Novel Iterative Algorithm for the Solution of Electromagnetic Scattering From Layered Random Rough Surfaces

In this paper we propose an efficient and accurate iterative numerical approach to analyze EM scattering from 1-D dielectric rough surfaces. It is based on a new splitting of the impedance matrix Z to improve the asymptotic convergence rate of the resultant iterative system. The structure of split matrix is then fully explored, in combination with the application of an identity for inverse of block matrix, to further reduce the computational and storage complexity. The embedded matrix-vector product is computed using the spectral acceleration technique. Extensive numerical simulations demonstrate a couple of appealing features of this proposed method for Gaussian surface with Gaussian spectrum: (1) It converges faster than both forward-backward method (FBM) and FBM with spectral acceleration (FBM-SA); (2) For HH polarization, the proposed method is about twice as fast as FBM-SA. For VV polarization, the proposed method is better when the rms slope is not larger than 16° or interestingly when rms height is beyond 2.0 wavelengths. Moreover, it converges for cases where FBM-SA fails for both polarizations. These features indicate that the proposed method can be effectively used to analyze EM scattering from 1-D dielectric Gaussian surface with Gaussian spectrum.

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.

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.

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.

The iterative forward backward (FB) method has been proposed to solve the magnetic field integral equation for smooth one-dimensional rough surfaces. This method has proved to be very efficient, converging in a very small number of iterations. Nevertheless, this solution becomes unstable when some obstacle, like a ship or a large breaking wave, is included in the original problem. In this paper we propose a new extension of the FB method: the generalized forward backward (GFB) method, to solve such kinds of composite problems.

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.

Basing on the exact spectral formalism, using the composite method that combines the numerical and approximate algorithms, the reconstruction problem for the rough surface is investigated. For the direct problem, the scattering data is obtained by the numerical algorithm-the method of moments (MOM), the Banded-Matrix-Iterative-Approach/Canonical Grid method (BMIA/CAG), and the forward-backward iterative method (FBM); For the inverse problem, the profile of rough surface with different roughness is reconstructed by two approximate algorithms - the small perturbation approximation (SPA) and the Kirchhoff approximation (KA) combined with the method of moments, the Banded-Matrix-Iterative-Approach/ Canonical Grid method, and forward-backward iterative method (FBM). The numerical results of reconstructed rough surface with different roughness are presented with the composite method, and the data are compared and analyzed.

A novel forward method to establish the three-dimensional parametric scattering center models is developed to extract scattering centers from the combined target/rough surface models. Both scattering centers from the ship, including single-order and higher order scattering contributions, and from the multiple interactions between the ship and random rough sea surface would be described concisely with physically relevant parameters by this proposed method. Due to the statistical nature of the random rough surface for the Monte Carlo simulation, we acquire a large number of realizations for estimations of the amplitude and position parameters to overcome the problem that single realization cannot extract scattering centers effectively. This method is validated through parametric models of the ship in free space and on the sea surface, and a good agreement has been demonstrated between the constructed and simulated radar characteristics. Furthermore, we analyze the composite target/surface model's physics and feature stability in a visually spatial range and direct connections between scattering centers and scattering sources, which would be valuable to future target recognitions and classifications. Finally, we quantitatively calculate and analyze the coupling scattering centers from interactions between the ship and the ocean-like surface that provide more abundant contour information of the inverse synthetic aperture radar (ISAR) image to facilitate contour detections.

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.

Surface roughness is a persistent challenge that may significantly reduce NMR T2 relaxation time, leading to the misinterpretation of formation and fluid properties. Of particular interest to accurately characterizing pore structures from NMR T2 responses, it is critical to define and quantify surface roughness before modeling its impact on NMR T2 relaxation. Some sophisticated microscope techniques can provide accurate surface roughness measurements; however, these methods probe the surface roughness of selected 2D regions on the rock surface, which may not fully represent surface roughness in 3D space. As the most commonly used 3D imaging technology, micro-computed tomography (micro-CT) digitizes core plugs into voxelized images. The actual surface roughness cannot be visualized as the length scale of surface textures is smaller than the image resolution. However, when modeling NMR T2 relaxation in digitized pore structures, the irregular pore shape increases surface relaxation. From the macroscopic point of view, the irregularity of solid-pore interfaces serves as the visible "roughness" at the given resolution. Thus, in this study, we treat it as surface roughness, and this raises a practical question of how to characterize surface roughness from micro-CT images. We proposed an image-based pore surface roughness characterization method, called 3D PSR, which utilizes a plurality of 2D cross-sectional images to approximate the surface roughness of a 3D volumetric pore structure. The accuracy and reliability of 3D PSR are influenced by pore morphology, as well as the number and orientation of cross-sectional planes. To resolve these issues, in this study, we upgrade the workflow by directly characterizing pore surface roughness in 3D space, which is named 3D PSR 2.0. The key to the success of 3D PSR 2.0 is calculating spherical harmonic (SH) coefficients to reconstruct the pore surface and then building the reference surface to characterize surface roughness. The proposed workflow consists of five steps, including image segmentation, pore separation and diagnosis, surface reconstruction, roughness evaluation, and roughness parameterization. Numerical results demonstrate the successful application of spherical harmonics for 3D pore surface roughness characterization.

To numerically calculate bistatic scattering from a fractal rough surface with high permittivity, a comprehensive approach of the forward-backward method (FBM) with spectral acceleration algorithm (SAA) combined with the physics-based two-grid (PBTG) method is developed. Bistatic scattering from and transmitting through one-dimensional (1-D) fractal rough surface with high permittivity, under TE and TM tapered wave incidence, are numerically simulated. Angular reflectivity and transmittivity demonstrate the energy conservation and the functional dependences upon the surface parameters.

Modeling and prediction of surface topography and surface roughness in dual-axis wheel polishing of optical glass

An advanced two-scale model of EM backscattering from rough surfaces

The aim of this work is to design an off-line system, method and experimental set-up for predicting surface roughness (Ra) of metal surfaces with the help of audio signals. The frictional contact between a metal surface and sharp pencil like scratching tool will produce audio signals which vary based on the roughness of the surface. The samples considered to design and validate the concept are work pieces machined with metal cutting processes such as Turning and Grinding. Several audio signals are generated from various types of metal surfaces produced by these processes after the completion of the machining process away from the machining area in an enclosed chamber. The audio waves are captured with the help of a microphone fixed inside the chamber. These audio signals are processed to generate the surface pattern of the relevant surface. The audio signals are then converted to spectrogram and normalized histogram plots with the help of MATLAB, based on which the roughness of the surfaces is predicted. An experimental set-up is designed which provides a sound-proof environment to capture and record the audio signals. The proposed system, method and set-up are validated with the actual surface roughness of the chosen surfaces measured with the help of a surface roughness measurement instrument.

In this paper we study the depolarized backscatter enhancement phenomenon for electromagnetic wave scattering from rough surfaces. Some new experimental data on light scattering from rough metallic surfaces shows a phenomenon of backscattering enhancement existing in the antispecular direction under some conditions, such as the surface parameters, wave polarization and operating frequency. From a roughly random surface the backscattering enhancement is predicted due to the constructive interference of multiple surfaces scattering. The study is based upon the integral equation method modified to be able to predict the phenomenon of multiple scattering and backscattering enhancement. From the study we found the backscattering enhancement takes place on the specialized surface parameters large compared with the incident wavelength. Further we also conclude that the depolarized multiple scattering makes much contribution along the plane of incidence from random rough surfaces, but depolarized single scattering makes little contributions as our expectation. In comparison of model prediction of total multiple scattering strength with measured data along the specular plane, excellent agreement is obtained.