurements on roughened and smooth firm surfaces are compared, as for example contact angles on smooth and roughened paraffin surfaces. If the figures for the contact angles on a smooth surface are 90° or > 90°, they will be bigger on a roughened surface; if they are <90° on a smooth surface, they will be smaller on a roughened surface. These results obtained with paraffin were confirmed by contact angle measurements made on plant leaves. The contact angles, measured on plant leaves with the help of the three different measuring methods, show a high degree of uniformity.

The apparent temperatures of smooth and rough terrain surfaces are calculated for frequencies between 1 and 75 kMc, for angles of incidence between <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5\deg</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">80\deg</tex> , and for observation altitudes between 2 km and 32 km. The attenuation and thermal radiation caused by the atmosphere are accounted for by an experimental model atmosphere, and the surface emissivities are based on measured complex dielectric constants (for the smooth surfaces) and measured radar return (for the rough surfaces). It is found that perpendicular polarization provides the greatest temperature contrast between rough and smooth surfaces, and that the contrast decreases as the altitude of observation increases; at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f=75</tex> kMc (approximately the resonant frequency of the oxygen molecule), there is likely to be little, if any, contrast between rough and smooth surfaces.