This paper presents various Iterative Progressive Numerical Methods (IPNMs) for the computation of electromagnetic (EM) wave scattering from many objects. We previously modified the original IPNM from the standpoint of the classical and the IDR-based linear iterative solvers. We demonstrate the performance of the IDR(s)-based IPNMs through some numerical examples of EM wave scattering from regularly placed 27 perfectly electric conducting spheres.

In this paper, an electromagnetic plane wave diffraction by finite number of loaded thick slits on infinitely long perfectly electric conductor (PEC) screen is analyzed. Here we formulate the problem by utilizing the Kobayashi Potential (KP) method, which is a kind of eigenfunction expansion method in terns of Weber-Schafheitlin discontinuous integrals. The multiple scattering contributions between the slits are analytically included in the formulation. The solution derived here may provide us with precise numerical result, so it may be considered as a reference solution to other numerical and approximate analyses.

This paper presents the iterative progressive numerical methods (IPNMs) based on the induced dimension reduction (IDR) theorem. The IDR theorem is mainly utilized for the development of new nonstationary linear iterative solvers. On the other hand, the use of the IDR theorem enables to revise the classical linear iterative solvers like the Jacobi, the Gauss-Seidel (GS), the relaxed Jacobi, the successive overrelaxation (SOR), and the symmetric SOR (SSOR) methods. The new IPNMs are based on the revised solvers because the original one is similar to the Jacobi method. In the new IPNMs, namely the IDR-based IPNMs, we repeatedly solve linear systems of equations by using a nonstationary linear iterative solver. An initial guess and a stopping criterion are discussed in order to realize a fast computation. We treat electromagnetic wave scattering from 27 perfectly electric conducting spheres and reports comparatively the performance of the IDR-based IPNMs. However, the IDR-based SOR- and the IDR-based SSOR-type IPNMs are not subject to the above numerical test in this paper because of the problem with an optimal relaxation parameter. The performance evaluation reveals that the IDR-based IPNMs are better than the conventional ones in terms of the net computation time and the application range for the distance between objects. The IDR-based GS-type IPNM is the best among the conventional and the IDR-based IPNMs and converges 5 times faster than a standard computation by way of the boundary element method.

The coupled mode equation describing the propagation of light in a disordered waveguide system composed of randomly different cores in size is analytically solved by the perturbation method and the average amplitude of light is derived. In the summation of a perturbation series only successive scatterings from different cores are taken into account. The result obtained shows that the average amplitude behaves as if in an ordered waveguide system composed of identical cores at short distance and decreases exponentially with increasing distance at large distance. The result is compared with the result obtained by the coherent potential approximation and the both results are in good agreement with each other. The results are also compared with the results obtained by numerically solving the coupled mode equation.

This paper deals with the scattering of a TM plane wave from a perfectly conductive sinusoidal surface with finite extent. For comparison, however, we briefly discuss the diffraction by the sinusoidal surface with infinite extent, where we use the concept of the total diffraction cross section per unit surface introduced previously. To solve a case where the sinusoidal corrugation width is much wider than wave length, we propose an undersampling approximation as a new numerical technique. For a small rough case, the total scattering cross section is calculated against the angle of incidence for several different corrugation widths. Then we find remarkable results, which are roughly summarized as follows. When the angle of incidence is apparently different from critical angles and diffraction beams are all scattered into non-grazing directions, the total scattering cross section increases proportional to the corrugation width and hence the total scattering cross section per unit surface (the ratio of the total scattering cross section to the corrugation width) becomes almost constant, which is nearly equal to the total diffraction cross section per unit surface in case of the sinusoidal surface with infinite extent. When the angle of incidence is critical and one of the diffraction beams is scattered into a grazing direction, the total scattering cross section per unit surface strongly depends on the corrugation width and approximately approaches to the total diffraction cross section per unit surface as the corrugation width gets wide.

Point-to-point optical and millimeter wave communication has recently been of interest, especially in urban areas. Its benefits include simpler and easier installation compared with a land-based line. However, this technology suffers when adverse weather conditions are present, such as rain, fog and clouds, which induce scattering and absorption of the optical wave. The effects of scattering and absorption degrade the quality of the communication link resulting in increase of bit-error-rate. Therefore, there exists a need for accurate channel characterization in order to understand and mitigate the problem. In this paper, radiative transfer theory is employed to study the behavior of amplitude modulated signal propagating through a random medium. We show the effect of the medium to a modulated signal and relate the outcome on the quality of the communication link.

This paper deals with the scattering problem of a layer where many spherical lossy particles of high dielectric constant are randomly distributed. A radiative transfer equation is used to calculate the scattering cross section of the layer. Four different multiple scattering methods are applied to determine the coefficients of the equation. The scattering cross sections of the four methods are compared by changing the incident angle and polarization of incident waves and the layer thickness. The comparison shows that the scattering cross section fairly depends on the multiple scattering methods and that we need to use an appropriate multiple scattering method for a scattering problem when using a radiative transfer equation.

There has been an increasing interest in multiple scattering phenomena in recent years. This is primarily due to the discovery of new multiple scattering phenomena and an increasing awareness that a common thread underlies the work of many researchers in such diverse fields as atmospheric optics, ocean acoustics, radio physics, astrophysics, condensed matter physics, plasma physics, geophysics, bioengineering, etc. In addition, waves in random media is one of the most challenging problems to theoreticians. Thus the field of wave propagation and scattering encompasses the most practical as well as the most theoretical questions. The strong interest in this subject is reflected in the launch of a new journal, Waves in Random Media, by the Institute of Physics, United Kingdom in 1991. This paper reviews some of the most recent developments and discoveries in the field of wave propagation and scattering in turbulence and volume and surface scattering. Included are new discoveries of backscattering enhancement and memory effects which may be applicable to tissue optics, ultrasound imaging, ocean acoustics and geophysical remote sensing. Also indicated are recent developments of numerical Monte-Carlo techniques and experimental studies on this subject.

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.

Physical and optical parameters within the atmosphere-ocean system have been retrieved by a multiple scattering analysis of the reflectance and degree of linear polarization data measured by the airborne POLDER sensor in Medimar campaign in 1991. Assuming an atmosphere-ocean system with a Cox-Munk type rough sea surface model, the theoretical reflectance and -degree of linear polarization were computed by the doubling and adding method for several different models. In this study the retrieval was made by assuming a fixed refractive index of the aerosol particles, i.e., Nr=1.33-0.0i. We obtained several important results in this study as follows: 1) By comparing computed results with the observed data at 0.85m, we rejected the oceanic type aerosol model and found Junge type aerosol model with its index range of 4.0v4.5 as an appropriate model for aerosols at the observation time. 2) The reflectance data analysis in the perpendicular plane rejected an isotropic Cox-Munk model, but it indicated that an anisotropic Cox-Munk model should be used in the sea surface wind field retrieval. 3) The surface wind speed was estimated to be 10.0m/secV15.0m/sec with an best estimate of V=12.5m/sec, which agrees with the observed wind speed of V=14.4m/sec. The range of the water column reflectance was also estimated to be 0.025rwc0.045 from Medimar reflectance data at 0.45m. 4) Further study should be made for other refractive indices of the aerosol particles. More refinement of the present multiple scattering code to include upwelling polarization components from below the sea surface is also necessary.

The Bidirectional Reflectance Distribution Function (BRDF) is an intrinsic measurement of directional properties of the earth's surface. However, the estimation of the BRDF requires many remote sensing measurements of a given surface target from different viewing angles. In addition, a good atmospheric correction scheme is a prerequisite for such an attempt. The airborne POLDER sensor measures successively reflected radiation by terrestrial surfaces in a framed image form at different viewing angles during a single airplane pass, like taking snap-shot pictures. A specially improved atmospheric correction algorithm which is applicable to a framed image data by POLDER sensor is presented. The observed reflectance images taken successively by the airborne POLDER at slightly different viewing angles are converted to a series of surface albedo images by applying our atmospheric correction algorithm. Then, the BRDFs for three surface covers, namely, "River Water," "Forest," and "Rice Field," are estimated by using successive albedo images. It is found that the BRDF for "River Water" follows Lambert law at both 550nm and 850nm. It is also found that the BRDFs for "Forest" and "Rice Field" follow Lambert's law at 550nm, but they follow an anisotropic reflection law at 850nm and fitting parameters for their BRDFs are presented.

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.