## 3 Experimental Approach
### Signal Processing  
Figure 5a shows the first and second reflected pulses from the interface of the solid-air contact (reference). This solid-air reflection acts as a reference. Since almost all the sound energy will be reflected from a solid-air interface, this is equivalent to the incident signal. Figure 5d shows the same pulses from a solid-solid contact at nominal contact pressure 4 MPa. In the present analysis, only the first reflected pulse was used as this contains most information from the interface.  
This first peak was extracted and a Hanning window function and a zero-pad function were applied to increase the resolution of the signals (Figure 5b,e). It should be noted that the type of window function as well as the length of zero-pad function are dependent on the quality of captured signals. In this study, other window functions, such as Hamming  
Figure 5: Signal processing of the reflected pulses from interface using a 140 V excitation with incident frequency 2 MHz: (**a–c**) solid-air contact (reference signal); (**d–f**) solid-solid contact at nominal contact pressure 4 MPa; (**a,d**) time domain of generated, first and second reflected pulses; (**b,e**) Hanning window and zero pad result of the first reflected pulse; (**c,f**) Fast Fourier Transform (FFT) results of the first reflected pulse.  
window function and Blackman window function were employed, but showed insignificant difference in the results, so the Hanning window function was adopted throughout.  
The time domain signals cannot precisely (in most cases this is impossible) indicate the existence of a super-harmonic (higher harmonics), subharmonic, or a mix of both. Therefore, a Fast Fourier Transform was employed to convert the time domain reflected signal to the frequency domain as shown in Figure 5c,f. These peaks are clearly visible corresponding to the fundamental frequency, as well as both, and even and odd (second) harmonics.  
Since Figure 5c shows solid-air contact, the source of the higher order harmonics in this case cannot be due to the interfacial contact. This nonlinearity might be generated by the bulk material, bonding nonlinearity (transducers to the specimen), the transducers themselves, or in the amplifier circuitry [29; 33; 44]. A test to see whether the interface (in the solid-solid case) is a source of harmonics is to increase the nominal contact pressure; this causes a reduction in the amplitude of higher harmonics indicating that the interface is also the source of nonlinearity generated in the reflected signals. To eliminate all sources of nonlinearity apart from those generated by the contact [45; 46], Equation (38) is reformulated as:  
\[\gamma=\left|\frac{A_{2}}{A_{1}^{2}}-\frac{A_{2\ ref}}{A_{1\ ref}^{2}}\right|= \frac{K_{2}}{\rho c\omega\sqrt{1+\left(K_{1}/\rho c\omega\right)^{2}}} \tag{40}\]  
where \(A_{1\ ref}\) and \(A_{2\ ref}\) are amplitudes of fundamental frequency and second order harmonic from a solid-air contact, respectively. In this way all nonlinearities not associated with the interface are subtracted out.  
The amplitude of the fundamental frequency of the reflected pulse in solid-solid contact (Figure 5f) was divided by the amplitude of the corresponding harmonic from the reference solid-air contact (Figure 5c) to derive the reflection coefficient \(R\) (Equation (36)). For the second order nonlinear parameter \(\gamma\), the amplitude of the fundamental frequency was divided by the square of the amplitude of the second harmonic (Equation (40)).