As technology progresses, especially with the maturation of virtual reality, three-dimensional (3D) light field display (LFD) emerges as a focal point in both scientific research and industry. This technology enables users to view lifelike 3D scenes without any external devices, offering a unique immersive visual experience. In 3D-LFD, the parameters such as viewing angle, spatial resolution, and viewpoint density are essential in assessing the 3D image quality. Moreover, viewpoint density, indicative of the density in constructing 3D scenes, is a critical metric for evaluating the fidelity of 3D-LFD, directly influencing the realism and accuracy of the reconstructed scenes. Recently, our research group has been dedicated to enhancing viewpoint density and a method based on spatial multiplexing for increasing viewpoint density has been proposed, utilizing 64 projectors to capture information of 3D objects from different angles, and then reproducing the spatial information of these objects through a holographic screen in front of the projectors. This method successfully creates a large-scale, true-color, real-time 3D display system with a viewpoint density of 1.42/(°). However, existing methods often face a common challenge: an increase in the total volume of information. In traditional 3D-LFD systems, enhancing viewpoint density typically requires more data transmission and processing, leading to increased system complexity and higher demands on computational and bandwidth resources. Furthermore, traditional 3D display technologies have an inherent contradiction: under a fixed volume of information, there is a trade-off among viewing angle, viewpoint density, and spatial resolution. In other words, simply increasing viewpoint density might reduce the viewing angle or spatial resolution. We hope that our strategy and work will be helpful for the design of large-angle 3D-LFDs and the optimization of viewpoint density.

Firstly, the impact of viewpoint density on the image quality of 3D-LFD is analyzed. Black and white striped patterns with identical spatial frequencies are used as test images, and computational simulations are employed to reconstruct them on the same depth plane, determining the central and peripheral viewpoint densities and fitting the relationship curve between viewing angle and viewpoint density. Subsequently, a novel lens is designed to realize the optical path distribution outlined in the relationship curve. Unlike traditional single lenses, the designed lens structure needs to be able to modulate the light emitted from pixels non-uniformly and also meet the distribution requirements of viewpoint density. This design must satisfy three conditions: 1) a viewing angle of 100° with a lens period of 1.12 mm; 2) the root mean square radius of the optical diffuse spot on the liquid crystal display (LCD) surface should be less than the size of its sub-pixels (62.5 μm); 3) the main light density distribution of the pixels after modulation by the lens should be consistent with the required viewpoint density curve distribution. Finally, to reconstruct a natural and smooth 3D scene, multi-view information of the scene must be collected and recorded. Using a virtual camera array with off-axis pickup, digital sampling of the direction and intensity of the target virtual 3D object is conducted. By deriving the formula for the propagation of light rays in the 3D-LFD system, the mathematical mapping relationship between the sub-pixels and the designed viewpoints can be calculated. This allows for determining the sub-pixel positions in the synthesized image loaded on the LCD corresponding to the parallax image seen by an observer at a certain position, thereby calculating the arrangement of sub-pixels in the lens unit.

To validate the feasibility of the proposed method, related simulations and optical experiments are conducted. The display system is composed of an LCD panel and the designed compound lens array with gradual main light density (GDLA). The LCD is used to load encoded images containing 3D information, and after modulation by the GDLA, 3D images are constructed in space, forming the viewpoint distribution that is dense in the center and gradually sparser towards the edges (Fig. 12). With a viewing angle of 100° and an off-screen depth of 300 mm, the simulation results of the 3D light field are compared between traditional and proposed methods (Fig. 13). The proposed GDLA, while suppressing aberrations, also achieves a distribution of viewpoint density that is dense in the middle and gradually sparser towards the edges. Therefore, the structural similarity (SSIM) value of the edge viewing area 3D image is lower than that of the traditional viewpoint density uniformity (TVDU). But because GDLA achieves a higher viewpoint density in the central region, the SSIM value of 3D image in the central viewing area is 0.954, which is higher than that of the traditional method. The GDLA optimizes the viewpoint density, effectively enhancing the density in critical areas and improving the quality of 3D images (Fig. 14). Further, an experimental optical display system is set up, achieving a high-definition 3D-LFD with a display size of 65 inches (1 inch≈2.54 cm), a viewing angle of 100°, and a display depth of 300 mm with a gradual viewpoint density (Fig. 15). This system holds significant potential for applications in medical education and auxiliary medical diagnosis.

Considering the inherent trade-offs among the number of viewpoints, viewing angle, and depth range, we propose a large-angle 3D-LFD with gradual viewpoint density. The primary objective of this system is to increase the viewing angle and optimize the viewpoint distribution. It is capable of displaying clear 3D images with smooth parallax and correct geometric occlusions across the entire visible range of 100°. The core optical control structure, GDLA, plays a pivotal role. It optimizes the distribution of viewpoints, ensuring a concentration of more effective viewpoint information in the middle of the viewing area. Additionally, to suppress aberrations and further improve image quality, the lens is designed with a specific composite structure. Compared with traditional 3D displays, this system is characterized by a dense distribution of viewpoint information in the middle of the viewing area and a gradually decreasing viewpoint density towards the sides. This design not only significantly enhances the clear maximum off-screen depth in the middle of the viewing area but also increases the viewing angle of the system. In experimental verification, the high-performance 3D-LDF system is obtained with the viewing angle of 100°. The 3D scene captured at a 0° viewing angle has a clear focus depth of up to 300 mm. From a commercial perspective, this prototype has the potential for mass production and exhibits good stability in most situations. We firmly believe that this 3D-LFD system has a broad application prospect in the future, especially in fields such as aviation simulation, industrial design, architectural design, and multimedia educational presentations.