## 2 Materials and Methods
### Force Sensor  
Figure 2a shows a photo of the developed force sensor. The force sensor was used for many reasons. First, it is important to monitor the force with which the surface under examination is \"hit\", for obvious reasons of safe conservation. Furthermore, the sensor signal is used as a trigger for the acquisition window of the sound picked up by the microphone, to optimize the amount of digital data to be examined by the calculation system (Figure 2c). Finally, we measure the impact-force to implement the CTT procedure described in the previous paragraph: the signal from the force sensor is sampled by the ADC (analog to digital converter) section that is inside the hardware at 500 kHz, a high sampling frequency for this type of signal (this signal is in a band up to 10-20 kHz); this sampling frequency was chosen to accurately measure the impact-time.  
The device is manufactured in a classic way, using two piezoelectric ceramic rings (type PZZ7 Ferroperm, Meggitt A/S, Kvistgaard, Denmark) connected in parallel and prestressed by a screw and inserted in a metal case that represents both a protection for the delicate ceramics used, and the system for transferring the force to the ceramics themselves (Figure 2b).  
Figure 1: Schematic of the measurement system. The electronic board (for the acquiring, controlling, and calculating of the signals) is connected by wires to the infrared (IR) camera and to the hitting device (probe).  
It is well known [16] that the exertion of a force \(F\) on a PZT transducer results in the generation of a charge \(Q=-d_{33}{}^{*}F\) (\(d_{33}\) is the piezoelectric charge constant). This charge is completely independent of the dimensions of the PZT element. However, if \(n\) PZT rings are stacked and connected electrically in parallel results \(Q=-n{}^{*}d_{33}{}^{*}F\) since the force acts simultaneously on \(n\) plates. The open circuit voltage \(V\) on a disc of height \(t\) is given by: \(V=-g_{33}{}^{*}t{}^{*}T_{3}\), where \(g_{33}\) is the piezoelectric voltage constant, and \(T_{3}\) is the stress in axial direction. In the case of the stack, the rings are connected in parallel, so the resulting voltage is the same. The advantage of a stack is more charge, higher capacitance and thus a lower impedance. Since the voltage increases almost linearly with mechanical stress, the PZT transducer can be used as force sensor. It is possible to rewrite the equation of the open circuit voltage to calculate the force exerted on the stack of the rings, in function of the material properties and of the geometrical dimensions, remembering that the stress T is dimensionally equivalent to a force acting on an area:  
\[|F|=\frac{V{\cdot}\pi{\cdot}\left(d_{o}^{2}-d_{i}^{2}\right)}{4{\cdot}g_{33}{ \cdot}t} \tag{1}\]  
where \(V\) is the measured voltage, \(d_{o}\) and \(d_{i}\) are the outer and the inner diameter of the PZT ring, \(g_{33}\) is the piezoelectric voltage constant, defined as the electric field generated in a material per unit of mechanical stress applied to it (for PZT27 Ferroperm, \(g_{33}=26.7{\cdot}10^{-3}\frac{V{\cdot}m}{N}\)), and \(t\) is the thickness of the ceramic. In our case, \(d_{o}=5\) mm, \(d_{i}=2.3\) mm, \(t=1\) mm and hence \(F=0.58{\cdot}V\). With our setup, we obtain an impact force of about 0.3-2 N.