Abstract

The use of pixel-level tunable liquid crystal (LC) lenses to steer the images shown on a flat panel display in full resolution for auto-stereoscopic applications was proposed. Micro lenticular LC lenses of different full widths ranging from 40 to 140 µm were designed and fabricated with laser patterned transparent ITO electrodes as narrow as 10 µm in width and two LC materials of high birefringence. Optical characterization of the lenses showed consistent parabolic phase profiles closely matched to that of ideal lenses. A proof-of-concept device with an array of tunable micro LC lenses each covers two sub-pixels of different colors was fabricated and applied on a standard computer monitor to confirm its capability of sub-pixel-level image steering.

© 2014 Optical Society of America

1. Introduction

Stereoscopic displays have been widely used in the products of consumer televisions and specialist image observation screens. As the separated views for left and right eyes are displayed simultaneously, the resolution of each view is limited to half of that of the display panel. Such a fundamental limitation is a particular concern for mobile phone displays, because of the small display area (usually a few inches in diagonal) and the finite size of sub-pixels for different colors (currently 20 + µm). It would be ideal that a mobile phone display with “a glass-free 3D experience” could have the same resolution as that of its 2D images and further have the viewing mode switchable between 2D and 3D if needed such as when viewing text contents [1,2]. Conventional auto-stereoscopic displays based on spatial multiplexing with fixed lenticular lens arrays or parallax barriers are not suitable for this purpose because of the reduced image resolution and brightness and the difficulty in switching between different viewing modes [3,4]. Other 3D display techniques also have their limitations. Holographic 3D displays are in principle capable of delivery high resolution 3D images but it needs complicated optics setup and a lot of computing power and are currently only practical for display still images [5]. A newly developed guided-wave illumination device based on light-emitting diodes permits the rendering of high-resolution, full-parallax 3D images in a very wide view zone [6], but the image resolution remains to be improved and the display of all the 64 images as suggested for real time videos without crosstalk will be very challenging.

Liquid crystal (LC) optical devices have already been extensively used in adaptive optical systems to compensate aberrations [7], and as spatial light modulators [8], active/adaptive lenses [9,10]and bandpass filters [11]. The reported size of the demonstrated LC lenses, defined here as the short length of the circular/lenticular configuration, ranges mostly between a few hundred micrometers and a few tens of millimeters [1215]. There was also a report of less than twenty micrometers with the lenses formed using a carbon nanotube based electrode structure [16]. However, there are a number of issues regarding the operation and performance of these LC lenses which remain to be resolved, such as high driving voltages and in particular non-ideal phase profiles prone to optical distortions. This makes it difficult to apply the developed LC lens technology directly to create high quality lenses of 20 + µm sub-pixel size for a high definition 3D viewing experience on modern mobile phones. Moreover, the latest developments in auto-stereoscopic 3D displays utilized a lenticular LC lens array on top of a tablet PC display (10.1 inch) to switch between 2D and 3D views [17,18]. Each LC lens covers two or more sub-pixels spatially, but even with spatial multiplexing it can only achieve a resolution which is half of the original display resolution and the viewing distance as reported was around 800-900 mm which is a bit far for mobile phone displays. Separately, a multi-electrode driven scheme was also proposed to form a refractive index curve to emulate that of an ideal lens in order to reduce the crosstalk between different views, however, the lens size was rather large because of the width of the electrodes [19].

In this study, we propose a scheme for full resolution glass-free 3D experience. Sub-pixel-level tunable lenticular LC lens array is designed and fabricated to preserve the maximum possible resolution as the 2D display panel. High birefringent nematic LCs are used to realize the large steering angles, and the transparent electrodes made of Indium Tin Oxide (ITO) are patterned with an infrared (IR) fiber laser to fabricate the high quality LC phase lenses. A proof-of-concept demonstrator consisting of lenticular array LC lenses is assembled to confirm the color separation and image steering at the sub-pixel level on a computer monitor.

2. An auto-stereoscopic approach for mobile displays

A multiplexing scheme using interlaced spatial and temporal beam steering for auto-stereoscopic displays is proposed [20]. It is based on the use of a carefully designed array of lenticular micro LC lenses with a layered structure and a thin form factor, suitable to be employed on top of small size display panels. Each of the lenticular micro LC lenses is realized using a parabolic phase profile generated by LC materials between patterned electrodes. The electrodes are shared between neighboring lenses to reduce the lens foot prints. Every such a lenticular lens covers two columns of the sub-pixels on the display panel, and each half of the lens will be able to steer the light from the corresponding single column of sub-pixels. If the light emission from a single sub-pixel can be regarded as collimated and it only illuminates an area near the center of a half lens, to the first order approximation, we can treat all the half lenses as simple linear phase ramps, as illustrated in Fig. 1.

 figure: Fig. 1

Fig. 1 The proposed multiplexing scheme using interlaced spatial and temporal beam steering to obtain the maximum resolution for an auto-stereoscopic display. The phase profile of each half of the lenses illustrated here is approximated as a linear phase ramp. The multiplexing operation can be described in two steps: (a) Frame 1 – odd sub-pixels deflected to the left eye and even sub-pixels deflected to the right eye. (b) Frame 2 – odd sub-pixels deflected to the right eye and even sub-pixels deflected to the left eye. The phase pattern is shifted by one sub-pixel resulting in the swap of deflection directions.

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The light coming from two neighboring sub-pixels in the first frame will therefore be steered into two different directions for the left and right eyes, respectively, as shown in Fig. 1(a). For the subsequent image frame, the whole phase profile for the lens array will be shifted by one sub-pixel, as shown Fig. 1(b), in order to steer the light from each sub-pixels to the direction opposite to that in the previous frame. Due to the residual viewing effect of human eyes we will be able to “see” the two time sequential images as a single image with the same image resolution as that of the display panel itself.

Assuming that the light incident on the LC layer is collimated, and we wish to deflect the light by an angle of ϒ using a continuous linear phase ramp across the facet, as shown in Fig. 2. The maximum optical beam deflection angle, ϒmax, is given by

tan(γmax)=dΔna,
where d is the LC element thickness, Δn the LC birefringence, and a the width of display sub-pixels. The maximum phase delay δmax that can be imparted by the cell is given by Eq. (2),
δmax=2πΔndλ
where λ is the wavelength of the incident light.

 figure: Fig. 2

Fig. 2 Deflection of a plane wave by a LC cell with a linear phase ramp.

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It is appreciated that the light emitted from the sub-pixels in conventional liquid crystal displays (LCDs) is usually not collimated. As a result, the emitted light from each sub-pixel can illuminate more than one lenticular lens and generate undesired crosstalk. Because the proximity of the LC lens and the exit aperture of the corresponding sub-pixel, most of the energy will go through the aligned lenticular lens, especially when the distance between the LC lenticular layer and sub-pixel layer is equal to the effective focal length (EFL) of the LC lenticular lens and the output beam will be collimated and steered to the targeted eye. To further address this matter, additional optical measure can be taken to minimise the crosstalk.

3. Characterization methods

The LC cells used in this work consist of a LC layer sandwiched between two soda lime display glass substrates. All the LC devices were made in a cleanroom environment. The substrates are 0.55 mm thick with a 23 nm thick ITO layer on the inner surfaces. The sheet resistance of ITO layer is 100 Ω/□. The ITO coatings on the glass substrates were patterned by using a single mode nanosecond pulsed fiber laser (G3 SM-S00044_1, SPI Lasers, Southampton, UK.) working at 1062 nm wavelength, which is capable of achieving a ~10 µm patterning resolution. A homogeneous polyimide layer (AL-3046, JSR Co.) was spin coated and rubbed in an anti-parallel configuration on two substrates for the nematic LC alignment.

Two high birefringent nematic proprietary LC materials, denoted as LC1 and LC2, were used. LC1 has a birefringence of 0.29 at 510 nm wavelength at room temperature, and LC2 has a birefringence of 0.45 under the same conditions. We used cells of a thickness of 8 µm. Thus LC1 will theoretically be able to provide a maximum phase delay of 9.1π based on Eq. (2), and LC2 a phase delay of 14.1π.

When a square wave of 1 kHz is applied to the ITO electrode, the patterned electrode structure introduces a spatially varying electric field. This leads to a spatial variation in LC director orientations, hence changing the phase of the light passing through the lens. The measurement data of the LC cells filled with LC1 is presented in the following sub-sections as an example.

3.1 Cell configuration

A single LC test cell was used to measure the phase profile near the edges of a patterned ITO electrode, as shown in Fig. 3(a). It consists of four regions, denoted as zones A, B, C and D, respectively. These regions of interests are essentially the same as that of the LC lens that would be used in the auto-stereoscopic display for four different director/electrode geometries. The dashed line indicates the bottom substrate glass, the solid line indicates the top substrate glass, and the red arrows denote the rubbing directions of the alignment layers on the two substrates, respectively. Note that the electric field along the edges of the electrodes in zones A and B is perpendicular to the rubbing direction, which may generate disclination defects around the corners of the electrodes. The blue areas of Fig. 3(a) are covered with ITO. In the case of our test cell, the average LC layer thickness is 7.36 µm with a standard deviation of 0.41 µm. The center of cell gap is slightly thinner than edges, shown as color difference in Fig. 3(b) under white light illumination between crossed-polarizers [21].

 figure: Fig. 3

Fig. 3 (a) Schematic of a cell configuration with the rubbing directions marked for the top and bottom substrates and (b) the image taken as the cell is placed between two crossed-polarizers with the rubbing direction oriented at 45° with respect to the polarizer’s transmission axis.

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3.2 Phase profile measurement approach

The light steering ability of a LC cell is achieved by forming a spatially varying phase delay across the LC layer. To measure such a phase profile experimentally the method described in [22] was used, in which the optical transmission of the cell through crossed-polarizers is measured using a quasi-monochromatic light source and a high resolution microscope. By analyzing the resulting spatial variation of the intensity distribution we can calculate the corresponding phase profile using Eqs. (3) and (4), as well as using the calculated maximum phase delay value as the reference.

|δ|=Nπ+2tan1IcIp,N=0,2,4,
|δ|=(N+1)π2tan1IcIp,N=1,3,5,
where Ic is the light intensity transmitted through the crossed-polarizers, Ip the light intensity transmitted through parallel polarizers, and N an integer determined by the maximum phase delay value.

3.3 Phase profile measurement results

Each zone in Fig. 3(a) was examined separately, with a maximum phase delay of 8.4π based on Eq. (2). The LC director orientations, intensity profiles and the calculated phase profiles for each zone are presented.

Zones A & B

Sketches of the cross sections of zones A and B are shown in Figs. 4(a) and 4(b), respectively. The rubbing directions of both zones are parallel to the edges of patterned ITO electrodes, with a pretilted angle around 3-5 degrees. When a driving voltage is applied, LC directors in the region where both ITO are present are re-orientated to the resulting electrical field direction normal to the cell surfaces, with the degree of re-orientation depending on the magnitude of the field. As we move away from the region with two electrodes to the region with only one electrode, there is a gradual change of the electric field strength and direction in the LC layer (i.e. the fringe field region), which results in the LC director being re-orientated less and less. Eventually, the LC directors will remain uniformly in the pretilted angle and not be affected by the applied field as shown in the far left and far right ends of the Figs. 4(a) and 4(b), respectively.

 figure: Fig. 4

Fig. 4 LC director orientations of (a) zone A and (b) zone B when a voltage is applied between the two ITO coated substrates.

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The measured intensity profiles of zone A at various driving voltages are shown in Fig. 5. The bright and dark areas in the 1.4 V image are of the regions with the ITO electrodes on both sides of the LC layer and on one side only, respectively. The transition area in between is the fringe field region. The subsequent images with larger driving voltages are aligned to the 1.4 V image so the edge of the patterned ITO electrode stays at the same position. Each increase of the voltage represents one additional π phase change in the region with the ITO electrodes on both sides except the 5 V case, where the intensity can be seen to change between the maximum (bright) and minimum (dark) in sequence as shown in Fig. 5.

 figure: Fig. 5

Fig. 5 Intensity profiles of zone A at various driving voltages.

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The measured intensity profiles in zone B are mirror images of the ones in zone A, and, as a result, they are not presented here. The spatial phase variations in both zones were calculated from the intensity profiles using Eqs. (3) and (4). The resulting phase profiles measured at 510 nm are plotted in Fig. 6 for different applied voltages.

 figure: Fig. 6

Fig. 6 Phase profiles of (a) zone A and (b) zone B at varying driving voltages.

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In Figs. 6(a) and 6(b), the ITO electrodes are patterned at one side only and they are from 25 µm up and until 5 µm, respectively. Each curve represents a relative phase delay under a given voltage, with the zero phase set in the region with the ITO electrodes on both sides. As the applied voltage increases, the maximum phase delay in each case increases. All phase profiles exhibit some discontinuities in the transition region. This is mainly caused by the non-collimated nature of the microscope light source which has a finite (~10 nm) bandwidth and more importantly relatively large (~5°) half angle. Also the LC thickness is relative large (~8 µm), which is larger than the depth of field of the 40x microscope objective lens used in the measurement. Nevertheless a near-linear region can be seen around the middle of the phase transition, and this region can be used to steer the incoming light from a mobile display sub-pixel. We define the LC phase profile width, as the distance between the 10% and 90% of the maximum phase value at a specific driving condition. This increases from ~5 µm to ~20 µm as the applied voltage increases.

Zones C & D

The intensity profiles and LC director orientations of zones C and D were also measured as shown in Fig. 7. The rubbing direction was perpendicular to the patterned ITO edges in both zones. However, there is a defect region in zone C, as circled in Fig. 7(a), which breaks the continuity of the phase profile. These so called disclinations happen as the symmetry of LC director rotation is broken [23]. As a result we will only focus on using zones A and B for lens construction because no disclination defects appearing as the rubbing direction is parallel to the edges of the patterned ITO electrodes.

 figure: Fig. 7

Fig. 7 Intensity profile of (a) zone C and (b) zone D at 8.5 V, where the circle in (a) highlights the region of LC disclinations.

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4. Liquid crystal lens array

Based on the measured phase profiles of zones A and B in Fig. 6, the LC cylindrical lens was designed with a radius of ~20 µm, and an array of such LC lenses were fabricated with laser patterned ITO glass substrates. The laser used was working at 1062 nm wavelength and 10 W average power, and the patterned ITO electrodes have very smooth edges as shown in Fig. 8. The non-machined ITO tracks are ~10 µm wide, and the distance between two neighboring electrodes is ~40 µm.

 figure: Fig. 8

Fig. 8 Microscope image of patterned ITO electrode tracks.

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The intensity profiles of the resulting LC lens array made with LC1 were measured between crossed-polarizers at three driving voltages as shown in Fig. 9. As the driving voltage increases, more intensity fringes develop across the lens region between two electrode tracks.

 figure: Fig. 9

Fig. 9 Intensity images of the LC lens array made with LC1 at driving voltages of (a) 2.52 V, (b) 3.52 V and (c) 6.00 V.

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The measured phase profiles using our two high birefringent materials, LC1 and LC2, are plotted in Fig. 10 as a function of driving voltage. The maximum phase delay achieved by the LC lens was measured to be ~8.3π for LC1 and ~14.1π for LC2. The experimentally determined phase profiles were compared to the equivalent ideal parabolic lens profiles having the same phase delay and lens radius. The phase profiles of the ideal lens were calculated based on the GRIN lens structure described in [24] and converted to phase values through Eq. (2). An excellent agreement between the ideal phase profiles and the measured LC phase profiles can be seen in Fig. 11, showing that the fabricated LC lens not only has an excellent performance as a micro-lens, but it also has the potential of being able to reduce crosstalk in the proposed 3D display [19].

 figure: Fig. 10

Fig. 10 The measured phase profiles at varying driving voltages for the LC lenses made with (a) LC1 and (b) LC2, respectively.

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 figure: Fig. 11

Fig. 11 The comparison of the measured LC lens phase profiles to the ideal parabolic lens profiles.

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5. Proof-of-concept demonstration

A lenticular LC lens array was fabricated to demonstrate the steering effect for an auto-stereoscopic display based on the design shown in Fig. 1. Here we use only half of a LC lens to steer beams for the auto-stereoscopic application. A previously reported ZEMAX simulation based on the measured phase profile of our LC lenses showed a similar steering angle and irradiance distribution at the viewing plane to an equivalent ideal paraxial steering lens [25]. A 24 inch HD LCD monitor (Samsung S24B300B) was chosen for its relative large pixel size, ~277 µm in the horizontal direction for three sub-pixels (RGB). The design of the ITO electrode pattern is shown in Fig. 12, the ITO tracks are intended to cover the gaps between sub-pixels. The 80 µm regions between tracks are designed to cover one sub-pixel so that each of the half lens can steer one sub-pixel beam. The electrodes on each side, V1/V2, are driven in turn so that each sub-pixel is directed to each of the two eyes sequentially. The whole LC lens array panel is 40x50 mm in dimensions.

 figure: Fig. 12

Fig. 12 The LC lens design (top-down view) intended to steer the images at sub-pixel level on a 24” HD monitor.

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A schematic shown in Fig. 13 outlines the principle of our demonstrator, where the LC lens array is placed on top of the monitor. The distance between the LC layer and monitor pixels is greater than 1.1 mm, taking into account the LC lens substrate thickness and front cover of the monitor. As a result, the non-collimated light emitted from one sub-pixel may get into about nine half LC lenses, based on the assumption of a 30° diverging angle for each sub-pixel. Part of the neighboring sub-pixel colors can enter the half LC lens for the target sub-pixel and get directed to the wrong eye. Hence spatial crosstalk is expected during sub-pixel color separation and steering in this demonstration.

 figure: Fig. 13

Fig. 13 The schematic of the demonstrator (side view) with the LC lens array placed on top of the monitor.

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The red and green colors in every other pixel were switched on simultaneously for the demonstration, shown as the colored sub-pixels in Fig. 13. The LC lens array separates red and green colors so that only one color can be seen by each eye. The letter ‘R’ and ‘G’ are embedded in the red and green images, respectively. As a result when the eye sees the red (green) image, only the letter ‘R’ (‘G’) can be seen.

In this demonstration the LC lens sheet was simply taped to the monitor. The results were captured by a camera (Nikon D7000), showing the original designed pattern in Fig. 14(a) and the separated red and green colors in Figs. 14(b) and 14(c), respectively. The images of the separated colors were taken at the same position as the voltage applied to V1 and V2 shown in Fig. 12 sequentially.

 figure: Fig. 14

Fig. 14 Photos showing (a) the original designed pattern, (b) the separated red color and (c) the separated green color.

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The color separation here is obvious. When a user sits ~600 mm in front of the monitor with his/her eyes in different color regions, each eye can see a full resolution color image with the voltage fast switching between the two electrodes. The video source can be programed so that each eye sees a slightly different image to form stereo parallax.

Some issues are present with the current demonstration, namely crosstalk and switching time. There is a color leakage during the color separation due to the large distance between the LC lens layer and monitor pixel plane. This crosstalk needs to be minimized to improve the user experience. The cell switching time between the two colors was measured to be in the range of 80-100 ms with a 10 V driving voltage. The long response time, due to the LC material property and the thick LC layer in use, cannot provide the auto-stereoscopic experience at video rate. We believe that the switching speed can be improved. This demonstration is for a 70 µm sub-pixel. The cell gap therefore the switching time can be reduced when we reduce the LC lens width to 20-30 µm for a mobile display, and the steering angle will not be compromised by such as reduction according to Eq. (1).

6. Conclusion

We proposed the use of sub-pixel-level tunable lenticular LC lens array to construct an auto-stereoscopic display for mobile phones with the maximum possible resolution as the 2D display panel. We designed and fabricated LC lenses with a width of the same order as that of a typical mobile display pixel on the market, so that the full resolution of the 2D display can be preserved after switching to the stereoscopic ‘3D’ mode. The characterization results showed that such a small LC lens can be made with the high quality of an ideal parabolic phase profile. The lens array as designed can be integrated directly onto an existing mobile display panel, and can deliver stereoscopic ‘3D’ viewing experience while maintaining 2D viewing capability. Large steering angles were realized by the use of high birefringent nematic LCs. The evaluated phase profiles of the LC lenses showed an excellent agreement with that of ideal parabolic phase profiles. Finally a proof-of-concept demonstrator consisting of lenticular array LC lenses on a computer LCD monitor was assembled to confirm the color separation and image steering at the sub-pixel level. The next step is to work on reducing the crosstalk, due to the interplay between the non-collimated light emission and the finite glass substrate thickness, and LC switching time in order to realize a high quality auto-stereoscopic video display.

References and links

1. A. Gotchev, G. B. Akar, T. Capin, D. Strohmeier, and A. Boev, “Three-dimensional media for mobile devices,” Proc. IEEE 99(4), 708–741 (2011). [CrossRef]  

2. J. Harrold and G. Woodgate, “Autostereoscopic display technology for mobile 3DTV applications,” Proc. SPIE 6490, 6490 (2007).

3. A. Boev and A. Gotchev, “Comparative study of autostereoscopic displays for mobile devices,” Proc. SPIE 7881, 78810B (2011).

4. L. Hill and A. Jacobs, “3-D liquid crystal displays and their applications,” Proc. IEEE 94(3), 575–590 (2006). [CrossRef]  

5. N. A. Dodgson, “Optical devices: 3D without the glasses,” Nature 495(7441), 316–317 (2013). [CrossRef]   [PubMed]  

6. D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).

7. Q. Mu, Z. Cao, D. Li, L. Hu, and L. Xuan, “Liquid Crystal based adaptive optics system to compensate both low and high order aberrations in a model eye,” Opt. Express 15(4), 1946–1953 (2007). [CrossRef]   [PubMed]  

8. I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471(5), 221–267 (2009).

9. A. F. Naumov, M. Y. Loktev, I. R. Guralnik, and G. Vdovin, “Liquid-crystal adaptive lenses with modal control,” Opt. Lett. 23(13), 992–994 (1998). [CrossRef]   [PubMed]  

10. H. Ren, D. W. Fox, B. Wu, and S.-T. Wu, “Liquid crystal lens with large focal length tunability and low operating voltage,” Opt. Express 15(18), 11328–11335 (2007). [CrossRef]   [PubMed]  

11. B. Bagwell and D. Wick, “Liquid crystal based active optics,” Proc. SPIE 6289, 628908 (2006).

12. M. Reznikov, Y. Reznikov, K. Slyusarenko, J. Varshal, and M. Manevich, “Adaptive properties of a liquid crystal cell with a microlens-profiled aligning surface,” J. Appl. Phys. 111(10), 103118 (2012). [CrossRef]  

13. V. V. Presnyakov and T. V. Galstian, “Electrically tunable polymer stabilized liquid-crystal lens,” J. Appl. Phys. 97(10), 103101 (2005). [CrossRef]  

14. H.-C. Lin, M.-S. Chen, and Y.-H. Lin, “A review of electrically tunable focusing liquid crystal lenses,” Trans. Electr. Electron. Mater. 12(6), 234–240 (2011). [CrossRef]  

15. S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual-frequency liquid-crystal varifocal lens,” Jpn. J. Appl. Phys. 39(2A), 480–484 (2000).

16. K. Won, R. Rajasekharan, P. Hands, Q. Dai, and T. D. Wilkinson, “Adaptive lenticular lens array using a hybrid liquid crystal–carbon nanotube nanophotonic device,” Opt. Eng. 50(5), 054002 (2011). [CrossRef]  

17. S.-C. Liu, C.-L. Tsou, and C.-W. Chang, “Autostereoscopic 2D/3D display using liquid crystal lens and its applications for tablet PC,” Proc. SPIE 8043, 80430P (2011).

18. D. Liang, J. Luo, W. Zhao, D.-H. Li, and Q.-H. Wang, “2D/3D switchable autostereoscopic display based on polymer-stabilized blue-phase liquid crystal lens,” J. Disp. Technol. 8(10), 609–612 (2012). [CrossRef]  

19. Y.-P. Huang, C.-W. Chen, T.-C. Shen, and J.-F. Huang, “Autostereoscopic 3D display with scanning multi-electrode driven liquid crystal (MeD-LC) lens,” 3D Res. 1(1), 39–42 (2010).

20. D. Chu, B. Robertson, J. Yao, and J. Zhou, “Apparatus, methods and display for stereo imaging,” 201310307101.9, China (2013).

21. Z. Zhang, H. Yang, B. Robertson, M. Redmond, M. Pivnenko, N. Collings, W. A. Crossland, and D. Chu, “Diffraction based phase compensation method for phase-only liquid crystal on silicon devices in operation,” Appl. Opt. 51(17), 3837–3846 (2012). [CrossRef]   [PubMed]  

22. S. T. Wu, U. Efron, and L. D. Hess, “Birefringence measurements of liquid crystals,” Appl. Opt. 23(21), 3911 (1984). [CrossRef]   [PubMed]  

23. M. Kleman and O. D. Lavrentovich, Soft Matter Physics: An Introduction (Springer New York, NY, 2003) pp. 388–399.

24. E. Hecht, Optics, 4th ed. (Addison Wesley, UK, 2002) pp. 273–276.

25. K. Li, B. Robertson, M. Pivnenko, D. Chu, J. Zhou, and J. Yao, “Pixel-level tunable liquid crystal lenses for auto-stereoscopic display,” Proc. SPIE 9005, 900505 (2014). [CrossRef]  

References

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  1. A. Gotchev, G. B. Akar, T. Capin, D. Strohmeier, and A. Boev, “Three-dimensional media for mobile devices,” Proc. IEEE 99(4), 708–741 (2011).
    [Crossref]
  2. J. Harrold and G. Woodgate, “Autostereoscopic display technology for mobile 3DTV applications,” Proc. SPIE 6490, 6490 (2007).
  3. A. Boev and A. Gotchev, “Comparative study of autostereoscopic displays for mobile devices,” Proc. SPIE 7881, 78810B (2011).
  4. L. Hill and A. Jacobs, “3-D liquid crystal displays and their applications,” Proc. IEEE 94(3), 575–590 (2006).
    [Crossref]
  5. N. A. Dodgson, “Optical devices: 3D without the glasses,” Nature 495(7441), 316–317 (2013).
    [Crossref] [PubMed]
  6. D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
  7. Q. Mu, Z. Cao, D. Li, L. Hu, and L. Xuan, “Liquid Crystal based adaptive optics system to compensate both low and high order aberrations in a model eye,” Opt. Express 15(4), 1946–1953 (2007).
    [Crossref] [PubMed]
  8. I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471(5), 221–267 (2009).
  9. A. F. Naumov, M. Y. Loktev, I. R. Guralnik, and G. Vdovin, “Liquid-crystal adaptive lenses with modal control,” Opt. Lett. 23(13), 992–994 (1998).
    [Crossref] [PubMed]
  10. H. Ren, D. W. Fox, B. Wu, and S.-T. Wu, “Liquid crystal lens with large focal length tunability and low operating voltage,” Opt. Express 15(18), 11328–11335 (2007).
    [Crossref] [PubMed]
  11. B. Bagwell and D. Wick, “Liquid crystal based active optics,” Proc. SPIE 6289, 628908 (2006).
  12. M. Reznikov, Y. Reznikov, K. Slyusarenko, J. Varshal, and M. Manevich, “Adaptive properties of a liquid crystal cell with a microlens-profiled aligning surface,” J. Appl. Phys. 111(10), 103118 (2012).
    [Crossref]
  13. V. V. Presnyakov and T. V. Galstian, “Electrically tunable polymer stabilized liquid-crystal lens,” J. Appl. Phys. 97(10), 103101 (2005).
    [Crossref]
  14. H.-C. Lin, M.-S. Chen, and Y.-H. Lin, “A review of electrically tunable focusing liquid crystal lenses,” Trans. Electr. Electron. Mater. 12(6), 234–240 (2011).
    [Crossref]
  15. S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual-frequency liquid-crystal varifocal lens,” Jpn. J. Appl. Phys. 39(2A), 480–484 (2000).
  16. K. Won, R. Rajasekharan, P. Hands, Q. Dai, and T. D. Wilkinson, “Adaptive lenticular lens array using a hybrid liquid crystal–carbon nanotube nanophotonic device,” Opt. Eng. 50(5), 054002 (2011).
    [Crossref]
  17. S.-C. Liu, C.-L. Tsou, and C.-W. Chang, “Autostereoscopic 2D/3D display using liquid crystal lens and its applications for tablet PC,” Proc. SPIE 8043, 80430P (2011).
  18. D. Liang, J. Luo, W. Zhao, D.-H. Li, and Q.-H. Wang, “2D/3D switchable autostereoscopic display based on polymer-stabilized blue-phase liquid crystal lens,” J. Disp. Technol. 8(10), 609–612 (2012).
    [Crossref]
  19. Y.-P. Huang, C.-W. Chen, T.-C. Shen, and J.-F. Huang, “Autostereoscopic 3D display with scanning multi-electrode driven liquid crystal (MeD-LC) lens,” 3D Res. 1(1), 39–42 (2010).
  20. D. Chu, B. Robertson, J. Yao, and J. Zhou, “Apparatus, methods and display for stereo imaging,” 201310307101.9, China (2013).
  21. Z. Zhang, H. Yang, B. Robertson, M. Redmond, M. Pivnenko, N. Collings, W. A. Crossland, and D. Chu, “Diffraction based phase compensation method for phase-only liquid crystal on silicon devices in operation,” Appl. Opt. 51(17), 3837–3846 (2012).
    [Crossref] [PubMed]
  22. S. T. Wu, U. Efron, and L. D. Hess, “Birefringence measurements of liquid crystals,” Appl. Opt. 23(21), 3911 (1984).
    [Crossref] [PubMed]
  23. M. Kleman and O. D. Lavrentovich, Soft Matter Physics: An Introduction (Springer New York, NY, 2003) pp. 388–399.
  24. E. Hecht, Optics, 4th ed. (Addison Wesley, UK, 2002) pp. 273–276.
  25. K. Li, B. Robertson, M. Pivnenko, D. Chu, J. Zhou, and J. Yao, “Pixel-level tunable liquid crystal lenses for auto-stereoscopic display,” Proc. SPIE 9005, 900505 (2014).
    [Crossref]

2014 (1)

K. Li, B. Robertson, M. Pivnenko, D. Chu, J. Zhou, and J. Yao, “Pixel-level tunable liquid crystal lenses for auto-stereoscopic display,” Proc. SPIE 9005, 900505 (2014).
[Crossref]

2013 (2)

N. A. Dodgson, “Optical devices: 3D without the glasses,” Nature 495(7441), 316–317 (2013).
[Crossref] [PubMed]

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).

2012 (3)

M. Reznikov, Y. Reznikov, K. Slyusarenko, J. Varshal, and M. Manevich, “Adaptive properties of a liquid crystal cell with a microlens-profiled aligning surface,” J. Appl. Phys. 111(10), 103118 (2012).
[Crossref]

D. Liang, J. Luo, W. Zhao, D.-H. Li, and Q.-H. Wang, “2D/3D switchable autostereoscopic display based on polymer-stabilized blue-phase liquid crystal lens,” J. Disp. Technol. 8(10), 609–612 (2012).
[Crossref]

Z. Zhang, H. Yang, B. Robertson, M. Redmond, M. Pivnenko, N. Collings, W. A. Crossland, and D. Chu, “Diffraction based phase compensation method for phase-only liquid crystal on silicon devices in operation,” Appl. Opt. 51(17), 3837–3846 (2012).
[Crossref] [PubMed]

2011 (5)

H.-C. Lin, M.-S. Chen, and Y.-H. Lin, “A review of electrically tunable focusing liquid crystal lenses,” Trans. Electr. Electron. Mater. 12(6), 234–240 (2011).
[Crossref]

K. Won, R. Rajasekharan, P. Hands, Q. Dai, and T. D. Wilkinson, “Adaptive lenticular lens array using a hybrid liquid crystal–carbon nanotube nanophotonic device,” Opt. Eng. 50(5), 054002 (2011).
[Crossref]

S.-C. Liu, C.-L. Tsou, and C.-W. Chang, “Autostereoscopic 2D/3D display using liquid crystal lens and its applications for tablet PC,” Proc. SPIE 8043, 80430P (2011).

A. Gotchev, G. B. Akar, T. Capin, D. Strohmeier, and A. Boev, “Three-dimensional media for mobile devices,” Proc. IEEE 99(4), 708–741 (2011).
[Crossref]

A. Boev and A. Gotchev, “Comparative study of autostereoscopic displays for mobile devices,” Proc. SPIE 7881, 78810B (2011).

2010 (1)

Y.-P. Huang, C.-W. Chen, T.-C. Shen, and J.-F. Huang, “Autostereoscopic 3D display with scanning multi-electrode driven liquid crystal (MeD-LC) lens,” 3D Res. 1(1), 39–42 (2010).

2009 (1)

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471(5), 221–267 (2009).

2007 (3)

2006 (2)

B. Bagwell and D. Wick, “Liquid crystal based active optics,” Proc. SPIE 6289, 628908 (2006).

L. Hill and A. Jacobs, “3-D liquid crystal displays and their applications,” Proc. IEEE 94(3), 575–590 (2006).
[Crossref]

2005 (1)

V. V. Presnyakov and T. V. Galstian, “Electrically tunable polymer stabilized liquid-crystal lens,” J. Appl. Phys. 97(10), 103101 (2005).
[Crossref]

2000 (1)

S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual-frequency liquid-crystal varifocal lens,” Jpn. J. Appl. Phys. 39(2A), 480–484 (2000).

1998 (1)

1984 (1)

Akar, G. B.

A. Gotchev, G. B. Akar, T. Capin, D. Strohmeier, and A. Boev, “Three-dimensional media for mobile devices,” Proc. IEEE 99(4), 708–741 (2011).
[Crossref]

Bagwell, B.

B. Bagwell and D. Wick, “Liquid crystal based active optics,” Proc. SPIE 6289, 628908 (2006).

Beausoleil, R. G.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).

Boev, A.

A. Gotchev, G. B. Akar, T. Capin, D. Strohmeier, and A. Boev, “Three-dimensional media for mobile devices,” Proc. IEEE 99(4), 708–741 (2011).
[Crossref]

A. Boev and A. Gotchev, “Comparative study of autostereoscopic displays for mobile devices,” Proc. SPIE 7881, 78810B (2011).

Brug, J.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).

Cao, Z.

Capin, T.

A. Gotchev, G. B. Akar, T. Capin, D. Strohmeier, and A. Boev, “Three-dimensional media for mobile devices,” Proc. IEEE 99(4), 708–741 (2011).
[Crossref]

Chang, C.-W.

S.-C. Liu, C.-L. Tsou, and C.-W. Chang, “Autostereoscopic 2D/3D display using liquid crystal lens and its applications for tablet PC,” Proc. SPIE 8043, 80430P (2011).

Chen, C.-W.

Y.-P. Huang, C.-W. Chen, T.-C. Shen, and J.-F. Huang, “Autostereoscopic 3D display with scanning multi-electrode driven liquid crystal (MeD-LC) lens,” 3D Res. 1(1), 39–42 (2010).

Chen, M.-S.

H.-C. Lin, M.-S. Chen, and Y.-H. Lin, “A review of electrically tunable focusing liquid crystal lenses,” Trans. Electr. Electron. Mater. 12(6), 234–240 (2011).
[Crossref]

Chu, D.

Collings, N.

Crossland, W. A.

Dai, Q.

K. Won, R. Rajasekharan, P. Hands, Q. Dai, and T. D. Wilkinson, “Adaptive lenticular lens array using a hybrid liquid crystal–carbon nanotube nanophotonic device,” Opt. Eng. 50(5), 054002 (2011).
[Crossref]

Date, M.

S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual-frequency liquid-crystal varifocal lens,” Jpn. J. Appl. Phys. 39(2A), 480–484 (2000).

Dodgson, N. A.

N. A. Dodgson, “Optical devices: 3D without the glasses,” Nature 495(7441), 316–317 (2013).
[Crossref] [PubMed]

Efron, U.

Fattal, D.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).

Fiorentino, M.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).

Fox, D. W.

Galstian, T. V.

V. V. Presnyakov and T. V. Galstian, “Electrically tunable polymer stabilized liquid-crystal lens,” J. Appl. Phys. 97(10), 103101 (2005).
[Crossref]

Gotchev, A.

A. Gotchev, G. B. Akar, T. Capin, D. Strohmeier, and A. Boev, “Three-dimensional media for mobile devices,” Proc. IEEE 99(4), 708–741 (2011).
[Crossref]

A. Boev and A. Gotchev, “Comparative study of autostereoscopic displays for mobile devices,” Proc. SPIE 7881, 78810B (2011).

Guralnik, I. R.

Hands, P.

K. Won, R. Rajasekharan, P. Hands, Q. Dai, and T. D. Wilkinson, “Adaptive lenticular lens array using a hybrid liquid crystal–carbon nanotube nanophotonic device,” Opt. Eng. 50(5), 054002 (2011).
[Crossref]

Harrold, J.

J. Harrold and G. Woodgate, “Autostereoscopic display technology for mobile 3DTV applications,” Proc. SPIE 6490, 6490 (2007).

Hess, L. D.

Hill, L.

L. Hill and A. Jacobs, “3-D liquid crystal displays and their applications,” Proc. IEEE 94(3), 575–590 (2006).
[Crossref]

Hu, L.

Huang, J.-F.

Y.-P. Huang, C.-W. Chen, T.-C. Shen, and J.-F. Huang, “Autostereoscopic 3D display with scanning multi-electrode driven liquid crystal (MeD-LC) lens,” 3D Res. 1(1), 39–42 (2010).

Huang, Y.-P.

Y.-P. Huang, C.-W. Chen, T.-C. Shen, and J.-F. Huang, “Autostereoscopic 3D display with scanning multi-electrode driven liquid crystal (MeD-LC) lens,” 3D Res. 1(1), 39–42 (2010).

Jacobs, A.

L. Hill and A. Jacobs, “3-D liquid crystal displays and their applications,” Proc. IEEE 94(3), 575–590 (2006).
[Crossref]

Khoo, I. C.

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471(5), 221–267 (2009).

Li, D.

Li, D.-H.

D. Liang, J. Luo, W. Zhao, D.-H. Li, and Q.-H. Wang, “2D/3D switchable autostereoscopic display based on polymer-stabilized blue-phase liquid crystal lens,” J. Disp. Technol. 8(10), 609–612 (2012).
[Crossref]

Li, K.

K. Li, B. Robertson, M. Pivnenko, D. Chu, J. Zhou, and J. Yao, “Pixel-level tunable liquid crystal lenses for auto-stereoscopic display,” Proc. SPIE 9005, 900505 (2014).
[Crossref]

Liang, D.

D. Liang, J. Luo, W. Zhao, D.-H. Li, and Q.-H. Wang, “2D/3D switchable autostereoscopic display based on polymer-stabilized blue-phase liquid crystal lens,” J. Disp. Technol. 8(10), 609–612 (2012).
[Crossref]

Lin, H.-C.

H.-C. Lin, M.-S. Chen, and Y.-H. Lin, “A review of electrically tunable focusing liquid crystal lenses,” Trans. Electr. Electron. Mater. 12(6), 234–240 (2011).
[Crossref]

Lin, Y.-H.

H.-C. Lin, M.-S. Chen, and Y.-H. Lin, “A review of electrically tunable focusing liquid crystal lenses,” Trans. Electr. Electron. Mater. 12(6), 234–240 (2011).
[Crossref]

Liu, S.-C.

S.-C. Liu, C.-L. Tsou, and C.-W. Chang, “Autostereoscopic 2D/3D display using liquid crystal lens and its applications for tablet PC,” Proc. SPIE 8043, 80430P (2011).

Loktev, M. Y.

Luo, J.

D. Liang, J. Luo, W. Zhao, D.-H. Li, and Q.-H. Wang, “2D/3D switchable autostereoscopic display based on polymer-stabilized blue-phase liquid crystal lens,” J. Disp. Technol. 8(10), 609–612 (2012).
[Crossref]

Manevich, M.

M. Reznikov, Y. Reznikov, K. Slyusarenko, J. Varshal, and M. Manevich, “Adaptive properties of a liquid crystal cell with a microlens-profiled aligning surface,” J. Appl. Phys. 111(10), 103118 (2012).
[Crossref]

Mu, Q.

Naumov, A. F.

Peng, Z.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).

Pivnenko, M.

Presnyakov, V. V.

V. V. Presnyakov and T. V. Galstian, “Electrically tunable polymer stabilized liquid-crystal lens,” J. Appl. Phys. 97(10), 103101 (2005).
[Crossref]

Rajasekharan, R.

K. Won, R. Rajasekharan, P. Hands, Q. Dai, and T. D. Wilkinson, “Adaptive lenticular lens array using a hybrid liquid crystal–carbon nanotube nanophotonic device,” Opt. Eng. 50(5), 054002 (2011).
[Crossref]

Redmond, M.

Ren, H.

Reznikov, M.

M. Reznikov, Y. Reznikov, K. Slyusarenko, J. Varshal, and M. Manevich, “Adaptive properties of a liquid crystal cell with a microlens-profiled aligning surface,” J. Appl. Phys. 111(10), 103118 (2012).
[Crossref]

Reznikov, Y.

M. Reznikov, Y. Reznikov, K. Slyusarenko, J. Varshal, and M. Manevich, “Adaptive properties of a liquid crystal cell with a microlens-profiled aligning surface,” J. Appl. Phys. 111(10), 103118 (2012).
[Crossref]

Robertson, B.

Shen, T.-C.

Y.-P. Huang, C.-W. Chen, T.-C. Shen, and J.-F. Huang, “Autostereoscopic 3D display with scanning multi-electrode driven liquid crystal (MeD-LC) lens,” 3D Res. 1(1), 39–42 (2010).

Slyusarenko, K.

M. Reznikov, Y. Reznikov, K. Slyusarenko, J. Varshal, and M. Manevich, “Adaptive properties of a liquid crystal cell with a microlens-profiled aligning surface,” J. Appl. Phys. 111(10), 103118 (2012).
[Crossref]

Strohmeier, D.

A. Gotchev, G. B. Akar, T. Capin, D. Strohmeier, and A. Boev, “Three-dimensional media for mobile devices,” Proc. IEEE 99(4), 708–741 (2011).
[Crossref]

Suyama, S.

S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual-frequency liquid-crystal varifocal lens,” Jpn. J. Appl. Phys. 39(2A), 480–484 (2000).

Takada, H.

S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual-frequency liquid-crystal varifocal lens,” Jpn. J. Appl. Phys. 39(2A), 480–484 (2000).

Tran, T.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).

Tsou, C.-L.

S.-C. Liu, C.-L. Tsou, and C.-W. Chang, “Autostereoscopic 2D/3D display using liquid crystal lens and its applications for tablet PC,” Proc. SPIE 8043, 80430P (2011).

Varshal, J.

M. Reznikov, Y. Reznikov, K. Slyusarenko, J. Varshal, and M. Manevich, “Adaptive properties of a liquid crystal cell with a microlens-profiled aligning surface,” J. Appl. Phys. 111(10), 103118 (2012).
[Crossref]

Vdovin, G.

Vo, S.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).

Wang, Q.-H.

D. Liang, J. Luo, W. Zhao, D.-H. Li, and Q.-H. Wang, “2D/3D switchable autostereoscopic display based on polymer-stabilized blue-phase liquid crystal lens,” J. Disp. Technol. 8(10), 609–612 (2012).
[Crossref]

Wick, D.

B. Bagwell and D. Wick, “Liquid crystal based active optics,” Proc. SPIE 6289, 628908 (2006).

Wilkinson, T. D.

K. Won, R. Rajasekharan, P. Hands, Q. Dai, and T. D. Wilkinson, “Adaptive lenticular lens array using a hybrid liquid crystal–carbon nanotube nanophotonic device,” Opt. Eng. 50(5), 054002 (2011).
[Crossref]

Won, K.

K. Won, R. Rajasekharan, P. Hands, Q. Dai, and T. D. Wilkinson, “Adaptive lenticular lens array using a hybrid liquid crystal–carbon nanotube nanophotonic device,” Opt. Eng. 50(5), 054002 (2011).
[Crossref]

Woodgate, G.

J. Harrold and G. Woodgate, “Autostereoscopic display technology for mobile 3DTV applications,” Proc. SPIE 6490, 6490 (2007).

Wu, B.

Wu, S. T.

Wu, S.-T.

Xuan, L.

Yang, H.

Yao, J.

K. Li, B. Robertson, M. Pivnenko, D. Chu, J. Zhou, and J. Yao, “Pixel-level tunable liquid crystal lenses for auto-stereoscopic display,” Proc. SPIE 9005, 900505 (2014).
[Crossref]

Zhang, Z.

Zhao, W.

D. Liang, J. Luo, W. Zhao, D.-H. Li, and Q.-H. Wang, “2D/3D switchable autostereoscopic display based on polymer-stabilized blue-phase liquid crystal lens,” J. Disp. Technol. 8(10), 609–612 (2012).
[Crossref]

Zhou, J.

K. Li, B. Robertson, M. Pivnenko, D. Chu, J. Zhou, and J. Yao, “Pixel-level tunable liquid crystal lenses for auto-stereoscopic display,” Proc. SPIE 9005, 900505 (2014).
[Crossref]

3D Res. (1)

Y.-P. Huang, C.-W. Chen, T.-C. Shen, and J.-F. Huang, “Autostereoscopic 3D display with scanning multi-electrode driven liquid crystal (MeD-LC) lens,” 3D Res. 1(1), 39–42 (2010).

Appl. Opt. (2)

J. Appl. Phys. (2)

M. Reznikov, Y. Reznikov, K. Slyusarenko, J. Varshal, and M. Manevich, “Adaptive properties of a liquid crystal cell with a microlens-profiled aligning surface,” J. Appl. Phys. 111(10), 103118 (2012).
[Crossref]

V. V. Presnyakov and T. V. Galstian, “Electrically tunable polymer stabilized liquid-crystal lens,” J. Appl. Phys. 97(10), 103101 (2005).
[Crossref]

J. Disp. Technol. (1)

D. Liang, J. Luo, W. Zhao, D.-H. Li, and Q.-H. Wang, “2D/3D switchable autostereoscopic display based on polymer-stabilized blue-phase liquid crystal lens,” J. Disp. Technol. 8(10), 609–612 (2012).
[Crossref]

Jpn. J. Appl. Phys. (1)

S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual-frequency liquid-crystal varifocal lens,” Jpn. J. Appl. Phys. 39(2A), 480–484 (2000).

Nature (2)

N. A. Dodgson, “Optical devices: 3D without the glasses,” Nature 495(7441), 316–317 (2013).
[Crossref] [PubMed]

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).

Opt. Eng. (1)

K. Won, R. Rajasekharan, P. Hands, Q. Dai, and T. D. Wilkinson, “Adaptive lenticular lens array using a hybrid liquid crystal–carbon nanotube nanophotonic device,” Opt. Eng. 50(5), 054002 (2011).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rep. (1)

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471(5), 221–267 (2009).

Proc. IEEE (2)

L. Hill and A. Jacobs, “3-D liquid crystal displays and their applications,” Proc. IEEE 94(3), 575–590 (2006).
[Crossref]

A. Gotchev, G. B. Akar, T. Capin, D. Strohmeier, and A. Boev, “Three-dimensional media for mobile devices,” Proc. IEEE 99(4), 708–741 (2011).
[Crossref]

Proc. SPIE (5)

J. Harrold and G. Woodgate, “Autostereoscopic display technology for mobile 3DTV applications,” Proc. SPIE 6490, 6490 (2007).

A. Boev and A. Gotchev, “Comparative study of autostereoscopic displays for mobile devices,” Proc. SPIE 7881, 78810B (2011).

B. Bagwell and D. Wick, “Liquid crystal based active optics,” Proc. SPIE 6289, 628908 (2006).

S.-C. Liu, C.-L. Tsou, and C.-W. Chang, “Autostereoscopic 2D/3D display using liquid crystal lens and its applications for tablet PC,” Proc. SPIE 8043, 80430P (2011).

K. Li, B. Robertson, M. Pivnenko, D. Chu, J. Zhou, and J. Yao, “Pixel-level tunable liquid crystal lenses for auto-stereoscopic display,” Proc. SPIE 9005, 900505 (2014).
[Crossref]

Trans. Electr. Electron. Mater. (1)

H.-C. Lin, M.-S. Chen, and Y.-H. Lin, “A review of electrically tunable focusing liquid crystal lenses,” Trans. Electr. Electron. Mater. 12(6), 234–240 (2011).
[Crossref]

Other (3)

D. Chu, B. Robertson, J. Yao, and J. Zhou, “Apparatus, methods and display for stereo imaging,” 201310307101.9, China (2013).

M. Kleman and O. D. Lavrentovich, Soft Matter Physics: An Introduction (Springer New York, NY, 2003) pp. 388–399.

E. Hecht, Optics, 4th ed. (Addison Wesley, UK, 2002) pp. 273–276.

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Figures (14)

Fig. 1
Fig. 1 The proposed multiplexing scheme using interlaced spatial and temporal beam steering to obtain the maximum resolution for an auto-stereoscopic display. The phase profile of each half of the lenses illustrated here is approximated as a linear phase ramp. The multiplexing operation can be described in two steps: (a) Frame 1 – odd sub-pixels deflected to the left eye and even sub-pixels deflected to the right eye. (b) Frame 2 – odd sub-pixels deflected to the right eye and even sub-pixels deflected to the left eye. The phase pattern is shifted by one sub-pixel resulting in the swap of deflection directions.
Fig. 2
Fig. 2 Deflection of a plane wave by a LC cell with a linear phase ramp.
Fig. 3
Fig. 3 (a) Schematic of a cell configuration with the rubbing directions marked for the top and bottom substrates and (b) the image taken as the cell is placed between two crossed-polarizers with the rubbing direction oriented at 45° with respect to the polarizer’s transmission axis.
Fig. 4
Fig. 4 LC director orientations of (a) zone A and (b) zone B when a voltage is applied between the two ITO coated substrates.
Fig. 5
Fig. 5 Intensity profiles of zone A at various driving voltages.
Fig. 6
Fig. 6 Phase profiles of (a) zone A and (b) zone B at varying driving voltages.
Fig. 7
Fig. 7 Intensity profile of (a) zone C and (b) zone D at 8.5 V, where the circle in (a) highlights the region of LC disclinations.
Fig. 8
Fig. 8 Microscope image of patterned ITO electrode tracks.
Fig. 9
Fig. 9 Intensity images of the LC lens array made with LC1 at driving voltages of (a) 2.52 V, (b) 3.52 V and (c) 6.00 V.
Fig. 10
Fig. 10 The measured phase profiles at varying driving voltages for the LC lenses made with (a) LC1 and (b) LC2, respectively.
Fig. 11
Fig. 11 The comparison of the measured LC lens phase profiles to the ideal parabolic lens profiles.
Fig. 12
Fig. 12 The LC lens design (top-down view) intended to steer the images at sub-pixel level on a 24” HD monitor.
Fig. 13
Fig. 13 The schematic of the demonstrator (side view) with the LC lens array placed on top of the monitor.
Fig. 14
Fig. 14 Photos showing (a) the original designed pattern, (b) the separated red color and (c) the separated green color.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

tan( γ max )= dΔn a ,
δ max = 2πΔnd λ
| δ |=Nπ+2 tan 1 I c I p , N= 0, 2, 4,
| δ |=(N+1)π2 tan 1 I c I p , N= 1, 3, 5,

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