# Resolution Enhancement of Spherical Wave-Based Holographic Stereogram with Large Depth Range +
## 3 Reducing CDP Depth \(L\)  
Reducing \(L\) means to capture the 3D object at a closer distance. It is apparent that by reducing \(L\), the first term in Equation (5) will decrease while the second term will increase. Thus, for the reconstructed 3D image near the CDP, reducing \(L\) will always be beneficial to the resolution enhancement. But for the reconstruction away from the CDP, reducing \(L\) may have a negative influence on the resolution. Reducing \(L\) is effective only when the reduction of the first term exceeds the increment of the second term. At a small \(\Delta z\), it is always satisfied. However, as \(\Delta z\) increases, this condition needs to be examined. The limiting case occurs when the reduction of the first term equals the increment of the second term at a given \(\Delta z\). In this case, the resolution is enhanced within the total depth \(\Delta z\), and an appropriate \(L\) should be chosen. Assuming the parameters are \(L=80\) mm,\(f=3\) mm, \(\Delta x_{1}=\Delta x_{2}=5\) um, \(\lambda=500\) nm, the relationship between image spot size \(S\) and defocused depth \(\Delta z\) is drawn by the black solid line in Figure 3a. It can be seen that at the CDP, the image spot has the minimum size. As \(\mid\Delta z\mid\) increases, the image spot size also increases, resulting in a degraded resolution. To enhance resolution, we try to reduce \(L\) to 30 mm, which is shown by the green dash-dotted line. The resolution at the CDP is greatly improved, but at \(\mid\Delta z\mid\) = 20 mm, the resolution is degraded, indicated by the upward arrow. Thus, the resolution is enhanced at a price of decreased depth range. This case can be avoided by choosing a proper \(L\). As shown by the red dashed line with \(L=45\) mm, the resolution at the CDP is improved compared with \(L=80\) mm. In addition, at \(\mid\Delta z\mid\) = 20 mm, its image spot size just equals that of \(L=80\) mm. It means that the resolution is enhanced within the total depth \(\Delta z\), without the price of decreased depth range. It is just the limiting case as mentioned above, with an appropriate \(L\). The suitable value of \(L\) can be found by a numerical method. Figure 3b shows the relationship between L and image spot size at \(\Delta z\) = 20 mm. First, the image spot size with \(L=80\) mm can be obtained, represented by the red point. Then, a horizontal line starting from the red point is generated, and it intersects with the curve to form a green point. The \(x\)-coordinate of the green point is just the proper value of \(L\). However, the proper value of \(L\) cannot be found at any situation. Figure 4a shows the case with the same parameters as Figure 3 except for \(\Delta x_{1}=3\) um. It can be seen that reducing \(L\) will always decrease the resolution away from the CDP, indicated by the upward arrows. On the contrary, Figure 4b shows the case with \(\Delta x_{1}=8\) um. It can be seen that  
Figure 3: **(a)** The relationship between image spot size \(S\) and defocused depth \(\Delta z\) at different capturing depth \(L\), with \(\Delta x_{1}=5\) μm. **(b)** The relationship between \(L\) and image spot size at \(\Delta z=20\) mm, with \(\Delta x_{1}=5\) μm. reducing \(L\) will always enhance the resolution within the total depth range, indicated by the downward arrows. These two results can be easily understood in Figure 4c, which shows the relationship between \(L\) and image spot size at \(\Delta z\) = 20 mm. In the case of \(\Delta x_{1}\) = 3 \(\upmu\)m, represented by the black solid line, reducing \(L\) will cause the increase of the image spot size at the marginal depth, which means reducing \(L\) will always cause decreased depth range. Contrastingly, in the case of \(\Delta x_{1}\) = 8 \(\upmu\)m, represented by the red dashed line, reducing \(L\) will cause the decrease of the image spot size at the marginal depth, which means reducing \(L\) is always effective. In both cases, the proper value of \(L\) cannot be found using the method in Figure 3b.