Verification of a rigorous 2D model of rough surface scattering (original) (raw)
Journal of the Optical Society of America A, 2001
The sparse-matrix-flat-surface iterative approach has been implemented for perfectly conducting surfaces and modified to enhance convergence stability and speed for very rough surfaces. Monte Carlo simulations of backscattering enhancement using a beam decomposition technique are compared with millimeter-wave laboratory experimental data. Strong but finite conductivity for metals or thin skin depth for dielectrics is simulated by an impedance approximation. This gives rise to a nonhypersingular integral equation derived from the magnetic field integral equation. The effect of finite conductivity for a metal at visible wavelengths is shown.
2001
"We consider the scattering from a two-dimensional periodic surface. From our previous work on scattering from one-dimensional surfaces (Waves in Random Media 8, 385(1998)) we have learned that the spectral-coordinate (SC) method was the fastest method we have available. Most computational studies of scattering from two-dimensional surfaces require a large memory and a long calculation time unless some approximations are used in the theoretical development. Here by using the SC method we are able to solve exact theoretical equations with a minimum of calculation time. We first derive (in PART I) in detail the SC equations for scattering from two-dimensional infinite surfaces. Equations for the boundary unknowns (surface field and/or its normal derivative) result as well as an equation to evaluate the scattered field once we have solved for the boundary unknowns. Special cases for the perfectly reflecting Dirichlet and Neumann boundary value problems are presented as is the flux-conservation relation. The equations are reduced to those for a two-dimensional periodic surface in PART II and we discuss the numerical methods for their solution. The two-dimensional coordinate and spectral samples are arranged in one-dimensional strings in order to define the matrix system to be solved. The SC equations for the two-dimensional periodic surfaces are solved in PART III. Computations are done for both Dirichlet and Neumann problems for various periodic sinusoidal surface examples. The surfaces vary in roughness as well as period and are investigated when the incident field is far from grazing incidence (“no grazing”) and when it is near-grazing. Extensive computations are included in terms of the maximum roughness slope which can be computed using the method with a fixed maximum error as a function of azimuthal angle of incidence, polar angle of incidence, and wavelength to period ratio. The results show that the SC method is highly robust. This is demonstrated with extensive computations. Further the SC method is found to be computationally efficient and accurate for near-grazing incidence. Computations are presented for grazing angles as low as 0.01o. In general we conclude that the SC method is a very fast, reliable and robust computational method to describe scattering from two-dimensional periodic surfaces. Its major limiting factor is high slope and we quantify this limitation."
Physical Review B, 2001
The small perturbations method has been extensively used for waves scattering by rough surfaces. The standard method developped by Rice is difficult to apply when we consider second and third order of scattered fields as a function of the surface height. Calculations can be greatly simplified with the use of reduced Rayleigh equations, because one of the unknown fields can be eliminated. We derive a new set of four reduced equations for the scattering amplitudes, which are applied to the cases of a rough conducting surface, and to a slab where one of the boundary is a rough surface. As in the one-dimensional case, numerical simulations show the appearance of enhanced backscattering for these structures.
A new theory for scattering of electromagnetic waves from conducting or dielectric rough surfaces
IEEE Transactions on Antennas and Propagation, 1992
The problem of scattering of electromagnetic waves from a conducting or dielectric rough surface with arbitrary shape is studied. An exact solution, using a differential method, is provided for a plane wave with one-dimensional irregularity of the interface. The proposed formalism involves using the covariant form of Maxwell equations written in nonorthogonal coordinate system. This permits the analytical writing of the exact boundary conditions. The problem is reduced to the resolution of a linear system of partial differential equations with constant coefficients, and to the computation of eigenvalues and eigenvectors of truncated infinite matrix. Numerical application is made to show the angular distribution of energy density in the case of an arbitrary profile of the scattering surface and its evolution when the nonperiodic profile tends to become periodic. The near field is computed on the interface and its enhancement in the illuminated region is well observed. It increases with the height of the irregularity and with the frequency.
2001
"We consider the scattering from and transmission through a two-dimensional periodic surface. We use the spectral-coordinate (SC) method for all the computations. It was the fastest method for one-dimensional problems and proved optimal for the scattering from two-dimensional surfaces where computation time can prove to be excessive. In particular we can avoid approximation methods and solve the exact equations. The SC equations are derived for an infinite surface and reduced to coupled equations for a periodic surface which are solved numerically for the two boundary unknowns. Solutions of the SC equations for various periodic sinusoidal surface examples are studied. The surfaces vary in roughness ands period. Extensive computations are included in terms of the maximum roughness slope which can be computed using the method with a fixed maximum error as a function of azimuthal angle of incidence, polar angle of incidence, wavelength to period ratio, density ratio and wavenumber ratio. Examples of reflectionless interfaces as a function of density and wavenumber are presented. Particular attention is paid to the case of near-grazing incidence. As a result of these extensive computations we conclude that the SC method is stable and robust (a) over the entire incident azimuthal variability, (b) over a 50-fold change in value of the wave number ratio, and (c) as the density parameter varies over two orders of magnitude. In addition SC works very well under extreme near-grazing conditions even for very rough surfaces with large slopes over a very broad parameter range in density and wavenumber. Spectral based methods can thus play an important role in the description of the scattering from two-dimensional periodic surfaces."
Frontiers in Physics, 2013
A formalism is introduced for the non-perturbative, purely numerical, solution of the reduced Rayleigh equation for the scattering of light from two-dimensional penetrable rough surfaces. As an example, we apply this formalism to study the scattering of p-or s-polarized light from twodimensional dielectric or metallic randomly rough surfaces by calculating the full angular distribution of the co-and cross-polarized intensity of the scattered light. In particular, we present calculations of the mean differential reflection coefficient for glass and silver surfaces characterized by (isotropic or anisotropic) Gaussian and cylindrical power spectra. The proposed method is found, within the validity of the Rayleigh hypothesis, to give reliable results. For a non-absorbing metal surface the conservation of energy was explicitly checked, and found to be satisfied to within 0.03%, or better, for the parameters assumed. This testifies to the accuracy of the approach and a satisfactory discretization.
Models for Scattering from Rough Surfaces
Electromagnetic Waves, 2011
Electromagnetic Waves 204 modelling scattering of electromagnetic waves from random rough surfaces. We will also define the bistatic scattering coefficient due to the importance of this type of measurement in many remote sensing applications.
Assessment of Scattering of Plane Waves on Optically Illuminated Area of Rough Surface
Progress In Electromagnetics Research B
In this paper, a new robust computational method that applies the geometrical theory of diffraction (GTD) in conjunction with the ray tracing (RT) technique is developed to evaluate the electromagnetic scattering pattern due to a plane wave incident on a rough surface of quite arbitrary statistical parameters. The Fresnel reflection model is applied under the assumption of arbitrary electrical and optical properties of the rough surface material to obtain the scattering patterns for both the power reflected to the upper half-space and the power transmitted into the medium covered by the rough surface. Also the polarization of the plane wave primarily incident on the rough surface is taken into consideration. The algorithm developed in the present work accounts for multiple bounces of an incident ray and, hence, it can be considered arbitrary higher-order GTD-RT technique. The accuracy of the obtained results is verified through the comparison with the experimental measurements of the scattering pattern of a light beam incident on rough sheets with specific statistical properties. Also, some of the obtained results are compared to other published results using the geometrical optics (GO) and the second-order Kirchhoff's approximation. The numerical results of the present work are concerned with investigating the dependence of the scattering pattern on the surface roughness, refractive index, angle of incidence, and the resolution of the geometric model of the rough surface. Also, it is shown that for limited resolution of the rough surface model, the accuracy of the calculated scattered field depends on the angle of incidence of the primary beam and the surface roughness.
The scattering of electromagnetic waves from a randomly rough 2D metallic surface
Optics Communications, 1994
By a computer simulation approach we study the scattering of a finite beam of p-polarized light from very rough two-dimensional metallic surfaces. Enhanced backscattering is observed. It is found that the approximation of a metal surface by a perfectly conducting surface in the visible region of the optical spectrum is less good for in-plane, co-polarized and out-of-plane, crossedpolarized scattering than it is for in-plane, crossed-polarized and out-of-plane, co-polarized scattering.
Journal of The Optical Society of America A-optics Image Science and Vision, 1994
Electromagnetic scattering of an incident plane wave from a rectangular strip and strip grating, are presented semi-analytically. The strip and strip grating are simulated by joining parallel perfect electromagnetic conductor (PEMC) circular cylinders and are illuminated by a TM z incident plane wave. The PEMC medium does not allow electromagnetic energy to enter. An interface of this medium serves as an ideal boundary to the electromagnetic field. The solution is based on the application of the boundary conditions on the surface of each cylinder in terms of its local coordinate system. The technique is used to predict the scattered field pattern of PEMC strip and PEMC strip grating.
IEEE Transactions on Antennas and Propagation, 2009
An asymptotic method is described for predicting the bistatic normalized radar cross section of a rough homogeneous layer made up of two rough surfaces. The model is based on iteration of the Kirchhoff approximation to calculate the fields scattered by the rough layer, and is reduced to the high-frequency limit in order to obtain numerical results rapidly. Shadowing effects, significant for large incidence or scattering angles, are taken into account through the use of shadowing functions. The model is applicable for moderate to large surface roughnesses having small to moderate slopes, and for both lossless and lossy inner media. It was validated for a rough layer with a rough surface over a perfectly flat surface in a preceding contribution. Here, the extension of the model to a rough layer with two rough surfaces is developed, and results are presented to validate the asymptotic model by comparison with a numerical reference method.
Monte Carlo simulation of electromagnetic scattering from two-dimensional random rough surfaces
IEEE Transactions on Antennas and Propagation, 1997
The fast multipole method-fast Fourier transform (FMM-FFT) method is developed to compute the scattering of an electromagnetic wave from a two-dimensional rough surface. The resulting algorithm computes a matrixvector multiply in O(NlogN) operations. This algorithm is shown to be more e cient than another O(NlogN) algorithm, the multi-level fast multipole algorithm (MLFMA), for surfaces of small height. For surfaces with larger roughness, the MLFMA is found to be more e cient. Using the MLFMA, Monte Carlo simulations are carried out to compute the statistical properties of the electromagnetic scattering from two-dimensional random rough surfaces using a workstation. For the rougher surface, backscattering enhancement is clearly observable as a pronounced peak, in the backscattering direction, of the computed bistatic scattering coe cient. For the smoother surface, the Monte Carlo results compare well with the results of the approximate Kirchho theory.
Numerical determination of scattered field amplitudes for rough surfaces
The Journal of the Acoustical Society of America, 1996
In theory, when an incident plane wave strikes a perfectly reflecting periodic surface, the resulting scattered field is comprised of a discrete spectrum of plane waves. Upon applying Dirichlet boundary conditions to the surface, one can construct what is referred to as a spectral-coordinate ͑SC͒ formalism for the scattered amplitudes. A Fredholm integral equation of the first kind is involved, and the integration is performed over a single surface period. Since the Rayleigh approximation is not utilized in the construction of this formalism, one may use this method to determine the exact scattered field above the highest surface excursion. The problem will be approached numerically by directly discretizing the mixed SC representation, then solving the system using a pseudoinverse SVD technique. It is very important to note that the scattered amplitudes are obtained without constraining the value of normalized energy. This particular approach is unique. It differs from others in which the discretizations are implemented entirely in coordinate space or entirely in spectral ͑i.e. Bragg͒ space. It is thus an additional computational tool designed for cases when a mixed representation is appropriate. Although this numerical scheme has been developed for arbitrary periodic surfaces, the results presented in this paper are restricted to sinusoidal surfaces. Particularly interesting features of this approach are the high level of accuracy attained for near-grazing incident fields and the maintenance of stability even for badly conditioned systems of equations.
Exact spectral formalism for rough-surface scattering
Journal of the Optical Society of America A, 1985
The spectral amplitudes of the scattered and transmitted fields for plane-wave incidence on an arbitrary rough interface in one dimension are derived exactly and simply by using Green's theorem. Results are stated in terms of integrals on values of the field and its normal derivative on the interface. The energy constraint is derived, and individual energy contributions in each region are also related to the surface-field values. The latter contributions can be calculated from coupled linear equations that are also derived using Green's theorem. The interface separates media of different but constant densities and sound speeds (acoustics) or different dielectrics (electromagnetics).
Electromagnetic scattering from multi-scale rough surfaces
Waves in Random Media, 1997
It is shown that the wavelet correlation dimension is a very relevant quantity for the characterization of rough surfaces by remote sensing means. First, the concept of correlation length is generalized to surfaces with wide power spectrum. Second, it is demonstrated that, in the framework of the small-perturbation theory, the wavelet correlation dimension can be retrieved from a knowledge of the backscattered cross section for a discrete set of frequencies.
A comparison study of the surface scattering models and numerical model
2001
Abstract This paper describes a comparison study of surface scattering models and a numerical model for dielectric surfaces. Two surface scattering models namely the integral equation model (IEM) and the small slope approximation (SSA) model are used to calculate the backscattering coefficients of rough surfaces and the results are compared with numerical simulations based on the moment method (MoM). Analysis of the results obtained is also presented
The method of the local parabolic approximation for rough surface scattering
The Journal of the Acoustical Society of America, 1993
A method for evaluation of scattering from rough surfaces which is similar to the Kirchhoff approximation is considered. However, it is based on a local parabolic approximation of the surface irregularities rather than a tangent plane approximation and two iterations of the surface field integral equation. The method, first proposed by Belobrov and Fuks [Izv. VUZ Radiofiz. 29, 1083-1089 (1986); Soy. Phys. Acoust. 31, 442-445 (1985)], accounts for local diffraction effects. Important modifications to the original method are introduced and extensive numerical results for Gaussian, one-dimensional randomly rough surfaces for both the Dirichlet and Neumann problems are provided. The validity of the local parabolic approximation is assessed by comparison with results from Monte Carlo simulations. It is demonstrated that the local parabolic approximation improves the Kirchhoff approximation for large and intermediate values of the surface correlation length especially in the backscattering region.