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Abstract
A four-mode 2D/3D switchable display using a 1D/2D convertible liquid crystal (LC) lens array is proposed in this paper. The LC lens array is composed of two orthogonal LC lens arrays, with a λ/2 film in the middle to rotate the polarization by 90°. Based on the LC lens array, a four-mode 2D/3D switchable display is realized, which is switchable between the turn-off and turn-on states: when the operating voltage V1 = 0, V2 = 0, the display operates in mode I, which is 2D display; when the operating voltage V1 = 0, V2 = 0, the display operates in mode II, and the 3D display effect is in x direction; when the operating voltage V1 = 0, V2 = 0, the display operates in mode III, and the 3D display effect is in y direction; when the operating voltage V1 = 0, V2 = 0, the display operates in mode IV, the 3D display effect is in x-y plane. Experimental results indicate that the LC lens array has simple fabrication process, low operating voltage (∼5.4V), and short focal length. Moreover, based on the designed LC lens array, the 2D/3D switchable display shows no moiré pattern.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, with the popularity of remote video conference and virtual medical technology/combat system, the autostereoscopic three-dimensional (3D) display attracts considerable academic and industrial attention for its realistic images with extra depth information, which can’t be offered by traditional two-dimensional (2D) displays [1–6]. Autostereoscopic 3D displays utilizing spatial-multiplexing and time-multiplexing 3D technologies for providing binocular disparities have certainly entered the mainstream due to the convenience of presenting 3D visual effects without wearing 3D glasses [7,8]. To date, however, most of the display information is still based on the 2D images for 2D display screen. Although several 3D display technologies have been developed, as mentioned above, when combined with 2D images, the display quality is significantly reduced [9]. Therefore, there is an increasing demand for the displays to be switchable between 2D and 3D displays, which can provide real visual experience while maintaining the 2D image display quality. In order to realize the 2D/3D switchable function, a straightforward way is to use the adaptive optical lens such as liquid lens [10–12]. Notably, the liquid lens has the potential of higher optical power and bigger size, but some technical problems such as slow response time, high operating voltage, thick and heavy, gravity effect are still needed to be solved.
To address these problems, LC lenses, of which the focal length can be electronically continuous controlled, have been used for the 2D/3D switchable displays in recent studies. The LC lenses exhibit some unique advantages, such as fast response, low operating voltage, light/thin, and simple fabrication process. The basic operation principle of the LC lens is to obtain the electric-field-induced parabolic phase distribution across the LC layer [13–20]. Currently, various types of 2D/3D switchable displays using LC lens have been proposed, such as the 2D/3D switchable lens using bistable ferroelectric LC layer [21], such as the 2D/3D switchable mobile display using a polarization-dependent switching liquid crystalline polymeric (LCP) lens array film [22], a multi-view 2D/3D switchable display with adaptive tilted LC lens array [9], a 2D/3D mixed frontal projection system based on InIm [23]. However, these new types of displays improve the performance to some extent at the expense of bring new disadvantages. For example, although the 2D/3D switchable mobile display using a polarization-dependent switching LCP lens array film shows a low crosstalk, fast response and low operating voltage, but the extra TN cell increases the thickness of the LC lens; the multi-view 2D/3D switchable display with adaptive tilted LC lens array shows no moiré pattern and fast response, but the 3D display effect is only in one direction; the 2D/3D mixed frontal projection system based on InIm show a compact, simple and space-efficient system, but the thicker LC layer also causes the light scattering.
In this paper, we propose a four-mode 2D/3D switchable display using a 1D/2D convertible LC lens array. The LC lens array is composed of two orthogonal cylindrical LC lens arrays, with a λ/2 film in the middle to rotate the polarization by 90°. The LC lens array can be totally turned on and off by switching between the voltage on and off states, and can also be locally turned on and off by operating the local voltage. Besides, when the global voltage is on, the LC lens array switches from 1D to 2D. Based on the LC lens array, a four-mode 2D/3D switchable display is realized. The experimental results show that the LC lens array has a low operating voltage (∼5.4 V), short focal length, and simple fabrication process. Moreover, the 2D/3D switchable display based on the LC lens array shows no moiré pattern.
2. Device structure and principle
The structure of the four-mode 2D/3D switchable display using 1D/2D convertible LC lens array is illustrated in Fig. 1(a). The 2D/3D switchable display consists of LC lens arrays, a λ/2 film (the optical axis is 45°), and a 2D display screen. The LC lens array is composed of two orthogonal cylindrical LC lens arrays. In order to rotate the polarization by 90°, a λ/2 film is placed between the two orthogonal cylindrical LC lens arrays. For the structure of the two LC lens arrays, two nematic LC layers are sandwiched between substrates 1, 2, 3 and 4. The surfaces facing the nematic LC layer of substrates 1 and 4 are coated with planar indium tin oxide (ITO) layers, working as the grounding electrode. The surfaces facing the nematic LC layer of substrates 2 and 3 are coated with strip ITO electrodes, acting as the driving electrode. The strip electrodes on substrate 2 are in the direction of the x axis while the strip ITO electrodes on substrate 3 are in the direction of the y axis. The inner surfaces of substrates 1, 2, 3 and 4 are coated with polyimide films and rubbed in two directions which are perpendicular to the strip ITO electrodes. Then the directors in the two LC layers are initially aligned homogeneously in the perpendicular directions with a small pretilt angle (less than 3 degrees) in the voltage off state, and the small pretilt angle cannot affect the performance of the LC lens array. The LC lens array is driven by the voltage V2 across the upper strip ITO electrode and the voltage V1 across the lower strip ITO electrode. The upper and lower electrodes are both grounded and the operating voltage V1 and V2 are the same.
Fig. 1. (a) Structure of the 2D/3D switchable display using 1D/2D convertible LC lens array, (b) the 3D display effect in the x direction, (c) the 3D display effect in the y direction, (d) the 3D display effect in the x-y plane.
In the voltage on state, the voltage across the strip ITO electrodes and the planar ITO electrode generates spatially nonuniform and nearly centrosymmetrical electric fields between the strip electrodes. In the aperture area between the strip electrodes, the spatially nonuniform electric field is the smallest at the gap center of the strip electrodes and becomes the largest at the edge of strip electrodes. The LC directors are then reorientated by the spatially nonuniform electric field and the local tilt angle θ of the LC directors increases with local spatially nonuniform electric field, which means that the tilt angle θ of the LC directors is the smallest at the gap center of the strip electrodes while becomes the largest at the boundary of strip electrodes. As a linearly polarized light beam is incident parallel to the rubbing direction, the effective refractive index experiences [24–26]:
By calculating the final effective refractive index (neff) distribution, the difference of phase retardation between the center and the boundary of each LC lens is determined. The accumulated phase retardation φ of the incident light beam is calculated by [27,28]:
where d is the thickness of the LC layer.The focal length value of the proposed LC lens array can be calculated according to the Fresnel’s approximation [29–31]:
where r is the effective half pitch of each LC lens, δn is the index difference between the LC lens array center and border.In order to obtain a relatively wide 3D viewing angle, a short focal length of the LC lens array is required. In addition, each LC lens needs to cover at least two sub pixels of the 2D display screen, and the more sub pixels covered, the denser the 3D viewpoints.
The principle of the locally switchable LC lens array and the driving method are shown in Figs. 1(b), (c) and (d). Due to the orthogonal strip ITO electrodes, the direction of the LC lens array is controllable via the proposed driving method. As shown in Fig. 1(b), when the turn on voltage (V1>0) is applied to the lower strip ITO electrodes, and the voltage V2 is in turn off state, a cylindrical LC lens array is formed in the y direction (mode II), and the 3D display effect is generated in the x direction. In order to control the LC lens array in the other directions, the turn on voltage (V2>0) is applied to the upper strip ITO electrodes, and the voltage V1 is in turn off state. Consequently, a cylindrical LC lens array is formed in the x direction (mode III), and the 3D display effect is generated in the y direction, as shown in Fig. 1(c). In mode IV, the turn on voltage V1>0 and V2>0 are applied to the lower strip ITO electrodes and upper strip ITO electrodes, respectively. With the λ/2 film, the polarization direction of polarized light is rotated by 90°. Therefore, by using InIm 3D display technology method, the 2D LC lens array is realized and the 3D display effect is generated in the x-y plane, as shown in Fig. 1(d). To be more specific, the electrode structure on the substrates 2 and 3 is illustrated in Fig. 2, in which d is thickness of the LC layer; w is the width of each strip electrode; l is the gap between the two strip electrodes; r is the effective half pitch of each LC lens.
3. Results and discussion
To assess the optical performance and the optical characteristics of the proposed LC lens array, we carry out the electro-optical simulations by using the commercial simulation software Tech Wiz LCD 3D (Sanayi System Co., Ltd., Incheon, Korea) and MATLAB (MathWorks Co., Ltd., Natick, America). The parallax images are generated by software 3ds Max (Discreet Co., Ltd., Montreal, Canada). In the simulation, the results of all models are calculated by Jones matrix, the polarized light propagating along the z-axis is expressed as [32]:
The LC material used in the simulation and experiment is the JC-TNLC-E7 (King Optronics Co. Ltd., Suzhou, China), with the birefringence Δn = 0.224, dielectric constant Δɛ = 11.4, viscosity γ = 29mPa.s, K11 = 16.7pN, K22 = 7.3pN, K33 = 18.1pN, ne = 1.741, and no = 1.517. The thickness of the λ/2 film (Ginza Optical Film Equipment Co. Ltd., Xuzhou, China) is 600µm, and the working wavelength is 400-700 nm. The parameters of the proposed cylindrical LC lens array are as follows: w = 10µm, l = 300µm, d = 65µm, r = 155µm, and the thickness of all the ITO electrodes is 0.04µm. In the following simulation and experiments, the region of each LC lens is from −155 µm to +155 µm. The 2D display screen used in the experiment is a mobile phone with 4k resolution.
3.1 Simulation results and discussion
For the convenience of understanding, the single-layer LC lens array is selected in the simulation. Figures 3(a) and 3(b) respectively show the simulated cross-section view and top view of the electric potential distribution within the LC layer of the LC lens array at Von = 6V. The electric potential distribution of the LC layer for a single LC lens is framed by a dashed frame. In Fig. 3, we observe that the electric potential lines in the LC layer become sparse from the edges to the center of the single LC lens. As a result, the tilt angle of the LC directors is smaller in the LC lens center than that at the edges. The electric potential distribution in Fig. 3 is conducive to the ideal parabolic phase profile. Figures 4(a)-(d) show the simulated top view of the refractive index for the extraordinary rays of the single LC lens array at Von = 4V, Von = 5V, Von = 6V, and Von = 7V, respectively. As shown in Fig. 4, with different operating voltages, the refractive index distributions of the single LC lens array are all axisymmetric. The refractive index difference between the center and the edge of the single LC lens are 0.1081 at Von = 4V, 0.1366 at Von = 5V, 0.1551 at Von = 6V, 0.1821 at Von = 7V, respectively. When the voltage is higher than 6 V, the refractive index difference between the center of the LC lens and the edge of LC lens is very large. It seems that the phase profile is triangular waveform, as shown in Figs. 5(a) and 5(b), which is not conducive to obtaining good image quality. As shown in Fig. 4(d), the effective diameter of the LC lens becomes shorter at Von = 7V, implying that the operating voltage of proposed LC lens array is relatively low. On the other hand, as depicted in Fig. 4, the gradient of the refractive index distribution is better at Von = 5V.
Fig. 3. Simulated (a) cross sectional view and (b) top view of the electric potential distribution within the LC layer of the proposed LC lens array at Von = 6V.
Fig. 4. Simulated top view of the refractive index along x axis for the extraordinary rays of the proposed LC lens array at (a) Von = 4V, (b) Von = 5V, (c) Von = 6V, and (d) Von = 7V.
The simulation results in Fig. 6(a) indicate that when the operating voltage is 5.4V, the refractive index distribution curve of the LC lens array shows the match with the ideal parabola model. Under such circumstances, almost all the LC directors from the LC lens array edge to the LC lens array center are beneficial to the focusing of the extraordinary ray. The difference between the maximum and the minimum refractive index is 0.1413. Besides, the refractive index distribution curve fits well with the ideal parabolic. For the 3D display based on the LC lens array, the shorter the focal length of the LC lens array, the larger the viewing angle of the 3D display. The voltage dependent focal length is depicted in Fig. 6(b). In the voltage off state, the LC lens array is in the non-focus state. With the increase of operating voltage, the focal length of the LC lens array decreases dramatically due to the inverse proportional relationship between the focal length f and the phase difference φ, as calculated by Eq. (3). When Von = 2V, the focal length of the LC lens array is about 72.0mm. The variation of the focal length is smaller when the operating voltage exceeds 3V because the LC directors on both edges of the LC lens array tend to be saturated. When Von = 5.4V, the focal length of the LC lens array reaches the shortest (∼6mm). The simulations are consistent with the experimental results.
Fig. 6. Simulated (a) refractive index distribution and (b) voltage-dependent focal length of the LC lens array.
In order to verify the 2D/3D switchable display effect of the proposed LC lens array, the virtual 3D scenes of the two modes are built in 3ds Max, as shown in Figs. 7 and 8, a 32×32 camera array is built to obtain the parallax images. For 3D display, the methods and the display effect of mode II and mode III are the same, so mode II is taken as an example. As depicted in Fig. 7, in the virtual object, the “pear” is placed in front of the “apple”, and the gap between the “pear” and “apple” is 5mm. The distance between the camera and the center depth plane of the photographed object is 1000mm, and the gap between each camera is 5mm. For mode II, only the parallax images taken by the middle row of cameras (in the yellow frame) are selected as the 3D image source, as shown in Fig. 7(a), and then 32 parallax images are obtained. Figure 7(b) shows the final composite tilt elemental image arrays (EIAs). The EIAs are in the y direction, with the slope of 0.4 [9]. For mode IV, the parallax images taken by all cameras (in the yellow frame) are selected as 3D image source, as shown in Fig. 8(a), and then 1024 parallax images are obtained. Figure 8(b) shows the final composite EIAs, which lie in the x-y plane.
3.2 Experimental results and discussion
Figure 9(a) shows the two fabricated LC lens arrays with the size of 14cm × 7cm and the pitch of 310µm. Figure 9(b) shows the two orthogonal LC lens arrays. In order to demonstrate the 1D/2D convertible functionality of the LC lens array, the line focus direction becomes a standard by which to determine the direction of the LC lens array. The line focus of the LC lens array is measured by using a collimator. A CCD is placed in the focal plane of the LC lens array. The distance between the CCD and the LC lens array is about 5.5 mm. During the experiment, a polarizer is added on substrate 4, and the polarization axis of the polarizer is consistent with the rubbing direction of substrate 4. When the parallel light traverses through the LC layer in the voltage off state (V1 = 0 V, V2 = 0 V), there is no line focus pattern on the CCD, as depicted in Fig. 10(a). If the operating voltage V1 = 0 V, V2 = 5.4 V, the cylindrical LC lens array forms in the x direction, and the line focus appear on the CCD, as depicted in Fig. 10(b). When the operating voltage V1 = 5.4 V, V2 = 0 V, the cylindrical LC lens array forms in the y direction, as depicted in Fig. 10(c). When the operating voltage V1 = 5.4 V, V2 = 5.4 V, the 2D LC lens array forms with the appearance of the focus on CCD as shown in Fig. 10(d). Therefore, based on the LC lens array as designed, the 2D display and 3D display can be switched freely, and at the same time, the 3D display effect can also be switched in different viewing directions. Besides, the line focus is smooth and continuous, and the quality of the LC lens array is good.
Fig. 10. Test experiment of focusing effect of the LC lens array: (a) V1 = 0V, V2 = 0V, (b) V1 = 0V, V2 = 5.4V. Test experiment of focusing effect of the LC lens array: (c) V1 = 5.4 V, V2 = 0 V, (d) V1 = 5.4 V, V2 = 5.4 V.
To verify the performance of the 2D/3D switchable display based on LC lens array, the 2D/3D switchable display effect under the two modes is demonstrated experimentally. The sub pixel of the 2D display screen is about 10.5µm, therefore the number of the viewpoints in mode II is set to 32 (the 3D display effect and viewpoints of mode II and mode III are the same, so mode II is taken as an example). Figure 11(a) shows the original 2D image with the LC lens array in the voltage off state. At this state, the LC lens array is equivalent to a transparent glass substrate, and the viewers can see a very clear 2D image without any reduction of the brightness or clarity of the 2D image.
Fig. 11. Experiment results of the (a) 2D image with the LC lens array in the voltage off state, mode I, (b) 3D display in mode II (V1 = 5.4V, V2 = 0V).
Figure 11(b) shows the 3D display of mode II, in which the operating voltages of the LC lens array respectively are V1 = 5.4 V, V2 = 0 V, and the 3D display effect is in the x direction. Compared with Fig. 7(b), due to the convergence of rays by the LC lens array, the EIAs are combined into a complete 3D image and a clear 3D image without no moiré pattern is displayed. In order to further demonstrate the 3D display effect under different viewpoints, the 3D display effect under different viewing directions is tested. In mode II, the 3D display effect in left, middle and right viewpoints are shown in Figs. 12(a), 12(b) and 12(c), respectively. From different viewpoints, we can see the occlusion (or interposition) relationships between the “apple” and “pear”. Visualization 1 shows the details of the occlusion (or interposition) relationships between the “apple” and “pear”, where the different information of the “apple” and “pear” can be observed.
Fig. 12. Experimental results of 3D display effect in (a) left (b) middle and (c) right viewpoints in mode II.
For mode IV, as shown in Fig. 13, the operating voltages of the LC lens array respectively are V1 = 5.4 V, V2 = 5.4 V. Using the λ/2 film and the two orthogonal LC lens arrays, the 3D display effect is generated in the x-y plane. In this way, the EIAs in Fig. 8(b) are synthesized into the 3D image in Fig. 13. In order to further demonstrate the 3D display effect under different viewpoints, the 3D display effect under different viewing directions is tested. The reconstructed 3D images from five viewpoints in mode IV are shown in Figs. 14(a)-(e). From different viewpoints of left, right, middle, up and down, we can also see the occlusion (or interposition) relationships clearly between the “apple” and “pear”. The details of the occlusion (or interposition) relationships between the “apple” and “pear” are shown in Visualization 2.
Fig. 14. Experimental results of the 3D display effect in (a) up (b) down (c) left (d) middle and (e) right viewpoints in mode IV.
Multiple layer structures will reduce the optical efficiency and limit the viewing angle. In order to improve these problems, the glass with thinner thickness and high transmittance can be used as ITO substrate. In addition, high brightness display screen can also solve these problems. The 2D/3D switching time is also a very important performance for the 2D/3D switchable display. The transmittance of the LC lens array (Von = 5.4 V) placed in the crossed polarizers is measured. The transmittance of the LC lens array is about 57.14%. The focusing time of the LC lens array is 28 ms when the transmittance reaches 57.14% under the operating voltage of 5.4 V.
4. Conclusion
A four-mode 2D/3D switchable display using a 1D/2D convertible LC lens array is demonstrated. The LC lens array is composed of two orthogonal LC lens arrays and a λ/2 film. The different display modes can be switched between the turn-off and turn-on state of the LC lens array. In modes II and III, the 3D display effect is in one direction, while in mode IV, the 3D display effect is in x-y plane. Experimental results show that the LC lens array has a low operating voltage (∼5.4 V), short focal length, and simple fabrication process. In addition, based on the designed LC lens array, the 2D/3D switchable display shows no moiré pattern. The proposed four-mode 2D/3D switchable display using the 1D/2D convertible LC lens array has applications for tabletop and portable displays.
Funding
National Natural Science Foundation of China (61927809).
Acknowledgement
The authors would thank Wu-Xiang Zhao from Sichuan University for his technical assistance in tilted elemental image array generation method.
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.
References
1. K. Wakunami, P. Y. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y. P. Huang, and K. Yamamoto, “Projection-type seethrough holographic three-dimensional display,” Nat. Commun. 7(1), 12954 (2016). [CrossRef]
2. M. Martínez-Corral and B. Javidi, “Fundamentals of 3D imaging and displays: a tutorial on integral imaging, light field, and plenoptic systems,” Adv. Opt. Photonics 10(3), 512–566 (2018). [CrossRef]
3. L. Shi, A. K. Srivastava, A. M. W. Tam, V. G. Chigrinov, and H. S. Kwok, “2D-3D switchable display based on a passive polymeric lenticular lens array and electrically suppressed ferroelectric liquid crystal,” Opt. Lett. 42(17), 3435–3438 (2017). [CrossRef]
4. D. Wang, C. Liu, C. Shen, Y. Xing, and Q. H. Wang, “Holographic capture and projection system of real object based on tunable zoom lens,” PhotoniX 1(1), 1–15 (2020). [CrossRef]
5. T. Zhan, J. Zou, J. Hao Xiong, X. M. Liu, H. Chen, J. L. Yang, S. Liu, Y. J. J. Dong, and S. T. Wu, “Practical chromatic aberration correction in virtual reality displays enabled by cost-effective ultra-broadband liquid crystal polymer lenses,” Adv. Opt. Mater. 8(2), 1901360 (2020). [CrossRef]
6. I. J. Chen and C. W. Tarn, “A 2D/3D switchable autostereoscopic display system, an acousto-optic lens approach,” Optik 126(23), 4061–4065 (2015). [CrossRef]
7. H. Y. Chen, H. W. Liang, W. H. Lai, C. C. Li, J. H. Wang, J. Y. Zhou, T. H. Lin, I. C. Khoo, and J. T. Li, “A 2D/3D switchable directional-backlight autostereoscopic display using polymer dispersed liquid crystal films,” J. Disp. Technol. 12(12), 1738–1744 (2016). [CrossRef]
8. Y. C. Chang, T. H. Jen, C. H. Ting, and Y. P. Huang, “High-resistance liquid-crystal lens array for rotatable 2D/3D autostereoscopic display,” Opt. Express 22(3), 2714–2724 (2014). [CrossRef]
9. F. Chu, D. Wang, C. Liu, L. Li, and Q. H. Wang, “Multi-view 2D/3D switchable display with cylindrical liquid crystal lens array,” Crystals 11(6), 715 (2021). [CrossRef]
10. J. Kim, D. Shin, J. Lee, G. Koo, C. Kim, J. H. Sim, G. Jung, and Y. H. Won, “Electro-wetting lenticular lens with improved diopter for 2D and 3D conversion using lensshaped ETPTA chamber,” Opt. Express 26(15), 19614–19626 (2018). [CrossRef]
11. J. H. Sim, J. Kim, C. Kim, D. Shin, J. Lee, G. Koo, G. S. Jung, and Y. H. Won, “Novel biconvex structure electrowetting liquid lenticular lens for 2D/3D convertible display,” Sci. Rep. 8(1), 15416 (2018). [CrossRef]
12. C. Kim, J. Kim, D. Shin, J. Lee, G. Koo, and Y. H. Won, “Electrowetting lenticular lens for a multi-view autostereoscopic 3D display,” IEEE Photonics Technol. Lett. 28(22), 2479–2482 (2016). [CrossRef]
13. P. F. Mcmanamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996). [CrossRef]
14. N. A. Riza and M. C. Dejule, “Three-terminal adaptive nematic liquid-crystal lens device,” Opt. Lett. 19(14), 1013–1015 (1994). [CrossRef]
15. H. C. Lin, M. S. Chen, and Y. H. Lin, “A review of electrically tunable focusing liquid crystal lenses,” Trans. Electr. Electron. Mater. 12(6), 234–240 (2011). [CrossRef]
16. T. Nose, S. Masuda, and S. Sato, “Optical properties of a liquid crystal microlens with a symmetric electrode structure,” Jpn. J. Appl. Phys. 30(Part 2, No. 12B), L2110–L2112 (1991). [CrossRef]
17. M. Wahle, B. Snow, J. Sargent, and C. Jones, “Embossing reactive mesogens: a facile approach to polarization-independent liquid crystal devices,” Adv. Opt. Mater. 7(2), 1801261 (2019). [CrossRef]
18. Y. H. Lin, Y. J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Cryst. Rev. 5(2), 111–143 (2017). [CrossRef]
19. Y. Li, S. J. Huang, P. C. Zhou, S. X. Liu, J. G. Lu, X. Li, and Y. K. Su, “Polymer-stabilized blue phase liquid crystals for photonic applications,” Adv. Mater. Technol. 1(8), 1600102 (2016). [CrossRef]
20. T. H. Jen, X. Shen, G. Yao, Y. P. Huang, H. P. D. Shieh, and B. Javidi, “Dynamic integral imaging display with electrically moving array lenslet technique using liquid crystal lens,” Opt. Express 23(14), 18415–18421 (2015). [CrossRef]
21. V. G. Chigrinov, “Liquid Crystal Photonics,” (Nova Science Pub Inc, 2014).
22. M. K. Park, H. Park, K. I. Joo, T. H. Lee, and H. R. Kim, “Polarization-dependent liquid crystalline polymeric lens array with aberration-improved aspherical curvature for low 3D crosstalk in 2D/3D switchable mobile multi-view display,” Opt. Express 26(16), 20281–20297 (2018). [CrossRef]
23. H. Deng, Q. Li, W. He, X. W. Li, H. Ren, and C. Chen, “2D/3D mixed frontal projection system based on integral imaging,” Opt. Express 28(18), 26385–26394 (2020). [CrossRef]
24. M. Ye, B. Wang, and S. Sato, “Liquid-crystal lens with a focal length that is variable in a wide range,” Appl. Opt. 43(35), 6407–6412 (2004). [CrossRef]
25. L. G. Wang, H. A. Hsien, and Y. H. Lin, “Electrically tunable gradient-index lenses via nematic liquid crystals with a method of spatially extended phase distribution,” Opt. Express 27(22), 32398–32408 (2019). [CrossRef]
26. H. Dou, F. Chu, Y. Q. Guo, L. L. Tian, Q. H. Wang, and Y. B. Sun, “Large aperture liquid crystal lens array using a composited alignment layer,” Opt. Express 26(7), 9254–9262 (2018). [CrossRef]
27. M. Ye, B. Wang, and S. Sato, “Double-layer liquid crystal lens,” Jpn. J. Appl. Phys. 43(No. 3A), L352–L354 (2004). [CrossRef]
28. B. Wang, M. Ye, and S. Sato, “Liquid crystal negative lens,” Jpn. J. Appl. Phys. 44(7A), 4979–4983 (2005). [CrossRef]
29. Y. H. Fan, H. Ren, X. Liang, H. Wang, and S. T. Wu, “Liquid crystal microlens arrays with switchable positive and negative focal lengths,” J. Disp. Technol. 1(1), 151–156 (2005). [CrossRef]
30. F. Chu, L. L. Tian, R. Li, X. Q. Gu, X. Y. Zhou, D. Wang, and Q. H. Wang, “Adaptive nematic liquid crystal lens array with resistive layer,” Liq. Cryst. 47(4), 563–571 (2020). [CrossRef]
31. L. L. Tian, F. Chu, H. Dou, L. Li, and Q. H. Wang, “Short-focus nematic liquid crystal microlens array with a dielectric layer,” Liq. Cryst. 47(1), 76–82 (2020). [CrossRef]
32. A. Lien, “The general and simplified Jones matrix representations for the high pretilt twisted nematic cell,” J. Appl. Phys. 67(6), 2853–2856 (1990). [CrossRef]
