For enhancing the spatial resolution of the LF imaging without causing a degradation in the angular sampling resolution, the approach of the lens shifting method, the virtual-moving MLA is implemented to obtain the time-sequential elemental image acquisition as shown in Fig. 1. The virtual-moving MLA is obtained through the integration of two polarization-dependent MLAs (PDMLAs), and the elemental lens position of the two PDMLAs are relatively shifted by half the pitch of the elemental lens array. Each PDMLA consists of a birefringent liquid crystalline polymer (LCP) layer having a planar-convex lens shape and an isotropic polymer layer having a concave-planar shape, wherein the ordinary refractive index (n o ) of the LCP layer is the same as the refractive index (n p ) of the isotropic polymer layer, and the extra-ordinary refractive index (n e ) of the LCP layer is larger than n p . The n e axes of the LCP layer of the top and bottom PDMLAs are aligned orthogonally with each other, i.e., along the x-axis direction (0°) and y-axis direction (90°), respectively. In this structure, in the case of the y-axis polarization state, the incident rays propagate through the top PDMLA without an optical refraction owing to the index-matching condition between the LCP layer and the isotropic polymer layer, and they are periodically focused in propagating through the bottom PDMLA, as shown in Fig. 1a. In contrast, when the incident polarization state is switched to the x-axis direction, the periodic ray focusing is obtained during propagation through the top PDMLA as shown in Fig. 1b. Figure 1c shows the top-view schematic of the relative elemental lens arrangement of the stacked PDMLAs. The position of the top PDMLA is shifted along the diagonal direction by half the pitch of the elemental lens array as compared to that of the bottom PDMLA.

Figure 1 Device structure and operating principle of the virtual-moving MLA. (a,b) Laterally shifted periodic beam-focusing states obtained by the bottom and top polarization-dependent MLA (PDMLA) according to the applied field conditions of the polarization-switching optically compensated bend (OCB) LC layer. (c) Top-view schematic of the virtual-moving MLA, wherein the lateral displacement of the bottom and top PDMLA arrangement is set as half the pitch of the elemental lens array in the diagonal direction. Full size image

Figure 2 shows the fabrication process of each PDMLA layer and the procedure of its stacking for fabricating the virtual-moving MLA. First, for each PDMLA, by performing a UV-nanoimprinting process, the isotropic polymer layer with the concave-planar MLA shape was formed using a UV-curable polymer resin of NOA89 (Norland Products Inc.; n p = 1.51) as shown in Fig. 2a. In this experiment, the square-arranged bed-pillow-shaped MLA template (MLA-S100-f4, RPC Photonics) was used for the preparation of the soft mould template required for the UV-nanoimprinting process. The oblique view of the surface profile of the MLA template is shown in Fig. 3a with the scanning electron microscope (SEM) image. With the periodic surface topology shown in Fig. 3a, the PDMLA with a fill factor of nearly 100% can be achieved, wherein the pitch and height of the square-shaped elemental lens is 100 μm and 5.3 μm, respectively. After the UV-nanoimprinting process, in order to obtain the anisotropic optical properties of the LCP molecules on the planar–concave isotropic MLA, we applied bottom–up and top–down interfacial alignment effects with a rubbing process on the bottom planar–concave MLA and on the other upper flat film surface, which are shown in Fig. 2b,c. The surface of the planar–concave MLA structure and the upper flat film were treated using a UV ozone process for 30 min in order to create a hydrophilic surface for the post-coating process. Polyvinyl alcohol (PVA) dissolved in water was coated onto the planar–concave MLA structure and the upper flat film, and they were thermally annealed at 90 °C for 30 min. The PVA layers were then bi-directionally rubbed to avoid shading regions on the planar–concave MLA surface. For the LCP layer, we used a UV-curable reactive mesogen (RM) (RMM727, Δn = 0.19, Merck). The LCP layer was formed by casting the LC RM on the planar–concave MLA structure, laminating the upper film substrate onto it, and polymerizing the RM using UV irradiation (for 90 s at 50 mW/cm2) in a uniaxially aligned state. Subsequent to the UV-induced polymerization of the RM LCP layer, the upper film substrate applied for the top–down LC alignment was peeled off, as shown in Fig. 2c. For the virtual-moving MLA, the other set of the PDMLA was prepared using the same method described above; however, the rubbing direction used was orthogonal to each other. The two PDMLAs with the orthogonal slow axis of the LCP layer were laminated with each other using an optically clear resin (NOA1625, Norland Products Inc.; n = 1.625), as shown in Fig. 2d, wherein the elemental lens positions of the two PDMLAs were aligned to be shifted by half the pitch of the elemental lens along the diagonal direction utilizing a micro-moving stage with a microscope. As all the optical layers consisting of the stacked PDMLAs were UV-curable polymeric layers on the film substrates, the printing process is viable without inflicting chemical, thermal, or mechanical stress damages being inflicted on the flexible film substrates.

Figure 2 Schematics of the fabrication procedures of the virtual-moving MLA: (a) ultraviolet (UV) nano-imprinting process for fabricating the planar–concave MLA structure made of the optically isotropic UV-curable resin, (b) UVO surface treatment on the replica-moulded planar–concave MLA structure, spin-coating and curing of the alignment layer (PVA), bi-directional rubbing treatment, and preparation of the top–down alignment film by spin-coating and curing of the PVA layer and rubbing treatment. (c) One-drop filling process of the reactive mesogen (RM) solution, lamination of the top–down alignment film, UV curing for the polymerization of the RM layer, and peel-off procedure of the top–down alignment film. (d) Lamination of the top PDMLA on the bottom PDMLA using the UV curable adhesive material between two MLAs, and the final structure of the virtual-moving MLA. Full size image

Figure 3 (a) Oblique view of the scanning electron microscope (SEM) image of the MLA with the square-arranged bed-pillow-shaped elemental lens surface topology, which is used as the master mould during the nano-imprinting process. (b) Cross-sectional view of the SEM image of the single PDMLA. (c,d) Polarizing optical microscope images of the single PDMLA observed between the crossed polarizers, wherein the rubbing direction is (c) parallel and (d) at 45° with respect to the transmission axis of one of the polarizers. (e,f) Measured and ideal relative phase delay profiles of the single PDMLA, wherein the measured results are derived from the phase unwrapping of the fringe ring patterns shown in (d) along the sampling directions of (e) a–a’ and (f) b–b’. Full size image

Figure 3b shows the cross-sectional SEM image of one of the fabricated PDMLAs before it was laminated. The total thickness of a single PDMLA layer was approximately 120 μm including the film substrate (100 μm), where the residual thickness of the LCP layer on the film substrate was approximately 3.5 μm. The optically clear resin layer used for laminating the two PDMLAs with each other was approximately 20 μm thick, and the total thickness of the stacked structure as the virtual-moving MLA was approximately 260 μm including the two film substrates—this stacked structure was thus thin and flexible. As shown in Fig. 2d, two polymerized PDMLA films could be stacked with a very thin adhesion layer without additional guiding substrates between them in contrast to the case of an LC-based switchable lens, and the longitudinal deviation of the focal planes between the top and bottom PDMLAs could be minimized for the time-multiplexed LF imaging.

Figure 3c,d show the polarized optical microscope (POM) images of the PDMLA observed through the crossed polarizers. As the slow axis of the LCP layer of the PDMLA was set such that it was parallel to the transmission axis of one of the polarizers, a completely dark LCP texture could be obtained without any optical leakage observation, as shown in Fig. 3c. In this figure, the RM molecules were well aligned along the alignment direction without an optic axis deviation due to the bottom–up and top–down interfacial alignment effects, although there were the periodic square-arranged planar–concave topology as the LCP alignment bottom surface. As the slow axis of the LCP layer of the PDMLA was rotated to 45° with respect to the transmission axes of the crossed polarizers, bright and dark ring patterns could be observed owing to the positional retardation variation of the planar–convex LCP layer, as shown in Fig. 3d, wherein a green filter was inserted into the POM for observing clear fringe patterns. The results show that all the phase profiles of each elemental lens were ideally centro-symmetric, and a fill factor of the PDMLA of nearly 100% could be achieved using the square-shaped bed-pillow-shaped MLA structure. Using the bright and dark ring patterns and the positional relative light transmittance levels shown in Fig. 3d, the effective positional relative retardation within an elemental lens was derived after the phase unwrapping. Figure 3e,f show the relative phase delay of the PDMLA for one region of the elemental lens array along the horizontal (a–a’) and diagonal (b–b’) directions shown in Fig. 3d. The focal length of the PDMLA can be estimated using the following equation30,31:

$$f=\pi {r}^{2}/\phi \lambda ,$$ (1)

where r is the aperture radius of each elemental lens, φ is the maximum phase difference between the centre and edge positions of the elemental lens, and λ is the wavelength of the incident light (λ = 550 nm). The derived focal length and f-number obtained using Eq. (1) were 1.60 mm and f/16, respectively.

Figure 4a–c show the focused beam patterns of the virtual-moving MLA according to the polarization states of the incident cool white beam. When the polarization state of the incident beam is parallel to the slow axis of the bottom PDMLA, the periodic focused beam pattern is determined by the bottom PDMLA, as shown in Figs 1a and 4a. In contrast, when the incident polarization is parallel to the slow axis of the top PDMLA, the periodic focused beam pattern is determined by the top PDMLA, as shown in Figs 1b and 4b. Figure 4c shows the focusing behaviour obtained under the incident polarization condition of 45° with respect to both alignment directions of the LCP layers of the top and bottom PDMLAs, which exhibits both beam patterns focused by the top and bottom PDMLAs. In Fig. 4c, as the lens planes can be considered to have approximately the same longitudinal position in our stacked PDMLAs, the beam profiles focused by the top and bottom PDMLAs were almost identical at the same focal plane.

Figure 4 (a–c) Optical microscope images of the focused beam patterns obtained using the virtual-moving MLA that are captured at the focal plane when the incident polarization states are parallel with the rubbing direction for the RM layer of (a) the top PDMLA and (b) bottom PDMLA and (c) rotated by 45° with respect to both the rubbing directions. (d) Time-dependent switching characteristics of the polarization switching layer (OCB mode LC cell) according to the applied field conditions. (e,f) Enlarged graphs of (d) presented to characterize the switching dynamics of the virtual-moving MLA. For the moving picture showing the fast-switching laterally moved focusing properties, see Movie S1. Full size image

Considering the full-colour LF imaging utilizing the virtual-moving MLA scheme, two dispersion characteristics of the n o values of the planar-convex LCP layer and the n p values of the planar-concave isotropic polymer layer should be matched each other over the whole visible range to avoid the optical crosstalk between two sets of the laterally shifting LF image acquisitions by the time-sequentially operating stacked PDMLAs. When we measured the refractive indices of n o and n e for the LCP and the n p refractive index for the isotropic polymer with an interferometric method, the wavelength-dependent refractive indices are n o = 1.5592, n e = 1.7511, and n p = 1.5652 at λ = 450 nm (blue), and n o = 1.5136, n e = 1.6794, and n p = 1.5111 at λ = 550 nm (green), and n o = 1.4952, n e = 1.6508, and n p = 1.4892 at λ = 650 nm (red). From the measured values, we found the dispersion equations of n o (λ), n e (λ), and n p (λ) by curve-fitting using the Cauchy equation (See Supplementary Section 1). Two dispersion curves of n o (λ) and n p (λ) showed that the index matching condition between the planar-convex LCP and planar-concave isotropic polymer layers of the stacked structure of the PDMLAs were preserved well over the whole visible range for the ordinary incident rays. The average value of the index mismatching amount over the visible range (400 nm~700 nm) was extremely low with \( < |{n}_{o}-{n}_{p}| > \) = 0.005615. The experimental results of the polarization-dependent focused beam patterns shown in Fig. 4a,b also show ideal switching characteristics without a crosstalk in the virtual-moving focused beam patterns although the incident beam condition for Fig. 4a,b were the broadband cool white visible source. For the operation of the beam-focused state of the PDMLA using the incident polarization condition of the extraordinary ray, the dispersion curve of n e (λ) is different with n p (λ) unlike the refractive index relationship between n o (λ) and n p (λ) because of the more dispersive characteristics of n e (λ) than n o (λ) of the uniaxial molecular structure of the LCP. This caused the chromatic aberration at the focused state of the PDMLA. In our experiment, to acquire the full colour LF imaging, the depth of field condition of the PDMLA was designed to be sufficiently large by adopting the large f-number (f/16) elemental lens condition. The details on the characterization methods and their results of the material dispersions (Fig. S1a), the index matching properties (Fig. S1a,b) between n o (λ) and n p (λ) for the polarization-dependent switching function in the stacked structure, and the chromatic aberration properties with the wavelength-dependent focusing (Fig. S1c) and wavelength-dependent imaging evaluated by the modulation transfer function (Fig. S1d) are presented in Supplementary Information (See Supplementary Section 1).

In our resolution-enhanced LF imaging system that uses the time-multiplexing scheme with the virtual-moving MLA, the time-sequential periodic ray sampling by each PDMLA layer is switched by the incident polarization change of the underlying polarization switching layer made by the fast-switching LC cell. Thus, the fast-switching property for the incident polarization control is important, and an optically compensated bend (OCB) LC mode cell is used as the polarization switching layer in our implementation of the LF imaging system. The OCB mode can provide an extremely short field-off response time as compared to those of the other types of LC modes owing to the field-off initial LC geometry of the large band elastic deformation. Figure 4d–f illustrate the switching dynamics between the two orthogonal output polarization states of the polarization switching layer required for two sets of the periodic ray sampling performed using the virtual-moving MLA. In Fig. 4d, the field waveform applied to the OCB mode LC cell used as the polarization switching layer was co-plotted. For the focusing states obtained by the bottom and top PDMLAs, 30 V p and 3 V p at 1 kHz, respectively, were applied to the polarization switching layer, wherein the polarization switching LC layer had a zero and half wave phase retardation for λ = 532 nm at the high and low applied voltages, respectively. For the half retardation condition, the signal voltage (3 V p at 1 kHz) is not zero, and the transition of the LC geometry from bent to splayed does not occurr32. Thus, as shown in Fig. 4d–f, the fast-switching dynamics can be obtained: the field-on and field-off response times of the polarization switching layer are 270 μs and 180 μs, respectively. The switching dynamics is sufficiently fast such that the presented resolution-enhanced LF imaging system can be applied to real-time image capturing in the case of a moving object. The moving picture showing the switching dynamics of the virtual-moving MLA is presented in Movie S1, wherein the switching results of the periodic focused beam patterns are provided at the low and fast-switching frequencies between two focused states. In Table 1, the detailed specifications of the LF imaging system comprising the virtual-moving MLA are listed.