# A Content Hiding Method for Digital Hologram Using Multiple Fresnel Diffraction
## 4 Numerical Simulation
### Experiments for the Scaling Factor and Diffraction Distance  
First, we performed experiments on the scaling factor \(w_{s}\) in Equation (5) and the diffraction distance \(z_{2}\) in Equation (9). The results are shown in Figure 8, which shows the NC values for the three diffraction distances of 1, 5, and 20 m as increasing the scaling factor to 10. In all cases, the NC values decrease to certain scaling factor values and then increase as the scaling factor increases further. The lowest NC values were obtained at the scaling factors of about 0.5, 0.7-1.3, and 2.4-4.4 and the encryption ratios were 0.094%, 0.0075-0.0252%, and 0.0053-0.0181% for the distances of 1, 5, and 20 m, respectively.  
Figure 9 shows some example results from encrypting the Rabbit DH with the optimal scaling factors of 0.5, 0.7, and 2.4 and being reconstructed for the diffraction distances (a) 1 m, (b) 5 m, and (c) 20 m. As you can see from the figures, the size of pattern by encryption gets larger as the distance increases. In each case the information contained by the DH was completely hidden unrecognizably in the reconstructed image.  
Because the encryption efficiency was better at the diffraction distance of 20 m than the other distances--Figure 8--we performed more experiments on the diffraction distance of 20 m. A few representative results for the Rabbit (class 1), Sujin (class 2), Baby (class 3), and Billiard (class 4) images are shown in Figure 10. For all the DHs, the results were almost the same as those of the lowest scaling factor value of about 2.5, giving the highest encryption effect.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Specification** \\ \hline Hologram resolution & 1024 \(\times\) 1024 \\ \hline \multirow{3}{*}{2 nd Fresnel Transform} & Distance (\(z_{2}\)) & 1 m, 5 m, 20 m \\ \cline{2-3}  & Pixel Pitch (\(\delta x_{2}\)) & 10 \(\mu\)m \\ \cline{2-3}  & Wavelength (\(\lambda_{2}\)) & 633 nm \\ \hline \multicolumn{2}{c}{Scale Factor (\(w_{s}\))} & 0.1 to 10 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters used in the experiments for the digital hologram encryption.  
Figure 8: C (normal correlation) values according to the transform distance and scale factor of the second Fresnel transform in the proposed digital hologram encryption technique.  
For the four DHs their encrypted and reconstructed images are shown in Figure 11, for some scaling factors: (b,f,j,n) with 2.5, (c,g,k,o) with 3.5, and (d,h,l,p) with 5; and the images reconstructed without encryption (a,e,i,m). From the figures it is clear that the image gets more unrecognizable as the scaling factor increases but also it is clear that in each image the scaling factor 2.5 is enough to hide the information almost completely. The encryption ratios when the scaling factor was 2.5, 3.5, and 5 were 0.0058%, 0.0115%, and 0.0231%, respectively. Figure 12 shows the result of decrypting the encrypted hologram at a transform distance of 20 m by inputting the incorrect key and the correct key. As a result of decoding, it can be confirmed that object information is not known at all when an incorrect key is used.  
Figure 11: _Cont._  
Figure 10: NC values and scale factor of the second Fresnel transform at the transform distance 20 m in the proposed digital hologram encryption technique.  
Figure 9: Examples of encryption results with the optimal scaling factor at the diffraction distances of (a) 1 m (s = 0.5), (b) 5 m (s = 0.7), (c) 20 m (s = 2.4).