A major difficulty in physical interpretation of radio wave scattering from geophysical surfaces is the lack of detailed information on the signatures of geologically plausible discrete objects. Although the aggregate response will never be dominated by any single object, differences in the population of discrete objects on or near the surface (their sizes and shapes, for example) can change the character of a radio echo markedly. When the average surface is modelled as a flat, homogeneous half-space, the field that "drives" the scattering process is a composite consisting of the incident plane wave and the reflected and transmitted plane waves, all of which are known quantities; the total field can then be defined as the sum of the driving field and the scattered field. When a discrete object is near the surface, the total field can be calculated using finite-difference time-domain (FDTD) techniques, and the scattered near field can be calculated accordingly. The Green's functions for electric and magnetic currents above and below the surface, obtained by Sommerfeld theory and employed in conjunction with Huygens' principle, transform the local scattered fields to the far field. The FDTD implementation accommodates discrete lossy dielectric and magnetic scatterers in the vicinity of a dielectric surface; extension to a lossy half-space is straightforward. Two-dimensional results for scattering from perfectly conducting circular cylinders above and below a dielectric surface agree with moment method solutions within a few percent. Results for scattering from a dielectric wedge exhibit expected forward diffraction and internal reflection phenomena.

A three-wave FDTD approach to surface scattering with applications to remote sensing of geophysical surfaces

A total-field/scattered-field (TF/SF) plane-wave source is developed for the finite-difference time-domain analysis of general (possibly lossy) planar layered media. A 1-D auxiliary grid is created to generate the incident field in the presence of the layered medium. Inhomogeneous plane waves are also allowed for lossless layers and narrowband excitation.

A Total-Field/Scattered-Field Plane-Wave Source for the FDTD Analysis of Layered Media

Near- to far-zone transformation for the finite-difference time-domain (FDTD) method can be performed by integration of the equivalent electric and magnetic currents originating from scattered electric and magnetic fields on a surface enclosing the object. Normally, when calculating the surface integrals, either the electric or magnetic fields are averaged since the electric and magnetic fields are spatially shifted in the FDTD grid. It is shown that this interpolation is unnecessary and also less accurate than if an integration is performed on two different surfaces. It is also shown that the accuracy of the far-zone transformation can be further improved if the phase is compensated with respect to a second-order dispersion corrected wavenumber. For validation, scattering results for an empty volume, a circular disk, and a sphere are compared with analytical solutions.

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An improved near- to far-zone transformation for the finite-difference time-domain method

In the application of two-dimension (2D) finite-difference time-domain (FDTD) to scattering analysis of object embedded in layered media, the incident electromagnetic wave propagation is much more complicated, it can not inject the plane wave source by traditional method. To solve this problem, the Π-shape total-field/scattering- field (TF-SF) boundary scheme is presented. The side TF-SF boundaries are governed by the modified 1D Maxwell's equations, but the discretization for which to p-wave is more difficult than n- wave. Then an auxiliary magnetic variable is used, which can develop the modified 1D-FDTD to p-wave without any approximately. To truncate the modified 1D-FDTD, the convolutional perfectly matched layer (CPML) absorbing boundary condition (ABC) is also given. Examples showthe feasibility and applicability of proposed Π-shape TF/SF boundaries scheme.

/pdf/analysis-of-tf-sf-boundary-for-2d-fdtd-with-plane-p-wave-e4puv4xu56.pdf

Analysis of TF-SF Boundary for 2D-FDTD with Plane P-Wave Propagation in Layered Dispersive and Lossy Media

Inverse light scattering analysis seeks to associate measured scattering properties with the most probable theoretical scattering distribution. Although Mie theory is a spherical scattering model, it has been used successfully for discerning the geometry of spheroidal scatterers. The goal of this study was an in-depth evaluation of the consequences of analyzing the structure of spheroidal geometries, which are relevant to cell and tissue studies in biology, by employing Mie-theory-based inverse light scattering analysis. As a basis for this study, the scattering from spheroidal geometries was modeled using T-matrix theory and used as test data. In a previous study, we used this technique to investigate the case of spheroidal scatterers aligned with the optical axis. In the present study, we look at a broader scope which includes the effects of aspect ratio, orientation, refractive index, and incident light polarization. Over this wide range of parameters, our results indicate that this method provides a good estimate of spheroidal structure.

/pdf/application-of-mie-theory-to-assess-structure-of-spheroidal-2rqnvtg4d8.pdf

P. B. Wong

Papers

A three-wave FDTD approach to surface scattering with applications to remote sensing of geophysical surfaces

Finite Difference-Time Domain Model for Surface Scattering with Application to Magellan at Venus