An Algorithm for Efficient and Effective Evaluation of Scattering From Fractal Surfaces

In recent years, it has been shown that use of the Kirchhoff approximation allows expressing the field scattered by a fractal surface in terms of two series expansions. A rigorous analysis of the properties of such two series has been addressed in the recent literature, aimed at finding suitable truncation criteria to compute, with a controlled absolute error, the field scattered by a fractal surface. In this paper, we first of all note that aforementioned analysis applies not only to the Kirchhoff approach, but also to more advanced approaches for surface scattering evaluation. Then, we address the use of the aforementioned series and truncation criteria to achieve a controlled relative rather than absolute error. According to such an analysis, an algorithm is provided, which allows to automatically choose which of the two series, if any, can be used, and how it can be properly truncated for efficient and effective (i.e., with a controlled relative error) computation of the field scattered by natural surfaces. An example of the application of the proposed algorithm to synthetic aperture radar data simulation is also provided.