*Article* **Holographic Element-Based Effective Perspective Image Segmentation and Mosaicking Holographic Stereogram Printing**

**Fan Fan 1,2, Xiaoyu Jiang 1,\*, Xingpeng Yan 1, Jun Wen 1, Song Chen 1, Teng Zhang <sup>1</sup> and Chao Han <sup>1</sup>**


Received: 5 February 2019; Accepted: 25 February 2019; Published: 4 March 2019

**Abstract:** Effective perspective image segmentation and mosaicking (EPISM) method is an effective holographic stereogram printing method, but a mosaic misplacement of reconstruction image occurred when focusing away from the reconstruction image plane. In this paper, a method known as holographic element-based effective perspective image segmentation and mosaicking is proposed. Holographic element (hogel) correspondence is used in EPISM method as pixel correspondence is used in direct-writing digital holography (DWDH) method to generate effective perspective images segments. The synthetic perspective image for holographic stereogram printing is obtained by mosaicking all the effective perspective images segments. Optical experiments verified that the holographic stereogram printed by the proposed method can provide high-quality reconstruction imagery and solve the mosaic misplacement inherent in the EPISM method.

**Keywords:** holographic printing; holographic stereogram; holographic element

#### **1. Introduction**

Holographic stereogram printing technology is used in many fields. Since Dennis Gabor invented holographic technology in 1948, holographic printing techniques can be categorized into three types: synthetic holographic stereogram printing, holographic fringe printing, and wavefront printing. The most widely used technology is holographic stereogram printing.

Holographic stereogram printing was first proposed by DeBitetto [1] in 1969. The perspective images sampled by a camera are exposed to a holographic recording medium by using a slit, generating a horizontal parallax holographic stereogram. In 1970, King [2] proposed a two-step horizontal parallax holographic stereogram printing technique. This two-step printing technique first records the master holographic plate, Then the second-step of the process is to record the reproduced image of the master holographic plate onto the transfer holographic plate. The production of a holographic stereogram that reproduces with white light and generates an orthoscopic real image is realized.

In 1990, Yamaguchi [3–5] proposed to print a full parallax holographic stereogram in a single step; based on this, a series of studies were carried out. In 1991, Halle [6–12] proposed a single-step holographic stereogram printing technique called Ultragram; this method processes the perspective image obtained by the sampling camera to generate a holographic stereogram that can be used for single-step printing. In this manner, arbitrary depth, full parallax, and undistortion holographic stereogram printing can be realized.

In 2001, Brotherton-Ratcliffe [13] proposed a technique for holographic stereogram printing by using pulsed lasers. In 2008, a single-step direct-writing digital holography printing technology [14,15] was proposed and used in Geola's holographic printing system. This technique employs a pixel corresponding method, replaces the image pixels loaded onto the spatial light modulator (SLM) with the pixels of the perspective image, and accurately reproduces the recorded scene. In 2017, Su and Yuan [16] proposed a method called effective perspective image segmentation and mosaicking (EPISM) method to simulate two-step method by a single-step process. Further research on the EPISM method was carried out by Su and Yan [17–19] to improve image quality and printing efficiency. In addition, many researchers have made valuable research in recent years [20,21].

The EPISM method uses the correspondence between the observation point and hogel to obtain an effective perspective images segments, and the resolution of the perspective image can be fully used by the EPISM method, but the use of an observation point will cause a mosaic misplacement of the reconstruction image when focusing away from the reconstruction image plane. To solve this problem, by using the idea of pixel correspondence of the DWDH method, the hogel correspondence is used as pixel correspondence to generate effective perspective images segments, and holographic element-based EPISM method is proposed.

This paper is divided into the following sections: In Section 2, the basic principles of the DWDH method, the EPISM method, and the holographic element-based EPISM method are introduced. In Section 3, the basic algorithms of holographic element-based EPISM method are given. In Section 4, the proposed method is verified by optical experiments, and the optical experiment results are compared with the experiment results of the EPISM method. In Section 5, conclusions are presented.

#### **2. The Basic Principles**

#### *2.1. The Basic Principle of the DWDH Method and the EPISM Method*

#### 2.1.1. The Basic Principle of the DWDH Method

The DWDH method converts sampled perspective images into a rearranged image for exposing. This algorithm is actually a pixel transformation from the film plane of the camera to the SLM plane of hogel. It is usually called 'I to S' transformation. The principle of the DWDH method is shown in Figure 1, There are six main planes: hologram plane, SLM plane, projected SLM plane, camera plane, film plane, and projected film plane.

**Figure 1.** Ray-tracing principle of "I to S" transformation by DWDH method.

In this conversion, the camera lens and the print head of the holographic optical printer are regarded as a point, and a test ray passes through the camera lens and hogel. The pixel where the ray intersects the SLM plane is replaced by the pixel where the ray intersects the film plane, the 'I to S' transformation of a pixel is completed. All pixels on the SLM are replaced by pixels on the film plane,

a rearranged image for exposing is obtained. All the hogels on the hologram plane were exposed, and the DWDH holographic stereogram was obtained.

The pixel correspondence of the DWDH method can accurately reproduce the 3D scene, but the resolution of the sampled image is determined by the number of hogels; high-quality holographic stereograms often require hundreds of thousands of sampled images.

#### 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 H2 plate can be computer-generated directly. As shown in Figure 2, the EPISM method takes the center of the hogel on H2 plate as an observation point. According to ray-tracing principle, when observing the hogel on virtual H1 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 H1 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 H2. Record all the synthetic perspective images corresponding to the hogel on H2 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 H2 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 H2 plate, the more obvious the mosaic misplacement.

**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.

#### *2.2. 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 H1 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 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 H1 plate. The position of the hogel on virtual H1 plate and the effective perspective images segments of its reconstruction images are determined by the position of the hogel on the H2 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.

**Figure 3.** The effective perspective images segments of adjacent hogels are aliased When holographic element is used for the corresponding.

**Figure 4.** The holographic elements are used as pixels to solve the aliasing problem of adjacent hogels.

The principle of this method is described as follows: as shown in Figure 5, to treat a hogel as a pixel, this requires the same hogel dimensions on the virtual H1 and H2 plates, and the dimension of the effective perspective images segments are also the same as the hogel dimension, denoted as *l*. The dimension of the LCD panel is fixed, and the LCD panel is partitioned according to the dimension of the effective perspective images segments. It is necessary to choose a suitable distance to make the rectangle area formed by the hogel on H2 plate and the segment of the LCD panel coincide with the hogel on the virtual H1 plate. The reproducing image of the hogel on the virtual H1 plate intersecting the segment of LCD generates the effective perspective image segments. For this purpose, as shown in

Figure 6, when the distance between the virtual H1 plate and the LCD panel is denoted as *L*1, we need to make *L*<sup>1</sup> be an integer multiple of *L*<sup>2</sup> which is the distance between the H2 plate and the LCD panel. This ensures that the rectangular area formed by the hogel on H2 plate and the segment of the LCD panel just falls on the hogel of virtual H1 plate.

**Figure 5.** Holographic element-based effective perspective image segmentation and mosaicking methods (**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.

**Figure 6.** Parameter setting of holographic element-based EPISM methods.

#### **3. The Basic Algorithm of the Holographic Element-Based EPISM Method**
