Ping-Ping Ding

Fast calculation of scattering by 3-D inhomogeneities in uniaxial anisotropic multilayers

A fast algorithm to calculate the response of uniaxial layered media on a rectilinear mesh is proposed in order to handle scattering phenomena due to inhomogeneities within them. The uniaxial layered media are with their optical axes parallel to the interfaces of the layered structure. The generalized Poisson summation formula is used to efficiently calculate the discrete Fourier transform of spatial responses of the layered media from its continuous Fourier spectrum. Using the windowing technique, the integral involved in constructing the discrete Fourier spectrum can be performed in a small domain without compromising the accuracy of the result. Furthermore, a fast numerical integration method based on the recently proposed Padua points is used, which, together with the windowing technique, yields a fast solution to such scattering problems. Numerical simulations illustrate the accuracy and efficiency of the proposed algorithm.

On inverse scattering and imaging solutions for objects buried within uniaxially anisotropic media

Electromagnetic imaging of damaged uniaxially anisotropic composite materials certainly remains a challenging task yet it is in need for whatever concerns quality, viability, safety and availability of systems involving manufactured composite parts, e.g., in aeronautics and in automotive industry. The contribution first surveys in some depth the investigation topic with examples being drawn from the most recent literature by the authors and others. Then, upon introduction of a rigorous full-wave 3-D electromagnetic modeling and asymptotic first-order counterpart, retrieval of volumetric defects hidden in such materials via MUSIC approaches (under various guises), in the case of defects small enough, and Subspace Optimization Methods, for larger ones, will be exhibited from single-frequency multi-static data acquired in the reflection mode.

Fast calculation of electromagnetic scattering in anisotropic multilayers and its inverse problem

A rigorous and robust algorithm is presented for solving the electromagnetic scattering problems in the planar multilayered anisotropic and composite media. The Lippman-Schwinger integral formulation is exploited and integrated with the wave iterative technique in the derivation of the spectral-domain state equation. The presented algorithm relies on the accurate expressions of the dyadic Green’s function and the introduction of polarization tensor. The Padua-Dominguez interpolation-integration technique is used for improving the computational efficiency. Then, the MUltiple SIgnal Classification (MUSIC) method is utilized for dealing with the inverse imaging problem for the planar multilayered composite structure. The validity of the presented algorithm and the effectiveness of the inverse imaging are verified through numerical examples.

MUSIC imaging method for electromagnetic inspection of composite multi-layers

A first-order asymptotic formulation of the electric field scattered by a small inclusion (with respect to the wavelength in dielectric regime or to the skin depth in conductive regime) embedded in composite material is given. It is validated by comparison with results obtained using a Method of Moments (MoM). A non-iterative MUltiple SIgnal Classification (MUSIC) imaging method is utilized in the same configuration to locate the position of small defects. The effectiveness of the imaging algorithm is illustrated through some numerical examples.