# Computer-Generated Holography Methods for Data Page Reconstruction Using Phase-Only Medium
## 5 Analysis of Reconstructed Data Page Images  
First, in the case of double-phase holograms, it appeared impossible to reconstruct the data page image in an on-axis configuration without being distorted by zero order. So, for the experiments, we decided to shift the data page image into the off-axis zone during CGH synthesis. In Figure 5b, the result of the registration of the output field formed by double-phase off-axis Fourier CGH is illustrated. One can see the presence of sharp zero order, and the image of the data page shifted from it to a certain distance great enough to avoid the cross-section. The registered data page images were analyzed. The complex amplitude modulus (square root of intensity) of the images was subjected to analysis. The mathematical expectations \(M_{1}\) of the pixel values in the true locations of the bits corresponding to the units were determined. The mathematical expectation \(M_{0}\) for the zeros is equal to 0. The standard deviations \(\sigma_{1}\) and \(\sigma_{0}\) of units and zeros were also calculated. Two following cases were considered. Elements of the data page were decoded:  
* Without taking into account the presence of zeros next to units;
* Taking into account the presence of zeros next to units. Figure 6 shows histograms for the data page elements' amplitude modulus. They correspond to the 0 and \(\pm 1\) elements. Both mentioned cases taking features into account are given. Blue columns correspond to the pixel numbers of \(\pm 1\) elements. Orange columns correspond to the 0 elements. Gray parts of columns correspond to pixel numbers of \(\pm 1\) and zero elements. Figure 5: Registered images of a reconstructed data page (**a**,**b**) and its informative parts (**b**,**d**). Fourier CGHs were synthesized by the bipolar intensity (**a**,**c**) and double-phase coding (**b**,**d**) methods. It can be seen that the double-phase coding method provides a lower quality of reconstructed images. Without taking features into account, this method gave a significant intersection of the zeros and \(\pm 1\) elements (see Figure 6b). Herewith for the bipolar intensity method, the intersection is almost absent (see Figure 6a). Taking the features of data page representation into account improves the quality even more. For the double-phase coding method, the intersection almost disappears (see Figure 6d). There is no intersection for the bipolar intensity method (see Figure 6c). At the same time, there was even a clear range separation between zeros and \(\pm 1\) elements. To access the improvement, signal-to-noise ratio and bit error rate values were determined. The SNR was calculated using the following equation:  
\[SNR=\frac{M_{1}-M_{0}}{\sigma_{1}+\sigma_{2}} \tag{14}\]  
The probability of BER value was estimated using Equation (1). Obtained values for both cases of data page consideration are shown in Tables 1 and 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Synthesis Method** & \(M_{1}\) & \(M_{0}\) & \(\sigma_{1}\) & \(\sigma_{0}\) & **SNR** & **BER** \\ \hline Double-phase coding & 13.24 & 0 & 1.14 & 6.42 & 1.8 & \(6.4\times 10^{-3}\) \\ Bipolar intensity & 15.04 & 0 & 0.23 & 6.21 & 2.3 & \(4.8\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Obtained results for data page image analysis in the case of ignoring data page specificities. Figure 6: Amplitude modulus histograms of zero and unit elements of the registered data pages. Fourier CGH were generated with the bipolar intensity (**a,c**) and double-phase coding (**b,d**) methods. The top row (**a,b**) does not consider the data page features. The bottom row (**c,d**) takes the data page features into account. It can be seen that all obtained results are better for the bipolar intensity method. The SNR value is higher at 1.3 (ignoring features; see Table 1) and 1.7 times (taking features into account; see Table 2). The BER values for the bipolar intensity method are more than ten times higher than that for the double-phase method.