High-resistance liquid-crystal lens array for rotatable 2 D / 3 D autostereoscopic display

A 2D/3D switchable and rotatable autostereoscopic display using a high-resistance liquid-crystal (Hi-R LC) lens array is investigated in this paper. Using high-resistance layers in an LC cell, a gradient electric-field distribution can be formed, which can provide a better lens-like shape of the refractive-index distribution. The advantages of the Hi-R LC lens array are its 2D/3D switchability, rotatability (in the horizontal and vertical directions), low driving voltage (~2 volts) and fast response (~0.6 second). In addition, the Hi-R LC lens array requires only a very simple fabrication process. ©2014Optical Society of America OCIS codes: (220.0220) Optical design and fabrication; (230.3720) Liquid-crystal devices. References and links 1. B. Javidi and F. Okano, Three-dimensional television, video, and display technologies, (Springer-Verlag, 2002), pp. 461. 2. H. H. Refai, “Static volumetric three-dimensional display,” IEEE J. Displ. Technol. 5(10), 391–397 (2009). 3. M. Gately, Y. 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Introduction
There is interest in pursuing more realistic images on displays permitted by advancements in technology.Because 3D displays provide depth information that is lacking in 2D displays, 3D displays play an important role in next-generation display technology.Autostereoscopic 3D displays have certainly entered the mainstream in recent years, thanks to the convenience of achieving the 3D effect without wearing glasses [1][2][3][4][5][6][7][8][9][10].The most common methods in autostereoscopic 3D technology are fixed parallax barriers and lenticular lenses [11][12][13][14].However, the 2D image quality is degraded by the use of these approaches; when the ability to switch between 2D and 3D display modes is a necessary function, the image quality in 2D mode must be maintained.In addition, the use of portable devices has been rising sharply for the past decade, and the displays of such devices do not only show images in the vertical direction but also offer the horizontal mode (Fig. 1).Therefore, rotatable functionality is a standard requirement for a portable 3D display.There are several technologies can achieve 2D/3D switchable functionality, such as sequential backlight systems [15], switchable barriers [16] and switchable LC lenses [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].Sketches and the various features of these technologies are shown in Table 1.The main advantage of sequential backlight technology is that it can provide a full-resolution 3D image to the observer.However, the viewing freedom in 3D mode is narrow; a 3D image can be shown only in the normal direction.In contrast, switchable barriers and switchable LC lenses can provide wider viewing freedom than sequential backlight systems.However, only switchable barriers and switchable LC lenses have the potential for rotatable functionality.

3D 3D
Nonetheless, the switchable barrier has a significant drawback: low brightness.Therefore, according to the above consideration of desirable features, an LC lens is the best candidate for mobile applications.Among current types of LC lenses, only an electric-field-driven LC lens (ELC lens) has the potential to yield 2D/3D rotation because it has no fixed physical lens structure.In a previous work, an external-electrode LC lens (Fig. 2 (a)) has been proposed that utilizes a glass substrate as a high-K material to smooth the electric field, producing a gradient distribution of the electric field in the LC cell.However, such a high-K material also increases the operating voltage (> 50 volts).Thus, an internal-electrode LC lens (Fig. 2 (b)), which can provide a lower operating voltage than the external-electrode lens, has been proposed [18].However, without high-K material, the fringing electric field spreads only around the electrodes; therefore, the LC molecules in the central region are not driven, and an internal-electrode LC lens cannot form an ideal lens shape.
In this paper, we propose an internal-electrode LC lens with 2D/3D switchable and rotatable functionality by incorporating a high-resistance (Hi-R) layer [32].The Hi-R LC lens is coated with a high-resistance layer within the cell, thus permitting the establishment of a continuous electric field with a gradient profile.In this manner, a lens-like profile can be formed.The most important concern when using a Hi-R layer is to avoid the electric-field distortions caused by crossed electrodes, thus maintaining high-performance 3D images in both the horizontal and vertical directions.A low operating voltage and fast switching time can be obtained using this design, as well.Moreover, the proposed Hi-R LC lens array requires only a very simple layout circuit with a similarly simple fabrication process.

Structure of single-layer Hi-R lenticular LC lens
Placing internal electrodes in an LC lens can yield lower driving voltages because the applied voltage can affect the LC molecules directly.However, because of the large slit between the electrodes, an internal-electrode LC lens can only share a weak electric energy and distribution of phase retardation.Most of the energy concentrates on the electrodes; the LC molecules can only be driven near the electrodes.Therefore, to overcome these issues, a high resistance-layer is coated onto the electrodes to generate a gradient voltage distribution in the LC cell.The LC molecules under the slits can also be affected by the electric field.As shown in Fig. 3(b), V D and V com are applied to the side and central electrodes of the LC lens, respectively.According to the function of the resistance layer, the voltage takes on gradient distribution on the resistance layer, and the voltage gradually changes from high to low for better phase retardation [33].Therefore, the LC lens profile is not controlled by the fringing field but directly by the gradient voltage.In addition, if all electrodes on the same substrate are driven by V com , the entire layer will perform as a flat ground electrode.As shown in Fig. 3(b) and Fig. 3(c), by changing the driving method, we can switch the electrodes from a strip to a flat form in the same layer.

Modeling of Hi-R LC lens
To further investigate the high-resistance LC lens, we construct an R-C circuit model to determine the parameters of the LC cell, as shown in Fig. 4. The resistance R in Fig. 4 is calculated using Eq.(1).To calculate the capacitance C in Fig. 4, the structure is first considered to be controlled by a uniform electrode field.The induced dipole moments of the two directions parallel and perpendicular to the LC direction are used.The equivalent polarization is shown in Eq. ( 2) and Eq. ( 3).The electric field is along the z direction, which induces the polarizations P and P  .The equivalent capacitance, C, can be calculated from z  as shown in Eq. ( 4).
From the model, it can be seen that the resistance of the high-R layer should be controlled within the proper range.If the resistance is chosen to be too low, the resistance from the hetero junction will consume a large proportion of the applied voltage.However, if the resistance of the Hi-R layer is too large, only a small proportion of the current can reach the center region if V 1 is higher than V 0 .These two situations both result in no phase retardation in the central region.

Control Layer (ITO)
High R Layer LC Layer Resistance from hetero junction :

Resistance of high R layer :
Capacitance of LC layer : Fig. 4. The R-C circuit model of the high-resistance LC lens.
where r  is the resistivity of the Hi-R layer.  22 0 sin cos sin cos sin cos where d and A are the thickness and area of the meshed element, respectively.

Rotatable lenticular LC lens
Because of the increasing popularity of portable devices, the rotatable functionality of a display in 3D mode has become a requirement that must be considered.To achieve rotatable functionality in a lenticular LC lens, the two sets of stripe electrodes should be arranged in different directions.The structure is shown in Fig. 5 (a).However, when we apply a voltage to a top or bottom electrode in this structure, there is no full flat electrode on the other side.
According to the structures and electrode fields of the LC cell, the LC cell will not behave as a lenticular lens.To form the shape of a lenticular lens, the variation of the electrode field should be changed only in one direction.The high-resistance layer can be used to overcome this issue.
According to the switchable functionality of the electrodes, we propose a rotatable lenticular LC lens with a high-resistance coating on both inner electrodes.To form a lenticular lens in two directions, the top electrodes and the bottom electrodes should be nearly perpendicular to each other.To achieve switchable functionality in two directions, the top and bottom electrodes are coated with high-resistance material, as shown in Fig. 5 (b).When all bottom electrodes are connected to V com and the top electrodes are driven by alternating voltages, V D and V com , an LC lenticular lens shape will form in the horizontal direction, as shown in Fig. 5 (c).Because of the application of the same driving voltage on each electrode, the bottom electrodes behave as a full electrode with the ground voltage.However, the voltage distribution on the top side becomes a gradient and continuous distribution because of the function of the high-resistance layer.Furthermore, in the vertical direction, the LC lens can be operated in the same manner, as shown in Fig. 5 (c).The bottom electrodes are driven by V D and V com alternately, and all electrodes on the top are driven by V com .

Specifications
We designed the Hi-R LC lens to generate 2 views of an autostereoscopic image in the vertical direction on an LCD panel and 4 views of an autostereoscopic image in the horizontal direction on the same panel.The specifications and parameters are shown in Table 2.

Fringe pattern
To prove the effect of the high-resistance layer, a fringe pattern is an obvious method of demonstrating the result of the LC phase.In Fig. 6, the operated LC cell is observed under a crossed polarizer; the alternate white and black patterns represent the phase variations.Here, V D and V com are 2 and 0 volts, respectively.And the waveforms were square wave with constant 1 KHz frequency.The phase variation in the LC lens without the Hi-R layers is discontinuous and bent under the horizontal electrodes, as shown in Fig. 6 (b).Because V com is applied only on the electrodes of the bottom substrate, the electric field cannot reach the centers of the slits between the electrodes.Thus, the electric fields of the vertical electrodes bend strongly toward the horizontal electrodes.Therefore, without the Hi-R layers, the electric-field distribution cannot form a lenticular LC lens profile.In contrast, the fringe pattern in the Hi-R LC lens exhibits a continuous and smooth phase variation, so it can produce a good lens shape, as shown in Fig. 6 (a).The result demonstrates that the n eff does not change gradually near the positions of the electrodes.Although there is a high-resistance layer, the electrode and high-resistance layer are connected in parallel.This means that the effective resistance must be smaller than the total resistance of the electrode, and the Hi-R layer, so the electrode will interfere with the driven gradient.
Therefore, a narrower electrode width will generate better performance.The electrical fields propagate smoothly from the vertical electrode to the planar electrode, which is a horizontal electrode coated with a Hi-R layer.Therefore, the phase distribution of the lenticular lens in the Hi-R LC cell is better than that in the LC cell without Hi-R layers.

Rotatable function
To demonstrate the 2D/3D switchable and rotatable functionalities on the same LC lens, the focusing ability becomes a criterion by which to judge the direction of the lenticular lens.The focusing ability of the Hi-R LC lens can be observed by using a parallel light, and the CCD locate at the focal plane of LC lenticular lens.When the parallel light passes through an LC cell voltage applied to the cell, there is no significant pattern on the CCD, as shown in Fig. 7 (a).If the driving voltage is applied along the vertical direction of the cell, the LC lenticular lens array forms in the horizontal direction.Therefore, the focused lines appear on the CCD as shown in Fig. 7 (b).The result is similar when the driving voltage is applied to the horizontal electrodes; the LC lenticular lens array forms in the vertical direction, as shown in Fig. 7 (c).The full video is available at the following web address: http://youtu.be/5LA9o0XPABw.

Angular crosstalk distribution
The angular distribution of the 2D/3D switchable autostereoscopic display achieved by operating the Hi-R LC lens array in the horizontal direction is shown in Fig. 8.The Hi-R LC lens simulation results indicate that defects near the electrodes cause leakage.The width ratio of all electrodes and lenses corresponds to a pitch of approximately 0.3.This defect will cause a high crosstalk in 3D mode.When the cell is operated at 1.5 volts, the multi-view crosstalk in the horizontal direction is 34.3%, as shown in Fig. 8 (b).In the vertical direction, the width ratio of all electrodes and lens corresponds to a pitch of approximately 0.06, as shown in Fig. 8 (a).When the cell is operated at 2 volts, the crosstalk in the vertical direction is 9.8%.(c) (d)   To find out what is the reason will cause the crosstalk on Hi-R lens, the effective refractive index (n eff ) is measured and show on Fig. 9. Compare with the profile of ideal lens, the distribution of n eff is too flat at the center and the edge of LC-lens.Therefore, the light will not refract to the designed angle.We believe this phenomenon comes from the electrode width of the Hi-R LC lens.Because of manufacturing limitations, the electrode width of the Hi-R LC lens of our sample is around 15 μm.According to these parameters, the effective refractive index was simulated using 2DiMOS.The ratio of electrode width to lens size varies from 10% to 40%, and the sketch is shown on Fig. 10 (a) and (b).The parameters of LC lens on simulation are shown in Table 3.The result indicates that the n eff does not change gradually near the position of the electrode, as shown in Fig. 10 (c).Although there is a highresistance layer, the electrode and the high-resistance layer are connected in parallel.This means that the effective resistance must be smaller than the total resistance of the electrode and the Hi-R layer, and the electrode with interfere with the driven gradient.Therefore, a narrower electrode width will generate better performance.Figure 10 (d) shows the n eff distribution of an ideal Hi-R LC lens with a very small electrode width.Therefore, lower crosstalk could be achieved if narrower electrodes were used.The 5μm electrode width can be easily achieved by conventional TFT-LCD company, thus shall be able to yield much lower crosstalk for the dual-directional Hi-R LC-lens.

Response time
To fit the power of the lens, the cell gap of LC Lens is 50 μm in our experiment.According to rising time, rise  of LC devices, larger cell gap results slow focusing time which is proportional to 2 d from relaxing state to focusing state, as Eq. ( 5) shows.
  where rise  is the function of cell gap d, rotational viscosity 1  , elastic constant K, threshold voltage th V , and applied voltage V .To overcome slow response of LC cells, over-drive is employed for accelerating the response times in LCD industry.By optimized the over driving voltages and switching to target operation, the LC response time can be much reduced.In our experiment, the optimized over-drive value is about 4 volts, and the rising time is close to 0.6 second.Figure 11 shows the sequential photograph of LC lens form non-focusing to focusing on different period.
To fit the power of the lens, the cell gap of LC Lens is 50 μm in our experiment.According to rising time, rise  of LC devices, larger cell gap results in slow focusing time which is proportional to 2 d from relaxing state to focusing state, as Eq. ( 5) shows.
  where rise  is the function of cell gap d, rotational viscosity 1  , elastic constant K, threshold voltage th V , and applied voltage V .For current LCD, which has cell gap around 5um, the response time is about 6ms with over-driving technology [34].According to the listed equation, LC-lens with 50um cell gap shall be around 6ms × 10 2 = 600ms.In our experiment, the optimized over-drive value is about 4 volts, and from the experiment results, our rising time is close to 600ms which is similar to the theoretical calculation.Figure 11 shows the sequential photograph of LC lens form non-focusing to focusing on different period.

Conclusion
A High-Resistance Liquid Crystal (Hi-R LC) lens that is capable of 2D/3D switching and 3D rotation is proposed.Using high-resistance layers, a continuous gradient electric-field distribution can be generated within the cell.Consequently, high-quality 3D images for horizontal and vertical viewing can be obtained.In our prototype, the crosstalk of the twoview system is below 10%, but in the rotated direction, the crosstalk of the multi-view system is approximately 34.3% because of the slanted 4-view design, but could be much improved by narrowing the electrode width.The Hi-R LC lens requires only a low operating voltage and a simple driving system.Finally, the Hi-R LC lens was successfully implemented on an LCD for 2D/3D switching and 3D rotation functionality, thereby demonstrating its high potential for application in future mobile autostereoscopic displays.

l
are the cross section and length of the resistance.s R is the sheet resistance.According to the equation, to have an optimized distribution of gradient voltage, the range of resistivity of the Hi-R layer is from 1 to 10 m  .

Fig. 5 .
Fig. 5. Sketch of the rotatable high-resistance liquid-crystal lens (Hi-R LC lens): (a) without high-resistance layer, (b) with high-resistance layer, (c) the structure in the X-Z(horizontal) plane, and Y-Z(vertical) plane.

Fig. 6 .
Fig. 6.The experimental results of a fringe pattern in a cross-electrode LC lens (a) with highresistance layers and (b) without high-resistance layers.

Fig. 7 .
Fig. 7. Test of the focusing ability the Hi-R LC Lens: (a) without any driving voltage, (b) operating the Hi-R LC lens in the horizontal direction, and (c) operating the Hi-R LC lens in the vertical direction (Media 1).

Fig. 8 .
Fig. 8.The angular distribution of the Hi-R LC Lens in (a) the vertical direction and (b) the horizontal direction.

Fig. 9 .
Fig. 9.The comparison of the effective refractive index between ideal lens and Hi-R LC Lens.

Fig. 10 .
Fig. 10.The influence of the ratio of electrode width on the effective refractive index (neff): (a) structure of low ratio of electrode width, (b) structure of high ratio of electrode width, (c) various ratios of electrode width and (d) the ideal case.

Table 1 . Review of 2D/3D Switchable Technology
 Full resolution  Narrow viewing freedom  Simple process  Wide viewing freedom  Low brightness  Wide viewing freedom