A Study of the Fourth-Order Small Perturbation Method for Scattering From Two-Layer Rough Surfaces

The rigorous evaluation of the NRCS (Normalized Radar Cross Section) of an object above a one-dimensional sea surface (2D case) needs to numerically solve a set of discretized integral equations involving a large number of unknowns. Thus, the direct solution of the impedance matrix equation via LU decomposition becomes the most expensive step in the MoM (Method of Moments) procedure. So, in order to minimize the computation cost, the iterative domain decomposition method called EPILE (Extended Propagation-Inside-Layer Expansion) was used and then was combined with the FBSA (Forward-Backward with Spectral Acceleration) to calculate the local interactions on the rough sea surface. The resulting fast method is called EPILE+FBSA. In this paper, we take advantage of the rank-deflcient nature of the coupling matrices, corresponding to the object-surface interactions, to further reduce the complexity of the method by using the ACA (Adaptive Cross Approximation). Thus, the coupling matrices are strongly compressed without a loss of accuracy and the memory requirement is then strongly reduced. For a cylinder above a rough sea surface, the results show the e-ciency of the accelerated EPILE+FBSA+ACA method.

Analytical expressions for the cross-polarization components of the normalized radar cross sections (NRCS) of three-dimensional stratified media with two rough surfaces are presented. In a recent paper, the zeroth- and the first-order scattering solutions of a two-rough-surface structure with arbitrary dielectric profiles were presented using the small perturbation approach based on the extended boundary conditions (EBC). In this study, the proposed method is extended to obtain the second-order solutions including cross-polarized fields. Unlike copolarizations, the main contribution of cross-polarizations is determined by the second-order solutions. A direct extension of the recently proposed formulation leads to difficult and lengthy manipulations; hence, first a compact recursive matrix formulation for the unknown surface fields of an arbitrary order is derived. Then, for the second-order fields, the matrix system is efficiently and straightforwardly solved. Finally, the cross-polarized scattered fields and the normalized radar cross sections are derived. The final solutions are given in simple, compact, and closed-form expressions that make the computations very easy. The derived expressions are validated against known solutions of special cases, available in the literature. The results are shown to be exactly consistent with existing ones, both analytically and numerically.

Summarizes the scattering properties of a rough surface as a function of observation parameters, physic and geometric characteristics of the surface. This study is applied to the oceanic surface. Results are presented in the form of polarimetric signature as a function of the transmitter location and receiver location for a bistatic radio-link over the rough sea surface. The like- and cross-polarized received power are directly calculated using the scattering coefficients, without calculating the Mueller matrix. The Kirchhoff model and the small perturbation method are applied to determine the scattering coefficients. The polarization states, obtained for the minima and maxima received power in order to increase the performance of a bistatic radio-link, or to improve the discrimination power of a radar target are investigated. It is observed that for a fixed transmitter location and receiver location it is possible to choose a polarization state minimizing the scattered power from a rough sea surface, independently of the sea state. An electromagnetic wave scattered from a target is a vectorial quantity containing polarimetric information. This information is a function of the target, and also depends on the observation parameters. The purpose of this paper is to present, the polarimetric signature of the rough sea surface in order to increase the performance of a bistatic radio link (decreasing fading effect, for example), or to improve the discrimination power of a radar target or to identify a target.

A backscattering model for scattering from a randomly rough dielectric surface is developed. Both like- and cross-polarized scattering coefficients are obtained. The like-polarized scattering coefficients contain single scattering terms and multiple scattering terms. The single scattering terms are shown to reduce to the first-order solutions derived from the small perturbation method when the roughness parameters satisfy the slightly rough conditions. When surface roughnesses are large but the surface slope is small, only a single scattering term corresponding to the standard Kirchhoff model is significant. If the surface slope is large, the multiple scattering term will also be significant. The cross-polarized backscattering coefficients satisfy reciprocity and contain only multiple scattering terms. The difference between vertical and horizontal scattering coefficients increases with the dielectric constant and is generally smaller than that predicted by the first-order small perturbation model. Good agreements are obtained between this model and measurements from statistically known surfaces.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

For detection of a two-layered rough surface structure through ground-penetrating radar, the estimation of the profile of each layered rough surface is an important problem to be solved. In modeling and calculating the scattering of two-layered rough surfaces, we found that the profile of the upper rough surface can be observed directly through the figure of the echo from the upper surface. However, the echo of the lower rough surface has a quite different shape from its surface profile, because of the influence of the scattering of the upper rough surface. This is disadvantageous to the estimation and imaging of the profile of the lower rough surface. To solve this problem, a time-delay calibration method is proposed in this paper to be applied to the profile estimation of the lower rough surface in the case of two-layered rough interface detection. By introducing a smooth surface, the expression of time delay is derived to eliminate the influence of the scattering of the upper surface. Applying the derived expression of time delay to the echo data from the lower rough surface, the echo outline of the lower rough surface can be corrected to reflect the surface's profile shape. The calibrated B-scan echo shape shows good agreement with the profile of the lower rough surface. With this method, we can get the profile shape of the lower rough surface quickly and simply by calibrating the echo data directly. This method can be used for fast microwave imaging of two-layered rough surface and for eliminating the interference of scattering from rough surface on the echoes of nearby targets. The purpose of this paper is to solve the problem we have found in our previous work. The work of this paper is an extension of the previous work.

In this paper, we study the electromagnetic wave propagation in a parallel plate waveguide with rough surface walls, using a mode matching technique in combination with the method of moments (MoM). In the formulation, a line source in the smooth section of the waveguide excites a summation of modal fields. For each waveguide modal excitation, the modal response fields in the rough surface section of the waveguide are obtained by the solution of the governing surface integral equations through MoM. The total field distribution in the rough surface waveguide is a linear combination of the modal response fields. The coefficients are obtained by enforcing the continuity of tangential electric and magnetic fields at the junctions between smooth and rough surface waveguide sections. Results are illustrated for a variety of roughness spectra based on the parametric generalized power spectral density. The results are compared with the previously developed small perturbation method of second order (SPM2) results for the plane wave and waveguide models. With the numerical validation, the SPM2 waveguide model is proved to be able to capture the waveguide thickness effect especially for very rough surface profiles.

Terrestrial light detection and ranging (LiDAR) offers significant advantages over conventional techniques for measuring the centimeter-scale surface roughness of natural surfaces, such as sea ice. However, the laser scanning technique is inherently limited, principally by the following: 1) the high inclination scanning angle of the sensor with respect to nadir; 2) the precision of the laser ranging estimate; and 3) the beam divergence of the laser. In this paper, we introduce a numerical model that has been designed to simulate the acquisition of LiDAR data over a regular rough surface. Results from the model compare well $(r^2 = 0.97) $ with LiDAR observations collected over two experimental surfaces of known roughness that were constructed from medium-density fibreboard using a computer numerical control three-axis router. The model demonstrates that surface roughness parameters are not sensitive to minor variations in the LiDAR sensor's range and laser beam divergence, but are slightly sensitive to the precision of the ranging estimate. The model also demonstrates that surface roughness parameters are particularly sensitive to the inclination angle of the LiDAR sensor. The surface RMS height is underestimated, and the correlation length is overestimated as either the inclination angle of the sensor or the true roughness of the surface increases. An isotropic surface is also increasingly observed as an anisotropic surface as either the inclination angle or the true surface roughness increases. Based on the model results, we propose a set of calibration functions that can be used to correct in situ LiDAR measurements of surface roughness.

An analytical study of environmental and clutter effects on microwave radiometers used for the detection of buried objects is presented. To simplify the analysis, it is assumed that the soil/target medium has a constant physical temperature versus depth, so that Kirchhoff's law can be applied to determine emissivities, and a simple layered medium geometry is used to model a buried target. Changes in brightness temperatures which result due to the present of a buried target are illustrated for varying soil dielectric properties, radiometer frequencies, and target depths, and are contrasted with changes in brightness temperatures which can occur when no target is presented due to slight soil moisture or soil temperature variations. Brightness temperature clutter due to a small surface roughness is also analytically modeled, through application of the small slope approximation for the homogeneous medium case and the small perturbation method in the presence of a subsurface layer, and it is shown that surface clutter effects can be mitigated through proper choice of sensor polarization and observation angle. Particular attention is given to the relationship between passive and active microwave sensors; results demonstrate that these two can provide complementary information. Finally, the use of wideband radiometric measurements are discussed as a means for reducing environmental clutter effects and improving detection algorithms.

The normalized radar cross section (NRCS) measured by satellite ocean radar systems is representative of the sea surface roughness at the scale of gravity-capillary waves, which are not only dominated by winds, but also modulated by some secondary factors such as sea surface temperature (SST) and sea surface salinity (SSS). In this paper, the variations of NRCS due to SST changes, depending on scatterometer radar frequency, polarization, and incidence angle, are investigated on the basis of a physics-based radar backscatter model and a dataset of collocated ASCAT C-band and RapidScat Ku-band scatterometer measurements. The study shows that the SST effects are substantial at Ku-band, but rather negligible for C-band NRCS measurements. Furthermore, the SST effects are wind speed dependent and more pronounced in VV polarization and at higher incidence angles. SSS effects, due to dielectric constant, surface tension, and dynamic viscosity variations, on scatterometer winds are limited (within 1%). This study concludes that it is necessary to take SST into account in scatterometer wind retrieval for radar wavelengths smaller than C-band.

The geometric optics approximation is based on the Kirchhoff-tangent plane approximation (KA), which assumes that each point of the rough surface can be considered as locally flat. Here, the extension of the KA to the case of rough layers for calculating the scattered field is presented, for either flat or rough lower surfaces. Then, for fast computation of the normalized radar cross section (NRCS), KA is reduced in the high-frequency limit to the geometric optics (GO) approximation, by using the method of stationary phase. Last, numerical results are presented by comparison with a reference numerical method to validate the asymptotic GO model.

This thesis is a contribution towards developing cost-effective ways for reducing outdoor traffic noise in outdoor environments by exploiting the interaction between sound travelling directly to a listener from the source and sound reflected by the intervening ground. Sound propagation over different kinds of porous, rough and mixed impedance ground surfaces have been studied experimentally and numerically. Measurements of short-range acoustic level difference spectra over outdoor ground surfaces and artificially-created surfaces outdoors and in the laboratory have been compared with predictions to establish suitable impedance models. Sound propagation over mixed impedance ground having single or multiple impedance discontinuities has also been studied. Acoustic transmission loss through vegetation, crops and hedges has been investigated. The phenomenon of sound diffraction and periodicity due to rough periodic ground surfaces has been explored through artificially created rough surfaces in the laboratory and outdoors. The phenomenon of surface wave propagation over rough hard surfaces and porous surfaces has been explored through laboratory experiments. Measured data indoors and outdoors have been used to validate numerical (BEM and FEM), empirical and analytical (MST) prediction techniques. The validated numerical methods have been used to make predictions at scales suitable for attenuating traffic noise by means of carefully designed ground treatments. The work has also been extended to railway and tramway noise. It has been found that replacing hard ground with porous ground, introducing single or multiple impedance discontinuities, growing vegetation and introducing low height roughness can all contribute between 3 and 15 dB additional attenuation of traffic noise. In respect of replacing hard ground by porous ground, it is concluded that the ground with lowest flow resistivity i.e. grassland left untouched and allowed to grow wild gives the best attenuation performance. However, dividing a single width of soft ground into alternating strips of hard and soft surfaces does not improve the insertion loss. The overall width of the soft surface is the main factor. Cultivating crops over porous ground can enhance the attenuation but the effect is not very significant for A-weighted levels as most of additional attenuation occurs at higher frequencies above 3 kHz. A 0.3 m high and at least 3 m wide lattice structure design is found to be very useful for traffic noise attenuation since it offers greater insertion loss than the same width and height of parallel low walls and the resulting attenuation is azimuthal angle independent. It has been shown also that the potentially negative effect on insertion loss due to propagation of roughness-induced surface waves over rough surfaces can be reduced by introducing sound absorbing material in between the walls.

Ultrashort pulsed (USP) laser machining is a promising approach for processing binderless nanopolycrystalline diamond (NPD), which combines isotropic ultra-high hardness and high thermal stability. This study systematically investigates USP laser ablation to identify suitable conditions for advanced microtool fabrication. The influence of pulse duration ( τ ), wavelength ( λ ), fluence ( F ), pulse frequency ( f ) and pulse and track overlaps ( O x , O y ) on orthogonal and quasi-tangential ablation of NPD was evaluated. The single-pulse ablation threshold ranged from 1.56 J / cm 2 for green fs irradiation to 8.82 J / cm 2 for IR ns irradiation. In orthogonal ablation, increasing f improved ablation efficiency under high-fluence conditions, with IR fs giving the highest material removal, while green fs at low frequency provided the best compromise between low roughness and high efficiency. In the overlap study, O x = 0.6 and O y = 0.8 yielded the lowest surface roughness. For quasi-tangential machining, an optimum parameter window was identified with R a = 13 nm and S a = 51 nm . Finally, NPD micro milling tools with sharp cutting edges ( r ϵ = 1.03 ± 0.13 μ m ) and low surface roughness were successfully fabricated. • Binderless nanopolycrystalline diamond showed the lowest ablation threshold under green femtosecond laser irradiation and the highest threshold under infrared nanosecond irradiation. • In orthogonal machining, green femtosecond irradiation at low frequency provided the best balance between smooth surfaces and efficient material removal, while infrared femtosecond irradiation at high frequency produced the highest removal rates. • A narrow optimum process window was identified for quasi-tangential machining, yielding very low surface roughness and high surface quality on cylindrical binderless nanopolycrystalline diamond. • Micro milling tools were successfully fabricated by combining orthogonal ablation for flute generation with quasi-tangential ablation for tool shaping, producing sharp cutting edges and low surface roughness in binderless nanopolycrystalline diamond.

A Gaussian Schell Model (GSM) might be a convenient way to model extended beacons created on diffuse targets. Earlier, we used a full wave computational technique called the Method of Moments (MoM) to evaluate the scattered field from a rough impedance surface in vacuum. The MoM model showed several deviations from GSM. The present work uses a simulation approach based on physical optics approximation to study the scattering behavior in presence of atmospheric turbulence. A fully coherent beam is propagated through weak turbulence and is incident on the rough surface. The light scattered from the rough surface is again propagated through turbulence back to the source plane and the properties of the scattered radiation are studied through numerical simulations. The simulation results are compared with a GSM.

ABSTRACTA generalized hybrid scheme combining finite element method (FEM) and the method of moments (MOM) is first presented to investigate scattering from a 3-D dielectric object above a 2-D dielectric rough surface. The hybrid FEM/MOM scheme is divided into the FEM region for the object based on Helmholtz’s equation and the MOM region for the rough surface based on coupled integral function, which can greatly reduce the computed region. With the rough surface getting larger, the unknowns of the rough surface get more. So MLFMA is employed to reduce computation complexity of MOM region itself and coupling interaction matrices between MOM region and FEM region. Consequently, the iterative process can be greatly accelerated. This generalized hybrid FEM/MOM is very suitable for investigating scattering from composite model of a complex material object and electrically large dielectric rough surface. Some examples verify this generalized hybrid FEM/MOM in high efficiency, low storage requirement, high precision and generality.

Wave scattering from rough surface is important in many diverse areas, including radio communications, microwave remote sensing, underwater acoustics. The recent interest in bistatic radar, or the study of radio links above the sea surface, has led to the need for information concerning bistatic reflectivity of clutter viewed by such systems, particularly for near grazing incidence. The problem of developing a model for a rough surface is very difficult since at best /spl sigma/ is dependent upon (at least) radar frequency, geometrical parameters, physical parameters, incident and observation angles, and polarization. Therefore, it is necessary to restrict the areas of applicability of such models. A first major new consideration in this paper is to study the domain of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case). Comparisons between the numerical calculations and the models are presented for various surface rms height and correlation length both normalized to the incident wave number (denoted by k/spl sigma/ and kL, respectively). These two parameters form a two-dimensional space, into which the approximate regions of validity are established. The second new major consideration is the development of the theoretical composite model describing bistatic reflectivity. One application is implemented for the ocean surface case. Numerical results for the cross sections are compared to those found using Kirchhoff approximation (Physical Optics), small-perturbation model, and the phase perturbation technique.