Characterization of Three - Dimensional Rough Fractal Surfaces from Backscattered Radar Data

Georgios Pouraimis,Panayiotis Frangos,Apostolos Kotopoulis,Evangelos Kallitsis

doi:10.5755/j01.eie.23.4.18721

Georgios Pouraimis, Panayiotis Frangos + Show 2 more

Open Access

https://doi.org/10.5755/j01.eie.23.4.18721

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Abstract

This paper discusses the scattering of electromagnetic (EM) waves from three – dimensional (3D) rough fractal surfaces using the Kirchhoff approximation. In particular, it introduces a novel method to characterize 3D rough fractal surfaces from spectral information of the backscattered EM wave in Synthetic Aperture Radar (SAR) applications. It represents an important extension of a previous recent paper by the same research group from 2D fractal surfaces to 3D fractal surfaces (the latter representing real – life SAR radar scenes). More specifically, in the present simulation scenarios it is assumed that the radar emits a burst of radar pulses of increasing carrier frequency [therefore a ‘stepped – frequency’ (SF) SAR radar]. By calculating the backscattered EM wave from 3D fractal surfaces as a function of the above radar frequencies (therefore, a ‘spectral method’), it is found here that the slope between the main backscattered lobe and its adjacent side lobes increases with increasing surface fractal dimension (i.e. with increasing surface roughness). In this way a characterization of 3D fractal rough surfaces from backscattered SAR radar data is achieved, as explained in detail in this paper.DOI: http://dx.doi.org/10.5755/j01.eie.23.4.18721

Highlights

In the last decades there has been a growing interest in the scattering of optical, electromagnetic and acoustical waves from rough surfaces
A very interesting and very popular approach to represent rough surfaces encountered in real – life has been proposed by Mandelbrot and other scientists, who presented the concept of fractals [1], [2]
Scattering of EM waves from fractal rough surfaces has been examined in the past in [3]–[7], where 2D self – similar fractal surfaces have been considered, the corresponding surface ‘fractal dimension’ has been introduced and the Kirchhoff approximation for EM wave scattering was used

Summary

INTRODUCTION

In the last decades there has been a growing interest in the scattering of optical, electromagnetic and acoustical waves from rough surfaces. Scattering of EM waves from fractal rough surfaces has been examined in the past in [3]–[7], where 2D self – similar fractal surfaces have been considered, the corresponding surface ‘fractal dimension’ has been introduced and the Kirchhoff approximation for EM wave scattering was used. A variant of 2D self – similar fractal surface representation, namely a ‘one-dimensional bandlimited Weierstrass function’, was introduced in [8], which will be generalized in this paper for 3D fractal. In those years (1994), a ‘twodimensional bandlimited Weierstrass function’ (i.e. a 3D surface) was proposed by Lin et al [9], in order to study the bistatic scattering of EM waves from 3D fractal surfaces.

PROBLEM GEOMETRY AND MATHEMATICAL FORMULATION

Findings

SIMULATION RESULTS