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Liquid crystal (LC) lenses with circular hole-patterned electrodes possess the excellent capabilities of tunable focal lengths. In this paper, we demonstrate the performance of a specific LC lens with tunable coaxial bifocals (CB) synthesized via photopolymerization of LC cells. The characteristics of tunable CB are clearly exhibited when the voltage applied is continuously increased, eventually disappearing until only one focus is left when significantly higher voltages are applied. We simultaneously demonstrate two types of tunable CB LC lenses fabricated via different photocurable processes and determine their optical functions.
©2012 Optical Society of America
1. Introduction
Given their specific electro-optical characteristics, liquid crystals (LCs) are usually used to study and fabricate optical devices for applications. The study on LC lenses began in the 1970s and became a popular topic because of their unique optical capabilities. Recently, numerous studies on LC lenses have focused on certain fields, including ophthalmic applications [1], aberration compensation for Blu-ray DVDs [2], imaging systems [3, 4], 3D display systems [5], and so on. In general, LC lenses and conventional LC cells are similarly structured: they have a LC layer sandwiched between parallel glass substrates with conductive thin films. When LC lenses are operated under applied voltages, the director distribution of LC molecules is induced to form a spatially quadratic distribution of refractive indices in the cells. Thus, an incident light beam passing through the cell will be focused or defocused. Numerous types of LC lenses have been proposed, such as the spherical-shaped LC lens [6], LC lenses with inhomogeneous polymer network [7], and hole-patterned LC lenses [8].
In general, LC lenses have electrically tunable focal lengths. Multi-focal lengths can be achieved by varying the applied voltages, with one focus corresponding to one applied voltage. Lenses with two coaxial focuses had been proposed and realized in liquid lenses [9, 10] and LC lenses [11, 12]. In the current study, they are referred to as the optical feature of coaxial bifocals (CB). Tunable CB LC lenses have potential applications in different fields. Single tunable CB LC lenses can be used in multi-layer [13] optical data storage because of its tunable focal lengths. For a microlens array composed of tunable CB LC lens units, the viewing depth in autostereoscopy, such as in integral photography [14], is largely improved. If these lenses are carefully designed and fabricated, suitable specifications can be achieved for more applications. In the present paper, we demonstrate a method of photopolymerization to obtain tunable CB LC lenses. Photopolymerization is a common process used to treat LC cells for certain applications, such as stabilization of LC molecules and improvement of the optical response time. Here, photopolymerization is used to modify properties in the central area of LC cells. Photopolymerized LCs located in the central area exhibit a reorientation behavior different from those located in the peripheral area without photopolymerization under applied voltages. If the central area is exposed to UV light for a significant length of time, the directions of LCs can be set to create an intrinsic focus. The peripheral area without UV exposure still retains the feature of tunable focal lengths. By contrast, if the UV-exposed area is treated for a short period of time, the slight change in the exposed area also affects the LC reorientation. Therefore, areas with and without UV exposure exhibit the characteristics of tunable focal lengths but have different properties.
2. Prior LC lens structure and tunable CB LC lens fabrication with photopolymerization
In Fig. 1 , a previously prepared LC lens with a circularly hole-patterned electrode [8] primarily consisting of two parallel glass substrates was adopted. A thick substrate with a circularly hole-patterned aluminum (Al) or indium tin oxide (ITO) electrode was used as the upper plate, whereas a thin substrate with a whole ITO film was used as the bottom plate. Both glass substrates were coated with polyimide (PI) and mechanically rubbed to promote a homogeneous LC alignment. Two strips of Mylar spacers were placed along the opposite sides of the cell boundary to control the cell gap. Finally, the completed empty cell was injected with material mixed with LCs, a reactive mesogen (RM257), and a photoinitiator via the capillary effect. In our previous work, we demonstrated occurrence of linkage formation between zigzag and disclination lines when LC lenses were operated for a long time [15]; this phenomenon should be prevented when fabricating this kind of LC lens. Some crucial specifications of the LC lenses are as follows: circularly hole-patterned diameter, 7 mm; LC layer thickness, 125 μm; upper glass substrate thickness, 1.4 mm; and bottom glass substrate thickness, 0.7 mm.
Fig. 1 Cross-section scheme of a liquid crystal (LC) lens with a circularly hole-patterned electrode. The hole-patterned electrode can be constructed with transparent or opaque conductive films such as indium tin oxide (ITO) or Al. The cell consists of a homogeneous alignment of LCs.
A material mixed with RM257 (Merck), a photoinitiator (Iragcure 651, Chiba), and LCs (E7, Merck) at a weight ratio (wt. %) of 3.0:0.14:96.86 was prepared. The completely mixed material was injected through capillary action into empty cells on the 100 °C hot plate. Voltages (from 0 Vrms to 100 Vrms) were applied to the completely injected LC at a slow increasing rate to prevent the occurrence of disclination lines. The applied voltages had a square waveform and a frequency of 1 kHz. The LC cells were further modified via special photopolymerization to fabricate tunable CB LC lenses. A homemade photo-mask from a printed slide film and with a clear circular area (~3.5 mm in diameter) over the cell was used and is schematically shown in Fig. 2 . The LC cells were exposed to UV light at a power of 6 mW/cm2 under applied voltages. The optical performance of the CB LC lenses differed at different UV exposure times. In this study, two LC lens types, namely, Type-A and Type-B, exposed in UV light for 2 and 2.5 minutes under 100 Vrms voltages, respectively, are reported. Both types exhibit the characteristics of tunable CB LC lenses, and their optical performances are demonstrated in the subsequent sections.
Fig. 2 Schemes of a photo-mask and the LC cell configuration for the fabrication of tunable CB LC lens via photopolymerization: (a) a homemade photo-mask from a printed slide film has a clear circular area approximately 3.5 mm in diameter; and (b) CB LC lens structure with a circularly patterned electrode. The photo-mask comes into contact with the cell during UV exposure under an applied voltage of 100 Vrms.
3. Optical characteristics of CB LC lenses with experimental measurements
The optical characteristics of the fabricated CB LC lenses were measured using a widely used experimental setup [16] to observe the interference patterns in the LC cells, which were recorded with a charge-coupled device (CCD) camera. The experimental setup had a He-Ne laser collimated and expanded light beam (λ = 632.8 nm), which was a normal incident when the tunable CB LC lens was placed between a pair of crossed polarizers. The rubbing direction of the LC cells was 45° with respect to the polarization of both polarizers. Figure 3 shows the interference patterns of two typical CB LC lenses (i.e., Type-A and Type-B) without an applied voltage. Figure 3(a) shows the experimental observation of an optical interference in a Type-A LC lens, which was developed via UV exposure for 2 minutes and has a circular central area ~3.5 mm in diameter. No interference pattern was observed in the cell without an applied voltage. By contrast, Fig. 3(b) shows the results of a Type-B LC lens under cell conditions similar to that of the cell shown in Fig. 3(a), except for a longer UV exposure time (2.5 minutes). An intrinsic interference pattern occurred in the cell without the applied voltage, which resulted in an intrinsic focus.
Fig. 3 Interference patterns for Type-A and Type-B LC lenses. (a) Type-A LC lens after UV exposure for 2 minutes. No interference pattern was detected in the cell without an applied voltage. The dark circle in the center of the LC cell after UV exposure represents the boundary of the UV-exposed area. (b) Type-B LC lens after UV exposure for 2.5 minutes, with other cell conditions the same as in Fig. 3(a). An intrinsic interference pattern can be seen in the cell without an applied voltage, indicating the existence of an intrinsic focus. The symbol on the right side of the figure shows the rubbing direction (labeled R) in the cell and the polarization of a pair of crossed polarizers (labeled A and P) in the experimental setup.
3.1. Type-A LC lenses
Type-A LC lenses are processed with a shorter of photopolymerization time. No obvious fixed interference patterns occurred in the entire circular area of the cell (7 mm in diameter) with or without UV exposure. When the voltages in the cells were gradually increased, the directions of the LC molecules with positive dielectric anisotropy were reoriented along the electric field so that the ideally spatially quadratic distributions of the refractive indices occurred in the form of interference patterns. Figure 4 shows a sequence of interference patterns for a Type-A LC lens under different applied voltages. The difference in the interference patterns in the UV-exposed and unexposed areas are highly obvious and imply that the reorientations of the LCs in the exposed and unexposed areas suffer different degrees of constraints. The difference in the interference patterns for both areas was gradually reduced when a higher voltage (100 Vrms) was applied. Finally, only one smooth and continuous interference pattern was left in the cell when voltages above 140 Vrms were applied.
Fig. 4 Interference patterns for a Type-A LC lens under different applied voltages: (a) 0, (b) 40, (c) 100, and (d) 180 Vrms. The red circle indicates the boundary of the UV-exposed areas. The difference in interference patterns in the exposed and unexposed areas is significant. When the applied voltages were increased, the variations in the interference patterns in both areas were independent. When a higher voltage (140 Vrms) was used, the interference patterns in both areas gradually merged into a single interference pattern. The symbol on the right side of figure indicates the rubbing direction (labeled R) in the cell and the polarization of a pair of crossed polarizers (labeled A and P) in the experimental setup.
We also observed and measured the focusing properties of the Type-A LC lenses. An expanded and collimated He-Ne laser beam was normally incident to the cell, in front of which a polarizer with a polarization parallel to the rubbing direction of the cell was placed. When a 40 Vrms voltage was applied to the cell, two focuses located 33 and 80 cm away from the cell were observed. The results are shown in Fig. 5 . The optical characteristics of the CB LC lens were clearly observed.
Fig. 5 Optical focuses for a Type-A LC lens at 40 Vrms: (a) one focus located 33 cm away from the cell, and (b) the other focus located 80 cm away from the cell. The focal lengths were measured through experimental observations of the focal points of the expanded laser beam.
We measured the variations in the CB of the cell under different applied voltages to evaluate the tunable capabilities of the Type-A LC lenses. The experimental results are shown in Fig. 6 . The coaxial bifocals were individually formed from two areas. One was the UV-exposed circular area with 3.5 mm in diameter, and the other was the 7 mm diameter circular unexposed area. When an expanded He-Ne laser beam was normally incident to the LC lens, the inner and external light beams were individually focused to monitor the variations in the LC distributions in both areas under different applied voltages.
Fig. 6 Characteristics of tunable CB for a Type-A LC lens under different applied voltages. At applied voltages below 30 Vrms, one tunable focus from an inner laser light was out of the focal length of 80 cm. At 40 Vrms, the properties of CB were observed. At 140 Vrms, only one focus was left in the cell.
3.2. Type-B LC lenses
Figure 7 shows the variations in the optical interference patterns for a Type-B LC lens with increasing applied voltages. A polymer network was formed after a long photopolymerization time, which stabilized the reorientation of the LC molecules located in the exposed area. Therefore, an intrinsically fixed interference pattern was observed regardless of the applied voltages. On the other hand, LC molecules located in the unexposed area still varied with varying applied voltages, which contributed to the development of tunable focuses in the cell. In Fig. 7(a), the strange circular texture near the interface between the exposed and unexposed areas may have been caused by diffraction during UV exposure. At much higher applied voltages, this strange texture gradually faded.
Fig. 7 Interference patterns for a Type-B LC lens under different applied voltages: (a) 0, (b) 30, (c) 100, and (d) 180 Vrms. The red circle indicates the boundary of the UV-exposed areas. An intrinsically fixed interference pattern is clearly seen in the exposed area after photopolymerization for 2.5 minutes. When the applied voltages increased, the interference patterns in the exposed area remained constant, whereas those in the unexposed area varied with the applied voltages. The symbol on the right side of the figure indicates the rubbing direction (labeled R) in the cell and the polarization of a pair of crossed polarizers (labeled A and P) in the experimental setup.
Figure 8 shows that two coaxial bifocals, located 42 and 30 cm away from the cell, were formed in the Type-B LC lens under an applied voltage of 30 Vrms.
Fig. 8 Optical focuses for a Type-B LC lens under an applied voltage of 30 Vrms: (a) one focus was located 42 cm away from the cell, and (b) the other was located 30 cm away from the cell. The focal lengths were measured through experimental observations of the focal points of the expanded laser beam.
We also measured the characteristics of the tunable CB for the Type-B LC lenses as shown in Fig. 9 . Initially, the two focuses were very different from each other, mainly because of the significant difference in the LC distributions of the exposed and unexposed areas in the cell. The two focuses gradually became closer as the applied voltages increased, and merged into one focus at 100 Vrms. At applied voltages higher than 100 Vrms, the two focuses gradually separated from each other. These results indicate that a smooth connection of interference patterns occurred when the cell was subjected to a 100 Vrms voltage.
Fig. 9 Characteristics of a tunable CB for a Type-B LC lens under different applied voltages. An intrinsically fixed focus existed in the inner part of the cell after photopolymerization, regardless of the applied voltages. The variation in the other tunable focus with the applied voltages is similar to that of conventional tunable LC lenses.
Finally, we demonstrate the capabilities of a Type-B LC lens used in an imaging system. A polarizer was placed in front of the CCD camera, with the polarization parallel to the X-axis in the coordinate. A Type-B CB LC lens was placed in front of the polarizer, and the mechanical rubbing direction was also parallel to the X-axis. A real object of text was placed a suitable distance away from the Type-B LC lens. We observed and recorded the text images with respect to the different conditions in the imaging system. The conditions are as follows: without a Type-B LC lens, with a Type-B LC lens but without an applied voltage, and with a Type-B LC lens and an applied voltages of 100 Vrms. The imaging system is shown in Fig. 10 .
Figure 11 shows the imaging performance of the tuning Type-B CB LC lens for an object of text words. Figure 11(a) shows a blurred text image when no Type-B LC lens was placed in the imaging system. When a Type-B LC lens was used in front of the CCD camera but without an applied voltage, a clearer image was obtained in the central area of the LC lens as shown in Fig. 11(b). This clearer text image resulted from the intrinsic focal length in the Type-B LC lens. The image outside red circle remained blurred. In Fig. 11(c), when a 100 Vrms applied voltage was used, the images in both areas became clearer because the same focal lengths were obtained. A small difference in the images in the central area with and without applied voltages was induced by changing the LC orientation. Some LC molecules were not fully aligned with the ideal directions after UV exposure, resulting in non-ideal intrinsic focus. When a 100 Vrms voltage was applied, the orientations of the LC molecules were modified, and a better focus was achieved.
Fig. 11 Comparisons of the imaging capabilities of a tunable Type-B LC lens in the imaging system: (a) without a Type-B LC lens; (b) with a Type-B LC lens but without an applied voltage; and (c) with a Type-B LC lens and an applied voltage of 100 Vrms. A blurred image was observed when no Type-B LC lens was used. When a Type-B LC lens was used but without an applied voltage, a clear image was observed in the central area. When a 100 Vrms voltage was applied with the Type-B LC lens, an overall clear image was obtained because the same focus was achieved in both areas.
4. Conclusion
We have demonstrated the development of tunable LC lenses via photopolymerization. Type-A and Type-B LC lenses are obtained when LC cells are exposed to UV radiation at different exposure times. For the Type-A LC lens, lens function is not possible without an applied voltage. When the applied voltage is increased, two tunable focal lengths are observed in the cell, which eventually merge into one focus at higher applied voltages. On the other hand, the Type-B LC lens possesses an intrinsically fixed focus without an applied voltage. When the applied voltage is increased, the intrinsic focus retains the same value, whereas the other focus is tunable with respect to various applied voltages. In the future, we will carefully design and fabricate a tunable CB LC lens array for use in integral photography to improve the viewing depth performance.
Acknowledgments
This work is supported by the National Science Council (NSC) in Taiwan under Contract No. 100-2221-E-006-167.
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