# Dynamic Identification of Tensile Force in Tie-Rods by Interferometric Radar Measurements
## 3 Microwave Radar Interferometry for Structural Vibration Measurements  
The radar interferometer is a coherent radar that allows detecting even small displacements of a target located at a great distance by generating, transmitting and receiving electromagnetic waves. The interferometric working principle allows measuring displacements by exploiting phase information of the back-reflected signal. The capability of remotely monitoring displacements of several points of a structure is the main advantage of this relatively new technology over other existing and well-established measurement techniques [43; 44; 45; 46]. Furthermore, the time sampling of the acquired data makes the radar interferometer also capable of vibrations measurements. In the dynamic structural field, the most advantageous features of this technology are the possibility of remote, contactless measurements (in principle, the access to the construction is not needed), the quick and easy installation (about 15 min); the possibility of operating day and night and in all weather conditions. Specifically, for the experimental tests described in the following Section, the employed interferometric radar system is a customized version of the IBIS-FS instrument, manufactured by IDS GeoRadar (Pisa, Italy) and aimed at remote static and dynamic monitoring of structures. The system basically consists of:  
1. The radar unit, including the transmitter, the receiver, and the antennas, capable of generating, emitting, receiving, and processing modulated microwaves of a specified frequency. In particular, the two antennas on the front side focus the radiated energy in the form of a beam of a suitable shape during the transmission and collect the echo signal during the receiving phase. The unit includes the interferometric sensor and the communication ports. 2. The power module. Two 12-volt batteries provide an independent power supply. 3. The control and recording module. A portable field computer, USB connected to the radar units, and equipped with the IBIS-FS CONTROLLER custom software, is used to manage the tests and to monitor and record the acquired data. 4. A sturdy tripod is provided with a movable head allowing the radar beam to be oriented in any direction. The accurate detection of differential displacements of the targets included in the cone of view of the antennas is performed by exploiting the following principles:  
1. The stepped frequency-continuous wave (SF-CW) technique [34] allowing for a large bandwidth even using long-duration microwaves (continuous waves) by linearly increasing the frequency of successive pulses in discrete steps (stepped frequency). This principle enables the sensor to detect the displacements of several targets at different locations, given that they are in the scenario illuminated by the emitted beams and are spaced more than the spatial resolution of the instrument (0.50 m for IBIS-FS). An SF-CW radar achieves a large effective bandwidth through a burst of N electromagnetic pulses (tones), whose frequencies are increased from tone-to-tone by a constant frequency increment \(\Delta f\) (see Figure 2, left). By taking the inverse discrete Fourier transform (IDFT) of the received complex signal sampled at N discrete frequencies, the response is reconstructed in the time domain of the radar, obtained the diagram called range profile (Figure 2, right), reporting the received echo intensity (amplitude) in the function of the distance of the target from the sensor. Peaks in the range profile diagram represent the locations of targets, reflecting a good quality signal. 2. The radar interferometry technique: the electromagnetic waves reflected back by moving targets are characterized by a phase shift \(\Delta\varphi\) compared to the emitted waves. This phase information can be exploited to detect differential radial displacements along the wave propagation direction.