# Multi-Object Deep-Field Digital Holographic Imaging Based on Inverse Cross-Correlation
## 5 Discussion  
### Factors Affecting Depth of Field  
In discussing the maximum achievable depth of field using this method, we summarize the following factors that influence the depth of field. The multi-plane depth of field is initially constrained by the single-plane depth of the field. Hence, the depth of field under the single plane is discussed first. The influencing factors include the sampling number (\(N\)) of the photodetector, the ideal position (\(Z_{i}\)) of the object reconstruction, the reconstruction algorithm, parameters relating to the optical instruments in the system (such as microscope parameters), etc. Since the angular spectrum reconstruction algorithm was used in this article and no additional optical instrumentation was employed, only the first two influencing factors are discussed herein. **Sampling number (\(N\)) of the photodetector. ** In the angular spectrum reconstruction algorithm, if it is assumed that the energy concentration of the point source within \(n_{\sigma}\) pixels in the reconstruction plane is the limiting condition for the depth of field, then the relationship between the actual reconstruction plane's position \(Z_{m}\) and \(Z_{i}\) that deviates from the ideal position is shown in the following equation (Equation (5)):  
\[|z_{m}-z_{i}|=\frac{3z_{i}}{n_{\delta}\cdot N} \tag{5}\]  
This equation indicates that the larger the sampling number (\(N\)) of the photodetector, the smaller the depth of field of its digital holography. **Ideal position (\(Z_{i}\)) for object reconstruction. ** Based on the above equation, the depth of field of a single-plane object increases as the ideal object reconstruction position (\(Z_{i}\)) is raised. The following section addresses the factors affecting the depth of field during the inverse cross-correlation calculation and experimental processes, which include the shape of the object itself, its position characteristics, threshold, and noise. **The morphology and position characteristics of the object itself. ** The reconstruction of multiplanar objects is affected by various factors, such as the shape, size, and position of the object being measured. In the case of complex diffraction profiles, an algorithm is more likely to capture the object's edge characteristics. Moreover, the size difference between the measured objects affects the accuracy of an algorithm. The larger the difference, the easier it is for the algorithm to ignore the edges of smaller objects, thus affecting their reconstruction. Position discrepancy refers to cases where the same measured object is placed at the same total distance but where the relative distance between the objects is inconsistent. In such cases, although the measured object is the same, the incidence of diffraction stripes on the  
Figure 10: Phase distribution. (**a**) Single-depth estimation operator. (**b**) Proposed method. photodetector differs, and the difference in the diffraction shape also affects the size of the depth of field. **Threshold. ** In the inverse cross-correlation calculation, the selection of the threshold value is a critical parameter for determining the coordinates of object edge positions. The number of location coordinates increases as the threshold value decreases. A larger threshold tends to result in missing the measured target, while a smaller threshold increases the difficulty of clustering and reduces accuracy. **Noise**. Speckles or other types of noise often appear in interferometric experiments, and they can affect depth-of-field results. In practical measurements, it is recommended to employ different noise reduction processes to mitigate the effects of noise. By considering these factors, a deeper understanding of the challenges and limitations associated with the multiplanar large-depth-of-field digital holographic imaging process can be gained.