The nondestructive characterization of cylindrical objects is needed in many fields, such as medical diagnostics, tree trunk inspection, or concrete column testing. In this study, the radar equation of Lambot et al. is combined with cylindrical Green’s functions to fully model and invert ultra-wideband (UWB) ground-penetrating radar (GPR) data and retrieve the properties of cylindrical objects. Inversion is carried out using a lookup table (LUT) approach followed by local optimization to ensure retrieval of the global minimum of the objective function. Numerical experiments were conducted to analyze the capabilities of the developed inversion procedure to estimate the radius, permittivity, and conductivity of the cylinders. The full-wave model was validated in laboratory conditions on metallic and plastic pipes of different sizes. The adopted radar system consists of a lightweight vector network analyzer (VNA) connected to a single transmitting and receiving horn antenna. The numerical experiments highlighted the complexity of the inverse problem, mainly originating from the multiple propagation modes within cylindrical objects. The laboratory measurements demonstrated the accuracy of the forward modeling and reconstructions in far-field conditions.

More and more applications of electrical resistivity tomography (ERT) for cylindrical objects have been rising in recent decades. This paper presents a 2.5-dimensional differential resistivity reconstruction scheme of cylindrical objects. The forward modeling algorithm incorporates the modified optimization wavenumbers to achieve an accurate 2.5-dimensional forward modeling. The modified optimization wavenumber selection is based on the approximate analytic solution of the circumference potential distribution of an infinitely long homogeneous cylindrical model, making it more accurate for cylindrical objects compared to the traditional optimization wavenumber selection which is only applicable for the half-space condition. In the laboratory, we measured the resistivity and resistance distributions of the sodium chloride solution-filled cylindrical tanks with/without a high resistivity rubber bar in the central. The modified and traditional optimization wavenumbers are included respectively to calculate the resistance distribution of the measured objects. The comparison results between the calculated and measured resistance distribution show that the modified optimization wavenumbers proposed in this paper can obtain higher calculation accuracy. The differential ERT incorporating the modified optimization wavenumbers is then employed to reconstruct the resistivity distribution of the cylindrical objects. The inversed resistivity values are in good agreement with the measured values. We, therefore, conclude that the modified optimization wavenumbers can result in better accuracy than the traditional one and the proposed 2.5-dimensional differential resistivity reconstruction scheme is time-saving and has great promise for the imaging of cylindrical objects.