# Transforming Monochromatic Images into 3D Holographic Stereograms Through Depth-Map Extraction
## 3 Proposed Method
### Digital Hologram Encoding and Hogel Generation  
To replicate the optical field from multiview image data, it is necessary to generate hogels that can be transferred to a digital hologram printer. A hologram is an array of small (dot-like) sub-holograms, called hogels. This requires rearranging multiview images into a data structure optimized for digital hologram printing [1; 25]. Figure 5 shows a conceptual diagram of digital-data rearrangement for hogel generation. Consider a 2D full-parallax 3D stereoscopic image with \(I_{m}(m\times n)\) pair of images (viewpoints) and a spatial light modulator (SLM) with a resolution of \(H_{ij}(i\times j)\). The diagram shows how the data are rearranged in this scenario.  
Figure 4: Hybrid translating/rotating camera configuration with fixed central target.  
Figure 5: Hogel formation by arranging digital data on SLM.  
The creation of a digital hologram begins with a set of multiview images, denoted by \(I_{11}\)-\(I_{mn}\), each representing a unique perspective on the desired scene, as shown in Figure 6. Using dedicated data-rearrangement software on a control computer, the pixels of the multiview images are sequentially loaded onto the SLM. The loading process follows a left-to-right and top-to-bottom order, starting with image \(I_{11}\) and proceeding to \(I_{m1}\) in the first iteration.  
The SLM--typically a liquid-crystal-on-silicon device--modulates a collimated laser beam through phase modulation, thereby encoding the information from an uploaded image. Crucially, the modulated beam interferes with a separate unmodulated reference beam of coherent light. The interference pattern created by the interaction of these two beams is then focused onto a holographic plate, which is a photosensitive material designed to record this intricate pattern. This recording process creates a single holographic element known as the hogel, \(H_{ij}\).  
The process is repeated iteratively. Each image is sequentially uploaded to the SLM, illuminated by the collimated laser and reference beams, and focused onto a holographic plate to record the corresponding hogel. This is repeated until the final iteration, where pixels from \(I_{m1}\) to \(I_{mn}\) are loaded, illuminated, and recorded, thereby generating the final hogel. The patterns displayed on the SLM are computationally generated through computer-generated holography. These calculations are highly complex and require substantial processing power. If both the input images \(I_{mn}\) and the resulting holes \(H_{ij}\) have a high-definition resolution of 1920 \(\times\) 1080 pixels, each hogel encapsulates an immense amount of information. Unlike conventional image pixels that contain a single intensity value, each hogel contains 2,073,600 (1920 \(\times\) 1080) unique data points, effectively encoding a complete perspective view. Consequently, to fabricate the digital hologram, the SLM displays a sequence of 2,073,600 distinct patterns for each hogel location, and each pattern is subtly modified to record a unique interference pattern on the holographic plate. These patterns are calculated to ensure accurate reconstruction of the optical field during viewing.  
Hogel \(H_{ij}\) serves as the fundamental building block for the final digital hologram. When properly illuminated, the recorded interference patterns within each hogel diffract light, recreating the original 3D scene as perceived from a specific viewpoint. All hogels are combined to reconstruct the entire holographic image.  
Figure 6: Conceptual diagram of digital-data rearrangement for hogel generation.