## 2 Depth Rescaling Process (Z Axis)
Depth Analysis: Obtain the depth information of the 3D scene in each captured elemental image and separate the 3D scene into multiple depth regions. 2. Reference Plane Calculation: Determine the number of reference planes. For each reference plane, obtain its position. 3. Virtual Pinhole Array Distance Calculation: Calculate the distance (\(d\)) between each reference plane and its corresponding virtual pinhole array. 4. Pixel Mapping: Map pixels from the real captured elemental images to the corresponding reference plane (simulated display). 5. Synthetic Capture: Generate new elemental images from each reference plane to their corresponding virtual pinhole array. 6. Superimposition: Combine the elemental image arrays to create a synthetic captured elemental image array with rescaled depth. In the proposed method, we adopt the depth estimation method in [11] to statistically estimate the depth information of the 3D scene. The depth estimation uses the statistics of spectral radiation in an object space to infer the depth of the surfaces in the 3D scene,  
Figure 2: Generation of the synthetic elemental image array (EIA) by multiple reference planes and multiple virtual pinhole arrays. This figure illustrates two reference planes in (**a**) and (**b**), respectively. and this method aligns well with the architecture of integral imaging optical sensing, sharing the same specifications and structural framework as the proposed process, which ensures procedural consistency. The number of the reference planes and the position of each reference plane can be calculated by segmenting the depth range of the original 3D scene into several sub-regions in the z direction. The boundary between two adjacent regions can be regarded as the position of the reference plane. For further explanation, we denote the number of the reference planes as \(N_{RP}\), and we set the \(N_{RP}\) reference planes to cover the depth range of the 3D scene. Note that the \(N_{RP}\) reference planes separate the depth range into \(N_{RP}-1\) sub-regions. The index of the reference planes ranges from 1 to \(N_{RP}\), and the first reference plane is set at the position where the surface of the object is closest to the lenslet array. The distance between the lenslet array and the \(i\)th reference plane in the simulated display stage can be expressed as follows:  
\[z_{RP}^{i}=z_{reur}+\frac{d_{o}}{N_{RP}-1}\times(i-1) \tag{1}\]  
where \(z_{narr}\) is the closest distance between the surface of the object and the lenslet array. \(d_{o}\) is the depth range of the 3D scene and \(N_{RP}\) is the number of reference planes. For optimal display, we set the rescaled depth of the 3D image to the depth range of the display system in order to fully utilize the capacities of the 3D display. To display both the real and virtual scene in the display system, the virtual pinhole array needs to be set at the center of the 3D scene in the synthetic capture stage [23]. The distance of \(d_{i}\) between the \(i\)th reference plane and the corresponding \(i\)th virtual pinhole array in the synthetic capture process is equal to the distance between the \(i\)th reference plane and the display plane in the 3D display process:  
\[d^{i}=\frac{d_{s}}{N_{RP}-1}\times[\frac{N_{RP}}{2}-(i-\frac{1}{2})] \tag{2}\]  
where \(d_{s}\) is the depth range of the display system. From Equations (1) and (2), the distance between the \(i\)th virtual pinhole array and the lenslet array can be calculated as follows:  
\[z_{p}^{i}=z_{RP}^{i}+d^{i} \tag{3}\]  
In the simulated display stage, the distance between two neighboring reference planes is \(\Delta RP=d_{o}/(N_{RP}-1)\), after the synthetic capture stage, a new elemental image array is generated by superimposing the synthetic captured elemental images. The distance between two reference planes recorded in the regenerated elemental image array is \(\Delta d=d_{s}/(N_{RP}-1)\). The range of the reference planes corresponds to the depth range of the 3D scene.