# Progress in the Synthetic Holographic Stereogram Printing Technique
## 2 Development of Synthetic Holographic Stereogram Printing Technique
In the single-step Lippmann method, the exposing images for hogels are acquired by the perspective projection, not by camera sampling, and the principle of this method is shown in Figure 3[29]. Based on the center of each hogel, scene points are projected to the position of liquid crystal display (LCD), respectively (see Figure 3a). According to the viewer's position, the occlusion relation of scene points in space should be considered and the hidden surfaces should be removed. The calculated images are then displayed on the LCD, converged through the lens, and recorded on the hogels (see Figure 3b). During the reconstruction of the scene, light rays are diffracted from each hogel in the same way as the image calculation; thus, the viewer can perceive the scene (see Figure 3c). The double-frustum algorithm can be also applied to the single-step Lippmann method. Figure 2: Transformation principle of perspective images in the infinite viewpoint camera method. (Reprinted with permission from ref [29], [OSA]). Geola Inc. has realized full parallax holographic stereogram printers with pulse lasers [35], while the commercial products provided by Geola Inc. are only HPO holographic stereograms. The DWDH method was proposed by [PERSON] and [PERSON]. The core idea of the DWDH method is the \(\mathrm{H_{1}-H_{2}}\) conversion, i.e., the image transformation from the camera film plane to the SLM plane, which is usually referred as \"I-to-S\" transforming [38]. The principle of the DWDH method is shown in Figure 4. There are six principal planes, i.e., the hologram plane, the SLM plane, the projected SLM image plane, the camera plane, the film plane, and the projected film plane. There is the assumption of a small-aperture camera and a \"point\" hogel, and each image of the SLM plane is acquired by the pixel swapping technique from different images of film planes according to the ray-tracing principle. The spatial location relations of these planes are easily established, and there is an exact pixel matching relationship between the SLM plane and film plane. In the two-step method, the process is relatively complex with double exposures, and it is difficult to make a large-size hologram since we can hardly achieve large-format collimating light during the second exposure. There is only single exposure in the infinite viewpoint camera method, in  
Figure 4: Principle of the direct-write digital holography (DWDH) method. Figure 3: Principle of the single-step Lippmann method. (**a**) Calculation of an exposing image. (**b**) Optical setup of the method. (**c**) Reconstruction geometry for the holographic stereogram. (Reprinted with permission from ref [29], [OSA]). the single-step Lippmann method, or in the DWDH method. Recently, a novel method based on effective perspective image segmentation and mosaicking (EPISM) was proposed by our group [29; 38]. The principle of the EPISM method is shown in Figure 5. On the basis of ray-tracing principle and the reversibility of light propagation, the viewing frustum effect of human eyes is analyzed and simulated (see Figure 5a). With the segmentation and mosaicking of effective perspective images, synthetic effective perspective images for single-step exposure can be achieved (see Figure 5b). By using the EPISM holographic stereogram printing method, the image processing is simple and the reconstructed images are of high resolution. Principles of different synthetic holographic stereogram printing methods have been described. Except for the two-step method, there is only single exposure in the other printing methods. According to different models to generate the hogel images, the methods mentioned above can be classified as two types [39]. In the first type, hogel images are generated by a camera placed on the viewing zone of the holographic stereogram. As shown in Figure 6, the hologram plane coincides with the camera image plane, and the camera is placed on every point of view on the viewing zone.