## 4 Experimental Results  
To find the optimal spatial coherence of the LED in a holographic display, we performed experiments to reconstruct Fresnel holograms by changing the spatial coherence as shown in Figure 7. Figure 7a describes the optical scheme of the experiment, and the optical configuration of the experiment was equal up to that of the SLM compared to the Fourier hologram experiment described in Section 2. After the SLM in the optical path, a 4\(f\) optical system was inserted to remove the conjugate noise by the single-side bandpass filter. In the 4\(f\) optical system, the focal lengths of the two lenses were 100 mm. The experimental setup is shown in Figure 7b. Hence, the optimal size of the spatial filter was determined experimentally by measuring the image quality reconstructed by the hologram. Figure 8a shows a specific target image for generating Fresnel holograms. The target object consisted of three bars to evaluate the visibility \(v\). The average cross-section intensity distribution of the reconstructed objects was evaluated through the visibility \(v\), given by  
\[v=\frac{I_{max}-I_{min}}{I_{max}+I_{min}}, \tag{9}\]  
where \(I_{max}\) and \(I_{min}\) are the central maximum intensity and neighboring minimum intensity, respectively. Visibility is a value between 0 and 1, and a value close to 1 indicates that the reconstructed image has a high sharpness. The eight target objects were located in different positions, and they were formed into two groups. Group 1 was the target object closer to the optical axis and group 2 was the target object far from the optical axis. In each group, the target objects were rotated in specific directions to check visibility in the tangential and sagittal directions. It was expected that the visibility of the tangential direction would  
Figure 7: Experimental setup obtaining the optimal spatial coherence of the LED. **(a)** The optical scheme and **(b)** the experimental setup. decrease as the target object moved farther from the optical axis owing to the temporal coherence. Fresnel holograms with a \(z_{obj}\) of 50, 100, 150, 200, and 250 mm were generated as shown in Figure 8b-f. Figure 9 shows the reconstructed images for the spatial filter size of 97.2, 270.0, 507.6, 702.0, 896.4, and 1090.8 \(\upmu\)m. The target object located at a 50 mm distance from the hologram plane was reconstructed clearly without blurring even if the spatial filter size increases. However, it was definitely confirmed that target objects in other positions were blurred as the spatial filter size increased. Moreover, the target objects farther from the hologram plane were quickly blurred as the spatial filter size increased. Among the objects of group 2, which were far from the optical axis, the tendency to blur faster than group 1 in the tangential direction was also confirmed. Figure 8: Fresnel holograms for experiments. (**a**) The target object image and Fresnel holograms of the object positioned at (**b**) 50, (**c**) 100, (**d**) 150, (**e**) 200, and (**f**) 250 mm from the hologram plane. Figure 9: Reconstructed images depending on the spatial filter size of 97.2, 270.0, 507.6, 702, 896.4, and 1090.8 \(\upmu\)m.  
The change of the visibility according to the spatial filter size is shown in Figure 10. Overall, the visibility did not exceed 0.5 mainly because of speckle noise. The visibility of 0.4 was considered as the limit line because the visibility of the target object at the nearest distance, 50 mm from the hologram plane, was approximately 0.4. Visibility was expected to be improved when the spatial filter size decreased, because the expressible depth range increased when the coherence increases. This tendency was observed when the spatial filter size was larger than about 400. However, visibility decreased when the spatial filter size was smaller than about 200. This phenomenon can be attributed to two reasons. One is the dominance of speckle noise. As previously mentioned, an increase of the coherence results in speckle noise, and it deteriorates visibility.