1. Introduction

Three-dimensional (3D) displays can offer more realistic images to viewers with depth information that is absent in two-dimensional (2D) displays. Recently, autostereoscopic 3D displays utilizing a parallax barrier or a lenticular lens array for presenting binocular disparities have received much attention due to the convenience of achieving 3D visual effects without the need for 3D glasses [1–6]. In the development of 3D displays, since most of the content is still based on 2D images for 2D display panels, the mode convertible function between 2D and 3D conditions is an essential requirement and can be achieved using switchable optical elements. While the active barrier method using a liquid crystal (LC) cell easily offers the 2D/3D switching function [7–8], brightness degradation inevitably occurs in 3D mode images compared with 2D mode images because the active barrier method simply controls the directional transmittance levels of the panel images to form binocular disparities. For multi-view or super-multi-view 3D displays with increased 3D viewpoints, the brightness level at each 3D viewpoint is more seriously degraded after transmitting significantly reduced effective aperture ratio of the active parallax barrier in switching to the 3D mode. The switchable lens array methods can control the ray directions based on the relative phase delay profiles without optical loss, and those are more suitable approaches for multi-view or super-multi-view 3D displays [9–15]. In particular, in the case of mobile applications implemented with panels of high resolution pixel density and small pixel aperture ratio conditions, the optical efficiency level of an additional optical layer attached to the mobile display panel for achieving 2D/3D switchable display function becomes a more critical issue, compared to large-area panel applications such as a TV or monitor.

For a switchable lens array in 2D/3D switchable multi-view displays, an LC-based gradient refractive index (GRIN) profile is most widely utilized. One method to fabricate a switchable LC lens array is to create a GRIN profile using an in-plane or fringe electric-field generated by patterned indium-tin-oxide (ITO) electrodes [16–25]. In this case, to achieve a short focal length for a given lens pitch condition (i.e., to make a lens with a small f-number), the cell gap of the LC layer becomes quite thick, which increases the operating voltages and slows down the switching times [16–25]. The LC orientations with the field-induced gradient profiles are unstable in the central regions between the patterned electrodes, because of the reverse tilt distributions of the LC directors, which results in degradation of the focusing efficiency of the field-switching LC lens array. For ideal field-induced GRIN profiles, complex electrode patterns are needed to control the field-induced LC director profiles more precisely, which is difficult for the short-pitch lenticular lens arrays required in 2D/3D switchable mobile displays. More importantly, for high-resolution mobile applications, the lens fill factor of the field-switching LC-based lenticular lens array becomes degraded because the LC molecules on the patterned ITO regions cannot be effectively reoriented by the switching fields without contributing to the formation of the GRIN profiles of these regions. This results in the lower optical efficiency of the lens in the 3D mode.

Another approach to facilitate the switchable focusing function based on the LC lens array is the utilization of the polarization-dependent switching LC or liquid crystalline polymer (LCP) lens array for which the structure is constructed by assembling the planar-convex LCP (or LC) lens array on the planar-concave isotropic polymeric lens array [26–33]. The focusing behavior of the polarization-dependent LCP lens array can be switched by controlling the polarization state of incident light, which determines the refractive index matching or mismatching conditions between the planar-convex LCP layer and the planar-concave isotropic polymeric layer. The polarization state of the incident light can be controlled using an LC-based electrically switchable polarization control layer, which is implemented between the polarization-dependent LCP lens array and the display panel. In this case, owing to the separated optical structures with different optical functions of the field-induced polarization control part and the polarization-dependent focusing part, ideal GRIN profiles can be achieved for a lower 3D crosstalk level. This is possible by precisely designing the interfacial curvature between the planar-convex LCP layer and the planar-concave isotropic polymeric layer. A fast switching time can also be obtained with a low operating voltage because the field-induced switching layer is the polarization control layer, which has the field-induced homogeneously reoriented LC layer, unlike the field-switching LC GRIN lens array.

For both types of LC-based lenses, unlike passive planar-convex lens arrays, the exit rays from the LC lens experience additional nonlinear refraction at the interface between the flat-shaped lens surface and the air. This has not been seriously considered in the development of LC-based switchable lens arrays for 3D displays with large-area panels. However, the LC-based lens with the flat air interfaces can cause more aberration in the focusing properties compared to the passive planar-convex lens. In particular, in the case of using the LC-based lens for mobile 3D displays, the aberration problem becomes more serious because a relatively small f-number lens is required for the mobile applications. Since a proper viewing window should be provided by the lens in a short viewing distance, the field of view (FOV) of the lens for mobile applications should be designed to be larger than that for the large-area panel applications. Also, since the pixel sizes of the mobile panels are much smaller than TV panels, the ray distortion caused by aberrations of the LC-based switchable lens can more sensitively affect the binocular crosstalk levels in the 3D mode representation [9–10,12].

In this paper, we discussed the aberration effect at the passive planar-convex lens array and the polarization-dependent switching LCP lens arrays according to the f-number conditions which are differently required depending on the display applications. To resolve the aberration problems of the LCP (or LC) GRIN lens in the small f-number condition for mobile applications, we introduced an aspherical curvature interface between the planar-convex LCP layer and the concave-planar isotropic polymer layer, by considering the additional ray refraction at the air interface. The focusing properties of the polarization-dependent switching LCP lens arrays adopting the aspherical curvature interface and its 3D crosstalk effect were compared with those of the lens array with the conventional spherical curvature interface. With the specially designed elemental lens curvature, we fabricated the thin-film-type polarization-dependent switching LCP lens array of which the f-number, lens pitch, and lens fill factor were 3.8, 150 μm, 100%, respectively. The 2D/3D switchable display implemented using a 5.5-inch quad high definition (QHD; 2560 × 1440, 538 ppi) mobile panel was able to provide autostereoscopic 10-view 3D images with the viewing distance and viewing window angle of 500 mm and 15°, respectively. In the 10-view 3D mode, the experimentally measured binocular crosstalk level was 3.3%. In the 2D mode, a wide viewing angle condition could be achieved without distortion of the 2D image at the polarization-dependent LCP lens array owing to the index matching condition between the planar-convex LCP layer and the concave-planar isotropic polymer layer, which was well-preserved irrespective of the viewing angle condition in our lens design.

2. Aberration of LC-based GRIN lens according to f-number condition

Figure 1 shows the defocusing/focusing switching principle of the polarization-dependent LCP GRIN lens array, where a twisted nematic (TN) LC layer functions as a polarization switching layer under the polarization-dependent lens array. The LCP layer has an optically uniaxial property with an ordinary refractive index and an extraordinary refractive index, similar to conventional LC molecules. The birefringent LCP layer and the isotropic polymer layer have planar-convex and concave-planar shapes, respectively. The ordinary refractive index of the LCP layer is the same as the refractive index (n_p) of the isotropic polymer layer. Whereas, the extraordinary refractive index of the LCP layer is larger than n_p. In this configuration, when the incident polarization state is parallel to the fast axis of the LCP layer at the field-off state of the TN LC layer as shown in Fig. 1(a), the incident rays are not refracted for the 2D image mode because of the index matching condition between the LCP layer and the isotropic polymer layer. On the contrary, when the incident polarization state is switched to be parallel to the slow axis of the LCP layer at the field-on state of the TN LC layer as shown in Fig. 1(b), the incident rays are periodically refracted and focused at the designed focal plane for the 3D image mode because the extraordinary refractive index of the planar-convex LCP layer is higher than the refractive index of the concave-planar isotropic polymer layer.

 

Fig. 1 Structure and operating principle of the polarization-dependent LCP GRIN lens array with the polarization switching layer, where (a) is the defocusing state for the 2D mode by the field-off condition of the polarization switching layer and (b) is the focusing state for the 3D mode by the field-on condition of the polarization switching layer.

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Figure 2(a) shows the spherical aberration properties that occur in a conventional passive-type planar-convex lens array, where the focal length (f_M) of the marginal rays of each elemental lens is shorter than the focal length (f_P) of the paraxial rays [34–36]. In Fig. 2(a), two types of the spherical aberrations were described as the longitudinal spherical aberration (LSA) and the transverse spherical aberration (TSA) which affect the optical imaging systems. When we compare the ray refraction behaviors between the passive-type planar-convex lens array and the polarization-dependent switching LCP GRIN lens array, the focusing rays in the passive-type planar-convex lens array are obtained by the single refraction at the convex-shaped lens/air curvature interface, as shown in Fig. 2(a). On the other hand, in the polarization-dependent LCP lens array, the incident rays are first refracted at the curvature interface between the LCP and the isotropic polymer layers and then additionally refracted at the flat interface between the lens substrate and the air, as shown in Fig. 2(b). By comparing the spherical aberration effects between the two types of lens structures, we found the TSA and LSA values of the LCP GRIN lens array to be larger than those of the passive-type planar-convex lens array under the same f-number lens condition, owing to the additional nonlinear refraction occurring at the flat air-substrate interface. Although we assumed the polarization-dependent LCP lens array in this discussion to be the same as the experimentally demonstrated lens array in our work, the other types of the LC-based lens with the flat substrate interfaces, including the electrically switchable LC GRIN lens also have the same additional aberration effects at the substrate interfaces compared with the passive-type planar-convex (planar-concave) lens array, which has not been sufficiently investigated as yet.

 

Fig. 2 Illustrations of longitudinal and transverse spherical aberrations for (a) passive-type planar-convex lens and (b) active-switching-type LCP GRIN lens with flat air interfaces.

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To analyze and compare the spherical aberration effects in the planar-convex lens and the LCP GRIN lens according to the f-number lens condition, we performed optical simulations by using the optical modeling software of Advanced System Analysis Program (ASAP^TM, Breault Research Organization, Inc.). Among the two types of aberrations in Fig. 2, the TSA values more dominantly affect the 3D image quality and 3D image crosstalk levels in the autostereoscopic 3D displays. Figure 3 shows the simulated results of the TSA values of the planar-convex lens and the LCP GRIN lens according to the f-number and pitch of the elemental lens. In these cases, the paraxial ray is defined as the ray passing through the middle points of the elemental lens radii (positions at 0.5 × r) and the marginal ray is defined as the ray passing near the edges of each elemental lens (positions at 0.001 × r). In our simulations of both types of lens, the spherical curvatures applied were identical for us to be able to make comparisons. As shown in Fig. 3, the TSA values are increased for both types of lens because of the increased spherical aberration as the f-number and pitch conditions of the elemental lens decrease. However, in the case of the LCP GRIN lens, the spherical aberrations (A_i values in Fig. 3) becomes much worse than those (B_i values in Fig. 3) of the conventional passive-type planar-convex lens, as decreasing the f-number and pitch conditions of the elemental lens, as shown in Fig. 3. This can be explained by the fact that the lens curvature of the LCP GRIN lens needs to be larger than that of the planar-convex lens to achieve the same focusing properties. This means that the same autostereoscopic 3D images can be obtained in terms of viewing distance and 3D viewpoints considering that the LCP GRIN lens has a concave-planar isotropic polymer layer, unlike passive-type planar-convex lenses with a curvature-shaped air interface. In addition, the TSA effect of the additional nonlinear refraction at the air-substrate interface on the (f_P - f_M) amount becomes even more significant as the f-number condition becomes smaller. For mobile applications using the autostereoscopic 3D displays, the f-number condition of the switchable elemental lens should be smaller compared with the large-area panel applications to obtain a proper viewing window in a shorter viewing distance. Also, since the sub-pixel size of the mobile panel recently became less than 20 μm for high resolution displays, this short pixel pitch condition of the panel together with the increased spherical aberration effects at a smaller f-number lens design makes it difficult to obtain clear 3D images at each viewpoint formed by the elemental lenses. This results in a worse crosstalk property of the 3D images in the mobile applications than that of the large-area panel applications.

 

Fig. 3 Transverse spherical aberrations of the planar-convex lens (B_i) and the switchable LCP GRIN lens (A_i) according to f-number and pitch of the lenticular microlens arrays. The elemental lens conditions of the f-number, pitch, and focal length are co-presented in the table.

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To overcome this problem of the spherical aberration at the LCP GRIN lens which is especially severe for the small f-number lens condition, we applied an aspherical curvature boundary between the planar-convex LCP layer and the concave-planar isotropic polymer layer using optical modeling software. Considering the experimentally characterized refractive indices of the LCP layer and the refractive index of the isotropic polymer layer, we sectionalized sub-regionally each elemental lens along the lens cross-section direction and re-designed the curvature boundaries for each section to quadrate the incident rays at the same focal point. The final aspherical curvature boundary between the planar-convex LCP layer and the concave-planar isotropic polymer layer was obtained by utilizing a curve fitting procedure from each sectionalized curvature. In our design of the LCP GRIN lens array, each elemental lens was divided into the 150 sub-sections for the lens pitch condition of 150 μm to minimize the spherical aberration. However, the focusing properties were almost converged when performing the curve fitting of the spherical curvature by using over 50 sub-sections for each elemental lens. Figures 4(a) and 4(b) are the ASAP simulation results showing the focusing performances of the LCP GRIN lens with the spherical and aspherical boundary curvature, respectively, where the f-number and focal length of each LCP GRIN lens are identically 3.8 and 556 μm, respectively. It is obvious that the LCP GRIN lens with the aspherical curvature boundary shown in Fig. 4(b) has a better focusing ability than the LCP GRIN lens with the spherical curvature boundary shown in Fig. 4(a), for both of the normal-axis and off-axis incident rays. The TSA value of the LCP GRIN lens adopting the aspherical curvature boundary is also improved by about 4.8 times compared to that of the LCP GRIN lens with the conventional spherical curvature boundary. In Fig. 3, the TSA value of the LCP GRIN lens with the aspherical curvature boundary is co-plotted with the amount of 12.4 μm.

 

Fig. 4 Simulation results of ray distributions and positional flux densities for the LCP lenses (f-number = 3.8, f_lens = 556 μm for both lens types) with (a) spherical and (b) aspherical curvature interfaces between the LCP and isotropic polymer layers. (c) Interfacial curvature profiles applied to the LCP lenses shown in Figs. 4(a) and 4(b).

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Figure 4(c) shows the curvature profiles between the LCP and isotropic polymer layers of the LCP GRIN lenses used for Figs. 4(a) and 4(b), where the functions of the spherical and aspherical curvature boundary are $y=106-\sqrt{{106}^2-x^2}$ and y = 0.00559x² expressed in μm dimensions for x and y values, respectively. The slope of the aspherical curvature boundary is slightly larger than that of the spherical curvature for the paraxial rays. Whereas, for the marginal rays of each elemental lens, the slope of the aspherical curvature boundary is designed to be smaller than that of the spherical curvature. Therefore, compared with the positional focusing properties of the LCP GRIN lens with the spherical curvature boundary, the LCP GRIN lens with the well-designed aspherical curvature boundary can provide shorter and longer focal length properties for the paraxial and marginal rays, respectively, while reducing the spherical aberration even for a lens design with a small f-number intended for mobile 3D applications.

3. Fabrication of polarization-dependent LCP lens array

Figure 5 shows the fabrication process of the polarization-dependent switching LCP lens array. To reduce the aberration of the polarization-dependent LCP lens with a small f-number (f-number = 3.8) and a small lens pitch (P_lens = 150 μm) conditions, we made the aspherical-shaped lenticular lens array template following our curvature profile design of y = 0.00559x² shown in Fig. 4(c), which was manufactured by Fresnel technologies inc. The average surface roughness value of the template was about 4.75 nm. A planar-concave isotropic polymer lens array structure was formed on a transparent film substrate via a UV-nanoimprinting process using a UV-curable polymer of NOA89 (n_p = 1.52, Norland Products, Inc.), as shown in Fig. 5(a). The curvature-shaped surface of the planar-concave isotropic lens array was treated by a UV ozone process for 30 min to make it a hydrophilic surface for a uniform subsequent coating process. Then, polyvinyl alcohol (PVA) solution was spin-coated and thermally annealed at 90 °C for 30 min to provide a bottom-up alignment effect for the LCP alignment on the optically isotropic planar-concave lenticular lens array structure. To obtain anisotropic alignment properties of the LCP molecules on the lens array structure, the PVA layer was rubbed along the lenticular lens axis direction as shown in Fig. 5(b). For the LCP layer, we used a UV-curable reactive mesogen (RM) (RMM727, Merck; n_o = 1.52, n_e = 1.71, and Δn = 0.19). To obtain a well-aligned LCP layer, we applied the top-down and bottom-up alignment methods for RM alignment before the UV curing process, which was applied for achieving the UV-induced polymerization of the RM molecules. For this purpose, another PVA layer coated on the film substrate was prepared as shown in Fig. 5(c). After laminating the upper film substrate onto the bottom substrate with the planar-concave lenticular lens array structure, the RM molecules were filled into the cavities by the capillary force. Then, the RM molecules were polymerized into the solid film of the LCP layer by irradiating the UV light for 90 s at 50 mW/cm² of the UV dose condition as shown in Fig. 5(d). The upper film substrate used for enhancing the RM alignment was peeled off to reduce the gap between the polarization-dependent switching LCP lens array and the display panel, which is required to meet the mobile 3D viewing condition during assembling the lens array with the mobile panel. As an electrically switchable polarization control layer, a film-based TN LC cell was prepared. Finally, the polarization-dependent LCP lens film was laminated on the polarization-switching TN cell by using a UV curable adhesive material (NOA1625, Norland Products Inc.; n = 1.625) as shown in Fig. 5(e). All of the fabrication steps and their manufacturing materials were designed to be viable to printing process on film substrates.

 

Fig. 5 Schematic diagrams of the fabrication procedures for the polarization-dependent switching LCP lens array: (a) UV nano-imprinting process to form the planar-concave isotropic polymer layer, made of UV-curable resin, (b) UVO surface pre-treatment on the replica-molded planar-concave isotropic polymer layer and spin-coating and curing of the LC alignment layer, and rubbing process on it for the bottom-up alignment of RM, (c) preparation of the top substrate by spin-coating and curing of the LC alignment layer and rubbing treatment on it for the top-down alignment of the RM layer, (d) one-drop filling process of the RM solution, lamination of the top substrate, UV curing for polymerization of the RM layer, and the final structure of the polarization-dependent LCP lens array after peel-off of the top substrate, (e) lamination process for integration of the polarization-dependent LCP lens array film on the polarization-switching TN LC cell by using UV curable adhesive material.

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Figure 6(a) shows the cross-sectional scanning electron microscopic (SEM) image of the fabricated polarization-dependent switching LCP lens array. In the structure, the residual thicknesses of the isotropic polymer layer and the LCP layer were about 13.8 μm and 12.0 μm, respectively. Figures 6(b) and 6(c) show the polarized optical microscope (POM) images of the polarization-dependent LCP lens array observed through the crossed polarizers, where the RM molecules were aligned by the bottom-up and top-down alignment effects as shown in Fig. 5. When the LCP alignment direction of the polarization-dependent switching LCP lens array was set to be parallel to one of the transmission axes of the crossed polarizers, a completely dark texture could be ideally obtained without any RM alignment defect as shown in Fig. 6(b). When the LCP alignment direction of the lens was rotated to be 45° with respect to the transmission axes of the crossed polarizers, the bright and dark fringe-like line patterns could be observed owing to the positional retardation variation of the planar-convex LCP layer, which also showed the well-aligned LCP texture as shown in Fig. 6(c). For Fig. 6(c), a monochromic light source (λ = 633 nm) was used to obtain a clear fringe pattern. The positional light transmittance level ($T\propto {\sin }^2\left(\pi \Delta n_{LCP}{d}_{LCP}(x,y)/\lambda \right)$; d_LCP(x,y) is the positional thickness of the planar-convex LCP layer) within each elemental lens is determined by the positional retardation amount of the planar-convex LCP layer. In Fig. 6(c), the positional phase retardation difference between the brightest fringe patterns or between the darkest fringe patterns is 2π. Whereas, for the LCP lens array prepared by the conventional bottom-up alignment effect only, a uniform LCP alignment could not be obtained as shown in Fig. 6(d) because of the underlying concave-shaped surface topology with the periodic sharp edges and thick thickness of the LCP layer required for the short focal length property.

 

Fig. 6 (a) Cross-sectional scanning electron microscopic image of the LCP lens array. (b) and (c) Polarizing optical microscope (POM) images of the LCP lens, prepared with the top-down and bottom-up alignment methods. (d) POM image of the LCP lens, prepared only with the bottom-up alignment method without applying the top-down alignment method. (e) Measured and ideal relative phase delay profiles of the LCP lens for the incident polarization condition of the focusing state, where the measured ones are obtained from the dark and bright fringe patterns shown in Fig. 6(c).

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Using the fringe patterns and the positional relative light transmittance levels shown in Fig. 6(c), the effective amount of the positional relative retardation within each elemental lens was first derived after the phase unwrapping. In analyzing the experimentally obtained refractive indices of the LCP layer from the positional effective retardation measurement, the effective refractive index value of the LCP layer is highly dependent on the RM molecule orientations aligned on the planar-concave isotropic polymer layer, which can be varied from the ideal material condition of n_e when there is horizontally or vertically RM alignment deviation from the homogeneous planar LCP geometry ideally aligned along the lenticular lens axis. However, due to the optically uniaxial property of the LCP molecules, the n_o value of the LCP layer is determined independently of the RM orientation states in analyzing the positional effective retardation of the LCP layer. Note that the n_o value of the LCP layer is identical with the n_p value of the isotropic polymer layer in our device structure. Thus, using n_p, the positional relative phase delay distribution (δ(x,y) = 2π(n_e(x,y)-n_p)d_LCP(x,y)/λ) of the assembled GRIN lens structure with the planar-convex LCP and planar-concave isotropic polymer layers could be obtained for the incident polarization condition of the extraordinary rays as shown in Fig. 6(e). In Fig. 6(e), the measured values were compared with the ideal relative phase delay curve, which indicated that the RM molecules were well-aligned with the homogeneously planar LCP geometry on the periodic planar-concave isotropic polymer layer.

When we estimated the focal length of the polarization-dependent LCP lens array with the following equation which is widely used for the focal length characterization of the GRIN lens:

For the electrically polarization-switching layer shown in Fig. 1, a TN LC cell was prepared between the plastic (PET) films substrates, which was attached under the polarization-dependent LCP lens array using the UV-curable adhesive resin. The thickness of the ITO-coated PET film used for the substrates of the TN LC cell was about 125 μm (thickness of the ITO electrode: ~100 nm), and the cell gap between the film substrates was about 5 μm. The birefringence of the LC used for the TN LC layer is 0.094 (n_e = 1.575 and n_o = 1.481). At this TN LC condition, the polarization state incident onto the LCP lens array can be ideally switched into one of the orthogonal polarization states by minimizing the wavelength dependence of the incident light for visible ranges. Total thickness of the assembled structure of the polarization-dependent LCP lens array (~182 μm including one film substrate) and the TN LC cell (~255 μm including a pair of ITO film substrates) was below 440 μm. Figures 7(a) and 7(b) show the defocusing and focusing behaviors of the polarization-dependent LCP lens array that is electrically switched by the TN LC layer, which was observed with the polarized light incidence without an analyzer. When the TN LC layer is in the field-off state (V_a = 0 V), the incident polarization becomes orthogonal to the optic axis of the LCP layer, and the output rays after the polarization-dependent LCP lens array were completely defocused as shown in Fig. 7(a). Whereas, when the TN LC layer is switched to the field-on state (V_a = 5 V, 100 Hz), the incident polarization is changed to be parallel with the optic axis of the LCP layer, and the periodically focused beam patterns could be obtained at the focal plane as shown in Fig. 7(b). Figure 7(c) shows the switching dynamics between the defocusing and focusing states of the polarization-dependent LCP lens array according to the field-switching polarization states of the TN LC layer. The field-on response time for switching of the lens from the defocusing state to the focusing state and the field-off response time for the opposite switching state were about 15.0 ms and 7.1 ms, respectively. For a quantitative analysis of the imaging performance of the polarization-dependent LCP lens array, the modulation transfer function (MTF) curve of the lens was measured at the focused mode by using the 1951 USAF resolution test chart. The MTF value was about 0.4336 at 5.66 line pairs per millimeter, as shown in Fig. 7(d).

 

Fig. 7 Microscope images of the (a) defocused and (b) focused beams obtained at the focal plane, showing the switchable focusing behaviors of the polarization-dependent LCP lens array according to the switching states ((a) field-off and (b) field-on states, respectively) of the polarization switching layer. (c) Time-dependent focused beam intensity of the polarization-dependent LCP lens array as switching it from the defocusing to focusing state and from the focusing to defocusing state by changing the applied voltage condition of the polarization-switching TN LC layer. (d) MTF curve of the polarization-dependent switching LCP lens at the focusing mode, characterized by using the 1951 USAF resolution test chart.

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4. 2D/3D switchable mobile display using polarization-dependent LCP lens array

Figure 8 shows the cross-sectional schematic of the 2D/3D switchable mobile 3D display made by assembling the polarization-dependent LCP lens array attached on the TN LC cell with the 5.5 inch high-resolution (1440 (H) × 2560 (V): QHD) mobile LCD panel. The gap between the LCP lenticular lens array and the mobile panel was approximately 850 μm. To avoid the color moiré pattern phenomena at the 3D mode induced by the relative positional effects between the periodic refractive lenticular lens and the periodic color sub-pixels, the axis of the lenticular lens array was slanted by 9.46° with respect to the sub-pixel arrangements of the LCD panel. For the slanted lens axis condition, a polarization film was inserted between the assembled module of the LCP lens array with the polarization-switching layer and the LCD panel, of which transmission axis condition was slanted by 9.46° with respect to the transmission axis of the exit polarizer of the LCD panel, as shown in Fig. 8. The LC alignment directions of the top and bottom film substrates of the TN LC cell were also rotated as much as the slanted angle of the LCP lenticular lens array. Sub-pixel re-mapping was applied for the 3D image contents so that the 3D image resolution was reduced similarly along the horizontal and vertical image directions from the 2D image resolution. The horizontal and vertical resolutions in 3D mode were 432 (H) × 853 (V) under the aforementioned slanted lens alignment and sub-pixel mapping conditions.

 

Fig. 8 Cross-sectional schematic of the polarization-dependent LCP lens array assembled on the QHD (538 ppi) mobile panel for the 2D/3D switchable display.

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Figures 9(a) and 9(b) show the optical simulation result and the experimentally measured result, respectively, of the angular luminance distribution of our 10-view autostereoscopic 3D display. For the simulation and experimental results used for evaluation of the 3D crosstalk level, a white pixel condition for each view point was applied after the R/G/B sub-pixel rearrangement with considering the slanted lens axis. In Fig. 9(c), the experimental result of the angular luminance distribution at the 2D mode is plotted. In this characterization, the viewing distance, the pupil size of the photo-detector, and the angular sampling resolution were 500 mm, 3 mm, and 0.5°, respectively. In our lens assembling condition, the experimental results showed that the angle of the viewing window and the average value between the adjacent views were 15° and 1.5° (13.2 mm in the distance between the adjacent views), respectively, which were well-matched with the simulation results.

 

Fig. 9 Angular luminance distributions of the autostereoscopic multi-view (10-view) 3D mode of the 2D/3D switchable mobile display: (a) the simulation result, (b-c) the experimentally measured results at (b) the 3D mode and (c) the 2D mode.

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The 3D crosstalk level can be defined as follows [14]:

Table 1. Specifications of the 2D/3D switchable mobile multi-view display.

View Table

In conventional electrically LC-switching GRIN lens, the field-induced non-uniform LC distributions of the positionally different tilted LC orientations inevitably occur. On the other hands, the RM molecules of the LCP layers for the polarization-dependent switching LCP GRIN lens are homogeneously aligned along the lenticular lens axis without any tilt orientation. Thus, with the precise refractive index information on the planar-convex LCP and concave-planar isotropic polymer layers, the aberration properties which gets worse at the small f-number lens condition can be effectively improved by delicately designing the aspherical curvature boundary in our lens structure even considering the additional nonlinear refraction behavior at the flat air interfaces as shown in our results. In addition, this ideal lens phase profile can be well-maintained even under any external mechanical stress like the contact pressure because the well-oriented RM molecules of the planar-convex LCP layer becomes the solidified film after the UV-induced polymerization. In Table 1, the detailed specifications of the 2D/3D switchable mobile multi-view display are listed. As shown in Fig. 8 and Table 1, the total lens module of the polarization-dependent LCP lens array with the polarization-switching TN LC layer can be made as a type of very thin film, and its operating voltage is sufficiently low, and therefore the properties are also quite suitable for the 2D/3D switchable mobile display applications.

In Figs. 10(a) and 10(b), the original 2D content image used in our demonstration for the 2D display mode with the defocused lens state and the 3D content image after the sub-pixel rearrangement for the autostereoscopic 10-view 3D display mode with the focused lenticular lens state, respectively. When displaying the 2D content on the LCD panel under the field-on state (V_a = 5 V) of the polarization-switching TN LC layer, the distorted 2D images were observed as shown in Fig. 10(c) because of the periodic ray refractions by the LCP lens array. However, when the exit polarization state after the TN LC layer was orthogonally switched by removing the applied voltage (V_a = 0 V), clear 2D images were obtained without distorting the high-resolution QDH 2D images as shown in Fig. 10(d). Considering that watching 2D content is more common than watching 3D content, the switchable lens module was designed for the 2D mode to be presented in the field-off state of the TN-LC layer to reduce the power consumption of the 2D/3D switchable mobile display. Figure 10(e) shows the 3D images captured at different oblique view directions while displaying the 3D content on the LCD panel under the field-on state of the polarization-switching TN LC layer as the 3D mode, where the different perspectives of the object images can be observed (See Visualization 1). The enlarged figures in Fig. 10(e) show that there was neither severe color mixing problems nor 3D resolution degradation at measured under different perspective view conditions. Because the LCP molecules are horizontally oriented along the lenticular lens axis direction with optically uniaxial properties, the 2D and 3D images provided by our 2D/3D switchable mobile display demonstrated the wide viewing angle property of our display in 2D mode and the low crosstalk level within the viewing window in 3D mode.

 

Fig. 10 Photograph of visual images captured from the 2D/3D switchable mobile display: (a) the original 2D content image, (b) the 3D content image after the sub-pixel rearrangement for the autostereoscopic 10-view 3D, (c) display image of the 2D content observed at the 3D mode, (d) display image of the 2D content observed at the 2D mode, (e) directional view images of the 3D content observed at the 3D mode. (Visualization 1: the moving picture of the 2D/3D switching images).

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5. Conclusion

We demonstrated a 2D/3D switchable mobile display using an assembled optical film module of a polarization-dependent switching LCP lens array and a polarization-switching TN LC cell. For the LCP (or LC)-based GRIN lens, the aberration effects according to the f-number and pitch conditions of the elemental lens were discussed, which showed that the lens aberration became severely degraded with a decrease of the f-number condition in the LCP (or LC)-based GRIN lens compared with the passive-type planar-convex lens. However, in the presented lens structure, the aberration of the LCP lens could be effectively suppressed by applying the aspherical curvature boundary interface between the planar-convex LCP layer and the concave-planar isotropic polymer layer, where the TSA value could be improved by about 4.8 compared to that of the LCP lens with conventional spherical curvature boundary. With the well-designed curvature boundary condition, we fabricated the thin-film-type polarization-dependent switching LCP lens array exhibiting decreased aberration, short focal length, small lens pitch, and small f-number condition for mobile display applications. The evaluated optical properties of the polarization-dependent LCP lens array revealed that its f-number and elemental lens pitch are 3.8 and 150 μm, respectively. Utilizing the polarization-dependent switching lens module, we implemented the 2D/3D switchable mobile display based on a 5.5-inch QHD mobile panel, which showed the autostereoscopic 10-view 3D images with a sufficiently low binocular crosstalk level of 3.3%. The 2D and 3D images expression could be switched by a low operating voltage level of 5 V. The total thickness of the lens module part including the polarization-switching TN LC layer was sufficiently thin (~440 μm), which is also suitable for mobile applications. We believe that the presented lens design scheme and its fabrication method can be usefully applied in realizing 2D/3D switchable displays, especially for mobile applications.