## 3 Results and Discussion  
Figure 4b shows a reconstructed phase pattern. The phase value is shifted by \(\pi\)/4. The shift value is required by correcting initial phase in recording. It does not seem that the reconstructed phase pattern is similar to recording data page (Figure 4a). The extinction ratio of right-circular polarization component to left-circular polarization component is not zero in this system. Therefore, the right-circular polarization component is slightly included in the illumination beam. The reconstructed signal beam is superposed with the right-circular polarization component of transmitted illumination beam. Therefore, the reconstructed phase value was changed. By considering the coding method, the transmitted illumination component can be eliminated. In the coding method, the average of complex amplitude of a symbol is always zero when it is assumed that the intensity is homogeneous. When the complex amplitude values of the reconstructed signal pattern in a symbol were averaged, the transmitted signal beam component is obtained. A data pixel consisted of 10 \(\times\) 10 pixels. The central 6 \(\times\) 6 pixels in the 10 \(\times\) 10 pixels were used to average the complex amplitude. Then, the standard deviation of real and imaginary parts was calculated and an argument was calculated from the real and imaginary parts. When the phase difference at a pixel is larger than the argument value, the complex amplitude value at the pixel is not used to calculate average complex amplitude. By substituting the average complex amplitude from the reconstructed signal complex amplitude, corrected phase pattern is obtained. The corrected phase pattern is shown in Figure 4c. Furthermore, to evaluate symbol error rate (SER), the reconstructed phase pattern must be four-valued. The sine and cosine of the phase value are calculated  
Figure 3: Phase data page. (**a**) four-valued phase data phase; (**b**) four symbols. in a symbol and compared with 16 cases of symbol pattern. Then, the phase pattern is substituted by a symbol pattern with the least square of the sum of the difference. By the method, a phase data page was reconstructed. The reconstructed phase data page is shown in Figure 4d. The symbol error rates (SERs) of reconstructed 12 phase data pages are shown Table 1. As shown in Table 1, SERs were under 11%. Those values were enough low to make zero by using an error correction method. The symbol error rate is dependent on the resolution and the positioning accuracy of the linear stage because of shift selectivity. In this experiment, the resolution and the accuracy are 2 \(\upmu\)m and 10 \(\upmu\)m, respectively. In this study, the data pixel size of phase data pages was reduced from 200 \(\upmu\)m to 60 \(\upmu\)m. Then, the width of the data page was calculated to \(W=30\times 60=1.8\) mm. When the recording medium is thin, that is, \(z_{1}=z_{2}\), and it is located at \(z_{1}=z_{2}=-1\) mm, \(|x_{\mathrm{R}}^{\prime}|=W|z_{1}|/f=450\)\(\upmu\)m is required to record another phase data page. When the thickness becomes greater, that is \(z_{2}\) approaches zero, the reconstructed image is eliminated by shifting the recording medium with less than 450 \(\upmu\)m. Therefore, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Page no.** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline SER (\%) & 3.33 & 0 & 2.38 & 0.48 & 0 & 5.71 \\ Page no. & 7 & 8 & 9 & 10 & 11 & 12 \\ SER (\%) & 10.95 & 10.95 & 2.86 & 1.90 & 2.86 & 0.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Symbol error rate (SER) of reconstructed phase data pages. Figure 4: Reconstructing process. (**a**) Recording phase data phase; (**b**) Reconstructed phase pattern; (**c**) Corrected phase pattern; (**d**) Reconstructed phase data page. shift multiplex recording was realized with the shift amount of 100 \(\upmu\)m. When the shift amount is decreased, the crosstalk noise is increased. Therefore, SER is increased. For a shift amount of 100 \(\upmu\)m, it has been determined that the SERs fall below about 10%.