Abstract
This dissertation presents two new methods for analyzing electromagnetic scattering from perfect electrically conducting surfaces. The Spectral Projection Model and Direct Spectral Projection Model are spectral techniques for analyzing the scattering patterns from two-dimensional objects. The methods evolved from prior work done on analyzing scattering from perfect electrical conducting surfaces in two-dimensions in the sinusoidal spatial frequency domain using the Spatial Frequency Technique. By employing the addition theorem for Hankel and Bessel functions, the Spectral Projection Model represents the incident and scattered electric fields in the electric field integral equation and magnetic field integral equation as projections of spectral signatures. Using the addition theorem, the incident fields and the scattered fields are decomposed into the product of two matrices whose columns and rows are the spectral signatures of current sources that are projected onto the spectral signatures of the observation points. The Direct Spectral Projection Model, which evolved from Spectral Projection Model, identifies a set of virtual sources that are the eigenfunctions of the scattering problem. The currents induced on the surface are calculated by decomposing the spectral signature of the incident fields in terms of the spectral signatures of these virtual sources. The first analyses using the Spectral Projection Model were on infinitely long circular cylinders and produced results that agreed well with established techniques like the Method of Moments for transverse magnetic incident waves. Both the Spectral Projection Model and Direct Spectral Projection Model techniques were then applied to elliptical cylinders of different axial ratios for both transverse magnetic and transverse electric incident waveforms. The techniques produced good agreement with Method of Moments techniques but only for small axial ratios. The addition theorem failed to converge for ellipses with large axial ratios. In this dissertation, it is shown that the spectral signature of a point in space, which is represented by a vector, is equivalent to the convolution of the spectral signatures of two vectors, which when combined result in the original vector. In order to calculate the scattered fields from elliptical cylinders of larger axial ratios, it was necessary to use the addition theorem as a convolution sum for both the source and observation points. To accomplish this, elliptical patterns were generated by summing two constant magnitude vectors rotating in opposite directions. Known as the Two Vector Sum approach, a variety of two-dimensional surfaces may be generated using two constant amplitude vectors rotating at different rates. Elliptical surfaces are generated using two vectors rotating at the same rate in opposite directions. The Spectral Projection Model was extended to scattering from ellipses with large axial ratios by using the Two Vector Sum approach to describe the model as a convolution of spectral signatures. Calculation of the convolution operation was performed using Hadamard products in the Fourier domain. Far-field patterns calculated using the Spectral Projection Model are compared with those using the Method of Moments to validate the accuracy of the method for elliptical cylinders of both large major axis and large axial ratio. Computation of the current distribution on elliptical cylinders of large major axis and large axial ratio using the Direct Spectral Projection Model also indicate that Direct Spectral Projection Model and Method of Moments results closely match. Both methods are also used with a few different two-dimensional perfect electrical conducting cylinders other than elliptical cylinders to show the versatility of the two models. The primary motivation for developing these models was the projection process clearly shows the physics of the scattering process by separating the spectral signatures of the incident sources from those of the induced currents. This allows this model to be used as a tool for surface or target synthesis. The Spectral Projection Model and Direct Spectral Projection Model formulation also has the potential for speeding up the computation by using the well-established properties of the convolution operation and the Fast Fourier Transform algorithm. The computational aspects of this model will be investigated as a follow-up to this dissertation. In the future, the models may also be extended to dielectric objects and three-dimensional objects.