# Two-Dimensional Linear Inversion of GPR Data with a Shifting Zoom along the Observation Line
## 5 Experimental Results  
This section is devoted to presenting the data and the results of the processing performed on them, with and without a shifting zoom. The exploited GPR system consisted of a vector network analyzer (VNA), which comprised a stepped-frequency continuous-wave (SFCW) radar system (ZVRE, Rohde & Schwarz, Munich, Germany) and a linearly polarized, double-ridged broadband horn antenna (BBHA 9120 A, Schwarzbeck Mess-Elektronik, Schonau, Germany) as the simultaneous transmitter and receiver. The antenna dimensions were as follows: height, 195 mm; aperture, 142 \(\times\) 245 mm. The antenna nominal frequency range was 0.8 to 5.0 GHz and its isotropic gain ranges were from 6 to 18 dB. The relatively high directivity of the antenna (45\({}^{\circ}\), 3 dB beam width in the E-plane and 30\({}^{\circ}\) in the H-plane at 1 GHz) made it immune to interferences from external sources or reflectors. The antenna was connected to the reflection port of the VNA via a high-quality N-type 50-Ohm coaxial cable. We calibrated the VNA at the connection between the antenna feed point and the cable using an Open-Short-Match calibration kit. The frequency-dependent complex ratio (\(S_{11}(f)\)) between the backscattered waves and the incident waves at the radar reference plane was measured at 1601 frequencies over a range of 800 to 4000 MHz, with a frequency step of 2 MHz. The radar measurements were performed over a 3 \(\times\) 3 m sand box, with the antenna aperture situated at about 1 cm above the sand surface. A copper sheet, assumed as a perfect electrical conductor (PEC), was installed at the bottom of the 0.86 m thick sand layer, to control the boundary conditions. The targets were three PVC pipes, 1.20 m in length and 50 mm in diameter, with a thickness of 1.8 mm, and were buried at depths of 0.07, 0.29, and 0.51 m, respectively. The three pipes were placed parallel to each other, and their horizontal distances from the start point of the B-scans were about equal to 0.47, 1.17 and 1.97 m, respectively. The pipes were filled with air. The radar system was installed on an  
Figure 7: Schematic for the shifting zoom. XYZ automated positioning table to automatically acquire the data over a 2.40 m long profile, with a position step of 1 cm. The radar profile was transverse to the pipes. In accordance with the near-field radar antenna model of [PERSON] (1996), the antenna global reflection and transmission functions were determined. Then, in order to remove a portion of the antenna effects, the free-space response of the antenna was subtracted from \(S_{11}(f)\). The frequency-domain radar data were subsequently converted into the time domain, using the inverse Fourier Transform (see Figure 8a), and zero timing with background removal was subsequently applied to highlight the targets (see Figure 8b). Let us now present some results relative to the entire collected experimental dataset presented in Figure 8. For the inversion, the same measurement/inversion parameters from the example described in the section above were used (in particular, observation and investigation domains were 0.8 m long), because the simulations were calibrated on the basis of the experimental results that had already been achieved beforehand. In particular, the sand was dry and its relative permittivity was estimated from the diffraction hyperbolas to be about equal to 2.37, as previously mentioned. The inversions were performed by means of a numerical TSVD, truncated at \(-30\) dB. The first result, shown in Figure 9, refers to subdivision of the overall domain, 2.4 m long, into three adjacent observation domains, each of which are 0.8 m long. As can be seen, two boundary lines are visible between the three investigation domains. In Figure 9, and in the following ones, the real cross section of the buried pipes is also depicted. Figure 8: The experimental radar data, in time domains, after free-space response removal (**a**), and after further (**b**) zero timing and background removal.