Microwave scattering model for grass blade structures

The EM scattering solution for a grass blade with complex cross-section geometry is considered. It was previously shown that the scattering solution for such problems, in the form of a polarizability tensor, can be obtained using the low-frequency approximation in conjunction with the method of moments. In addition, that study showed that the relationship between the polarizability tensor of a dielectric cylinder and its dielectric constant can be approximated by a simple algebraic expression. The results of that study are used to show that this algebraic approximation is valid also for cylinders with cross sections the shape of grass blades, providing that proper values are selected for each of three constants appearing in the expression. These constants are dependent on cylinder shape, and if the relationship between the constants and the three parameters describing a grass blade shape can be determined, an algebraic approximation relating polarizability tensor to blade shape, as well as dielectric constant, can be formed. This algebraic approximation can replace the cumbersome method of moments model. The moment method model is therefore used to generate a small but representative set of polarizability tensor data over the range of values commonly observed in nature. A conjugate gradient method is then implemented to correctly determine the three constants of the algebraic approximation for each blade shape. A third-order polynomial fit to the data is then determined for each constant, thus providing a complete analytic replacement to the numerical (moment method) scattering model