## 3 Experimental Results and Discussion  
The performance metrics were evaluated with the validation dataset, which consisted of six classes with 200 images in each class. For the CNN evaluation as the image classifier, a perfect classification was reached in the confusion matrix. The confusion matrix reached is shown in Figure 7. The confusion matrix obtained was a diagonal matrix, where the main diagonal elements reached the maximum classification percentage, i.e., the CNN correctly classified 100% of the images according with their classes.  
The performance of the Regressor as a phase difference estimator was also calculated, and the results obtained are shown in Table 5. The Regressor presented a high coefficient of determination (\(R^{2}\)) of 0.9986, which indicates that it is a high-quality model. Also, the Regressor presented low values of MAE and MSE errors, which indicates that the model presented a good capacity to estimate. It is noted that the regressor reached a high performance, however, there are errors that guarantee that the CNN was not overfitted (the CNN did not memorize the images).  
The training accuracy and training loss curves are shown in Figures 9 and 10, respectively. The CNN obtained a high value of accuracy of 90% in its first epochs; however, the CNN accuracy presented fluctuations until the epoch  
The concentration values estimated by the proposed method with all the validation dataset are shown in Table 6. The error relative between the true and predicted values, the standard deviation (STD), the mean absolute error (MAE), and the mean square error (MSE) per class are also listed in Table 6.  
According to the validation dataset, and the classes with which the CNN was trained, the proposed method presents a precision of \(\pm\)0.0147, and an accuracy of 0.0043%.  
In addition, five new classes with different phases of difference were used to verify the proposed method. The difference phases estimated by the proposed method are shown in Table 7. Also, the new holograms are shown in Figure 11. These holograms were not used before in the training process.  
It should be noted that the errors in Table 6 are smaller than the values obtained with the conventional DHI method [5]. However, in Table 7 the errors are slightly higher; however, the precision can be improved if the image dataset is increased.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Values**} & \multicolumn{6}{c}{**Classes**} \\ \cline{2-7}  & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline True value & 0.2500 & 0.5000 & 0.7500 & 1.0000 & 1.2500 & 1.5000 \\ Predicted value & 0.2503 & 0.5031 & 0.7568 & 1.0002 & 1.2406 & 1.4942 \\ Error & 0.0003 & 0.0031 & 0.0068 & 0.0002 & 0.0094 & 0.0058 \\ STD & 0.0184 & 0.0141 & 0.0108 & 0.0115 & 0.0133 & 0.0201 \\ MAE & 0.0148 & 0.0116 & 0.0101 & 0.0090 & 0.0131 & 0.0166 \\ MSE & 0.0003 & 0.0002 & 0.0002 & 0.0001 & 0.0002 & 0.0004 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Concentration estimated by the proposed method. Standard deviation (STD).  
Figure 11: New classes with holograms used to evaluate the proposed method.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Values**} & \multicolumn{6}{c}{**Classes**} \\ \cline{2-7}  & **7** & **8** & **9** & **10** & **11** \\ \hline True value & 0.3750 & 0.6250 & 0.8750 & 1.1250 & 1.3750 \\ Predicted value & 0.4647 & 0.7167 & 0.9134 & 1.0776 & 1.2766 \\ Error (\%) & 0.0897 & 0.0917 & 0.0384 & 0.0474 & 0.0984 \\ STD & 0.1219 & 0.0330 & 0.0569 & 0.0361 & 0.0746 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The estimated concentration of extra recorded holograms with the proposed method.  
Therefore, the proposed method can calculate concentration ranges from 0.25 gL\({}^{-1}\)L to 1.5 gL\({}^{-1}\), with a precision of \(\pm\)0.0645, and accuracy of 0.0731% based on data and classes that were not used to train the CNN.