Abstract

Information-dependent (active) polarization encoding can be used to simultaneously present two image-resolvable elements [elements of left and right views of a three-dimensional (3D) scene] in a single display pixel. Polarization decoding, with the help of passive polarization filters, makes it possible to separate elements of left and right views and to observe them independently by left and right eyes. In this paper the basic theory of such 3D displays is developed. The relevant solutions of the general equation of light elliptical polarization are obtained in all important cases: cases of controlled birefringence and/or optical activity as three basic controlled polarization encoders. The obtained formulas are essentially the forms of signals that should control the values of birefringence and optical activity to realize the required polarization encoding. Optical schemes of flat-panel direct-view stereoscopic and autostereoscopic displays with the use of liquid crystal polarization encoding matrices are considered.

© 2010 Optical Society of America

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References

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  1. V. Ezhov, “Stereo image observation method with joint presentation of the views and a device for implementation thereof,” R.U. patent 2,306,680 (13 March 2006). In Russian.
  2. V. Ezhov, “A new approach to stereoscopic display developed by solving general equation of light polarization,” in Proceedings of 27th International Display Research Conference(Society for Information Display, 2007), pp. 445–449.
  3. M. Born and E. Wolf, “Basic properties of the electromagnetic field,” in Principles of Optics (Cambridge U. Press, 2002), Chap 1, pp. 24–28.
  4. J. Gaudreau, M. Bechamp, B. MacNaughton, and V. Power, “Innovative stereoscopic display using variable polarization angle,” Proc. SPIE 6055, 605518 (2006).
    [CrossRef]
  5. V. Ezhov, “Stereo image observation method with full resolution for each view and a device for implementation thereof,” R.U. patent 2,377,623 (20 April 2007). In Russian.
  6. V. Ezhov, “World’s first full resolution (at each view) auto3D/2D planar display structure based on standard LCD technology,” in Proceedings of 29th International Display Research Conference (Society for Information Display, 2009), paper 10.4.
  7. P. Bos, “Rapid starting, high-speed liquid crystal variable optical retarder,” U.S. patent 4,566,758 (28 January 1986).
  8. M. Schadt and W. Helfrich, “Voltage dependent optical activity of a twisted nematic liquid crystal,” Appl. Phys. Lett. 18, 127–128 (1971).
    [CrossRef]

2006 (1)

J. Gaudreau, M. Bechamp, B. MacNaughton, and V. Power, “Innovative stereoscopic display using variable polarization angle,” Proc. SPIE 6055, 605518 (2006).
[CrossRef]

1971 (1)

M. Schadt and W. Helfrich, “Voltage dependent optical activity of a twisted nematic liquid crystal,” Appl. Phys. Lett. 18, 127–128 (1971).
[CrossRef]

Bechamp, M.

J. Gaudreau, M. Bechamp, B. MacNaughton, and V. Power, “Innovative stereoscopic display using variable polarization angle,” Proc. SPIE 6055, 605518 (2006).
[CrossRef]

Born, M.

M. Born and E. Wolf, “Basic properties of the electromagnetic field,” in Principles of Optics (Cambridge U. Press, 2002), Chap 1, pp. 24–28.

Bos, P.

P. Bos, “Rapid starting, high-speed liquid crystal variable optical retarder,” U.S. patent 4,566,758 (28 January 1986).

Ezhov, V.

V. Ezhov, “Stereo image observation method with full resolution for each view and a device for implementation thereof,” R.U. patent 2,377,623 (20 April 2007). In Russian.

V. Ezhov, “Stereo image observation method with joint presentation of the views and a device for implementation thereof,” R.U. patent 2,306,680 (13 March 2006). In Russian.

V. Ezhov, “A new approach to stereoscopic display developed by solving general equation of light polarization,” in Proceedings of 27th International Display Research Conference(Society for Information Display, 2007), pp. 445–449.

V. Ezhov, “World’s first full resolution (at each view) auto3D/2D planar display structure based on standard LCD technology,” in Proceedings of 29th International Display Research Conference (Society for Information Display, 2009), paper 10.4.

Gaudreau, J.

J. Gaudreau, M. Bechamp, B. MacNaughton, and V. Power, “Innovative stereoscopic display using variable polarization angle,” Proc. SPIE 6055, 605518 (2006).
[CrossRef]

Helfrich, W.

M. Schadt and W. Helfrich, “Voltage dependent optical activity of a twisted nematic liquid crystal,” Appl. Phys. Lett. 18, 127–128 (1971).
[CrossRef]

MacNaughton, B.

J. Gaudreau, M. Bechamp, B. MacNaughton, and V. Power, “Innovative stereoscopic display using variable polarization angle,” Proc. SPIE 6055, 605518 (2006).
[CrossRef]

Power, V.

J. Gaudreau, M. Bechamp, B. MacNaughton, and V. Power, “Innovative stereoscopic display using variable polarization angle,” Proc. SPIE 6055, 605518 (2006).
[CrossRef]

Schadt, M.

M. Schadt and W. Helfrich, “Voltage dependent optical activity of a twisted nematic liquid crystal,” Appl. Phys. Lett. 18, 127–128 (1971).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, “Basic properties of the electromagnetic field,” in Principles of Optics (Cambridge U. Press, 2002), Chap 1, pp. 24–28.

Appl. Phys. Lett. (1)

M. Schadt and W. Helfrich, “Voltage dependent optical activity of a twisted nematic liquid crystal,” Appl. Phys. Lett. 18, 127–128 (1971).
[CrossRef]

Proc. SPIE (1)

J. Gaudreau, M. Bechamp, B. MacNaughton, and V. Power, “Innovative stereoscopic display using variable polarization angle,” Proc. SPIE 6055, 605518 (2006).
[CrossRef]

Other (6)

V. Ezhov, “Stereo image observation method with full resolution for each view and a device for implementation thereof,” R.U. patent 2,377,623 (20 April 2007). In Russian.

V. Ezhov, “World’s first full resolution (at each view) auto3D/2D planar display structure based on standard LCD technology,” in Proceedings of 29th International Display Research Conference (Society for Information Display, 2009), paper 10.4.

P. Bos, “Rapid starting, high-speed liquid crystal variable optical retarder,” U.S. patent 4,566,758 (28 January 1986).

V. Ezhov, “Stereo image observation method with joint presentation of the views and a device for implementation thereof,” R.U. patent 2,306,680 (13 March 2006). In Russian.

V. Ezhov, “A new approach to stereoscopic display developed by solving general equation of light polarization,” in Proceedings of 27th International Display Research Conference(Society for Information Display, 2007), pp. 445–449.

M. Born and E. Wolf, “Basic properties of the electromagnetic field,” in Principles of Optics (Cambridge U. Press, 2002), Chap 1, pp. 24–28.

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Figures (10)

Fig. 1
Fig. 1

Separation of simultaneous resolvable elements of two views by polarization coding.

Fig. 2
Fig. 2

Voltage-controlled optically anisotropic plate: (a) united phase retarder–optical rotator, (b) pure phase retarder, (c) pure optical rotator.

Fig. 3
Fig. 3

Elliptical polarization dependence on phase retardation and optical activity.

Fig. 4
Fig. 4

Encoding functions in the case of voltage-controlled phase retardation.

Fig. 5
Fig. 5

Encoding functions in the case of voltage-controlled optical activity at ± 45 ° angles between the input polarization direction and the polarization decoder axis.

Fig. 6
Fig. 6

Encoding functions in the case of voltage-controlled optical activity at 0 ° 90 ° angles between the input polarization direction and the polarization decoder axis: (a) first orientation of axis and (b) second orientation of axis.

Fig. 7
Fig. 7

Stereoscopic observation with glasses.

Fig. 8
Fig. 8

Glasses-free (autostereoscopic) observation with switched phase grid.

Fig. 9
Fig. 9

Plots of two mutually orthogonal encoding functions.

Fig. 10
Fig. 10

Autostereoscopic observation with polarization grid.

Equations (30)

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J L mn B L mn ; J R mn B R mn ,
J 0 mn = J L mn + J R mn B L mn + B R mn .
J L mn / J R mn = B L mn / B R mn .
E mn = E o mn cos ( τ + δ mn ) ,
E x mn = E o mn cos φ mn cos ( τ + δ o mn ) ,
E y mn = E o mn sin φ mn cos ( τ + δ e mn ) ,
( E x mn ) 2 cos 2 φ mn + ( E y mn ) 2 sin 2 φ mn 2 E x mn E y mn cos φ mn sin φ mn cos δ mn = ( E o mn ) 2 sin 2 δ mn ,
tan 2 α mn = tan 2 φ mn cos δ mn ,
δ mn = δ S mn + δ con st mn ,
φ mn = φ S mn + φ const mn ,
J y = x mn ( 1 2 cos φ mn sin φ mn cos δ mn cos 2 φ mn sin 2 φ mn ) = ( E o mn ) 2 sin 2 δ mn ,
J y = x mn ( 1 + 2 cos φ mn sin φ mn cos δ mn cos 2 φ mn sin 2 φ mn ) = ( E o mn ) 2 sin 2 δ mn ,
J y = x mn J y = x mn = J L mn J R mn = B L mn B R mn = 1 + 2 cos φ mn sin φ mn cos δ mn 1 2 cos φ mn sin φ mn cos δ mn ,
J L mn J R mn = B L mn B R mn = 1 + sin 2 φ mn cos δ mn 1 sin 2 φ mn cos δ mn .
B L mn B R mn = 1 + cos δ s mn 1 cos δ s mn ,
δ s mn = arccos [ B L mn B R mn B L mn + B R mn ] .
δ s mn = arccos [ B R mn B L mn B L mn + B R mn ] .
δ s mn = arcsin [ B L mn B R mn B L mn + B R mn ] .
B L mn B R mn = 1 + sin 2 φ mn 1 sin 2 φ mn .
B L mn B R mn = 1 + sin [ 2 ( φ mn + 90 ° ) ] 1 sin [ 2 ( φ mn + 90 ° ) ] = 1 sin 2 φ mn 1 + sin 2 φ mn .
φ s mn = + 1 2 arcsin [ B L mn B R mn B R mn + B L : mn ] ,
φ s mn = 1 2 arcsin [ B L mn B R mn B R mn + B L : mn ] ,
B R mn B L mn = 1 + cos 2 φ mn 1 cos 2 φ mn = tan 2 φ .
B R mn B L mn = 1 cos 2 φ mn 1 + cos 2 φ mn = cot 2 φ .
φ S mn = arctan ( B L mn B R mn ) 1 / 2 ,
φ mn [ 0 , 90 ° ] ; φ s mn [ 45 ° , 45 ° ] ; ( B L mn B R mn ) 1 / 2 [ 0 , ] .
φ S mn = arccot ( B L mn B R mn ) 1 / 2 ,
φ mn [ 90 ° , 0 ] ; φ mn [ 135 ° , 45 ° ] ; ( B L mn B R mn ) 1 / 2 [ 0 , ] .
δ S m ( 2 n 1 ) = arccos ( B L m ( 2 n 1 ) B R m ( 2 n 1 ) B L m ( 2 n 1 ) + B R m ( 2 n 1 ) ) ,
δ S m ( 2 n ) = arccos ( B L m ( 2 n ) B R m ( 2 n ) ) B L m ( 2 n ) + B R m ( 2 n ) ) = π arccos ( B L m ( 2 n ) B R m ( 2 n ) ) B L m ( 2 n ) + B R m ( 2 n ) ) .

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