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

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

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

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)

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]

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

Proc. SPIE (5)

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]

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).

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).

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

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)

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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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