## 3 Results
### Spatial Resolution of the L-RFA  
A high spatial resolution, comparable to that of a single cell in soft-tissue tumor stiffness measurement, is essential for physical oncology. The spatial resolution of L-RFA was evaluated using a scanning Doppler vibrometer to visualize the natural vibration due to LIPTEW. Figure 8 presents the evaluation conditions and results. As shown in Figure 8a, the sample surface was irradiated using an excitation laser at oblique incidence, and the center of the laser irradiation, as indicated by the blue dot in the figure, was measured. Figure 8b presents the measurement positions for a total of 235 points evaluated using the  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Actual Values in True and Predicted Young’s Modulus**} \\ \hline True Young’s modulus (MPa) & 0.0424 & 0.129 & 0.241 & 0.388 & 0.539 & 0.627 & 0.957 & 1.22 & 1.37 \\ \hline Predicted Young’s modulus (MPa) & 0.0200 & 0.136 & 0.441 & 0.472 & 0.598 & 0.550 & 1.17 & 1.13 & 1.53 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Prediction results of Young’s modulus by machine learning-based analysis in Figure 7b.  
Figure 6: Laser-induced vibrational spectrogram of agarose with Young’s moduli of (**a**) 0.042 MPa, (b) 0.76 MPa, and (c) 2.3 MPa.  
scanning Doppler vibrometer. Figure 8c presents the evaluation results of the fundamental mode (924 Hz) and (d) second-harmonic mode (1848 Hz) for the agarose sample with a Young's modulus of 0.042 MPa. Figure 8e presents the results of the evaluation of the fundamental mode (924 Hz) and (f) the second harmonic mode (1848 Hz) for an agarose sample with a Young's modulus of 1.2 MPa. Due to oblique incidence, the laser irradiation spot was elliptical, and an oscillation range of approximately 2 mm was observed for an irradiation system of approximately 4 mm on average as shown in Figure 8c-e. This indicates that in the laser irradiation spot focused by the lens only a portion of the intensity, which was considered to exhibit a Gaussian distribution, oscillated. Moreover, when the laser irradiation scheme was optimized, the extremely high spatial resolution vibrational area, a small region with a diameter of less than one-tenth of the laser irradiation spot diameter, was provided as shown in Figure 8f. From the experimental results, it was necessary to utilize higher-order vibration modes for demonstrate high spatial resolution measurements. Also, materials with higher Young's modulus were easier to measure. In principle, the laser beam can be operated up to the abovementioned wave-length, and by scaling the results of this study it is expected that the laser beam can be operated to under several tens of micrometers, which would allow for a high spatial resolution (i.e., the size of a single cell).  
Figure 8: Evaluation settings of (**a**) overview and (**b**) scanning point of laser Doppler vibrometer, and behaviors of forced vibration obtained by L-RFA on agarose samples at different Young’s moduli as (**c**) 924 Hz at 0.042 MPa, (**d**) 1848 Hz at 0.042 MPa, (**e**) 924 Hz at 1.2 MPa, and (**f**) 1848 Hz at 1.2 MPa, respectively.  
Figure 7: Prediction results of Young’s moduli of agarose samples using machine learning-based analysis with (**a**) non-averaged data and (**b**) averaged data.