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Abstract
The depth of focus (DOF) of a lens is a crucial parameter in glasses-free 3D displays that affects the viewing distance range. Here we proposed a vector light field display based on intertwined flat lens for extended viewing distance. The gray-scale diffractive lens (GDL) is designed and fabricated with extended DOF for red (658 nm), green (532 nm), and blue (450 nm) colors. By integrating the intertwined GDLs with a liquid crystal display, four views form a smooth horizontal parallax with a cross talk below 26% over a viewing distance from 24 to 90 cm. The enhancement of the DOF is ${1.8} \times {{1}}{{{0}}^4}$-fold. The light efficiency of the pixelated GDL reaches 82%. The proposed vector light field 3D display has the advantages of a thin form factor, high efficiency, high color fidelity, and large viewing distance. The potential applications include portable electronics, 3D TVs, and tabletop displays.
© 2022 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. INTRODUCTION
Glasses-free three-dimensional (3D) displays are widely regarded as one of the most promising technologies that will redefine the display industry [1–8]. Holography [9–13] generates realistic 3D images by reconstructing both the amplitude and phase information from the image. However, due to the large data volumes, holographic displays with large field of view (FOV) and high resolutions are still quite challenging to achieve. Multiview 3D displays [14–16] discretize the light field into spaced views to provide a 3D stereoscopic experience for multiple observers simultaneously. The development of cylindrical barrier- or microlens array (MLA)-based 3D displays has made great progress in recent years [17–21]. However, issues such as short range of viewing distance, limited motion parallax, self-repeating views, and vergence–accommodation conflict hinder the extensive daily usage of 3D displays [22–24].
Microstructures/nanostructures provide a revolutionary light manipulation method for 3D displays to address the aforementioned critical issues [25]. Wan et al. [26] proposed a holographic sampling 3D display by adopting metagratings to form converged views. Shi et al. [27] proposed a 32-in. holographic combiner based on spatial multiplexing metagratings for glasses-free augmented reality 3D displays. Compared with geometric-optics-based multiview 3D displays, the proposed sampling 3D display has the advantages of a large FOV, natural motion parallax, and minimum vergence–accommodation conflict. However, the experimental diffraction efficiency of metagratings is approximately 20%. High power consumption due to the low light efficiency is unacceptable in portable electronics.
On this basis, multilevel diffractive optical elements (DOEs) have been further designed and fabricated for 3D displays. Multilevel DOEs have the same merit as metagratings with superior light manipulation capability for the sake of a large FOV, a thin form factor, and eliminated cross talk [28,29]. Moreover, the theoretical diffractive efficiency of 16-level diffractive elements can be as high as 99%. At a wavelength of 532 nm, the measured diffraction efficiency is up to 60% for four-level DOEs [28]. Finally, the depth of focus (DOF) can be significantly increased by the application of diffractive optics. In recent years, multilevel diffractive lenses have shown great capabilities in expanding the DOF [30–32]. Extremely large DOF from 5 to 1200 mm has been achieved at a wavelength of 850 nm [33]. With extended DOF, the range of viewing distance can be greatly enlarged.
In this paper, we showed that with a delicate design of the gray-scale diffractive lens (GDL), it is possible to significantly extend the DOF range at red, green, and blue wavelengths of 450 nm, 532 nm, and 658 nm, respectively. We further proposed a vector light field 3D display based on a pixelated GDL array. In a 4-in. prototype, the DOF ranged from 24 to 90 cm. The enhancement of the DOF was ${1.8} \times {{1}}{{{0}}^4}$-fold. The cross talk was maintained below 26% over a viewing distance of 66 cm. Moreover, the light efficiency of the pixelated GDL reached 82% in the experiment. We demonstrated that a pixelated GDL significantly increased the viewing distance for vector light field 3D displays. GDL-based 3D displays have a thin form factor and high light efficiency and are compatible with traditional flat panels, providing a promising approach for the potential applications of this study include mobile electronics, 3D television (TV), and tabletop displays.
Fig. 1. 3D topography of the flat lens and the comparison between the Fresnel lens and GDL. (a) 3D topography of the GDL; (b) 3D microscopic photo of the GDL captured by a laser confocal microscope (LEXT, OLS4100, OLYMPUS); (c) cross section of the traditional Fresnel lens (in blue) and optimized GDL (in red); (d) optical micrograph of the fabricated GDL; (e) imaging properties of the GDL; (f) topography of a Fresnel lens; (g) optimized topography of the GDL; (h)-(i) comparison between the light distributions of a Fresnel lens and the proposed GDL.
2. DESIGN OF FLAT LENS
The design and fabrication of flat lenses for glasses-free 3D displays is challenging. First, the viewing distance for mobile phones typically ranges from 25 cm (near the human eye) to more than 60 cm (the length of one arm). In other words, the proposed GDL for 3D displays needs an enhancement of DOF (eDOF) larger than ${{9}} \times {{1}}{{{0}}^3}$-fold. The eDOF is given by [33]
Second, color fidelity is crucial for display purposes. The spectral response of the GDL affects the standard red–green–blue (sRGB) color space because of chromatic dispersion. Third, the size of the optical device used for display purposes is usually between 4 and 100 in. From a practical point of view, state-of-the-art nanofabrication technology includes tight constraints on the minimum feature size of the designed microstructure over a 4-in. format.
Here, we optimized the sawtooth relief profile of a GDL based on a directed binary search technique [33]. Uniform illumination was assumed to normally impinge on the GDL. The GDL is polarization insensitive, and all experiments conducted here were illuminated by unpolarized light-emitting diode (LED) light. A conventional Fresnel diffraction integral is adopted to model the $x - z$ light distribution from the lens plane to the observation plane. We further investigated the light distribution of the GDL through finite-difference time-domain analysis (FDTD solution software, Lumerical). Both simulation results suggest identical optical properties, validating the theoretical design.
To prove the feasibility of the proposed design methodology, we designed and fabricated a GDL with $f_{\min} = {{20}}\;{\rm{mm}}$ and $f_{{\max}} = {{110}}\;{\rm{mm}}$ at selective wavelengths. We chose wavelengths of 658 nm, 532 nm, and 450 nm to characterize the RGB imaging behavior.
Figures 1(a)–1(c) show the 3D topography and the surface relief profile of the flat lens. The relief depth of all zones of the GDL is the same, determined by
where $m$ is the harmonic diffraction coefficient of a harmonic diffraction lens, ${\lambda _0}$ is the central operating wavelength of the lens, and $n$ is the refractive index of the material. The harmonic diffraction coefficient is set to 5. With a refractive index of 1.53, the groove depth is 5 µm. Thanks to the gray-scale lithography, each sawtooth is divided into 256 steps, providing a smooth surface profile. Figure 1(d) is a micrograph of the GDL. The minimum width of the sawtooth is 35 µm. Figure 1(e) shows a GDL with a diameter of 10 mm placed on top of a Soochow University logo. The magnified image formed through the GDL suggests a wide spectral response of the lens. The light intensity distribution in the $z - x$ plane was simulated and plotted for both the traditional Fresnel lens and the proposed GDL [Figs. 1(f)–1(g)]. From the simulation, there are multiple focal points along the $z$ direction within the main lobe of focus. In comparison, the Fresnel lens has only one focal point at a focal length of 50 mm [Figs. 1(h) and 1(i)].We further investigated the light distribution under the illumination of collimated light. The point spread functions (PSFs, or the light intensity distribution in the $x - y$ plane) at different $z$ positions (the distance from the GDL) are simulated in Fig. S1 of Supplement 1. To demonstrate the imaging capability, we used a standard test chart [United States Air Force (USAF) 1951] as the object. We obtained the image of USAF 1951 through a GDL with a monochrome charge-coupled device detector. The bandwidth of the illuminance is 10 nm. It is clear that the proposed GDL is capable of forming good images at RGB wavelengths over a large DOF range (20–110 mm). (The detail spatial resolution measurement results are attached in Supplement 1, Figs. S4–S6.) Figures 2(d)–2(f) show the measured modulation transfer function (MTF) for the GDL. The average cutoff frequency at the contrast of 10% is 133l p/mm, 153l p/mm, and 143l p/mm for red, green, and blue light over a DOF range of 20–110 mm (Fig. S7). While the conventional Fresnel lens has a narrow spectral response, we note that the GDL possesses similar optical behavior for RGB wavelengths within the extended focal length range. The optimized GDL with spectrally invariant MTF over an extended DOF can provide unique properties for full-color glasses-free 3D displays.
Fig. 2. (a)-(c) Distribution diagram of far-field diffraction light intensities at the wavelengths of 658, 532, and 450 nm. (d)-(f) Modulation transfer function for the GDL at the illuminance of red, green, and blue, respectively. (g)-(i) Image of the Air Force resolution chart at the different z distance under the illuminance of red, green, and blue, respectively.
3. VECTOR LIGHT FIELD 3D DISPLAY BASED ON GDLS WITH A LONG DOF
MLA-based light field 3D displays suffer from severe resolution degradation and limited FOV. Inspired by our recent studies in metagratings-based glasses-free 3D displays [26,27], the view modulator is composed of several intertwined flat lenses. We propose a vector light field 3D display where the vector of the light beam from each pixel is designed to form a converged view. The vergence–accommodation conflict is significantly eliminated by converged views [26]. An off-the-shelf purchased liquid crystal display (LCD) is adopted as the refreshable image generator. The corresponding surface-relief structures modulate the vector of the emergent beam from each pixel. Thus, the pixelated structures are aligned with the pixels of LCD panels. From the perspective of each view, the pixelated structures focus light beams to the view and work as a focusing lens. Take a 3D display with four views as an example, four axis-horizontally-shifted GDLs intertwined to form a view modulator. The function of each lens is to converge irradiant light into a view. A voxel is comprised of four pixels for four views. Multiple intertwined GDLs generate multiple views to form motion parallax, as shown in Fig. 3(a).
Fig. 3. Schematic diagram of the 3D display device. (a) Schematic of the pixelated GDL array. (b) Vector light field display device. (c), (d) Microscope picture of the view modulator. (e) Microscope picture of the pixel size.
Compared to an MLA-based 3D display, a view modulator composed of an intertwined GDL is superior for a dramatically reduced information redundancy. The views can be arranged arbitrarily within the viewing zone. In the preferred prototype, the views are evenly distributed in the horizontal direction according to the observation habit of human eyes.
Figure 3(b) is a schematic diagram of a vector light field 3D display based on a pixelated flat lens array. Collimated LED light uniformly illuminates the LCD panel. The modulated light passes through the color filter and normally impinges on the view modulator. The sawtooth microstructures redirect the emergent light to the corresponding view. The refreshable LCD information is designed to match the position of each view from the display screen. As a result, one can observe smooth motion parallax when transitioning from one view to another.
Figure 3(e) shows the color filter of an LCD panel with a pixel size of 78 µm, on which multiperspective images are refreshed at video rate. A gray-scale lithography system (Microlab, SVG) was used to fabricate pixelated GDL arrays on the view modulator. The surface relief structures can be further transferred to a flexible membrane by an ultraviolet imprinting process. With a thickness of 100 µm, the structured membrane can be easily integrated with the LCD panel for a compact form factor. The pixel size of the sawtooth microstructures is set to 78 µm for pixel-to-pixel integration with the LCD panel [Figs. 3(c) and 3(d)]. While we adopted the pixel-to-pixel alignment strategy for the vector light field 3D display, the GDLs with long DOF also can be used in the MLA-based 3D display to extend their viewing depth.
We tested the DOF of the view modulator with collimated white LED light. As the receiving plane moves away from the view modulator at distances from 24 to 90 cm, four converged views were captured, as shown in Fig. 4(a). The light distribution along the $z$ direction is further evaluated by cross talk and DOF.
Fig. 4. (a) Intensity distribution of four views at distances from 12 to 90 cm. (b) Light intensity distribution of the four viewpoints at a distance of 48 cm. (c) Measured cross-talk dependences on viewing distance compared with prior art [33]. (d) Measured light efficiency under collimated LED illumination.
Fig. 5. (a) Photos of the view modulator and LCD panel. (b) Photo of the vector light field 3D display prototype. (c) Color block matrix diagram observed at the viewpoints. (d)-(f) Images observed from different perspectives (see Visualization 1, Visualization 2, and Visualization 3).
Cross talk is an important parameter for evaluating the performance of a glasses-free 3D display device. The cross talk along the viewing angle can be defined as follows:
After integrating the 4-in. view modulator with an LCD panel [Figs. 5(a) and 5(b)], we tested the color fidelity and color mixing of the view modulator, as shown in Fig. 5(c). Three virtual models with different complexities were built to test the 3D display effect. The viewing angle range is ${-}{4.5}^\circ$ to 4.5°, and the resolution of each perspective image is ${{568}} \times {{320}}$ pixels. The angular separation is 3°. The images were captured by a camera (D810, Nikon). The natural motion parallax can be observed as shown in Figs. 5(d)–5(f) and the recorded videos in Visualization 1, Visualization 2, and Visualization 3.
4. CONCLUSION
The DOF and FOV can hardly be simultaneously increased in geometric-optics-based multiview 3D displays. Moreover, multiview 3D displays suffer from severe vergence–accommodation conflict, cross talk, and limited FOV.
Developments in micro-/nano-optics have provided revolutionary tools for light manipulation. In this paper, delicate design of a GDL was used to modulate the light field to form converged views over a significantly extended DOF with good spatial resolution for the human eye. We further proposed a vector light field 3D display where the vector of the light beam from each pixel is designed to form a converged view. In a 4-in. prototype, the viewing distance was between 24 and 90 cm with an enhancement of the DOF of ${1.8} \times {{1}}{{{0}}^4}$-fold. The cross talk was maintained below 26% over a range of 66 cm. Moreover, the light efficiency of the pixelated GDL reached 82% in the experiment. We demonstrated that an intertwined GDL significantly increased the viewing distance for vector light field 3D displays. Slight cross talk can be observed in the captured 3D image. This can be minimized by further improvement in the fabrication and assembly process.
With a 100 µm thick microstructured membrane, the proposed glasses-free 3D display based on the intertwined GDLs has the advantages of a thin form factor, high efficiency, high color fidelity, and large DOF. The potential applications include consumer electronics, window displays, 3D TVs, and tabletop displays.
The glasses-free 3D display is an encouraging application for diffractive lenses and metalenses. The design of flat lenses in 3D display is less critical than the design in imaging applications. While broadband spectrum response has to be considered in imaging, optical behavior at only three wavelengths (R/G/B) is optimized in 3D display. Moreover, only on-axis performance is used, since the view modulator is illuminated by collimated light. The issue of off-axis degradation in imaging is bypassed in 3D display applications. We envision flat lenses provide superior light manipulating capability, thus open the opportunities to solve the formidable problems such as limited motion parallax, cross talk, visual fatigue, and limited viewing distance in 3D display.
Funding
National Key Research and Development Program of China (2021YFB3600500); Leading Technology of Jiangsu Basic Research Plan (BK20192003); Key Research and Development Project in Jiangsu Province (BE2021010); National Natural Science Foundation of China (61975140, 62075145); Priority Academic Program Development of Jiangsu Higher Education Institutions.
Acknowledgment
The authors thank Jianyu Hua and Yang Chen for useful discussions and suggestions on the nanofabrication process.
W. Qiao and L. Chen conceived the research and designed the experiments. F. B. Zhou and F. Zhou conducted the experiment. W. Qiao and F. B. Zhou wrote the paper. All authors discussed the results and commented on the paper.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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