Laser pulse scattering from a moving one-dimensional rough surface

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.

One of the most popular methods for calculating the scattering of light from rough surfaces is the Kirchhoff approximation. A recent modification of the Kirchhoff approximation allows calculation of the scattering of electromagnetic radiation from rough surfaces with very high, or even infinite, slopes, which occurs frequently in, for example, imaging or testing of printed circuits or remote sensing applications. The modification involves a simple change in the way the surface normal is described which removes the explicit dependence of the resulting integral equations on the surface slope, and changing the sampling of the surface, removing the requirement of small slopes for application of the method. In this paper we present the application of the method to vector electromagnetic scattering, using the Stratton-Chu equation, from 2D rough metallic surfaces with infinite slope. The single and double scatter contributions to the total scattered intensity are calculated numerically with this new formulation. Geometrical shadowing is included by using ray tracing directly on the surface. The theoretical basis and preliminary numerical results of the application of this method to vector electromagnetic scattering from simple rough metallic surfaces (plane surfaces with single grooves or with a small number of identical grooves) with infinitely sloped structure are presented.

Starting with Zenneck and Sommerfeld wave propagation over a flat finitely conducting surface has been extensively studied by Wait (see IEEE Antennas Propagat. Mag., vol.40, p.7-24, 1998) and many other authors. We examine propagation over a finitely conducting rough surface, also studied by many people including Feinberg (1944), Bass and Fuks (1979), and Barrick (see Radio Sci., vol.6, p.517-26, and vol.6., p.527-33). This paper extends the multiple scattering theories based on Dyson and Bethe-Salpeter equations and their smoothing approximations. The theory developed here applies to rough surfaces with small root-mean-square (RMS) heights (/spl sigma/<0.1/spl lambda/). We limit ourselves to the one-dimensional (1-D) rough surface with finite conductivity excited by a magnetic line source, which is equivalent to the Sommerfeld dipole problem in two dimensions (x-z plane). With the presence of finite roughness, the total field decomposes into the coherent field and the incoherent field. The coherent (average) field is obtained by using Dyson's equation, a fundamental integral equation based on the modified perturbation method. Once the coherent field has been obtained, we determine the Sommerfeld pole, the effective surface impedance, and the Zenneck wave for rough surfaces of small RMS heights. The coherent field is written in terms of the Fourier transform, which is equivalent to the Sommerfeld integral. Numerical examples of the attenuation function are compared to Monte Carlo simulations and are shown to contrast the flat and rough surface cases. Next, we obtain the general expression for the incoherent mutual coherence functions and scattering cross section for rough conducting surfaces.

Compared with scattering from a rough surface only, composite scattering from a target above a rough surface has become so practical that it is a subject of great interest. At present, this problem has been solved by some numerical methods which will produce an enormous calculation amount. In order to overcome this shortcoming, the reciprocity theorem (RT) and the method of equivalent edge currents (MEC) are used in this paper. Due to the advantage of RT, the difficulty in computing the secondary scattered fields is reduced. Simultaneously, MEC, a high-frequency method with edge diffraction considered, is used to calculate the scattered field from the cone-cylinder target with a high accuracy and efficiency. The backscattered field and the polarization currents of the rough sea surface are evaluated by the Kirchhoff approximation (KA) method and physical optics (PO) method, respectively. The effects of the backscattering radar cross section (RCS) and the Doppler spectrum on the size of the target and the windspeed of the sea surface for different incident angles are analysed in detail.

This paper presents an analytical theory of rough surface Green's functions based on the extension of the diagram method of Bass and Fuks (1979), and Ito (1985) with the smoothing approximation used by Watson and Keller (1983, 1984). The method is a modification of the perturbation method and is applicable to rough surfaces with small RMS height. But the range of validity is considerably greater than the conventional perturbation solutions. We consider one-dimensional rough surfaces with Dirichlet, Neumann, and impedance boundary conditions. The coherent Green's function is obtained from the smoothed Dyson's equation by using a spatial Fourier transform. The mutual coherence function for the Green's function is obtained by the first-order iteration of the smoothing approximation applied to the Bethe-Salpeter equation in terms of a quadruple Fourier transform. These integrals are evaluated by the saddle-point technique. The equivalent bi-static cross section per unit length of the surface is compared to the conventional perturbation method and Watson-Keller's result. With respect to Watson-Keller's result, it should be noted that our result is reciprocal while the Watson-Keller result is nonreciprocal. Included in this paper is a discussion of the specific intensity at a given observation point. The theory developed will be useful for the RCS signature related problems and LGA (low grazing angle) scattering when both the transmitter and object are close to the surface.

The mutual coherence function (MCF) of strong-fluctuation theory as a result of optical energy passing through a transversely and longitudinally inhomogeneous aero-optic turbulent layer is studied. Solutions for the MCF equation are determined by decomposing the MCF solution into coherent and incoherent parts and by solving separately the equations that result from this decomposition. The MCF equations for an arbitrary three-dimensional inhomogeneous layer are presented. A simplified version of these equations for the case in which the turbulence inhomogeneity is longitudinally inhomogeneous and is transversely inhomogeneous in one dimension is also presented. A numerical method for solving the parabolic MCF equations by the Lax-Wendroff explicit finite-difference algorithm is given, and numerical examples of the MCF solution for three different inhomogeneous aero-optic layers are discussed. Equations to relate the point-spread function, the optical transfer function, and image formation to the MCF of an inhomogeneous aero-optic turbulence layer are derived. An approximate MCF Fourier integral solution is presented and compared with the exact finite-difference solution. A formula to estimate the validity of the approximate integral solution is given.

The Kirchhoff approximation (KA) for elastic wave scattering from two-dimensional (2D) and three-dimensional (3D) rough surfaces is critically examined using finite-element (FE) simulations capable of extracting highly accurate data while retaining a fine-scale rough surface. The FE approach efficiently couples a time domain FE solver with a boundary integration method to compute the scattered signals from specific realizations of rough surfaces. Multiple random rough surfaces whose profiles have Gaussian statistics are studied by both Kirchhoff and FE models and the results are compared; Monte Carlo simulations are used to assess the comparison statistically. The comparison focuses on the averaged peak amplitude of the scattered signals, as it is an important characteristic measured in experiments. Comparisons, in both two dimensions and three dimensions, determine the accuracy of Kirchhoff theory in terms of an empirically estimated parameterσ2/λ0(σis the RMS value, and λ0is the correlation length, of the roughness), being considered accurate when this is less than some upper boundc, (σ2/λ0&lt;c). The incidence and scattering angles also play important roles in the validity of the Kirchhoff theory and it is found that for modest incidence angles of less than 30°, the accuracy of the KA is improved even whenσ2/λ0&gt;c. In addition, the evaluation results are compared using 3D isotropic rough surfaces and 2D surfaces with the same surface parameters.

Approximate analytical solution of the matrix transport equation for the mutual coherence function (MCF) of an acoustic field in terms of normal modes was derived. The proposed approach is capable of including stochastically rough surface as well as volume fluctuations in the index of refraction, and allowed one to reduce the problem of the MCF calculation in a refractive channel to the analogous problem in a free space. These results have been then employed to simulate the statistical effects of long-range sound propagation in realistic deep-water environments from the North-West Pacific on the horizontal array detection performance for several beamforming techniques. The most attention was paid to the gain degradation for the sound frequency of 250 Hz over megameter ranges under the basic assumption that internal waves or surface wind waves are, respectively, the main source of acoustic signal fluctuations. Rough surface scattering has been shown to cause the most significant effects. In particular, for the array length of order 100 acoustic wavelengths and wind speed of 15 m/s the coherence loss was of about 6 dB even for optimal quadratic processor and, in comparison, of about 12 dB for conventional plane-wave beamformer. [Work supported by Russian Basic Research Foundation, Grant No. 94-02-04544a.]

The roughness of the material surface affects the THz nondestructive testing results. Roughness of the surface can be ignored in the microwave region, but should be considered in the terahertz frequency domain. The effect of scattering caused by rough surface at terahertz frequency on the reflection spectrum was studied and discussed. By consideration of the reflection model of a single sample, the reflection signal of a rough surface can be correlated with that of a smooth surface by using the Kirchhoff approximation. In addition, the glucose tablets with different roughness were measured by THz-TDS (Terahertz time domain spectroscopy) system and their reflection spectra were analyzed. The reflection spectrum results show that due to the roughness of the surface, diffuse scattering generated by the rough surface weakens the intensity of the reflection spectrum at the receiver. In order to reduce the influence of the roughness on the spectrum, a spectral Gaussian compensation method was proposed, which can restore the spectral characteristics of the smooth surface. The power spectrum of 360 mesh roughness was increased by about 3 dB and 9 dB at 0.5 THz and 1 THz, respectively. Therefore, it can be envisaged that the proposed rough-surface spectral compensation method has a specific reference value in the development of the THz nondestructive testing technology in the future.

The actual rough sea surface is described by Pierson-Moscowitz (PM) spectrum and Monte Carlo method; the composite electromagnetic scattering from the double rectangular crosssection conductor columns above the rough sea surface is investigated using the hybrid methodthe Method of Moment with the Kirchhoff approximation. Angular distribution curves of composite scattering coefficient are obtained; and this coefficient that varies with the parameter of sea surface, rectangular cross-section conductor columns and incident waves is calculated in detail. The characteristics of the composite scattering coefficient from the double rectangular cross-section conductor columns above the rough sea surface are also obtained. Results show that the hybrid methodthe Method of Moment with the Kirchhoff approximation, compared to the traditional Method of Moment, can obtain higher accuracy. Moreover, the hybrid method can effectively reduce the computation time and memory footprint, and the performance becomes more favorable with the increase of the sizes of rough surface.

A new iterative strategy combining analytical Kirchhoff Approximation (KA) with the powerful simulation tool finite elementboundary integral (FE-BI) method is presented in this paper to study the interactions between an object and the underlying rough surface. This hybrid FE-BI-KA scheme is an improved and generalized version of MOM-KA. Instead of using MOM, FE-BI is used to model scattering from the above object with the original incidence and scattered wave by the rough surface as the exciting source. Whereas scattering from rough surface is studied by the classical KA in order to reduce the computation resource and time required

There is a need for a solution to the problem of wave scattering from rough surfaces that is accurate when both the classical field perturbation and Kirchhoff approximations are not. In previous work it was shown numerically that the phase perturbation reflection and backscattering coefficients reduce to those of field perturbation theory and the Kirchhoff approximation in the appropriate limits; however, for cases when the classical solutions did not apply, the accuracy of the phase perturbation results could not be determined. In this paper we examine the validity of the phase perturbation technique for a region in parameter space when the two classical solutions fail. Numerical results for the bistatic scattering cross section are compared with exact numerical results for one-dimensional surfaces having a Gaussian roughness spectrum and satisfying a Dirichlet boundary condition. It is found that in the region considered the phase perturbation results agree with the exact results over all scattered angl...

This thesis consists of two parts. The first one is "Scattering of Waves in a Random Medium," and the second one is "Radiative Transfer in a Sphere Illuminated by a Parallel Beam: An Integral Equation Approach." In the first part, a new formalism tor partially coherent wave scattering in a random medium is developed. In this formalism the coherent wave is the solution of a phenomenological wave equation, and the mutual coherence function of the wave field satisfies a simple integral equation. Using this formalism, the Peierls equation can be readily derived. Also, an improved version of the Peierls equation is derived in which the intensity of the wave field and the first order derivative of the mutual coherence function are calculated at the same time. A simple problem is solved to find the mutual coherence function produced by a laser beam in the atmosphere. The similarity between the mutual coherence function and the density matrix or quantum mechanics is explored and a measure of the randomness is defined for the partially coherent wave field. In the second part of this work, the problem of multiple scattering of non-polarized light in a planetary body of arbitrary shape illuminated by a parallel beam is formulated using the integral equation approach. There exists a simple functional whose stationarity condition is equivalent to solving the equation of radiative transfer and whose value at the stationary point is proportional to the differential cross section. Our analysis reveals a direct relation between the microscopic symmetry of the. Phase function for each scattering event and the macroscopic symmetry of the differential cross section for the entire planetary body, and the intimate connection between these symmetry relations and the variational principle. The case of a homogeneous sphere containing isotropic scatterers is investigated in detail. It is shown that the solution can be expanded in a multipole series such that the general spherical problem is reduced to solving a set of decoupled integral equations in one dimension. Computations have been performed for a range of parameters of interest, and illustrative examples of applications to planetary problems are provided.

The electromagnetic wave transmission of the rough surface of Gaussian layered medium is studied with a hybrid algorithm which is based on MoM (method of moment) and combines with KA (Kirchhoff approximation). In the hybrid algorithm, the upper rough surface and the lower rough surface are placed in the MoM area and the KA area respectively, and the curve of transmission coefficient to change with the scattering angle of transmission wave is solved through numerical calculation. Finally, the relationships of transmission coefficient with the root-mean-square height, the dielectric constant and thickness of the middle-layer medium, and the frequency of incident wave of rough surface are discussed, and then a complete electromagnetic wave transmission characteristic is obtained.

Influence of fractal surface roughness on multiphase flow behavior: Lattice Boltzmann simulation