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Abstract
Conventionally, the fabrication of liquid crystal lenticular microlens arrays (LCLMLAs) is complicated and costly. Here, we demonstrate a one-step fabrication technique for LCLMLAs, which is prepared through the photopolymerization-induced phase separation in the LC/polymer composite. The LCLMLAs possess both polarization-dependent and electrically tunable focusing properties. Furthermore, we construct a 14-view 2D/3D switchable autostereoscopic display prototype based on a 2D LCD panel and the prepared LCLMLA, which has a viewing angle of 14° and a crosstalk of 46.2% at the optimal viewing zone. The proposed LCLMLAs have the merits of simple fabrication, large-scale production, and low cost.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Autostereoscopic displays have attracted intensive attention due to their high display quality, simplicity, compactness, and low cost [1–4]. Conventional autostereoscopic displays consist of a two-dimensional (2D) display panel covered by a lenticular sheet. With this configuration, the parallax images on the screen can be dispersed at different spatial positions using the lenticular sheet. Subsequently they enter the left and right eyes of a viewer, respectively. As a result, the viewer can experience binocular disparity and perceive 3D depth without the need for glasses. The lenticular sheet is the essential component of an autostereoscopic display, which is used to magnify and modulate the light rays emitted from specific subpixels to the desired area. Thus far, two major methods have been used to achieve this function: parallax barriers [5–7] and lenticular microlens arrays [8–29]. Comparatively, the parallax barriers are easy to fabricate and implement. However, they have low efficiency as they block a large portion of the illumination. Multi-view 3D displays are particularly affected by brightness degeneration due to the significant decrease in the effective aperture ratio. Instead of parallax barriers, lenticular microlens arrays provide high efficiency, making them a better choice for multi-view 3D displays.
Generally, the resolution of 3D images is significantly lower than that of 2D ones due to spatial multiplexing. Therefore, in practice, certain types of information, such as text and pictures, are better displayed in 2D mode to achieve a higher resolution. Therefore, it is highly important that autostereoscopic displays can switch between 2D and 3D modes for practical applications. To achieve a 2D/3D switchable autostereoscopic display, the use of an adaptive microlens array is a straightforward approach. Liquid crystal lenticular microlens arrays (LCLMLAs) are widely used as the tunable optical elements for 2D/3D switchable displays [11–29]. Liquid crystals (LCs) are a unique optically anisotropic material that is widely used for light field manipulation, including applications such as spatial light modulators [30], tunable microlens arrays [31–35], and dynamic metasurfaces [36–39]. In general, liquid crystal microlens arrays can be classified into two types. One type is that a spatially inhomogeneous electric field is generated by patterned electrodes in a homogeneous LC layer. Under the spatially inhomogeneous electric field, the LC molecules can be reorientated to produce a parabolic refractive index distribution known as the gradient refractive index (GRIN) profile [14,15,40]. Previously, the GRIN LC lens utilized a glass substrate as a high-K layer to generate a parabolic voltage gradient. However, the operating voltage is quite high (>50 V). Later, the high-K layer was replaced by a high-resistance layer (MΩ/sq) in a new design of the GRIN LC lens, known as the model control LC lens [17,20,21,41]. In this configuration, a gradient electric field distribution is generated across the LC layer by coating the patterned electrodes with a high-resistance layer. In such cases, the applied voltage is significantly reduced. However, it is crucial to precisely control the sheet resistance and the thickness of the high-resistance layer to match the parameters of the LC lens, such as the diameter and cell gap. In addition, due to the capacitive characteristic of the LC, the distribution of the electric field is frequency-dependent. This also requires precise control of the amplitude, frequency, and waveform of the driving voltage, making the control more challenging. The other type is to combine the lenticular microlens with an LC layer to form a double-layer composite structure [25–28,42]. The first step is to prepare a lenticular microlens array as the bottom substrate. Next, the LC cell is assembled, consisting of the top substrate with an alignment layer and the prepared bottom substrate. Finally, the LC is filled into the cell by the capillary force. To ensure a homogeneous alignment, the substrate with a lenticular microlens array should be coated with an alignment layer and uniaxially rubbed. Unfortunately, the rubbing process usually deteriorates the microlens structures, hence degrading the optical performance of the microlens.
To overcome the difficulties in fabrication, a one-step exposure technique is proposed to prepare LCLMLAs. LCLMLAs are formed through one-dimensional anisotropic polymerization-induced phase separation (PIPS). Ultraviolet (UV) exposure causes the polymer/LC composite to undergo phase separation, resulting in the formation of two adjacent layers. This configuration is similar to the second type of LCLMLAs, known as phase-separated composite films (PSCOFs) [43–47]. A grayscale photomask is exploited and positioned between the LC cell and the UV lamp. This mask is used to modulate the distribution of the UV light intensity, thereby allowing for control the structure of the polymer layer. Compared to the aforementioned preparation techniques, our proposed approach is advantageous, featuring simple fabrication, high-quality LC alignment, large-area producibility, and low cost. Furthermore, a 2D/3D switchable autostereoscopic display is demonstrated by utilizing the fabricated LCLMLAs and a 2D LCD panel, showing the great potential of our proposed LCLMLAs fabrication technique.
2. Results and discussion
2.1 LCLMLAs fabrication
Figure 1 shows the schematic diagram of LCLMLAs fabrication. First, an LC cell was assembled using two pieces of conductive indium-tin-oxide (ITO) glass substrates. Before assembling, an alignment layer of polyvinyl alcohol (PVA) was spin-coated on the bottom ITO glass substrate and then rubbed uniaxially with the purpose for LC alignment. The prepolymer mixture of the LC (E7) and UV-curable optical adhesive (NOA65) was filled into the cell by the capillary force. As shown in Fig. 1(a), a collimated UV light beam passes through the grayscale photomask and then illuminates the cell. The photomask is in close contact with the cell. Figure 1(b) shows the schematic processes of phase separation. At an elevated temperature, the photopolymerization of NOA65 first occurs near the top substrate where the UV intensity is higher. During the photopolymerization process, the concentration of NOA65 decreases in the high UV intensity region. Diffusion of the NOA65 monomers and counter-diffusion of LC molecules causes the phase separation of the polymer and the LCs, with the former and latter diffusing towards the high and low intensity regions both horizontally and vertically, respectively. As a result, following the UV light intensity distribution inside the cell, the composite film structure is formed once the NOA65 monomers are completely consumed. Finally, the LC molecules are uniformly aligned by the PVA alignment layer on the bottom substrate as the cell temperature gradually cools down to the room temperature. The patterns on the grayscale photomask determine the morphology of the microstructures of the polymer film. In this work, the patterns of the photomask are carefully designed for a lenticular microlens array, as shown in Fig. 1(c). The period of the photomask is 142 µm. The transmittance of the grayscale photomask is well controlled by the density of the randomly distributed square-shaped dots with the side length of 1 µm. The designed distribution of the random dot’s density is parabolic within a single period. In our experiment, there is a gap between the prepolymer and the photomask, which filled by the ITO glass substrate with a thickness of 400 µm. As a result, the UV light intensity distribution will become parabolic due to the diffraction effect. The light intensity distribution at this distance was measured with an optical microscope (Fig. 1(d)). Figure 1(e) shows the intensity distribution along the red dashed line in Fig. 1(d). In the center of the selected region, the intensity distribution is parabolic compared to the fitting curve.
Fig. 1. (a) Schematic configuration of LCLMLAs fabrication. (b) Schematic processes of phase separation of polymers and LCs. (c) Typical morphologies of the designed grayscale photomask. (d) Light intensity distribution at a propagation distance of 400 µm upon the collimated UV light beam passing through the grayscale photomask. (e) Experimentally measured and parabolically fitted intensity distribution along the red dashed line in (d).
2.2 LCLMLAs’ morphologies
The materials and fabrication details are described in the Supplement 1, Experimental Section. In our experiments, three LCLMLAs with different cell gaps of 15, 20, and 25 µm were fabricated using the PIPS technique. For experimental convenience, the prepared LCLMLAs had a working area of about 5 cm × 5 cm, containing approximately 350 microlenses. Additionally, samples with an effective area of 6.8 cm × 11.6 cm were demonstrated, as shown in Supplement 1, Fig. S1. The textures and morphologies of the samples were firstly investigated. Figures 2(a – c) show the polarizing optical microscope (POM) images of the three LCLMLAs with the cell gaps of 15, 20, and 25 µm, respectively. Under crossed polarizers, when the LCs’ director (i.e., the alignment direction) is parallel to the optical axis of either the polarizer or the analyzer, the samples appear totally dark, as shown in Figs. 2(a1 – c1). When the LCs’ director is 45° with respect to the optical axis of the polarizer/analyzer, the LC cells demonstrate periodically patterned structures. These observed results indicate high-quality alignment of LCs in the samples. To take a close look at a single period, one can clearly observe distinct interference colors changing from carmine to yellow from the center to the edge of each lenticular microlens in Fig. 2(a2). The thickness or birefringence Δn of LC can be estimated by observing their interference colors [48]. Since the birefringence of the LC is constant, it can be inferred that the thickness of the LC layer inside the cell changes gradually. Moreover, the interference colors change rapidly as the cell gap increases, indicating that the thickness of the LC layer increases proportionally. Overall, we can confirm that the light intensity patterns produced by the grayscale photomask were accurately replicated inside the LC cells.
Fig. 2. POM images of the prepared samples when the alignment direction of the LCs is (a1 – c1) 0° and (a2 – c2) 45° with respect to the optical axis of the polarizer for three different cells with the cell gaps of (a1, a2) 15, (b1, b2) 20, and (c1, c2) 25 µm, respectively. Insets are the magnified images of the half lenticular microlens.
To further confirm the inner structures inside the cells, the surface morphologies of the polymer films were investigated. Figures 3(a1 – c1) show the scanning electron microscope (SEM) images of the polymer films at a tilt angle of 30° for the three different LC cells with the cell gaps of 15, 20, and 25 µm, respectively. The magnified cross-section views of the polymer films are also shown in the insets in Figs. 3(a1 – c1). It is obvious from SEM images that the polymer films exhibit uniform lenticular microlens microstructures. The sag heights of the polymeric lenticular microlenses are measured using a step profiler, as shown in Figs. 3(a2 – c2). The averaged sag heights of the polymeric lenticular microlenses inside the three LC cells are 4.4, 8.2, and 9.8 µm, respectively. These results reveal that the sag height of the polymeric lenticular microlens increases as the cell gap increases, which is consistent with our expectations. Therefore, one can control the sag height and focal length of the lenticular microlens by adjusting the cell gap.
Fig. 3. (a1 – c1) SEM images taken at a tilt angle of 30° and (a2 – c2) measured sag height distribution of the polymeric films for three different cells with the cell gaps of (a1, a2) 15, (b1, b2) 20, and (c1, c2) 25 µm, respectively. Insets are the magnified cross-section views of the polymer films.
2.3 LCLMLAs’ focusing properties
In our design, the LC molecules will be aligned along the preset direction by the PVA alignment layer, hence demonstrating strong optical anisotropy. As a result, the LCLMLAs demonstrate both polarization-dependent and electrically tunable focusing properties. Figure 4(a) shows the experimental setup. A laser beam with the operating wavelength of 532 nm is expanded and then collimated. The polarization direction of the incident light can be rotated using a half-wave plate. In our experiments, we first investigate the LCLMLAs’ focusing properties by rotating the polarization direction of the incident light to different angles with respect to the LC alignment direction. Figure 4(b) shows the focusing images of the LCLMLAs with a cell gap of 15 µm. As the polarization direction of the incident light is gradually rotated from 0° to 90°, the intensities of the focal points gradually decrease until they disappear. This observation can be attributed to the change of the refractive index experienced by the incident light with different linear polarizations. When the polarization of the incident light is parallel to the LC alignment direction, the incident light will experience the effective refractive index (neff) of LCs of neff = ne. By contrast, when the polarization of the incident light is perpendicular to the LC alignment direction, the incident light will see neff = no. In our configuration, the refractive index of the polymer (np) is close to no, which means that as the angle is rotated from 0° to 90°, the refractive index difference between the LCs and the polymer gradually decreases to nearly zero. As a result, the LCLMLA has a strongest focusing intensity at 0°, but no focusing effect at 90°, as shown in Fig. 4(b1 – b4). Similar effects can be observed for the LCLMLAs with the cell gaps of 20 and 25 µm, as shown in Figs. 4(c) and 4(d). Therefore, one can conclude that all the LCLMLAs demonstrate excellent polarization-dependent focusing properties, further reflecting the high-quality alignment of LC molecules in the LC cells.
Fig. 4. (a) Schematic of experimental setup for investigating both polarization-dependent and electrically tunable focusing properties of LCLMLAs. (b – d) Polarization-dependent focusing of LCLMLAs with three different cell gaps of (b1 – b4) 15, (c1 – c4) 20, and (d1 – d4) 25 µm, respectively.
In addition to their polarization-dependent focusing properties, LCLMLAs also possess electrically tunable focusing properties, as shown in Fig. 5. When the polarization of the incident light is parallel to the LC alignment direction, as the applied voltage increases, the intensities of the focal points decrease. Similarly, when there is no applied voltage, the incident light will experience the effective refractive index (neff) of LCs of neff = ne. Upon applying a voltage above the threshold, an electric field will be created inside the LC cell, which causes the LC molecules to reorientate along the direction of the electric field. The effective refractive index, neff, can be calculated using the following equation,
Fig. 5. Captured focusing images at the focal planes of three prepared LCLMLAs under different applied voltages with the cell gaps of (a1 – a4) 15, (b1 – b4) 20, and (c1 – c4) 25 µm, respectively.
To further investigate the focusing properties of LCLMLAs, the intensity distributions of the focal points in the x-z plane were measured, as shown in Fig. 6(a1 – c1), where z = 0 denotes the LCLMLAs’ plane. The measured focal lengths are approximately 1000, 800, and 650 µm for the three LCLMLAs with the corresponding cell gaps of 15, 20, and 25 µm, respectively. To estimate the point spread function (PSF) of the prepared microlens, the calculated and experimental intensity distributions were extracted from the white dash lines in Fig. 6(a1 – c1), and shown in Fig. 6(a2 – c2). The calculation details are available in Ref. [35]. The parameters of LCLMLAs with different cell gaps are shown in Table 1. The experimental and theoretical results are in good agreement, indicating that the prepared LCLMLAs have high-quality, near-diffraction-limited focusing performance.
Fig. 6. (a1 – c1) Intensity distributions of the focal points in x-z plane and (a2 – c2) corresponding theoretically calculated and experimentally measured PSFs of LCLMLAs with the cell gaps of (a1, a2) 15, (b1, b2) 20 and (c1, c2) 25 µm, respectively.
Table 1. Results of the LCLMLAs with different cell gaps
For LC-based microlenses, switching time is another important factor for numerous applications. Therefore, the response times of the prepared LCLMLAs with different cell gaps were measured. The measured response times of the LCLMLAs with different cell gaps are shown in Fig. 7. Herein, the rising time and falling time are defined as the time taken for 90% to 10% and 10% to 90% change in transmittance, respectively. The rising time and falling time for homogeneous LC devices can be estimated by the following equations [49]:
Fig. 7. Measured response times of three LCLMLAs with the cell gap of (a) 15, (b) 20, and (c) 25 µm, respectively. (d) Response time versus the applied voltage ranging from 7 to 18 V for three LCLMLAs with different cell gaps.
2.4 Prototype of the 2D/3D switchable autostereoscopic display
Upon achieving the high-quality LCLMLAs, we exploited them to set up the prototype of a 14-view 2D/3D switchable autostereoscopic display, as shown in Fig. 8(a). A 5.5 inch 4 K LCD panel (VS055QUM-NH0-6KP0, BOE, China) was used as the 2D panel. In order to mitigate the decrease in horizontal resolution and the occurrence of color moiré pattern induced by the periodic LCLMLAs and the periodic pixels, the LCLMLA was placed obliquely with a slanted angle of 15.07°. In our experiment, the light emitted from the LCD panel is linearly polarized with the polarization direction being horizontal. To align the polarization direction of the incident light with the LC alignment direction of the LCLMLAs, we inserted a linear polarizer between the panel and the LCLMLAs. The optical axis of the polarizer was aligned with the LC alignment direction of the LCLMLAs. Although this reduces optical efficiency slightly, it improves the display performance significantly. The schematic of the cross-section view of the prototype is also shown in Fig. 8(b). To achieve optimal display quality, the focal length of the LCLMLA should match the distance between the microlens and the pixels. Therefore, the thickness of each element should be carefully considered. The thicknesses of the ITO glass substrate (d1), the polarizer (d2), and the cover glass plus polarizer of the panel (d3) are 0.4, 0.1, and 0.2 mm, respectively. Considering the refractive index of the cover glass, the focal length of the LCLMLA used for this panel should be slightly smaller than 0.7 mm. The calculation details are shown in Supplement 1, Fig. S2. Therefore, the LCLMLA with the cell gap of 25 µm was selected for the phototype accordingly.
Fig. 8. (a) Picture of the prototype of the 2D/3D switchable autostereoscopic display. (b) Elements arrangement of the prototype. Among them, the LCD panel is composed of a backlight, a color filter (CF), a cover glass, and a polarizer (POL).
In 3D mode, the microlens array disperses the subpixels into 14 views. The image displayed on the LCD panel, called the composite image, has to be calculated based on the geometrical parameters. First, the images were captured from different angles using the virtual 3D software “Cinema 4D”, as shown in Fig. 9(a). The object used was a cube with red, blue, and yellow colors. The 1 × 14 virtual camera array was positioned at a distance of 20 m from the object. The interval between each camera was 30 cm. Then, the images from different views should be reconstituted to a composite image, as shown in Fig. 9(b). The black line indicates a single lenticular microlens. The red, green, and blue rectangles represent the RGB subpixels of the LCD panel. The numbers in each rectangle refer to the viewpoint numbers. The composite method is based on the following equation,
where Nl,k is the corresponding views of the subpixels on the lth row and the kth column. l and k are the number of rows and columns to which the subpixel belongs, respectively. kini is the initial viewpoint of the first subpixel. X is the number of the subpixels covered by a microlens. Ntot is the number of views. $\alpha $ is the slanted angle between the lenticular microlens and the pixels. mod(a,b) is a modulo operation, which returns the remainder after division of a by b. Due to spatial multiplexing, the resolution of the multi-view display in the 3D mode is N times smaller than that in the 2D mode. Particularly, in our experiment, the resolution decreases by a factor of 14/3 horizontally and by a factor of 3 vertically. As a result, the horizontal and vertical resolutions are 463 and 1280 in the 3D mode, respectively. The parameters of the autostereoscopic display are shown in Table 2. Figure 9(c) shows the composite image calculated using the arrangement method depicted in Fig. 9(b).Fig. 9. The generation method of the composite image. (a) Capturing images from different views in the “Cinema 4D” software. (b) Arrangement of the views on subpixels. (c) Calculated composite image.
Table 2. The parameters of the 2D/3D switchable autostereoscopic display
To evaluate the performance of the 3D display, an experiment was carried out based on the prototype. A camera was positioned at the optimal observation distance and used to capture videos of 3D objects at angles ranging from −7° to +7° (see Visualization 1). In the video, as the camera moves, different images of the object from various perspectives are sequentially displayed, indicating that the prototype has motion parallax. Figure 10 shows the captured images of the 3D object at −7°, 0° and +7°. The different sides of the cube are clearly visible in the images. The magnified image of the right side of the cube is shown in Fig. 10 for comparison. It can be observed that the cube is slightly rotated with respect to the camera. Slight crosstalk from neighboring viewpoints caused a slightly perceptible ghost image.
Fig. 10. Captured image of the 3D object at (a) −7°, (b) 0°, and (c) + 7° (see Visualization 1). Insets show the magnified part of the images.
Crosstalk is a crucial parameter to estimate the performance in 3D displays. We measured the crosstalk of the prototype. The black-and-white testing images were generated in advance. The subpixels corresponding to the under-measured viewpoint were set to maximum brightness. The remaining subpixels were turned off. The photodetector was used to measure luminance along the horizontal direction at the optimal distances. At the optimal distance, crosstalk is minimized, resulting in improved image quality. However, when deviating from the optimal distance, crosstalk becomes more serious due to overlapping viewpoints and the image quality deteriorates with increasing viewing distance [50,51]. As a result, the camera/photodetector is positioned at the optimal distance when capturing images and measuring crosstalk. We measured the intensity distribution of each viewpoint’s white-black testing images, which were then subtracted from the environmental light intensity, as shown in Fig. 11. The crosstalk can be estimated by the equation,
Fig. 11. Measured horizontal intensity distribution of the 14 views in our autostereoscopic display.
According to the measured intensity distribution in Fig. 11, the calculated crosstalk is 46.2%, which is comparable to the results in other reports [14,15,21,25]. In addition, the binocular crosstalk is less than 5%. Therefore, one can still observe the 3D images under this level of crosstalk. The crosstalk arises from three possible reasons: the mismatch between the subpixels and the microlens array, errors during assembly and measurement, and the aberrations of the LCLMLA. As demonstrated in Fig. 3, the surface profile of the polymer film does not exhibit a perfect parabolic shape, resulting in the LCLMLA’s aberration and subsequently causing crosstalk between adjacent viewpoints. In general, aberrations can be corrected by using lens groups [52], aspherical lenses [25], or refractive-diffractive hybrid lenses [53]. Our prepared microlenses consist of a polymer layer and a LC layer, which can be considered as a combination of two lenses. To better eliminate aberrations, the curvature of the microlens will be optimized to minimize aberrations in future studies, which can be well controlled by the UV light intensity distribution through the grayscale photomask.
The 2D/3D switching function of the prototype was further investigated. Figure 12 shows the photographs of both 2D and 3D images in 2D/3D mode. Without applied voltages, the LCLMLA remains the focusing state, and the display is in 3D mode. The prototype displays a 2D image consisting of a group of lines with different widths, a circle, crossed arrows, and a paragraph of text, as shown in Fig. 12(a). All displayed contents are distorted on the screen due to the refraction of the light from the pixels by the microlens array. Thus, in 3D mode, the high-resolution 2D content can’t be displayed without distortion, whereas the 3D image can be displayed correctly, as demonstrated in Fig. 12(b). When a voltage of 10 V is applied to the LCLMLA, the focusing effect disappears, and the display switches to 2D mode. The high-resolution 2D content can therefore be displayed without any distortion, as shown in Fig. 12(c). By contrast, the display directly presented the composite image, as shown in Fig. 12(d). Visualization 2 displays the 3D content recorded at varying angles in 2D mode. The results demonstrate that the autostereoscopic display has a 2D/3D switching function.
Fig. 12. 2D/3D switching function of the prototype. Captured image of (a) 2D and (b) 3D contents in 3D mode. Captured image of (c) 2D and (d) 3D contents in 2D mode (see Visualization 2).
3. Conclusion
In summary, LCLMLAs with different focal lengths have been demonstrated using the simple PIPS technique. Both high-quality LC alignment and lenticular lens-like surface morphologies of the polymer layer have been achieved inside the LC cells. LCLMLAs demonstrate both polarization-dependent and electrically tunable focusing properties. Depending on the cell gaps, LCLMLAs have the focal lengths ranging from 650 to 1000 µm. Both theoretical calculations and experimental results indicate that the prepared LCLMLAs have high quality, near-diffraction-limited focusing. Furthermore, we have constructed a prototype of a 14-view 2D/3D switchable display, consisting of a 2D LCD panel and the prepared LCLMLA. The viewing angle is 14° and the crosstalk at the optimal viewing position is 46.2%. Compared to the reported LCLMLAs, ours have distinct advantages of simple fabrication, high-quality LC alignment, large-area producibility, and low cost, which could play a key role in the development of 2D/3D switchable displays.
Funding
National Key Research and Development Program of China (2021YFB2802300); National Natural Science Foundation of China (62075093, 62211530039); Guangdong Province Introduction of Innovative R&D Team (2017ZT07C071); Science, Technology and Innovation Commission of Shenzhen Municipality (JCYJ20220818100413030); Development and Reform Commission of Shenzhen Municipality (XMHT20220114005).
Acknowledgments
The authors acknowledge the assistance of SUSTech Core Research Facilities.
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
Supplemental document
See Supplement 1 for supporting content.
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