A method to reconstruct the surface shape of a scatterer from the relative intensity of the scattered field is proposed. Reconstruction of the scatterer shape has been studied as an inverse problem. An approach that employs boundary-integral equations can determine the scatterer shape with low computation resources and high accuracy. In this method, the reconstruction process is performed so that the error between the measured far field of the sample and the computed far field of the estimated scatterer shape is minimized. The amplitude of the incident wave at the sample is required to compute the scattered field of the estimated shape. However, measurement of the incident wave at the sample (measurement without the sample) is inconvenient, particularly when the output power of the wave source is temporally unstable. In this study, we improve the reconstruction method with boundary-integral equations for practical use and expandability to various types of samples. First, we propose new boundary-integral equations that can reconstruct the sample shape from the relative intensity at a finite distance. The relative intensity is independent from the amplitude of the incident wave, and the reconstruction process can be performed without measuring the incident field. Second, the boundary integral equation for reconstruction is discretized with boundary elements. The boundary elements can flexibly discretize various shapes of samples, and this approach can be applied to various inverse scattering problems. In this paper, we present a few reconstruction processes in numerical simulations. Then, we discuss the reason for slow-convergence conditions and introduce a weighting coefficient to accelerate the convergence. The weighting coefficient depends on the distance between the sample and the observation points. Finally, we derive a formula to obtain an optimum weighting coefficient so that we can reconstruct the surface shape of a scatterer at various distances of the observation points.

A piece of information on the polarization effects on the effective dielectric constant εeff of a medium whose dielectric circular cylinders are randomly distributed is obtained by analyzing εeff for both E-wave and H-wave incidences. Our numerical analysis shows clearly the difference of εeff between E-wave and H-wave incidences and also shows the difference of εeff between our method and the Foldy's approximation.

Coherent and incoherent electromagnetic (EM) waves scattered by many particles are approximately expressed as solutions of integral equations by unconventional multiple scattering method. The particles are randomly displaced from a uniformly ordered distribution, and hence the distribution of particles can change from total uniformity to complete randomness. The approximate expressions of the EM waves are systematically given, independent of the distributions of particles, on the following assumptions. First the particles are identical in material, shape, size and orientation. Second each random displacement of particles from the ordered positions is statistically independent of each other and homogeneous in space. These assumptions may be extended to more general ones but have been used here to make clear the derivation process of the coherent and incoherent EM waves. The approximate expressions of the EM waves are reduced to known ones for both limiting cases: a periodic distribution and a very sparse random distribution. The effective dielectric constant of a random medium containing randomly distributed dielectric spheres can be calculated from the coherent EM wave and compared with those given by conventional methods such as the quasi-crystalline approximation, using the previous results. The comparison indicates the advantage of the method presented here. The present method is expected to be useful for the study of interaction of EM waves with many particles.

The effective dielectric constant εeff of discrete random medium composed of many dielectric spheres has been analyzed by EFA (Effective Field Approximation), QCA (Quasicrystalline Approximation) and QCA-CP (Quasicrystalline Approximation and Coherent Potential) in the case where the optical path length is very large in the medium. These methods lead to a reasonable K for non-large dielectric constants of spheres, while their methods yield an unphysical dependence of εeff on large dielectric constants of spheres: that is, the εeff does not become large for increasing the dielectric constant. In this paper, we remove the unphysical dependence and present new results for εeff of our method, comparing with the results for εeff of EFA, QCA and QCA-CP.

A method is presented for analyzing the scalar wave scattering from a conducting target of arbitrary shape in random media for both the Dirichlet and Neumann problems. The current generators on the target are introduced and expressed generally by the Yasuura method. When using the current generators, the scattering problem is reduced to the wave propagation problem in random media.