On the Practical Applicability of Series Expansions for Kirchhoff Diffractals

Use of the Kirchhoff approach allows expressing the electromagnetic field scattered by a fractal surface in terms of two series with different convergence regions. Convergence properties of these series and problems arising in their numerical evaluation have been presented in recent literature. In particular, suitable truncation criteria have been devised, which allow practical use of these two series expansions for computation of the scattered field with a controlled error. Based on the analysis provided by the recent literature, in this work an algorithm is presented that, given the illumination and surface roughness parameters, computes the scattered power density by automatically selecting the most appropriate series and truncation criterion.