# Measurement of Absolute Acoustic Nonlinearity Parameter Using Laser-Ultrasonic Detection
## 4 Experimental Results  
### Laser-Ultrasonic Detection Results  
The absolute \(\beta\) parameter was measured using a laser-ultrasonic detection method. Before measuring \(\beta\), the capability of the absolute ultrasonic displacement amplitude measurement of the photorefractive interferometer was compared with that of the conventional Fabry-Perot interferometer. Because the surface roughness of the tested prepared specimens was rougher (Ra: 0.64 \(\upmu\)m) than the optically flat surface level (Ra: approximately several nanometers), where the Fabry-Perot interferometer was applicable, the copper and Al6061-T6 specimens were polished with a mirror-like finish (approximately 8 nm). Figure 5 displays the measurement results of the ultrasonic displacement amplitudes for the copper (blue circle) and Al6061-T6 (brown square) specimens using the photorefractive and Fabry-Perot interferometers, where the former used general milling machined specimens and the latter used the mirror-like specimens. The measurement results for the copper and Al6061-T6 specimens indicated a high correlation with the \(y=x\) function, within 10% deviation, demonstrating the capability of the absolute ultrasonic displacement amplitude of the photorefractive interferometer, even on a rough surface. Note that a deviation of about 10% is an acceptable level in consideration of the experimental environment or the effect of surface roughness of the specimen [26]. Figure 4: Picture of photorefractive interferometric system. Figure 3: Schematic diagram for measurement of \(\beta\) parameter using laser-ultrasonic detection. Figure 6 displays typical ultrasonic signals in the time-domain measured using the laser detection method, where the blue solid and brown dotted lines represent the signals obtained from the copper and Al6061-T6 specimens, respectively. The y-axis represents the ultrasonic displacement amplitude. For a clear comparison of the waveforms obtained from the two specimens, the waveform for the copper specimen was horizontally shifted in the time domain corresponding to that of the Al6061-T6 specimen. Note that because the longitudinal ultrasonic velocities for the copper (4750 m/s) and Al6061-T6 (6300 m/s) specimens are different from each other, the arrival times of the ultrasonic signals measured for the two specimens are different. The displacement amplitudes of the fundamental (\(A_{1}\)) and second-order harmonic (\(A_{2}\)) components were extracted in the frequency domain. Here, a Hanning window was applied to increase the frequency resolution, where a side-lobe effect generated by the fundamental component, which has the potential to bury the second-harmonic component, was minimized. The scaling factor was also compensated for by the energy loss according to the Hanning window [33]. The typical signals for the tested specimens in the frequency domain, which were Fourier transformed using fast Fourier transform, are displayed in Figure 7, where blue and dotted-brown lines present the signals for the copper and Al6061-T6 specimens, respectively. In Figure 7, while the ultrasonic displacement amplitude of the fundamental frequency component for the copper specimen corresponded to that of  
Figure 5: Performance comparison for absolute displacement measurement between photorefractive and Fabry–Perot interferometers. Figure 6: Typical ultrasonic signals in time-domain for copper (blue solid line) and Al6061-T6 (brown dotted line) specimens. The two signals aligned with the time axis overlap each other. the Al6061-T6 specimen, displacement amplitudes of the second-order harmonics for the copper and Al6061-T6 specimens are slightly different with each other. Although the surface roughness of both specimens was not optically flat, the spectra of the second-order harmonics and that of the fundamental frequency components can be clearly observed.