Method of moments evaluation of the two-dimensional quasi-crystalline approximation

In remote sensing, the propagation of electromagnetic fields through random media is often of concern. We may wish to characterize the effects of clouds or water droplets along the line of sight between an airplane and a radar installation, or we may be interested in using radar to probe the random medium itself, such as in determining snow depth and particle size. In all of these problems it is necessary to predict the propagation constant in the "random" medium. The purpose of this paper is to characterize the accuracy of the quasi-crystalline approximation and other associated methods of determining the effective permittivity for two-dimensional (2-D) random media. A numerical method based on the method of moments is used as a gauge for comparison with the theoretical methods. After deriving the 2-D quasi-crystalline approximation and presenting the numerical method, the behavior of the effective permittivity is analyzed for a range of particle sizes, volume fractions and dielectric losses. From this analysis, regions of validity for the theoretical methods are determined. An investigation is also given which explores the effect of particle arrangement methods on the pair distribution function which, in turn, is shown to have a significant effect on the imaginary component of the effective permittivity.