## 2 Materials and Methods
### Practical Calculation  
The \(f_{m}\), \(\phi_{m}\), and, \(\phi_{ref}\) values of each point were required to calculate the thickness and speed of sound of the samples. After the analog-digital converter, a Fast Fourier transform (FFT) of the signal  
Figure 3: Scanning acoustic microscope (SAM) system. (A-scan) was computed. The product of FFT was a complex number. The real and imaginary parts contained frequency and phase information, respectively. The interference of the two reflections (front and back sides of tissue) occurred at frequency \(f_{m}\) in condition [22]:  
\[f_{m}=\frac{nc}{2d},\ (\mathrm{n}=0,\ 1,\ 2,\ 3\ldots) \tag{7}\]  
where \(f_{m}\), c, d are the frequency that induces the interference, speed of sound in tissue and thickness of the tissue, respectively. The Equation (7) can assist the work in approximating the interference frequency when acoustic velocity and thickness are in a known range of values. Figure 4c shows that the magnitude (peak to peak) of the first reflection from the front side of the tissue is about 10% of the rear one. Consequently, obtaining the interferential frequency from the spectrum in Figure 4d was difficult. Therefore, the spectrum in Figure 4d was normalized by the reference spectrum in Figure 4b, which resulted in Figure 4e. The reference spectrum in Figure 4b was the product of FFT from the signal in Figure 4a, which was reflected from the substrate. The interferential frequency (\(f_{m}\)) was obtained from the nominal spectrum in Figure 4e. According to the derived frequency (\(f_{m}\)), its phase value (\(\phi_{m}\)) was determined in Figure 4f. The reference phase \(\phi_{ref}\) is the phase of the signal that reflected directly from the substrate at the calculating point. As a result, the reference phase at the calculating point was indirectly calculated owing to tissue coverage at this point. The determination of \(\phi_{ref}\) are mentioned below. Finally, the thickness and speed of sound of the point were determined by replacing \(f_{m}\), \(\phi_{m}\), and \(\phi_{ref}\) in Equations (5) and (6). The acoustic velocity of water coupling was measured by the time lag between two specific points when translating the transducer along the Z-axis. The transducer was scanned over the region of interest. Each point of the sample was calculated to create 2D images. Figure 4: _Cont._  
In this study, the mice skin containing the tumor region were used as the sample for scanning. We proposed a method that used data of the first vertical line (Y axis) and the first horizontal line (X axis) to detect the slope of the stage and the fluctuation pattern shown in Figure 5a,b. The slope of the stage was controlled by the slope adjustment stage, and the fluctuation was determined by the shaft of the motors. For this reason, the first vertical and horizontal lines (along Y and X axes, respectively) need to be reserved in empty (without tissue) as a setup condition, which is described in Figure 5d. Figure 5a,b are the graphs of the phase values at 60 MHz along the Y and X axes, respectively. The red straight lines in the graphs connecting the beginning point and the ending point demonstrate the mismatch between the fluctuated situation and plane function in terms of reference phase extraction. The X-axis was used for scanning and the Y-axis was used for advancing. Figure 5a demonstrates the significant fluctuation and slope of the stage along the Y-axis. The slope of the stage is intentionally regulated as a setup condition for this experiment. Figure 5c is the 2D acoustic velocity image using plane function. In such cases of slope and fluctuation, the plane function gives unreliable results. Previous studies have determined the reference phases by using the plane function. These studies were performed by obtaining the phase values at three corners of the scanning area. Then, the plane function was built, and the reference phase was extracted from this function to compensate for the slope of the scanning stage.