## 4 Experimental Results
The other is the increase of shot noise of the CMOS sensor. The optical power passing through the spatial filter decreases significantly in proportion to its area as the size of the spatial filter decreases. In the range between 200 and 400, the visibility did not change significantly regardless of the spatial filter size. In the tangential direction, it is obvious that the visibilities of group 2 were much lower than those of group 1. This is because a target object far from the optical axis is strongly affected by the temporal coherence. Conversely, the visibility in the sagittal direction did not change significantly, unlike in the tangential direction. This experiment is very consistent with the simulation in Section 3. For example, it is validated by comparing the visibility of the reconstructed object located at 150 mm in tangential group 1 of Figure 10. The visibility began to decrease below 0.4 when the spatial filter size exceeded 400. Similarly, it is also confirmed that the object located at 150 mm could not be expressed after a size of around 400 through a red line of Figure 6.  
Consequently, the optimal spatial filter size (OSFS) was estimated to be between 200 and 400. In the tangential direction of group 1, the OSFS for reconstruction at object distances of 50, 100, and 150 mm was around 350 because there was the highest visibility around the area. In the case of reconstructing at object distances of 200 and 250 mm, the OSFS was around 270. In the tangential direction of group 2, the OSFS was considered as 400 when object distances were 50 and 100 mm. In the case of object distances of 150, 200, and 250 mm, the OSFS was around 200. Similarly, the OSFS was obtained depending on the object distances in the sagittal direction. In group 1, in the case of object  
Figure 10: Visibility depending on the sagittal and tangential directions. distances of 50, 100, and 150 mm, the OSFS was around 350 \(\upmu\)m. When object distances were 200 and 250 mm, the OSFS was 270 \(\upmu\)m. In the case of group 2, the OSFS was around 450 \(\upmu\)m with an object distance of 250 mm. Also, we estimated an OSFS of 300 \(\upmu\)m at the object distances of 100, 150, and 200 mm. In case of an object distance of 250 mm, the OSFS was around 250 \(\upmu\)m. These results indicate the OSFS differs according to object distances and it is hard to decide the OSFS. However, among the specification of a holographic display, the expressible object distance range is an important characteristic. An increase of the spatial filter size induces a narrowing of the expressible object distance range, and this is demonstrated in our experiments. Therefore, we obtained the OSFS by analyzing a figure of merit which is the negative of the sum of the measured visibilities according to the spatial filter size, \(r_{s}\), and the figure of merit, \(M\), is calculated by  
\[M(r_{s})=-\sum_{z_{obj}}v(r_{s},z_{obj}), \tag{10}\]  
where a figure of merit, \(M\), signifies the criterion that a hologram can be accurately expressed. This indicates that the smaller the value, the better the hologram is expressed. Figure 11 shows the figure of merit, \(M\), depending on the spatial filter size. Blue circles denote the figure of merit of the measured result corresponding to the spatial filter size, and a blue line is a regression result of the figure of merit values. Considering the tendency of visibility of Figure 10, there is no significant change between 200 \(\upmu\)m and 400 \(\upmu\)m in \[v=\frac{I_{max}-I_{min}}{I_{max}+I_{min}}, \tag{9}\]0 When the spatial filter size is 270 \(\upmu\)m, the figure of merit, \(M\), is the minimum value.