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Abstract
In this paper, we propose an optofluidic lenticular lens array (OLLA) for a two-dimensional/three-dimensional (2D/3D) switchable display. The OLLA includes a bottom substrate layer with lenticular lens structure, a microfluidic layer with microchannels, and a top substrate layer with inlets as well as outlets. A micro gap is formed between the lenticular lens of the bottom substrate layer and the top substrate layer. When air is in the micro gap, the OLLA behaves as a lenticular lens array, which can realize 3D display. When fluid is filled in the micro gap, because the refractive index of the fluid is the same with the lenticular lens structure, the OLLA equivalents to a transparent flat panel, which can realize a 2D display. Experiments verify that a switchable 2D/3D display prototype based on this OLLA and a smartphone achieves both high-resolution 2D display and high-quality 3D display.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The three-dimensional (3D) display with depth information can provide a more realistic visual experience [1–7]. However, the 3D display usually causes display quality degradation [8], and the two-dimensional (2D) display is still the most convenient and more high-definition display technology [9]. Therefore, the 2D/3D compatible display is a popular research technology, which brings visual enjoyment for people in recent years [10–11].
The most common way to achieve a 2D/3D compatible display is based on the liquid crystal (LC) lens [12–18]. For example, the hexagonal LC lens array has been used to achieve a 2D/3D hybrid integral imaging display [16], which can improve the resolution of the 3D display. And the multi-view 2D/3D switchable display using cylindrical LC lens array has been proposed [17], and it has the advantages of low operating voltage, fast response, and much thinner thickness. However, their lens array pitch is relatively small, which can only be used for the specific screens with small pixels, since the sub-lens needs to cover at least two sub-pixels in the realization of 3D display, and the viewing angle of the 3D image is small. There is a 2D/3D mixed frontal projection system containing an LC microlens array and a quarter-wave retarding film with pinholes (QWRF-P) [18]. Nevertheless, although it can achieve a larger size of the LC lens array pitch, the addition of a QWRF-P and a polarization-preserving screen (PPS) leads to a relatively complicated system. On the other hand, since the LC material modulates polarized light, the light is lost during the conversion process, which reduces the display brightness. And polarization correlation will also limit its use in certain displays, such as organic light-emitting diode (OLED) and micro-LED displays.
The adaptive liquid lens [19–25] is based on the change of its own structure and shape, and the length of its optical path change can reach the millimeter level. Therefore, the liquid lens array has a potential ability to implement 2D/3D switchable display. For example, a liquid-filled tunable lenticular lens composed of transparent elastic membrane microchannels to realize 2D/3D switching display by changing the shape of membrane has been reported [19]. This method can be directly connected to a smart phone display and project a 2D image with the original resolution and a high-brightness 3D image. A more convenient way of 2D/3D switching display technology is based on the electrowetting liquid lenticular lenses [21–25]. The liquid surface is adjusted to a flat or convex surface by changing the applied voltage. The flat surface displays 2D images, and the convex surface displays 3D images. However, the liquid lens array needs to overcome some problems such as gravity effect, relatively high driving voltage, and complicated production process.
Fortunately, with the development of micromachining technology, many more precise lens arrays based on optofluidic technology for 3D display are proposed [26–28], and they have fast and accurate adjustment functions with a flexible lens size, which makes them suitable components for tunable optics in AR/VR devices. However, they have not been able to easily achieve large-size 2D/3D compatible displays.
In this paper, we propose a 2D/3D switchable display based on an optofluidic lenticular lens array (OLLA) and a smartphone. The OLLA can be switched between 2D mode and 3D mode by pressure switching fluid and air. And the optical characteristics in the two modes both meet the requirements of switchable 2D/3D display, including expected focal length, uniform light distribution, and reasonable response time. Experiments verify that the switchable 2D/3D display can achieve high-resolution 2D display and high-quality 3D display. The fabrication of the OLLA is simple and the proposed display is compact, easy to implement, and high optical efficiency.
2. Structure and principle
2.1 Design of the OLLA for a 2D/3D switchable display
Figure 1(a) shows the schematic diagram of the OLLA, which is composed of three layers. The bottom substrate is designed with a lenticular lens array structure and the top substrate contains a fluid-inlet, an air-inlet, and an outlet. And the refractive index of the lenticular lens arrays structure is nl. The microfluidic layer made of polydimethylsiloxane (PDMS) with micro-channels is sandwiched by two substrates. Since the thickness of the PDMS layer is slightly larger than the height of the lenticular lens, there is a micro gap in the lenticular lens arrays area, and the lenticular lens arrays area is named the display area, as shown in Fig. 1(a).
Fig. 1. Schematic diagram of structure and principle of the OLLA. (a) 3D structure of the OLLA. (b) 3D mode. (c) 2D mode.
When air is filled in the micro gap, because the refractive index of the lenticular lens is greater than that of air (na), the display area is in a focused state, as shown in Fig. 1(b), which is called the 3D mode of the OLLA. When the micro gap is filled with fluid (nf) with the same refractive index of the lenticular lens, the display area is equivalent to a transparent flat panel, as shown in Fig. 1(c), which is called the 2D mode of the OLLA.
2.2 Principle of the 2D/3D switchable display
The 3D display based on a lenticular lens is shown in Fig. 2(a) [29]. The display screen is located on the focal plane of the lenticular lens to provide a parallax synthetic image. In the arrangement direction of the lenticular lens units, the parallax image can be projected to different directions after the light of the screen passes through the lens arrays due to the beam splitting effect of the lenticular lens. The 3D image can be observed in 3D mode. When the lenticular lens is switched to a flat plate, the observer sees 2D image display in the 2D mode, as shown in Fig. 2(b).
Fig. 2. Schematic diagram and principle of the 2D/3D switchable display. (a) 3D display. (b) 2D display.
3. Calculation and fabrication
To fabricate the lenticular lens array structure, we first need to determine the radius of curvature (R) of the lens. The focal length and pitch of the lenticular lens are crucial for 3D display. In this study, a smartphone display (iPhone XR, Apple Inc. America), whose sub-pixel width (Wp) is 26µm, was used and the lens pitch was designed to be 423µm in consideration of the 17-view image. Figure 3 briefly shows the light splitting principle of the lenticular lens 3D display.
The display screen is located at the focal plane of the lens. According to the geometric principle, the sub-pixel width and focal length (f) satisfy the equation
where L is the optimal view distance (OVD), fixed at 300 mm, Q is the viewpoint distance between adjacent parallax images, Q = E/17, and E is the interpupillary distance of the human eyes (∼65 mm), so Q is about 3.82 mm. We calculated the focal length as about 2 mm. According to the basic principles of geometric optics, the focal length (f) and curvature radius (R) can be described by where n is the refractive index of lenticular lens, and it is 1.51. From Eq. (1) and (2), the curvature radius can be described by we calculated the curvature radius as 1.024 mm.Figure 4 shows the fabrication process of the OLLA. A lenticular lens array mold and a channel mold are printed with a 3D printer. The lenticular lens array mold has 90 lenticular lenses. The channel diameter of channel mold is about 1mm, and the display area is approximately 40mm×40mm. The PDMS prepolymer (10:1 mixture of the base and curing agent, Sylgard 184, Dow Corning) was poured onto the two molds and baked at 100°C for more than 1 hour on the hot plate, and peeled off the PDMS from the mold to get the PDMS reverse lens and the microfluidic layer, as shown in Figs. 4(a)–4(b).
Fig. 4. Fabrication process of the OLLA. (a) PDMS reverse lens obtainment. (b) Microfluidic layer obtainment. (c) Bottom substrate obtainment. (d) Plasma treatment. (e) Layers bonding. (f) Fabricated the OLLA and lenticular structure under microscope.
To obtain the bottom substrate with lenticular lens structure, the UV curable resin H807 is spin-coated on the glass substrate with a thin thickness, and then imprint with the PDMS reverse lens, and expose to UV light until the UV curable resin is cured before peeling off the PDMS reverse lens, as shown in Fig. 4(c). The refractive index of the solidified UV curable resin H807 is 1.51. A glass substrate with three holes, the microfluidic layer, and the bottom substrate are treated with O2 plasma. Subsequently, these three layers are bonded together, as shown in Figs. 4(d)–4(e). Figure 4(f) shows the fabricated OLLA and the lenticular lens structure under the microscope.
4. Experimental results and discussion
4.1 OLLA performance
To evaluate the optical characteristics of the OLLA, such as the focal length and the uniformity of light distribution, we built a testing system composed of a collimator (FPG-7, Hua Zhong Precision Instruments Co., Ltd., China), the OLLA, and a CMOS camera, as shown in Fig. 5. The light source is an incandescent lamp. The light from the lamp passes through a filter (wavelength range 600-650nm) and collimator to form a beam of collimated light, and the CMOS camera records the images.
When the OLLA is in 3D mode, a collimated light passes through the OLLA, and a set of parallel thin bright stripes are photographed on the CMOS camera. By moving the camera position and observing the changes of these stripes, the distance from the camera at the brightest and thinnest position of these stripes to the OLLA is the focal length of the lenticular lens, as shown in Fig. 5. The focal length of the lenticular lens is measured to be about 2mm, which meets the requirements of 3D display. The photographed result is shown in Fig. 6(a). We analyzed the light intensity distribution of Fig. 6(a), and the results of analysis are shown in Figs. 6(c). In order to realize the 2D mode, we use the phenyl silicone oil (refractive index 1.51) as the fluid to fill the micro gap. As a result, as the position of the camera moves, bright stripes are no longer observed on the camera, but a plane with uniform brightness, as shown in Fig. 6(b). Similarly, we analyzed the light intensity distribution of Fig. 6(b), and the results of analysis are shown in Figs. 6(d). The light intensity distribution in the two modes both are highly uniform, which means that the OLLA can achieve expected optical characteristics well in the two modes.
Fig. 6. (a) Light distribution in 3D mode. (b) Light distribution in 2D mode. (c) Intensity analysis in 3D mode. (d) Intensity analysis in 2D mode.
The response time of the OLLA to switch 2D/3D display is measured by a measuring system composed of laser source, attenuator, beam splitter (BS), reflector, the OLLA, and 2 photodetectors, as shown in Fig. 7(a). The photodetectors are placed near the two ports to monitor the light intensity of the OLLA. The measured light intensity in 3D mode is about 15mW. A constant pressure pump (WH-PMPP-12, Wenhao Co., Ltd., China) is used to provide pressure. When port-1 is opened, as the pressure increases, the phenyl silicone oil in the reservoir enters the OLLA through the microchannels of the microfluidic layer, and the 3D mode is switched to the 2D mode, and the light intensity at the two detectors changes to about 27.68mW successively. The time difference between the light intensity changes of the two photodetectors is used as the response time of the OLLA from 3D mode to 2D mode (3D-2D). Similarly, when port-1 is closed and port-2 is opened, the air enters the OLLA by pressure, the 2D mode is switched to the 3D mode, and the light intensity at the two photodetectors is restored to about 15mW successively. The time difference between the light intensity changes of the two photodetectors is used as the response time of the OLLA from 2D mode to 3D mode (2D-3D). Figure 7(b) shows the relationship of the light intensity at the two photodetectors with time when the pressure is 0.4MPa, and the response time of 3D-2D and the response time of 2D-3D are about 2.2s and 0.7s respectively. The response time is related to the pressure, and Fig. 7(c) shows the response time while pressure from 0.2MP to 0.4MPa. In order to prevent the OLLA from being damaged, the pressure cannot exceed 0.5MPa. In this experiment, the phenyl silicone oil has a large viscosity, which affects the response time. We can improve the response speed by choosing a liquid with a smaller viscosity in future work.
Fig. 7. Measurement of the response time. (a) Measuring system. (b) Light intensity change of the OLLA with applied pressure. (c) Relationship between the response time and applied pressure.
To evaluate the performance of the OLLA in switchable 2D/3D display, we contrasted the imaging of a 2D picture in the two modes. We placed the letters “B” and “H” (Fig. 8(a)) as the target under the OLLA, and used a camera to record the images. The distance between the target and the OLLA is about 6mm, and the distance between the camera and the OLLA is about 170mm. The result in 3D mode is shown in Fig. 8(b), and we obtained a deformed and blurred image due to the light focus of the lenticular lens. We could also obtain a high resolution and clear image in 2D mode, compared with Fig. 8(a), there is almost no difference for “BH”, as shown in Fig. 8(c), which means that the OLLA can achieve a portable 2D/3D display switching.
4.2 Display results
A 3D scene composed of a group of red blood cells and a coronavirus cell was built in 3 ds Max, and a camera array consisted of 17 cameras was built to obtain 17 parallax images, as shown in Fig. 9. In the scene, the coronavirus cell is wrapped by a group of red blood cells, and the distance between each camera is 10mm, and the distance from the camera to the central depth plane is 635mm.
In order to reduce the moiré patterns of the 3D image and match the pixel of the smartphone, the design synthetic image slope is 0.2750 [30]. And the synthetic image as the 3D image source is displayed on a smartphone display with a resolution of 828×1792 pixels, as shown in Fig. 10(a). Because the pitch of the lenticular lens is 423µm, matching 17 viewpoints, the resolution of the 3D display is about 49×1792 pixels (828/17×1792 pixels). One of the parallax images is selected as the 2D image source and displayed on the smartphone, as shown in Fig. 10(b). The resolution of the 2D display is 828×1792 pixels. The proposed switchable 2D/3D display prototype consists of a smartphone display and the OLLA, which is tilted and pasted tightly on the smartphone display with the same slope, as shown in Fig. 10(c).
Fig. 10. Image sources and proposed switchable 2D/3D display prototype. (a) 3D image source. (b) 2D image source. (c) Switchable 2D/3D display prototype.
Visualization 1 clearly shows the 3D display in 3D mode of the OLLA from each viewpoint, when the smartphone displays the 3D image source. We define the viewing area refers to the angular area where a complete 3D image can be seen without crosstalk and flippling, and the viewing area is about 12°. When viewing from a distance of 300mm from the smartphone, the maximum depth of the 3D scene recessed into the display screen is about 5mm, the maximum depth of the protruding display screen is about 15mm, and the depth of the 3D display is about 20mm [31]. And Fig. 11 shows the display results from 4 of these viewpoints. The display results show that the changes of the cells positions can be clearly observed from different viewpoints to obtain cell space position information. And since the cells are separated, the cell outlines can also be clearly observed. In this case, a specific cell can be isolated from the population of cells for individual observation, such as the coronavirus cell here.
When the smartphone displays the 2D image source and the OLLA is switched to the 2D mode. We observe a high-definition 2D image, as shown in Fig. 12. In this case, it helps to observe the appearance of the population of cells and the plane positional relationship between them, so as to quickly identify and locate a specific cell.
In this experiment, we fabricated an OLLA and a switchable 2D/3D display prototype that matched the screen of iPhone XR that is LCD. It is worth noting that the proposed method is also applicable to other types of screens, such as OLED, micro-LED, and mini-LED, and it is only necessary to change the OLLA parameters accordingly.
5. Conclusion
In this paper, an OLLA for 2D/3D switchable display is proposed, and the OLLA can switch between 2D mode and 3D mode by pressure switching fluid and air. And the optical characteristics meet the requirements of switchable 2D/3D display, including expected focal length, uniform light distribution, and reasonable response time. A switchable 2D/3D display prototype based on the OLLA and a smartphone is developed, and it can achieve a high-resolution 2D display in the 2D mode and a high-quality 3D display in the 3D mode. The fabrication of the OLLA is simple and the proposed display is compact, easy to implement, and high optical efficiency.
Funding
National Natural Science Foundation of China (61927809).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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.
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