# Dynamic Identification of Tensile Force in Tie-Rods by Interferometric Radar Measurements
## 3 Microwave Radar Interferometry for Structural Vibration Measurements
Indeed, radial displacements are proportional to the wave propagation velocity and to the phase shift \(\Delta\varphi\), and inversely proportional to the central frequency of the emitted waves [34]. The main features of the employed customized IBIS-FS radar interferometer are collected in Table 1.  
About data in Table 1, notice that the maximum allowed value of the sampling frequency of the standard IBIS-FS device is 200 Hz and that the displacement accuracy measured as line-of-sight displacement standard deviation depends on the distance between instrument and target and on the signal-to-noise ratio (SNR) of the received waves. The interferometric radar technique is still under investigation and development with the aim of overcoming some relevant drawbacks. First, the maximum accuracy of displacement measurements, of the order of hundredths of millimeters, can be considered a good value, but as recalled above, this accuracy is achievable only in the presence of targets with good reflectivity on the structure and decreases with the distance. Second, as suggested by Figure 2, right, the observed scenario is detected from the radar interferometer as divided into discrete ranges (the so-called range bins) along the line-of-sight direction. As a consequence, the radar interferometer is not able to distinguish two or more reflective elements located at the same range bin, i.e., at the same radial distance from the instrument, since they correspond to the same peak in the range profile diagram. Third, the system can measure only the component of displacements along the line-of-sight direction. The same three considerations hold for dynamic measurements. In conclusion, it is possible to say that a radar interferometer could provide high-precision measurements of the radial component of displacements but without accurate information about the location of the observed points. This, for example, prevents from determining e mode shapes of vibrating structures, unless they occur special conditions like, e.g., in the case of large structures with many well-spaced high reflectivity points: clearly, this is not the case of tie-rods of historic masonry constructions. Anyway, to improve the accuracy of measurements also in the presence of targets with low reflectivity and/or for clearly distinguish measurement points on the structure, some corner reflectors can be installed. A corner reflector is a pyramidal metallic element with high reflectivity to electromagnetic waves. Even though this is an effective solution, the need to access the construction nullifies one of the main advantages of the interferometric radar technique. On the other hand, the installation of corner reflectors is easier and quicker than installing accelerometers. \begin{table}
\begin{tabular}{c c} \hline Sampling frequency (Hz) & \(>\)300 \\ Radio-frequency band (GHz) & 17.05–17.35 (K\({}_{u}\)-band) \\ EIRP power (dBm) & 26 \\ Modulation & Linear frequency modulated continuous wave (LFMCW) \\ Displacement accuracy (mm) & 0.01 \(\div\) 0.1 \\ Range resolution (m) & 0.5 \\ Operating range (m) & Up to 1000 \\ Operating temperature (\({}^{\circ}\)C) & \(-20\)\({}^{\circ}\)C to +55 \({}^{\circ}\)C \\ \hline \end{tabular}
\end{table} 
Table 1: Radar interferometer: features. Figure 2: The SF-CW technique in (**a**) time and (**b**) frequency domain [34] (left) and the range profile diagram [41]. The cited improvements of the experimental setup, along with the research activities performed to take advantage of the above recalled appealing features of the interferometric radar technique, are opening increasing application field for this experimental approach, also involving application to architectural heritage constructions [45; 46; 47].