## 4 Experimental Results  
To evaluate the performance of our proposed method, 2 sets of holograms have been captured with the OSH system that has been configured to operate in the incoherent mode [22], and with the wavelength of the laser beam being 633 nm. The first hologram \"A\" is a pair of binary Chinese characters \"\(\mathbb{J}\)\" and \"\(\overline{\mathbb{H}}\)\", and second hologram \"B\" is a grey level image of a pair of partially overlapping coins. The pixel size of holograms (i.e., the sampling interval with which each hologram pixel is recorded) \"A\" and \"B\" are 5 \(\upmu\)m and 15 \(\upmu\)m, respectively. In both cases, the range of distance between the object space and the hologram plane is [0.015 m, 0.03 m], but there is no prior knowledge on the depth of individual objects in the scene. The sine and the cosine holograms of the 2 samples are shown in Figure 4a-d. Through a series of trial and error tests conducted with visual judgement, we estimated that there are mainly 2 focused planes that can be identified for sample 'A' at 0.021 m and 0.024 m. For 'B', again there are mainly 2 focused planes at 0.0197 m and 0.027 m. The reconstructed images of sample 'A' at the 2 focused planes are shown in Figure 5a,b. It can be seen that in both figures when certain regions of the image are in focused, the remaining ones are blurred. Similar observation is noted for the reconstructed image of sample 'B' at the 2 focused planes in Figure 5c,d. In both cases, it is not possible to have an EDF image where all the contents are in focus. Figure 4: (**a**) Sine hologram of hologram “A”; (**b**) Cosine hologram of hologram “A”; (**c**) Sine hologram of hologram “B”; (**d**) Cosine hologram of hologram “B”. Next, we apply stages 1 and 2 of our proposed method to obtain the depth map and the EDF image from the 2 holograms. The number of reconstruction planes and the block size are set to \(N=40\) and \(M=32\), respectively, to provide a sufficiently fine depth resolution of \(\Delta z=\frac{Z}{N}=\frac{0.015}{40}=0.375\) mm, and a reliable measurement of the entropy of each image block. The depth maps of the 2 samples are shown in Figure 6a,b, and the corresponding EDF images obtained with the above settings are shown in Figure 6c,d. We observe that all the objects in the scene represented by each hologram are reconstructed as focused images but the appearance, especially for sample \"B\", is rather blocky with obvious discontinuities along some of the object boundaries. Subsequently, we have applied Equation (12) to filter the depth map, and obtained the reconstructed images with Equations (13) and (14). Suppose the dynamic range of the reconstructed image is normalized to the range \([0,1]\), the threshold \(T\) is set to 0.0625, as image intensity lower than this value is hardly visible, and likely to represent empty background or noise signals. The filtered depth maps are shown in Figure 7a,b, and the reconstructed EDF images are shown in Figure 7c,d. In the EDF images of both samples, we observe that the objects in the scenes are reconstructed as sharp focused images, and the blocky appearance has been reduced significantly as compared with those obtained with the unfiltered depth maps. The computation time based on the typical PC is around 5.9 s. The correlation score of the EDF images of holograms 'A' and 'B' (with reference with the ones obtained with manual judgement) are 0.977 and 0.845, respectively. The high correlation scores reflect that the EDF images obtained with our proposed method are close to those derived from manual judgement. Figure 5: (**a**) Reconstructed image of hologram “A” at 0.021 m; (**b**) Reconstructed image of hologram “A” at 0.024 m; (**c**) Reconstructed image of hologram “B” at 0.0197 m; (**d**) Reconstructed image of hologram “B” at 0.027 m.  
We would like to point out that out proposed method can function for quite a wide range of \(M\).