## 4 Experimental Results  
### Rough Surfaces on both Sides  
Figures 5 and 6 show the absolute and relative nonlinear measurement results for Al 6061-T6 with rough transmission and reception surfaces (Ra = 0.5, 1.0, 1.5, 2.2, and 2.7 \(\upmu\)m). The marked points represent the average of the measured data, and the error bar represents the range of the max and min values (repeatability error is small within 1%; thus, most error bars overlap with the marked points). Figure 5a shows the variation in the displacement amplitude, \(A_{1}\), obtained from the absolute measurements and the voltage amplitude, \(A_{1}\)', obtained from the relative measurement of the fundamental frequency component with respect to the surface roughness by normalizing each initial value. The voltage amplitude, \(A_{1}\)', decreased sharply as the surface roughness increased; it decreased to 0.53 on the roughest surface (Ra = 2.7 \(\upmu\)m). However, in the absolute measurements, the displacement amplitude, \(A_{1}\), remained unchanged up to Ra = 1.0 \(\upmu\)m, and then decreased gradually as the surface roughness increased; it decreased to 0.75 on the roughest surface (Ra = 2.7 \(\upmu\)m). Figure 5b shows the variation in \(A_{2}\) and the voltage amplitude, \(A_{2}\)', of the second-order harmonic component with respect to the surface roughness by normalizing each initial value. In the relative measurements, the voltage amplitude \(A_{2}\)' of the second-order harmonic component decreased sharply as the surface roughness increased; it decreased to 0.30 on the roughest surface (Ra = 2.7 \(\upmu\)m). In contrast, in the absolute measurements, the displacement amplitude \(A_{2}\) was constant up to Ra = 1.0 and then decreased gradually as the surface roughness increased; it decreased to 0.57 on the roughest surface (Ra = 2.7 \(\upmu\)m). These experimental results show that voltage amplitudes \(A_{1}\)' and \(A_{2}\)' obtained from the relative  
Figure 5: Variations in (**a**) fundamental frequency component (\(A_{1}\) and \(A_{1}\)’); (**b**) second-order frequency component (\(A_{2}\) and \(A_{2}\)’) in absolute and relative measurements for Al 6061-T6 with respect to the surface roughness. Figure 6: Variations in the absolute and relative nonlinearity parameters for Al 6061-T6 with respect to the surface roughness. measurements exhibit a steeper decrease than displacement amplitudes \(A_{1}\) and \(A_{2}\) obtained from the absolute measurements because the calibration function, H(\(\omega\)), obtained through calibration increases slightly as the surface roughness increases (Figure 2b). In other words, the variations in the sensitivity of the receiving transducer caused by the surface roughness are compensated by H(\(\omega\)). Figure 6 shows the normalized absolute and relative nonlinearity parameters for Al 6061-T6 with respect to their surface roughness. The absolute nonlinearity parameter barely changes with the increasing surface roughness. In contrast, the relative nonlinearity parameter barely changes up to Ra = 1.5 \(\upmu\)m, as observed for the absolute nonlinearity parameter, and then increased sharply as the surface roughness increased; it increased to 1.15 on the roughest surface (Ra = 2.7 \(\upmu\)m). These results show that the absolute nonlinearity parameter changes by a smaller degree than the relative nonlinearity parameter according to variations in the surface roughness. The absolute nonlinearity parameter can compensate for the influence of the surface roughness using the calibration function obtained from the calibration process in the absolute measurements; thus, the influence of surface roughness is different from that observed for the relative nonlinearity parameter. Figure 7 shows the normalized absolute and relative nonlinearity parameters for SUS 304 specimens with respect to the surface roughness (Ra = 0.5, 0.9, 1.7, 2.2, and 2.9 \(\upmu\)m). The absolute nonlinearity parameter barely changes with the increasing surface roughness.