# Progress in the Synthetic Holographic Stereogram Printing Technique
## 2 Development of Synthetic Holographic Stereogram Printing Technique  
Synthetic holographic stereogram printing was first proposed by [PERSON] [27] and promoted by [PERSON] et al. [28]. The earliest synthetic holographic stereograms are horizontal-par parallax-only (HPO) holographic stereograms. When the viewer is not located at the slit plane of the stereogram, there will be image distortions. The problem will not occur in full parallax holographic stereograms. With the two-step method, we can achieve a real-virtual combined holographic stereogram, i.e., the reconstructed 3D scene is viewed inside or outside of the holographic recording medium. The production and reconstruction of the two-step method is shown in Figure 1[29]. Full parallax perspective images of the scene are acquired under incoherent illumination, and Fresnel holograms of them are recorded in different hogels (holographic elements) successively (see Figure 1a). When viewing the master hologram, eyes should be close to the positions of aperture pupils (see Figure 1b). To separate the aperture pupil plane and the viewing plane, the master hologram (H\({}_{1}\) plate) should be recopied to the transfer hologram (the H\({}_{2}\) plate) with the image hologram photographing method, i.e., there are double exposures in the two-step method (see Figure 1c). When viewing the transfer hologram from different virtual pupil positions, different perspective images can be captured by human eyes, and the stereoscopic vision is formed (see Figure 1d). Figure 1: Production and reconstruction of the two-step method. (**a**) The production of the master hologram. (**b**) The reconstruction of the master hologram. (**c**) The reproduction of the master hologram to the transfer hologram. (**d**) The reconstruction of the transfer hologram. (Reprinted with permission from ref [29], [OSA]). Since the 1990s, the media lab of Massachusetts Institute of Technology (MIT), the imaging science and engineering laboratory of Tokyo Institute of Technology, and the General Optics Laboratory (Geola) have been researching the synthetic holographic stereogram printing technique [30]. To simplify the process of the two-step method, they proposed the infinite viewpoint camera method [31; 32], the single-step Lippmann method [33; 34], and the direct-write digital holography (DWDH) method [3; 35; 36]. MIT studied the problem of image distortions in HPO holographic stereograms and proposed two predistortion techniques, i.e., the infinite camera predistortion method and the perspective slicing predistortion method. The infinite viewpoint camera method for synthetic holographic stereogram printing was proposed, whose core idea was to transform the perspective images into parallax related images. The perspective images are first captured by an infinite camera, and the light arriving at the hogels can be considered as bundles of parallel light approximately since the distance between the camera and the holographic recording medium is far enough. The transformation is just an operation on a series of arrays as shown in Figure 2[29]. Suppose there are \(s\times t\)\((s=1,2,\cdots,M,t=1,2,\cdots,N)\) perspective images, and each image contains \(i\times j\)\((i=1,2,\cdots,m,j=1,2,\cdots,n)\) pixels. The perspective image matrix is expressed as \(\mathbf{P}_{st}(i,j)\). All pixels at the same location of each \(\mathbf{P}_{st}(i,j)\) are extracted to form a new matrix \(\mathbf{H}_{ij}(s,t)\), which denotes a parallax-related image. During the holographic printing, a convex lens is used to control the refraction direction of light rays. The resolution of reconstructed images equates to the number of hogels. A double-frustum algorithm for rapidly generating image data for full parallax holographic stereograms was proposed by [PERSON] et al. [37]. There is a special renderer with an orthoscopic camera and a pseudoscopic camera together, and each exposing image is synthesized by using rendering images of these two cameras.