Wire-grid electromagnetic modelling of metallic cylindrical objects with arbitrary section, for Ground Penetrating Radar applications

For any wire-grid model, a fundamental question is the choice of the optimum wire radius and grid spacing. The most widely used criterion to fix the wire size is the so-called same-area rule [2], coming from empirical observation: the total surface area of the wires has to be equal to the surface area of the object being modelled. However, just few authors have investigated the validity of this criterion. Ludwig [3] studied the reliability of the rule by examining the canonical radiation problem of a transverse magnetic field by a circular cylinder fed with a uniform surface current, compared with a wire-grid model; he concluded that the same-area rule is optimum and that too thin wires are just as bad as too thick ones. Paknys [4] investigated the accuracy of the same-area rule for the modelling of a circular cylinder with a uniform current on it, continuing the study initiated in [3], or illuminated by a transverse magnetic monochromatic plane wave; he deduced that the same-area rule is optimal and that the field inside the cylinder is most sensitive to the wire radius than the field outside the object, so being a good error indicator. In [5], a circular cylinder was considered, embedded in a dielectric half-space and illuminated by a transverse magnetic monochromatic plane wave; the scattered near field was calculated by using the Cylindrical-Wave Approach and numerical results, obtained for different wire-grid models in the spectral domain, were compared with the exact solution. The Authors demonstrated that the well-known same-area criterion yields affordable results but is quite far from being the optimum: better results can be obtained with a wire radius shorter than what is suggested by the rule.