## 2 Materials and Methods
### Phase Difference Images  
Seven liquid samples were created by mixing 1 liter of distiller water with various masses of NaCl. The different masses of NaCl used are shown in Table 1.  
In order to measure the concentration difference between two liquid samples, two holograms were recorded at different moments or states. A hologram is obtained from a wave-front. The wave-front coming from certain liquid sample is represented as:  
\[U_{1}=u_{1}(x.y)\ e^{i\phi_{1}(x,y)} \tag{1}\]  
where \(u_{1}(x.y)\) is the amplitude, \(\phi_{1}\) is the phase of the wave-front, and \(x,y\) are the rectangular coordinates of the recording sensor plane.  
Then, a second hologram was obtained from a wave-front coming from another liquid sample or after slightly modifying the concentration of the liquid sample. The new wave-front is represented as:  
\[U_{2}=u_{2}(x.y)\ e^{i\phi_{2}(x,y)} \tag{2}\]  
where \(\phi_{2}\) is the new phase that indicates a change in the optical path length, i.e., \(\phi_{2}=\ \phi_{1}+\Delta\phi_{2-1}\).  
The procedure continued with the calculation of the phase difference from the individual phase terms \(\Delta\phi_{2-1}=\ \phi_{2}+\ \phi_{1}\). A phase term depends on the transverse distances and the refractive index  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Samples**} \\ \cline{2-7}  & **0** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline NaCl (g) & 0.00 & 0.25 & 0.50 & 0.75 & 1.00 & 1.25 & 1.50 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Liquid samples used.  
Figure 1: Schematic diagram of the experimental setup of digital holographic interferometry (DHI). _LA1_: laser; _BS1_ and _BS2_: cubic 50:50 beam splitters; _M1_ and _M2_: mirrors; _L1_, _L2_, _L3_, _L4_, and _L5_: lenses; _D1_: diffuser; _S1_: sample liquid (glass cylindrical tube; _A1_: rectangular aperture; CCD: charge-coupled device; _f\({}_{CX}\)_: the spatial carrier frequency along the x direction of the sensor plane.  
of the liquid mixture inside a glass tube. The refractive index difference is related to the change of concentration (\(CON\)) and the temperature (T) between liquid samples. In the case of aqueous salt mixtures, the liquid samples have a linear relationship between the refractive index and concentration (\(CON\)), which is considered to be constant at \(1.71\times 10^{-3}\) at a temperature of 20 \({}^{\circ}\)C. Therefore, the concentration difference between two liquid samples can be described as [5]:  
\[\Delta\phi_{2-1}(x,y)=k\Big{\{}d_{i}(x,y)\big{[}1.71\times 10^{-3}\big{]}[ CON_{2}(x,y)-CON_{1}(x,y)]\Big{\}} \tag{3}\]  
where \(k=\pi/2\lambda\), \(\lambda\) is the wavelength, \(CON_{1}\) and \(CON_{2}\) are the concentration values of two liquid samples, and \(d_{i}\) is the inner transversal distance of the glass tube.  
Therefore, the wrapped phase difference images were obtained from the difference between two holograms with different concentrations. The wrapped phase difference images were obtained from the difference between the different samples and the sample with only distilled water (0 g of NaCl), which did not require special preparation. In addition, six classes were created with different concentrations, and they are shown in Table 2. The wrapped phase difference images for each class are shown in Figure 2.