# Multi-Object Deep-Field Digital Holographic Imaging Based on Inverse Cross-Correlation
## 4 Experiment
### Large Depth-of-Field Reconstruction in the Non-Overlapping Case  
Unlike the simulation data, the holograms captured during the experimental process contained large noise, such as scattering noise and other types; thus, each point that met the threshold was reconstructed separately, and all the reconstructed images were merged together. The specific process employed was as follows: Assuming that there are a total of \(i\) extreme points within the threshold selected by the inverse cross-correlation coefficient \(Cc\) (and taking the position of each extreme point as the center coordinate), rectangular boxes with the respective dimensions of S \(\times\) S, M \(\times\) M, and L \(\times\) L are constructed (S \(<\) M \(<\) L); following this, \(3i\) rectangular boxes can be obtained. The rectangular boxes are used as the boundaries to find the reconstruction distances \(z_{\mu\sigma}\), which correspond to the \(3i\) regions (\(\mu=S,M,L;\sigma=1\) to \(i\)). After applying \(z_{\mu\sigma}\) globally, all the reconstructed images are then fused and processed to obtain the final results. The cross-correlation results are shown in Figure 7: Figure 7a shows the hologram obtained by CCD, and Figure 7b shows the inverse cross-correlation matrix \(Cc\) under \(z_{1}=10.0\) cm and \(z_{2}=10.5\) cm. Since the four measured objects do not overlap with each other at this time, only M \(\times\) M (M = 50 pixels) could be reconstructed by choosing the matrix box. Figure 7c shows a schematic diagram of the rectangular box. The color bar values indicate the normalized amplitude. Figure 6: The result of single-depth operators. (**a**) Normalized reconstruction distance coefficients. (**b**) The reconstructed image at the maximum point. The results are shown in Figure 8. Figure 8a shows the reconstructed phase distribution in the case of a single-depth estimation operator's extreme point; at this time, the reconstruction distance \(z=21.0\) cm. The color bars indicate the phase values. It can be seen that, due to the mutual interference of the various planes, the phase is blurred, and the actual different positions of the measured object are forced to be reproduced in the same plane and thus cannot be accurately distinguished. Additionally, the reconstruction of the phase represents the error. Figure 8b shows the reconstructed image under the method proposed in this paper. The phase of each plane is clearly visible, and the relative positional distance between planes can be obtained: BJ and T are 7.2 cm apart, and T and U are 6.1 cm apart. To better characterize the ability of the depth-of-field enhancement, the quality of the reconstructed image was quantified using the Fourier transform criterion. Firstly, the Fourier transform was applied to the reproduced image to obtain the sum of the spatial frequency components, \(S_{FT}\), whose expression is shown in Equation (4). \(M\) and \(N\) denote the number of horizontal and vertical pixels in the reconstructed image, and \(Re\) and \(Im\) are the real and imaginary parts of the spectrum, respectively. The higher the value of the \(S_{FT}\), the more information is available in the reconstructed image, and the higher the accuracy of the reconstruction. Figure 8: Phase distribution. (**a**) Single-depth estimation operator. (**b**) Proposed method. Figure 7: (**a**) Hologram. (**b**) Inverse cross-correlation coefficient matrix. (**c**) Schematic diagram of the rectangular box. \[S_{FT}=\sum_{m=1}^{M}\sum_{n=1}^{N}\sqrt{\text{Re}^{2}(F\{I(m,n)\})+\text{Im}^{2}(F \{I(m,n)\})} \tag{4}\]  
The \(S_{FT}\) of the single-depth operator was \(0.53\times 10^{8}\), as calculated using Equation (4) for the reconstructed image in Figure 8a, and the \(S_{FT}\) of the proposed algorithm was \(1.28\times 10^{8}\) in Figure 8b.