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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 26520–26526
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Liquid-crystal micro-lens array with two-divided and tetragonally hole-patterned electrodes

Marenori Kawamura, Kento Nakamura, and Susumu Sato  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 26520-26526 (2013)
http://dx.doi.org/10.1364/OE.21.026520


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Abstract

We propose a liquid crystal (LC) micro-lens array with the structure of two-divided and tetragonally hole-patterned electrodes. Each LC cell in the lens array behaves like cylindrical or spherical lens properties by electrically adjusting the applied voltages. The LC micro-lens array is useful for tuning optical properties such a focal length and deflection angle of a light emitting diode (LED) illumination system.

© 2013 Optical Society of America

1. Introduction

Nematic liquid crystals (LCs) with a large electrical and optical anisotropies are easily to be operated by low voltages. These materials have been used in flat display devices and optical devices. The LC molecular orientation is controlled by applying an external electric field and then optical properties of an LC device are changed. An LC lens with a lens-shaped cell for electrically varying the optical property such as a focal length was first reported [1

1. S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979). [CrossRef]

]. There are several methods for fabricating the LC lenses such as refractive lenses [2

2. 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]

, 3

3. M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41(Part 2, No. 5B), L571–L573 (2002). [CrossRef]

], polymer dispersed LC lenses [4

4. H. Ren and S. T. Wu, “Inhomogeneous nanoscale polymer-dispersed liquid crystals with gradient refractive index,” Appl. Phys. Lett. 81(19), 3537–3539 (2002). [CrossRef]

, 5

5. H. Lin and Y.-H. Lin, “An electrically tunable focusing liquid crystal lens with a built-in planar polymeric lens,” Appl. Phys. Lett. 98, 083503 (2010).

], and the variable optical properties of the LC lens have been proposed for use in mobile phone camera lenses and microscope lenses and so on. The LC lenses with severally-divided and circularly hole-patterned electrodes have been developed for steering and focusing a light beam; the foci can be movable off as well as along the lens axes [6

6. M. Ye and S. Sato, “Liquid crystal lens with focus movable along and off axis,” Opt. Commun. 225(4–6), 277–280 (2003). [CrossRef]

, 7

7. M. Ye, B. Wang, and S. Sato, “Study of liquid crystal lens with focus movable in focal plane by wave front analysis,” Jpn. J. Appl. Phys. 45(8A), 6320–6322 (2006). [CrossRef]

]. Recently, the optical aberrations of the low-voltage-driving LC lens with both low aberrations and a wide focal range are studied [8

8. M. Ye, B. Wang, M. Uchida, S. Yanase, H. Kunitsuka, S. Takahashi, and S. Sato, “Measurement of optical aberrations of liquid crystal lens,” Jpn. J. Appl. Phys. 52, 042501–042504 (2013). [CrossRef]

]. We proposed an optical manipulation system by using the LC lens with the beam steering function for controlling three-dimensional positions of captured spherical and/or cylindrical microscopic particles [9

9. M. Kawamura, M. Ye, and S. Sato, “Optical trapping and manipulation system by using a liquid crystal lens with focusing and deflection properties,” Jpn. J. Appl. Phys. 44(8), 6098–6100 (2005). [CrossRef]

, 10

10. M. Kawamura, H. Umeda, J. Onishi, M. Ye, and S. Sato, “Laser manipulator for rotating microscopic trapped particles by using liquid crystal optical devices,” Mol. Cryst. Liq. Cryst. 488(1), 238–245 (2008). [CrossRef]

]. The LC lens with two-dimensional micro-sized lens array; called an LC micro-lens array have also been proposed [11

11. T. Nose and S. Sato, “A liquid crystal microlens obtained with a non-uniform electric field,” Liq. Cryst. 5(5), 1425–1433 (1989). [CrossRef]

19

19. T. Sugita, S. Oka, T. Naganuma, T. Saito, S. Komura, and T. Miyazawa, “Refractive index distribution analysis of liquid crystal GRIN lens for autostereoscopic 2D/3D switchable displays,” SID Symp. Dig. Tech. 43 1452–1455 (2012). [CrossRef]

]. The one type of the LC micro-lens array with the micro-sized circularly or hexagonal hole-patterned electrode has been developed and based on the orientation effects of LC molecules in inhomogeneous electric fields. By controlling the applied voltage on the LC micro-lens array, the optical property such as the focal length can also be varied electrically. The advantage of the LC lenses is such that small size, lightweight, planer and low voltage. Among them some LC lenses have been used in optical information processing or autostereoscopic two-dimensional/three-dimensional switchable displays [19

19. T. Sugita, S. Oka, T. Naganuma, T. Saito, S. Komura, and T. Miyazawa, “Refractive index distribution analysis of liquid crystal GRIN lens for autostereoscopic 2D/3D switchable displays,” SID Symp. Dig. Tech. 43 1452–1455 (2012). [CrossRef]

].

In this study, we propose an LC micro-lens array with a new type electrode structure for electrically changing the focal length and deflection angle. The each LC cell in the micro-lens array behaves like cylindrical or spherical lens properties by adjusting the voltage applied to the divided electrodes without any mechanical movements.

2. Experimental

The structures of the side and top views of the LC micro-lens array are schematically shown in Figs. 1(a)
Fig. 1 The cross-section of the LC-micro-lens array. (a) Top view; (b) Side view
and 1(b). The LC micro-lens array consists of a upper glass substrate (1.1 mm-thickness) with the hole-patterned electrodes, transparent polymer film (5 μm-thickness) such as an exposy-based and high-resistive transparent UV curable polymer film for an insulation layer, LC layer and glass substrate with the transparent and uniform ITO electrode (1.1 mm-thickness). The upper substrate is prepared to be the hole-patterned electrodes by a photolithography etching of the aluminum (Al) thin film (about 0.1 nm-thickness) deposited on the glass substrate by using a vacuum deposition. The width of the electrode lines is 50 μm and the width between two electrode line is 30 μm. The aperture size of the hole-patterned region is ϕ = 300 μm. The distance between two neighboring patterned-electrodes is P = 430 μm, that is, the pitch (P/ϕ) is about 1.4. The transparent polymer film is fabricated by coating the solvent on the surface of the hole-patterned electrodes on the glass substrate and then exposing the UV light. The left electrode lines [blue lines as shown in Fig. 1(a)] and right electrode lines [red lines] at the square apertures operated as the LC microlens array are located on the same side since the square apertures shift to the neighbor columns along the y-direction and then their positions also shift to 67.5 μm along the transverse direction. Both electrode substrates are spin-coated with a polyimide parallel alignment film, and their surfaces are rubbed to obtain homogeneous alignment parallel to the electrode lines along y-axis as shown in Fig. 1(a). Two substrates are overlapped at anti-parallel rubbing directions, and the cell gap is controlled by using glass ball spacers at the diameter of 110 μm. Thenematic LC material with a positive dielectric anisotropy; RDP-85475 (DIC Co.) is filled into the cell under a room temperature. AC voltages of f = 1 kHz; VL and VR are applied to the left and right electrode lines by using a function generator.

3. Results and discussion

Figures 2(a)
Fig. 2 Interference fringe patterns under various voltages applied to the LC micro-lens (VL = VR) in a crossed polarizing microscope system. (a) VL = VR = 0; (b) VL = VR = 2.0 V; (c) VL = VR = 2.5 V; (d) VL = VR = 3.0 V.
2(d) show the interference fringe pattern images of the LC lens array at the apertures of the hole-patterned electrode in a crossed polarizing microscope system, where the polarization direction of the incident light is adjusted to 45° with respect to the rubbing direction of the LC cell. The LC molecular orientations can be obtained by observing fringe patterns produced by the interference between ordinary and extraordinary rays through the LC cell. When the electric field is applied to the cell, the LC molecules are tilted toward the normal direction of the substrates. Since there is distance between the hole-patterned electrodes and the LC layer, a non-uniform electrical field is produced and the induced electric charges at the transparent polymer film are distributed over the LC layer. As increasing both voltages VL and VR to the two electrode lines, the almost circular interference fringes which are centrally symmetric appear successively. The electric fields close to the electrode edges at the tetragonal patterned region become relative strong with increase of the applied voltage. The electric field distributions in the LC micro-lens seem to vary with the applied voltage, specially near the center of the hole pattern since the LC molecular orientations are experimentally investigated by observing the fringe patterns. The electricpotential becomes close to a parabolic function. As increasing the difference between the asymmetric voltages applied to the left and right electrodes, the fringes tend to become dense and the turbulence of the images occurs near the electrode where the further high voltage is applied because of effective refractive index distribution efficiencies. The behaviors of the reverse tilt and/or twist angle disclination lines at the boundary between the two different domains are not induced by the nonuniform electric field less than the applied voltage of 8 V to the hole-patterned electrode. With the increase of the applied voltage, the focal length can be changed from about 1.1 mm to infinity. When the voltage is increased over 3.0V, the optical properties of the LC lens will be worsened because the reflective index distribution in the hole-pattern becomes different from lens-like distributions. The zigzag track region at a width of 30 μm between the adjacent rows of tetragonal aperture would induce diffraction patterns and unnecessary light leakages. The diffraction light intensities would be modulated by changing the phase differences in the zigzag track region when the two different voltages were applied to the left and right electrode lines.

Figures 3(a)
Fig. 3 Interference fringe patterns of the LC micro-lens under different voltages. (a) VL = 2.0V, VR = 4.0V; (b) VL = 4.0V, VR = 2.0V.
and 3(b) show the interference fringes under crossed polarizers when the different voltage is applied to two-divided electrode lines, where the rubbing direction of the cells is also 45° with respect to both polarizer and analyzer. When the voltage VR ( = 4.0 V) applied to the right electrode is twice higher than that applied to the left electrode, the more interference fringes can be obtained on the right electric and the circular interference fringes become asymmetric. It can be seen that the center of the relatively circular fringe shifts to the left electrode as shown in Fig. 3(a). On the other hand, the center of the interference fringes shifts to the right electrode as shown in Fig. 3(b) when the applied voltage (VL = 4.0V) is higher than the voltage VR. The cause is that the LC molecules under the applied side of the electrode are tilted toward the normal direction of the substrates, resulting in the decrease of the effective refractive index and the appearance of the fringes.

Figures 4(a)
Fig. 4 Phase retardation distributions from the fringe patterns as shown in Fig. 3. (a) VR = 4.0 V; (b) VL = 4.0 V.
and 4(b) show cross-sectional distributions of the phase retardations corresponding to x-axis by estimating the interference fringes as shown in Figs. 3(a) and 3(b), since the phase retardation of the neighbour interference fringe is 2π (rad). The parabolic phase retardation can be obtained when the applied voltages VL and VR are same values. It is clear that the phase retardation decreases both in the center region of the hole-pattern and near the electrode line edge. This means that the LC molecules not only near the electrode line edges but in the center region are forced to tilt toward the normal direction of the substrates with increasing the applied voltage. By applying voltages, the refractive index distribution can be induced in the two-divided electrode. As increasing the difference between the asymmetric voltages applied to left and right electrodes, the tilt distribution of the LC molecules at the left and right electrodes increases and then the retardation becomes large. The LC molecules near the edges of the every upper and lower electrodes are twisted toward the perpendicular direction from the initial LC alignment direction when the high voltage is applied to the electrode lines.

Figures 5(a)
Fig. 5 Interference fringe patterns of the LC micro-lens under different voltages. (a) VL = 2.0V, VR = 0; (b) VL = 3.0V, VR = 0; (c) VL = 0, VR = 2.0V; (d) VL = 0, VR = 3.0V.
5(d) show the nearly linear interference fringe pattern images with cylindrical lens properties of the LC micro-lens array under crossed polarizers, when no voltage is applied to one of the two-divided electrodes. When the voltage is applied to one side of the electrode line, the deformed interference fringe seems to shift to the electrode side of the low voltage. Figures 6(a)
Fig. 6 Phase retardation distributions from the fringe patterns as shown in Fig. 5. (a) VR = 0 V; (b) VL = 0 V.
and 6(b) show the cross-sectional distributions of the phase retardation corresponding to x-axis by estimating the interference fringes. The phase retardation increases further as increasing the voltage applied to the either left or right electrode. By applying voltage to one side of the electrode lines, the cylindrical refractive index distribution can be induced in the tetragonal patterned area. The retardation as shown in Fig. 6 becomes higher than that as shown in Fig. 4 because the difference between the voltages applied to two electrodes more increases. With the voltage exceeds to about 4 V to one of two electrodes, the LC molecules in the side of the electrode without the applied voltage are also tilted, thus the interference fringe moves and the retardation decreases.

The spatial light intensity distributions passing through the LC micro-lens array are measured in an optical system using a He-Ne laser at a wavelength of 0.6328 μm as a light source, a collimator lens and a translucent screen. The collimated light beam is normally incident on the LC micro-lens array. The distance between two positions of the LC micro-lens array and the screen is about 200 mm. The polarization direction of the incident light is parallel to the rubbing direction of the LC cell. The deflection angle can be derived by measuring spatial intensity distributions passing through the LC micro-lens array projected tothe screen. When the voltage is applied to the left side electrode and the phase retardation becomes a cylindrical lens-like distribution as shown in Fig. 6(a), the light peak from the optical axis occurs, and moves to the right side as a positive direction on the screen with increasing the applied voltage; VL. On the other hand, the light peak can be deflected and moves to the left side as a negative direction on the screen with further increase of the voltage; VR. The deflection angle can be estimated and its range varies from −9.7° at the applied voltages of VL = 4.0 V and VR = 0 V to 10.1° at the voltages of VL = 0 V and VR = 4.0 V. In the current stage, the wavefront through the LC micro-lens array is deformed in its aperture. The appropriate beam steering will be realized to fabricate the new structure of the LC micro-lens array with an assist electrode to increase the electric field at the edge around the tetragonal electrode.

The response time was due to the thickness of the bulk LC in the LC layer. The response time of approximately and a decay time also several seconds have been achieved when LC material RDP-85475 (DIC Co.) with a 110 μm-thickness is used. However we also note that the refractive index distribution is rapidly changed with the increase of the voltage. These experiments are now in progress and the detail dynamic property on the properties of an LC microlens array will be reported in elsewhere.

4. Conclusion

An LC micro-lens array with two-divided and tetragonally hole-patterned electrodes was proposed. The refractive index distributions of the cylindrical and spherical lens properties of each LC cell in the micro-lens array were verified. The optical properties such as a focal length and deflection angle of the light beam were demonstrated by applying an appropriate applied voltage to the divided electrode. The LC micro-lens array with the light-scattering and deflecting effects is useful for an LED illumination system to control the light distributions without any mechanical movements.

References and links

1.

S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979). [CrossRef]

2.

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]

3.

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41(Part 2, No. 5B), L571–L573 (2002). [CrossRef]

4.

H. Ren and S. T. Wu, “Inhomogeneous nanoscale polymer-dispersed liquid crystals with gradient refractive index,” Appl. Phys. Lett. 81(19), 3537–3539 (2002). [CrossRef]

5.

H. Lin and Y.-H. Lin, “An electrically tunable focusing liquid crystal lens with a built-in planar polymeric lens,” Appl. Phys. Lett. 98, 083503 (2010).

6.

M. Ye and S. Sato, “Liquid crystal lens with focus movable along and off axis,” Opt. Commun. 225(4–6), 277–280 (2003). [CrossRef]

7.

M. Ye, B. Wang, and S. Sato, “Study of liquid crystal lens with focus movable in focal plane by wave front analysis,” Jpn. J. Appl. Phys. 45(8A), 6320–6322 (2006). [CrossRef]

8.

M. Ye, B. Wang, M. Uchida, S. Yanase, H. Kunitsuka, S. Takahashi, and S. Sato, “Measurement of optical aberrations of liquid crystal lens,” Jpn. J. Appl. Phys. 52, 042501–042504 (2013). [CrossRef]

9.

M. Kawamura, M. Ye, and S. Sato, “Optical trapping and manipulation system by using a liquid crystal lens with focusing and deflection properties,” Jpn. J. Appl. Phys. 44(8), 6098–6100 (2005). [CrossRef]

10.

M. Kawamura, H. Umeda, J. Onishi, M. Ye, and S. Sato, “Laser manipulator for rotating microscopic trapped particles by using liquid crystal optical devices,” Mol. Cryst. Liq. Cryst. 488(1), 238–245 (2008). [CrossRef]

11.

T. Nose and S. Sato, “A liquid crystal microlens obtained with a non-uniform electric field,” Liq. Cryst. 5(5), 1425–1433 (1989). [CrossRef]

12.

S. Masuda, S. Fujioka, M. Honma, T. Nose, and S. Sato, “Dependence of optical properties on the device and material parameters in liquid crystal microlenses,” Jpn. J. Appl. Phys. 35(Part 1, No. 9A), 4668–4672 (1996). [CrossRef]

13.

S. Masuda, S. Takahashi, T. Nose, S. Sato, and H. Ito, “Liquid-crystal microlens with a beam-steering function,” Appl. Opt. 36(20), 4772–4778 (1997). [CrossRef] [PubMed]

14.

S. Yanase, K. Ouchi, and S. Sato, “Molecular orientation states and optical properties of liquid crystal microlenses with an asymmetric electrode structure,” Jpn. J. Appl. Phys. 41(Part 1, No. 3A), 1482–1488 (2002). [CrossRef]

15.

M. Ye, H. Hayasaka, and S. Sato, “Liquid crystal lens array with hexagonal-hole-patterned electrodes,” Jpn. J. Appl. Phys. 43(9A), 6108–6111 (2004). [CrossRef]

16.

H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, “Tunable-focus microlens arrays using nanosized polymer-dispersed liquid crystal droplets,” Opt. Commun. 247(1-3), 101–106 (2005). [CrossRef]

17.

Y. H. Lin, H. S. Chen, H. C. Lin, Y. S. Tsou, H. K. Hsu, and W. Y. Li, “Polarizer-free and fast response microlens arrays using polymer-stablized blue phase liquid crystals,” Appl. Phys. Lett. 96(11), 113505 (2010). [CrossRef]

18.

M. Ye and S. Sato, “Transient properties of a liquid-crystal microlens,” Jpn. J. Appl. Phys. 40(Part 1, No. 10), 6012–6016 (2001). [CrossRef]

19.

T. Sugita, S. Oka, T. Naganuma, T. Saito, S. Komura, and T. Miyazawa, “Refractive index distribution analysis of liquid crystal GRIN lens for autostereoscopic 2D/3D switchable displays,” SID Symp. Dig. Tech. 43 1452–1455 (2012). [CrossRef]

OCIS Codes
(080.3630) Geometric optics : Lenses
(160.3710) Materials : Liquid crystals
(230.0230) Optical devices : Optical devices
(230.3720) Optical devices : Liquid-crystal devices
(130.3990) Integrated optics : Micro-optical devices

ToC Category:
Optical Devices

History
Original Manuscript: August 20, 2013
Revised Manuscript: October 15, 2013
Manuscript Accepted: October 15, 2013
Published: October 28, 2013

Citation
Marenori Kawamura, Kento Nakamura, and Susumu Sato, "Liquid-crystal micro-lens array with two-divided and tetragonally hole-patterned electrodes," Opt. Express 21, 26520-26526 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-26520


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References

  1. S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys.18(9), 1679–1684 (1979). [CrossRef]
  2. 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]
  3. M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys.41(Part 2, No. 5B), L571–L573 (2002). [CrossRef]
  4. H. Ren and S. T. Wu, “Inhomogeneous nanoscale polymer-dispersed liquid crystals with gradient refractive index,” Appl. Phys. Lett.81(19), 3537–3539 (2002). [CrossRef]
  5. H. Lin and Y.-H. Lin, “An electrically tunable focusing liquid crystal lens with a built-in planar polymeric lens,” Appl. Phys. Lett.98, 083503 (2010).
  6. M. Ye and S. Sato, “Liquid crystal lens with focus movable along and off axis,” Opt. Commun.225(4–6), 277–280 (2003). [CrossRef]
  7. M. Ye, B. Wang, and S. Sato, “Study of liquid crystal lens with focus movable in focal plane by wave front analysis,” Jpn. J. Appl. Phys.45(8A), 6320–6322 (2006). [CrossRef]
  8. M. Ye, B. Wang, M. Uchida, S. Yanase, H. Kunitsuka, S. Takahashi, and S. Sato, “Measurement of optical aberrations of liquid crystal lens,” Jpn. J. Appl. Phys.52, 042501–042504 (2013). [CrossRef]
  9. M. Kawamura, M. Ye, and S. Sato, “Optical trapping and manipulation system by using a liquid crystal lens with focusing and deflection properties,” Jpn. J. Appl. Phys.44(8), 6098–6100 (2005). [CrossRef]
  10. M. Kawamura, H. Umeda, J. Onishi, M. Ye, and S. Sato, “Laser manipulator for rotating microscopic trapped particles by using liquid crystal optical devices,” Mol. Cryst. Liq. Cryst.488(1), 238–245 (2008). [CrossRef]
  11. T. Nose and S. Sato, “A liquid crystal microlens obtained with a non-uniform electric field,” Liq. Cryst.5(5), 1425–1433 (1989). [CrossRef]
  12. S. Masuda, S. Fujioka, M. Honma, T. Nose, and S. Sato, “Dependence of optical properties on the device and material parameters in liquid crystal microlenses,” Jpn. J. Appl. Phys.35(Part 1, No. 9A), 4668–4672 (1996). [CrossRef]
  13. S. Masuda, S. Takahashi, T. Nose, S. Sato, and H. Ito, “Liquid-crystal microlens with a beam-steering function,” Appl. Opt.36(20), 4772–4778 (1997). [CrossRef] [PubMed]
  14. S. Yanase, K. Ouchi, and S. Sato, “Molecular orientation states and optical properties of liquid crystal microlenses with an asymmetric electrode structure,” Jpn. J. Appl. Phys.41(Part 1, No. 3A), 1482–1488 (2002). [CrossRef]
  15. M. Ye, H. Hayasaka, and S. Sato, “Liquid crystal lens array with hexagonal-hole-patterned electrodes,” Jpn. J. Appl. Phys.43(9A), 6108–6111 (2004). [CrossRef]
  16. H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, “Tunable-focus microlens arrays using nanosized polymer-dispersed liquid crystal droplets,” Opt. Commun.247(1-3), 101–106 (2005). [CrossRef]
  17. Y. H. Lin, H. S. Chen, H. C. Lin, Y. S. Tsou, H. K. Hsu, and W. Y. Li, “Polarizer-free and fast response microlens arrays using polymer-stablized blue phase liquid crystals,” Appl. Phys. Lett.96(11), 113505 (2010). [CrossRef]
  18. M. Ye and S. Sato, “Transient properties of a liquid-crystal microlens,” Jpn. J. Appl. Phys.40(Part 1, No. 10), 6012–6016 (2001). [CrossRef]
  19. T. Sugita, S. Oka, T. Naganuma, T. Saito, S. Komura, and T. Miyazawa, “Refractive index distribution analysis of liquid crystal GRIN lens for autostereoscopic 2D/3D switchable displays,” SID Symp. Dig. Tech. 43 1452–1455 (2012). [CrossRef]

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