Measurement of the Electromagnetic Field Backscattered by a Fractal Surface for the Verification of Electromagnetic Scattering Models

Abstract

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 and measurements are then discussed. Finally, fractal and classical surface models are compared as far as their use in the EM scattering is concerned.

Electromagnetic Scattering from Fractional Brownian Motion Surfaces via the Small Slope Approximation

“…We first consider an artificially manufactured aluminum fBm surface, with p scribed H and 𝑠 parameters reported in the first line of Table 1. The manufacturing this surface is described in detail in [32], and a photo of the surface is shown in Figure Measurements of the backscattering NRCS of this surface, under a controlled enviro ment, were performed at a frequency of 10 GHz for both VV and HH polarization and several incidence angles, as described in [33]. These measurements are reported as dots the plots of Figure 5, while SSA-1 results are reported as light-blue lines in the same figu We note that for natural surfaces (see the values of s 2 and H in Section 2.1), up to microwave frequencies, the effective slope variance σ 2 se f f is much smaller than one, so that also for near-specular directions SSA-1 can be applied.…”

“…The manufacturing of this surface is described in detail in [32], and a photo of the surface is shown in Figure 4. Measurements of the backscattering NRCS of this surface, under a controlled environment, were performed at a frequency of 10 GHz for both VV and HH polarization and at several incidence angles, as described in [33]. These measurements are reported as dots in the plots of Figure 5, while SSA-1 results are reported as light-blue lines in the same figure, results of SPM and KA are also plotted for reference.…”

Anisotropic Phase Unwrapping for Synthetic Aperture Radar Interferometry

“…As interesting as it is, we put this problem beyond the scope of this paper and invite interested readers to investigate, from the more physical bases, the relation of phase noise and fractal parameters of the observed natural surfaces. Informative materials that discuss microwave scattering from physical fBm surfaces are readily available in literature, including the theoretical foundations and developments [17]- [20], as well as a number of laboratory experiments using real surfaces to carefully evaluate their scattering properties [32], [33].…”

Buried metal detection within the wooden block by X‐band measurements

“…Ruello et al presents a study about the theory of Fractal geometry which 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 EM scattering theories highly desirable. They present a procedure for measuring their scattering properties.…”