## 2 The Basic Principles
### The Basic Principle of the DWDH Method and the EPISM Method
#### 2.1.2 The Basic Principle of the EPISM Method  
The EPISM method is proposed to achieve a two-step holographic stereogram printing effect by a single-step process. In the EPISM method, a liquid crystal display (LCD) panel is used as SLM. To achieve this purpose, by simulating the propagation process of information from different perspective images, the exposing synthetic perspective images for hogels on H\({}_{2}\) plate can be computer-generated directly. As shown in Figure 2, the EPISM method takes the center of the hogel on H\({}_{2}\) plate as an observation point. According to ray-tracing principle, when observing the hogel on virtual H\({}_{1}\) plate at point O, a viewing frustum with the observation point as the vertex and the hogel as the bottom is obtained. Since the reproduction image of the hogel on virtual H\({}_{1}\) plate is the corresponding perspective image, and the reproduction position is the position of the LCD panel when recording, the intersection of frustum and the reproduced image is the effective perspective image segments of the hogel for the observation point O. Mosaicking all effective perspective images segments together obtains a synthetic perspective image for recording onto the hogel of H\({}_{2}\). Record all the synthetic perspective images corresponding to the hogel on H\({}_{2}\) plate, and a full parallax holographic stereogram based on the EPISM method is received, as shown in Figure 2.  
The resolution of the sampled image is determined by the resolution of the LCD panel in the EPISM method. Since the observation point is used on the hogel on the H\({}_{2}\) plate to generate effective perspective images segments, the influence of the hogel size on the effective perspective images segments is ignored, and this ignorance leads to slight mosaic misplacement in the position away from the reconstructed image plane, and the larger the dimension of the hogel on H\({}_{2}\) plate, the more obvious the mosaic misplacement. The Basic Principle of the Holographic Element-Based Effective Perspective Image Segmentation and Mosaicking (EPISM) Methods  
Using holographic elements to replace pixels, the effective perspective images segments of adjacent hogels on virtual H\({}_{1}\) plate are mosaicked as shown in Figure 3, then the aliasing perspective images segments of adjacent hogel cannot be simulated by the LCD panel. To avoid the aliasing of effective perspective images segments of adjacent hogels, the pixel correspondence in the DWDH method is used to establish the hogel correspondence. The DWDH method uses the hogel (as a point) position and the pixel coordinates on the SLM plane to determine  
Figure 2: The primitive principle of the proposed method. (**a**) The extraction of effective perspective image segment corresponding to a single virtual hogel. (**b**) The synthetic effective perspective image mosaicked by effective images segments of multiple virtual hogels. the camera position and the pixel coordinates on the film plane. As shown in Figure 4, if the dimension of hogel is considered, the pixel on the SLM plane in the DWDH method should be replaced by a segment of the LCD panel in holographic element-based EPISM method, and the dimension of the segment of the LCD panel is equal to the dimension of the hogel on virtual H\({}_{1}\) plate. The position of the hogel on virtual H\({}_{1}\) plate and the effective perspective images segments of its reconstruction images are determined by the position of the hogel on the H\({}_{2}\) plate and the segment of the LCD panel. A synthetic perspective image based on the holographic element can be obtained by mosaicking all the perspective images segments, and the aliasing of perspective images segments is avoided. Based on this idea, holographic element-based EPISM method is proposed.