Synthesis, construction, and validation of a fractal surface

Abstract

Fractal geometry provides reliable models to describe geometrical properties of natural surfaces. Therefore, their use in the electromagnetic scattering methods deserves careful research. In order to have complete insight into the phenomenon, a measurement campaign on a fractal surface in a controlled environment is a key step. In this paper, we propose a technique for building a fractal surface that can be used for electromagnetic scattering evaluation purposes. The surface characteristics are imposed by computer synthesizing a bandlimited Weierstrass-Mandelbrot function, whose actual shape is constructed by means of a cheap innovative technique: the synthesized surface is made from cardboard covered with aluminum foil, which gives a conducting surface and creates the micro-scale conditions, useful to represent manufacturing errors. Statistics of the overall surface shape are then measured, analyzed and compared with the imposed ones, providing and verifying the rationale for a fully controlled surface to be applied in any kind of experiment on natural surfaces.