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Generally, the spatial resolution (multiview display pixels Nmul) and the angular resolution (angular separation ∆θ) determine the visual experience provided by a multiview 3D display3. Therefore, we adopt the information density (pixels per degree (PPD)) to evaluate the performance of the 3D display:
$$ {\rm{ID}}= \frac{{N_{\mathrm{mul}}}}{{\Delta}\theta} $$ (1) where ID represents the information density. A higher information density provides a higher spatial resolution with more fluidic motion parallax. In prior studies, constant information density was provided within the viewing angle by views with the same distribution pattern (Fig. 1a). In contrast, we propose 3D display with spatially variant information density by precisely manipulating the view distribution into hybrid dot/line/rectangle shape (Fig. 1b).
Fig. 1 Working principle of the foveated glasses-free 3D display.
a State-of-the-art glasses-free 3D display with uniformly distributed information. The irradiance distribution pattern of each view is a dot or a line for current 3D displays based on microlens or cylindrical lens array. b The proposed glasses-free 3D display with variant distributed information. The irradiance distribution pattern of each view consists of dots, lines, or rectangles. To make a fair comparison, the number of views (16 views) is consistent with a. c Schematic of a foveated glasses-free 3D display. An LCD panel matches the view modulator pixel by pixel. For convenience, two voxels are shown on the view modulator. Each voxel contains 3 × 3 pixelated 2D metagratings to generate View 1–View 9Figure 1c illustrates the schematic of the view modulator with 2DMCs. To generate a horizontally variant display information density, we define 9 irradiance patterns with variant widths. Pixelated 2D metagratings (3 × 3), which are grouped into a voxel, are designed to provide the predefined view distribution. We reserve detailed calculation of the 2D metagratings in the view modulator pixel by pixel to the Supplementary Information (Section 1). As a result, the information density distribution will be modulated as in the foveated vision.
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The cornerstone of the proposed display architecture is a large-scale 2DMC on the view modulator. With a size up to 9 inch, the data volume of 2DMCs is > 1.8 Tb. Due to the large data volume, both the design and fabrication of 2DMCs is nontrivial.
Figure 2a illustrates the schematic of the design process of 2DMCs. We first designed the phase hologram of the nanostructures according to the target view distribution by the Gerchberg–Saxton algorithm45. Four typical phase holograms responsible for typical view distributions are summarized in Table 1, and they can be applied in different scenarios. For example, dot-shaped views provide the highest information density. The vertically oriented and horizontally oriented line-shaped views reduce the information density in one direction while maintaining the information density in the other direction. The rectangular-shaped views reduce the information density along both directions, which are typically adopted for peripheral observing region. Although the diffractive pattern for each voxel is the same, the position of each pixel and the diffraction angle for the emergent beam varied. As a result, a unique nanostructure is donated to each pixel over the entire view modulator. Furthermore, with negligible tolerance, it has been proven that the 2D metagratings corresponding to the same view have similar shapes but with different scaling factors of periods and orientations (for additional information, see Section 2 in the Supplementary Information).
Fig. 2 Fabrication process flow of 2DMCs on the view modulator.
a Design and fabrication process for 2D metagratings in the view modulator: ① generating the phase hologram by the GS algorithm according to the target view distribution; ② fabricating the binary optical element (BOE) by a laser direct writing (LDW) system; ③ patterning 2DMCs on the view modulator by a self-developed interference lithography (IL) system. The red dashed line marks a pixelated 2D metagrating. b Schematic of the self-developed interference lithography system. c Illustration of controlling the BOE to adjust the scaling factor of periods and orientation of the patterned 2D metagratingsTarget view Simulated phase hologram Simulated reconstructed view Experimental reconstructed view aFor convenience, we maintained the first-order diffraction light and blocked out the other orders of light because only the first-order diffraction components were used Table 1. A summary of four typical phase holograms designed for various target viewsa
The fabrication of a view modulator with complex nanostructures remains a challenge. On the one hand, electron-beam lithography (EBL) is a typical nanopatterning tool in the laboratory46-49, but it suffers from limited throughput and size. On the other hand, laser direct writing (LDW) technology can fabricate patterns over several inches50, yet the minimum resolvable line width is diffraction limited to a submicron scale. Herein we developed a versatile IL system, as shown in Fig. 2b. A collimated and expanded laser beam illuminates a phase-modulated system, which consists of two Fourier transform lenses and a binary optical element (BOE) inserted in between. Then an interference pattern is formed by the multiple diffractive beams of the BOE at the back focal plane of the second Fourier transform lens. Finally, the interference pattern light field is minified by an objective lens and projected on the photoresist. The patterned structures on the photoresist are a minified multibeam interference pattern of the BOE. Details about the principles of our versatile IL system can be found in the Supplementary Information (Sections 2 and 3). Therefore, we enabled the fabrication of 2DMCs on the view modulator to form dot, linear, and rectangular hybrid shaped view distribution shown in Table 1.
Furthermore, the axial movement and axial rotation of the BOEs between two Fourier transform lenses lead to variations in the scaling factor of periods and orientation of the patterned 2D metagratings51, respectively (Fig. 2c). A pixelated 2D metagrating can be fabricated by pulse exposure. On the one hand, the 2DMCs for one view can be patterned by precisely controlling the scaling factor of periods and the orientation. On the other hand, the 2DMCs for views with different irradiance shapes can be achieved by inserting the corresponding BOEs in the homemade IL system. Furthermore, it is worth noting that the periodic tuning accuracy of fabricated 2D-metagrating can reach within 1 nm. The processing efficiency of the IL system can reach 20 mm2 mins−1, 500 times faster than the speed of EBL.
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Enabled by the homemade IL system, we fabricated several view modulators with different screen sizes and complexity (for details about the fabrication, see "Materials and methods"). The typical parameters of the three prototypes are summarized in Table 2. To prove the concept, we made a 6-inch view modulator with horizontal-variant information density. Figure 3a shows the variation of the scaling factor for periods of the 2D metagratings on the view modulator. The proposed 6-inch view modulator contains a total of 800 × 600 voxels, and each voxel is composed of 3 × 3 pixels for 9 views. That is to say, a total of 4, 320, 000 2D metagratings need to be patterned on the view modulator. A microscopic image of the 2DMCs on the view modulator is shown in Fig. 3b. Figures 3c and S4 presents the measured and simulated radiation pattern of the 9-view modulator prototype (for details about the simulation, see "Materials and methods"), respectively. Seven views (Views 2–8) are uniformly distributed in the central region with an angular separation of 10°, while the peripheral views (Views 1 and 9) cover 40° on each side of the central views. The crosstalk is measured as 14.88% (for detailed measurement, see Section 4 in the Supplementary Information). Compared with the theoretical value of 8%, a slight increment in experimental value is observed. Besides, the diffraction efficiency of 2DMC for red/green/blue (R/G/B) color is measured as 8.89, 7.72, and 11.92%, respectively. In contrast, the theoretical diffraction efficiency of 500 nm deep 2DMC is 20%. The experimental deviations for both crosstalk and diffraction efficiency are induced by nanofabrication inaccuracy and the misalignment in system assembly.
3D imaging characteristics View modulator in Fig. 3e View modulator in Fig. 5a View modulator in Fig. 5b Screen size 12 cm × 9 cm 5.4 cm × 5.4 cm 20.6 cm × 12.9 cm View number 9 36 9 Field of view 160° 160° 160° Number of pixels 2400 × 1800 3600 × 1200 1280 × 800 Sub-pixel size 50 μm × 50 μm 15 μm × 45 μm 108 μm × 108 μm Angular separation 10° (center) 3° (center) 10° (center) 30° (edge) 8.5° (edge) 30° (edge) Information densitya 80 PPD (center) 200 PPD (center) 42.6 PPD (center) 26.7 PPD (edge) 70.6 PPD (edge) 14.2 PPD (edge) aPPD: pixels per degree Table 2. Critical parameters of three typical prototypes
Fig. 3 A proof of concept with horizontally variant information density.
a Variation of the scaling factor for periods of the 2D metagratings. The blue dashed line marks an area containing 3 × 3 voxels. The red dashed line marks a voxel. b The microscopic image of the 2DMCs, captured by a laser confocal microscope (OLYMPUS, OLS4100). The red dashed line also marks a voxel. c The irradiance of view distribution and the intensity distribution along the white dashed line of the views. d The variant information density distribution (blue solid line) and its comparison with two cases for uniformly distributed information. Case A is that the angular separation between views is set to 10° with decreased FOV (green dashed line). In case B, the FOV is kept to 160°, but the information density is greatly reduced (red dashed line). e Images of numbers "1–9" observed from left to right views. A dinosaur toy is adhered to the left corner of the view modulator and is served as a reference for the viewing angle. See another 3D images in Figs. S5 and S7A shadow mask with hybrid images of numbers is adopted to match the 9-view modulator pixel by pixel. When the light from a collimated light-emitting diode (LED) illuminates the prototype, we record the "1–9" numbers projected to each view, as shown in Fig. 3e. The horizontal FOV is 160°, and the vertical FOV is 50° (Visualization 1). The information density is modulated to 80 PPD at the central region and 26.7 PPD at the periphery (Fig. 3d).
For video rate full-color 3D displays, we successively stack a liquid crystal display (LCD) panel, color filter, and view modulator together to keep the system thin and compatible (Fig. 4a). Since most LCD panels have already been integrated with a color filter, the system integration can be simply achieved by pixel to pixel alignment of the 2D-metagrating film with the LCD panel via one-step bonding assembly. The layout of 2DMCs on the view modulator is designed according to the off-the-shelf purchased LCD panel (P9, HUAWEI) (Fig. 4b). To minimize the thickness of the prototype, 2D metagratings are nanoimprinted on a flexible polyethylene terephthalate (PET) film with a thickness of 200 µm (Fig. 4c), resulting in a total thickness of < 2 mm for the whole system (Fig. 4d).
Fig. 4 A full-color and video rate spatially variant information density 3D display.
a Schematic of the full-color video rate 3D displays that contain an LCD panel, a color filter, and a view modulator. b The microscopic image of the RGB 2DMCs on the view modulator. The red dashed line marks a voxel containing 3 × 3 full-color pixels, and the blue dashed line marks a full-color pixel containing three subpixels for R (650 nm), G (530 nm), and B (450 nm). c Photo of the nanoimprinted flexible view modulator with a thickness of 200 µm. d A full-color, video rate prototype of the proposed 3D display. The backlight, battery, and driving circuit are extractedA white LED light illuminates the 2D metagratings from the back with a filtered wavelength and modulated intensity. The emergent beams from R/G/B 2DMCs are combined for full-color display (Fig. 5a, b, Visualization 2 and 3). The FOV reaches a record of 160°. The information density is modulated to 200 PPD at the central region and 70.6 PPD at the periphery.
Fig. 5 Performance of the foveated 3D display.
a Images of "Albert Einstein" and b "whales" and "lotus leaves" observed from various views with natural motion parallax and color mixing. The number shown in the lower left corner represents the viewing angle of the image. See other 3D images in Fig. S6