## 3 Results and Discussions
Linearly polarized light with rotation of its polarization angle was used as the probe beam incident on the surface of the sample. The polarization states of the reflected light were perturbed by the surface acoustic wave. By measuring the reflected light at four different polarization angles, I(0\({}^{\circ}\)), I(90\({}^{\circ}\)), I(45\({}^{\circ}\)), and I(135\({}^{\circ}\)), the Stokes parameters, the phase delay \(\delta\), and the polarization orientation angle \(\psi\) were calculated. The calculated polarization parametric images of the probe beam can be related to the ultrasonic wave field via the photo-elastic effect [31]. The visualization of the acoustic field is shown in Figure 6. The Stokes parameters S0, S1, S2, S3 phase delay \(\delta\) and polarization orientation angle \(\psi\) can be obtained from I(0\({}^{\circ}\)), I(90\({}^{\circ}\)), I(45\({}^{\circ}\)), I(135\({}^{\circ}\)). I(10\({}^{\circ}\)) is the intensity of the linearly horizontal polarized light component, I(90\({}^{\circ}\)) is the intensity of the linearly vertical polarized light component, I(45\({}^{\circ}\)) is the intensity of the linearly +45\({}^{\circ}\) polarized (L+45P) light component (L for linearly and P for polarization), I(135\({}^{\circ}\)) is the intensity of the linear \(-45^{\circ}\) polarized (L\(-45P\)) light components. From Figure 6, we found that S3 and \(\psi\) show high sensitivity to the laser-induced surface acoustic wave, while the wavefront can barely be seen in the phase retardation \(\delta\). As a comparison, the propagation of acoustic waves in the xy-plane induced by three acoustic emitters at the same locations as the laser array source was simulated using MATLAB's k-wave toolbox [32]. The heat sources in Model 1, Model 2, and Model 3 were replaced by sound sources with the same size, shape, distributions, and delay time. The simulation area was a square with a side length of 8 mm, and an 800 \(\times\) 800 mesh was used. The speed of sound in the medium was taken to be 2940 m/s, the same as the surface wave sound velocity of aluminum. The uniformly distributed source was defined by the acoustic pressure, which was assigned a value of \(-0.1\) Pa because thermally induced SAWs have a negative initial acoustic pressure. The initial frequency of the acoustic signal was specified as 3.3 MHz, approximately equal to the frequency of the sound wave excited in the FEM simulation. The input signals of the acoustic sources A, B, and C in Model 3 are shown \begin{table}
\begin{tabular}{c c c} \hline \hline
**j** & **n** & **Z\({}_{\textbf{j}}\)** \\ \hline
1 & 1 & y \\
2 & 1 & x \\
3 & 2 & 2 xy \\
4 & 2 & \(-1+2(x^{2}+y^{2})\) \\
5 & 2 & \(x^{2}-y^{2}\) \\
6 & 3 & \(3x^{3}-y^{3}\) \\
7 & 3 & \(-2y+3y(x^{2}+y^{2})\) \\
8 & 3 & \(-2x+3x(x^{2}+y^{2})\) \\
9 & 3 & \(x^{3}-3 xy^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: First 3 orders of the Zernike polynomial in Cartesian coordinate. in Figure 7. The input signal for source B has a time delay of 200 ns relative to sources. A and C.  
Figure 5: Processed data fitted with 2–5 order polynomials and Zernike polynomials at 1.2 μs. From top to bottom: original data interpolation results, second, third, fourth, and fifth-order polynomial fitting, Zernike polynomial fitting. (**a**) Model 1 (single heat source); (**b**) Model 2 (three heat sources without delay); (**c**) Model 3 (three heat sources with delay). Figure 6: Modeled Stokes parameter images of S0, S1, S2, S3, sin\(\delta\), \(\psi\).