## 4 Results
This kind of graphs allows us to study and evaluate the illumination, but it is not statistically significant to calculate Q-factor or BER per row (or column), because we only have 128 bits of data for each column or row in an image that use \(4\times 4\) pixels per bit. In the best case, we would have 512 bits per column when using \(1\times 1\) pixel per bit. In Figure 11, the number of errors is pseudocolored: blue represents few errors than red. We show the number of errors detected in a specific column in Figure 11a (row in Figure 11b). The column number is represented in the X-axis (when we use vertical stripes, this number refers to a specific row), and the evolution in the number of errors as a function of the threshold level is represented in  
Figure 8: Number of errors counted as a function of threshold level for a complete image: (**a**) horizontal orientation; and (**b**) vertical orientation. Figure 9: Zones defined for uniformity analysis. the Y-axis. This representation gives us some clues about the illumination and how sensitive is the threshold level selection. A wider blue zone, which is correlated with the large valley in Figure 8, implies that the selection of the threshold level is less critical. The ripples shown in Figure 11 come from the illumination inhomogeneities: we can see that the horizontal orientation (Figure 11a) is more sensitive to these inhomogeneities. For the different bit sizes and linear stripes orientations, we provide specific quantitative results in tabular form. Tables 1 and 2 shows the data page as a whole, and Tables 3 and 4 shows them in terms of the local characterization in four regions across the aperture of the data page. Figure 11: Number of errors for each column (horizontal stripes) and row (vertical stripes) as a function of threshold level. Data page with 4 \(\times\) 4 pixels per bit. (**a**) number of errors detected in a specific column; (**b**) number of errors detected in a specific row. Figure 10: Number of errors counted as a function of threshold level for vertical stripes orientation by zone: (**a**) Zone 1; (**b**) Zone 2; (**c**) Zone 3; and (**d**) Zone 4. First, in Tables 1 and 2, we show the measured Q-factor and BER for the different bit sizes and orientations considered. The Q-factor is calculated using Equation (1), and the data were obtained from the histograms (Figures 8 and 10). The BER was obtained applying Equation (2). We have also included the number of errors, counting directly, associated with the optimum threshold level. The first thing that we note is that the bit size of 2 \(\times\) 2 pixels presents a very high BER and a low Q-factor. This is because this bit size is in the resolution limit of our system, as we calculated from the 1951 USAF resolution test target shown in Figure 2. Therefore, this resolution is out of our scope due to the limitations imposed by the optical system, not to the LCoS display. Table 1 also reflect that the BER is in the order of \(10^{-3}\) or below before introducing error correction codes. This fact indicates that the reconstruction without errors is possible [28; 29]. From the results in Tables 1 and 2, we also see that the Q-factor and BER values are better, i.e., less image degradation, for the vertical stripes images. This contradicts the results in diffractive optical elements displayed on LCoS devices [8; 10; 11] where diffraction efficiency becomes smaller for vertically oriented elements, i.e., periodicity along the columns of the LCoS. One possible explanation for this difference is that in the HDSS application in the paper, where BIM data pages are introduced, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Pixel Size** & **Q-Factor** & **Errors** & **BER** \\ \hline \(8\times 8\) & 3.082 & 1 & \(1.0\times 10^{-3}\) \\ \(4\times 4\) & 2.473 & 25 & \(6.8\times 10^{-3}\) \\ \(3\times 3\) & 2.243 & 117 & \(12.5\times 10^{-3}\) \\ \(2\times 2\) & 0.574 & 18,097 & \(2.8\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Bit error rate and Q-factor for Horizontal stripes.