Measurement of the electromagnetic field backscattered by a fractal surface for the verification of electromagnetic scattering models

Abstract

Fractal geometry is widely accepted as an efficient theory for the characterization of natural surfaces; the opportunity of describing irregularity of natural surfaces in terms of few fractal parameters makes its use in direct and inverse electromagnetic (EM) scattering theories highly desirable. In this paper, we present an innovative procedure for manufacturing fractal surfaces and for measuring their scattering properties. A cardboard–aluminum fractal surface was built as a representation of a Weiestrass–Mandelbrot fractal process; the EM field scattered from it was measured in an anechoic chamber. A monostatic radarlike configuration was employed. Measurement results were compared to Kirchhoff approximation and small perturbation method closed-form results that were analytically obtained by employing the fractional Brownian motion to model the surface shape. Matching and discrepancies between theories andmeasurements are then discussed. Finally, fractal and classical surface models are compared as far as their use in the EM scattering is concerned.