| Perturbation Theory is used to calculate the scattered fields of several systems with rough boundaries. The boundary conditions are assumed to be of the impedance type with impedance constant $gamma$. This constant, $gamma$, is redefined as a dynamic variable of the roughness of the surface by inverting the boundary conditions to find an integral equation involving the impedance constant in terms of the perturbed fields. When followed by a successive approximation, a new impedance constant $gammasb0$ is so defined. By removing the degrees of freedom of the roughness of the surface and summing their contribution to the old impedance constant, the new impedance constant can be found to satisfy a rather simple first order differential equation, the flow of which determines the apparent type of problem an experiment could detect. The solution to this simple equation can be found exactly and successively, the later being equivalent to summing the major contribution to the appropriate order perturbation theory. Lastly, the implications toward calculating the scattering cross section are discussed. |
