Rigorous Integral Method Research Articles

Modelization of the Scattering of Electromagnetic Waves FROM the Ocean Surface

In this paper, two models for the solution of the electromagnetic bistatic scattering from sea surface are suggested. A rigorous formalism leading to weakly singular integral equations is presented, as well as the surface impedance approximation for low penetrable media and the beam simulation method to synthesize incident beams with arbitrary size. This rigorous integral method is used to test first order approximations, and it is shown that the Small Slope Approximation is very accurate in predicting the scattering crosssection from the high spatial frequencies of the sea surface. This result led us to suggest an improvement of the classical two-scale model, consisting in replacing the small perturbation theory by the small slope approximation. This change allows the cut-off spatial frequency to be shifted so that the use of geometrical Optics is restricted to the large scales.

Reconstruction of buried objects surrounded by smallinhomogeneities

This paper deals with the reconstruction of the boundary and the permittivity of homogeneous objects from synthetic data. Themethod is based on a rigorous integral method and a conjugategradient algorithm requiring the solution of only two directproblems at each step. To model some noise resulting from theinhomogeneity of the background, this object is surrounded by aset of point-like scatterers, arbitrarily distributed betweenthe two parallel lines of measurement. Since convergence of thealgorithm strongly depends on the initial guess, a method todetect a target in a random medium has been adapted. Statisticalnumerical results for reconstruction in a crosswellconfiguration are also presented.

Improved inverse scattering for dielectric homogeneous cylinders

A method for the reconstruction of the shape and of the permittivities of homogeneous cylindrical objects is described. It is based on a rigorous integral method and a conjugate gradient algorithm requiring the solution of only two direct problems at each step. The number of scatterers is directly estimated from the data and remains fixed during the iterative process. To ensure the stability of the method, some smoothness of the boundary is required. This is achieved through the in-process control of the number of Fourier coefficients in the representation of the boundary. Numerical examples showing the versatility of the approach are given.

Electromagnetic scattering from bounded or infinite subsurface bodies

The direct scattering problem from a stack of two rough interfaces or from a buried object with a rough interface above it is addressed. The two boundaries are separating three homogeneous and isotropic media. The profiles are assumed to be invariant in one (and the same) direction, and the probing field is time harmonic. The problem is solved with a rigorous integral method leading to a single boundary integral equation. This equation is converted into a linear system of equations, thanks to a boundary finite element method. To improve the accuracy, especially when the two boundaries are very close to each other, the singularity of the kernel is isolated and its integration is performed analytically. As shown through several examples, this versatile tool is well suited for the investigation of physical phenomena, especially the competition between surface and subsurface scattering.

Rigorous integral approach to the problem of scattering from a modulated periodic medium obtained through conformal mapping

The method described is an alternative way to solve, by means of a rigorous integral method, the problem of electromagnetic scattering from a typical periodic medium. This medium is issued from a particular conformal mapping that transforms a periodic surface-relief grating into a volume grating bounded by a perfect mirror. Thus the method indirectly solves the problem of scattering from a perfectly conducting rough grating and leads to a single integral equation of the Fredholm type with a simple kernel for each fundamental polarization. Numerical solution of the equation is computed through Gaussian integration, and computing time is less than 1 s per point on a workstation. Application is then made to different types of grating such as cycloidal, blaze, and N-level binary gratings coated with a highly conducting metal such as silver or gold.