Computing low‐frequency radar surface echoes for planetary radar using Huygens‐Fresnel's principle

Abstract

Radar echoes from planetary sounders often contain ambiguities between surface echoes (clutter) and subsurface reflections. Such problems severely constrain quantitative data analysis especially for rough terrains. We propose a physical optics approach to simulate planetary sounding radar surface echoes to address this specific issue. The method relies on the Huygens-Fresnel's principle which permits the recasting of Maxwell's equations in a surface integral formulation. To compute this integral, we describe the surface through a mesh composed of adjacent triangular elements for which we provide an analytical expression of the scattered electromagnetic fields. The main contribution of this work lies in the use of analytical integrals over triangular facet elements much larger than the wavelength of the electromagnetic field. Hence, the advantage of the proposed approach is its computation efficiency which reduces the computational requirements while maintaining the physical optics accuracy. This allows a systematic analysis of the continuously growing planetary sounding radar database. Equations and implementation are detailed in this paper as well as illustrations of obtained results for different instruments (namely, SHARAD and LRS). Our simulation results suggest that the method is able to accurately reproduce the observed clutter in both rough and smooth terrains of the planetary cases discussed in this paper.

Radar probing of Jovian icy moons: Understanding subsurface water and structure detectability in the JUICE and Europa missions

“…The distinguishable radar signature characterizing the furrow is the strong return from its bottom (11.a.2) that can be used to estimate its depth. Use of accurate Digital Elevation Models (DEMs) will constrain the surface clutter contribution and decrease it by mean of clutter-reduction techniques (Nouvel et al, 2004, Ferro et al, 2013and Berquin et al, 2015. As can be observed in image (b) of Figure 11, for this model the number and density of near-surface cracks is much smaller with respect to the bright terrain.…”

“…Clutter-reduction techniques and synthetic aperture processing will be of primary importance for the study of Callisto's topography (e.g. Berquin et al, 2015).…”

CLUSIM: A Synthetic Aperture Radar Clutter Simulator for Planetary Exploration

“…Berquin et al () make use of the vectorial Huygens‐Fresnel principle and derive an expression for polarized radar echo from the planetary surface: with the dyadic Green function where E and H denote electric and magnetic fields, respectively, is a unit normal to the surface, x is a point on the surface, is the characteristic impedance of the surface, ϵ and μ are the permittivity and permeability, k is the wave number and is the unit vector pointing in the scattering direction. Assuming the length of the synthetic aperture to be small compared to the spacecraft orbit height, we can regard as a constant and integrate over the synthetic aperture analytically, as is explained above for the scalar case.…”

“…Berquin et al () also derive an expression for the diffraction integral over the whole surface of the triangular facet as an approximate sum of an infinite series. These approximate expressions cannot be further integrated analytically, so the aperture synthesis can only be performed numerically on the postprocessing stage.…”

“…Probably, for this reason, most known clutter simulations are more or less simplified, for example, they lack the aperture synthesis (Fa & Jin, 2010;Smirnov et al, 2014). In other simulation algorithms, the aperture synthesis is performed at the postprocessing stages (Berquin et al, 2015).…”