Abstract

Cell-thickness dependence of a liquid crystal display that consists of a combination of a conventional 90° twisted nematic cell and neutral polarizers is studied from the aspects of theoretical analysis and colorimetric experiment. From a theoretical analysis of the Poincaré sphere we show the state of elliptically polarized light after the horizontal linearly polarized light passed through the cell and the transition state of elliptically polarized light when horizontal linearly polarized incident light passes through the cell. From the colorimetric experiment, it is found that chromaticity coordinates are shifted significantly at a cell thickness of 9 μm, although above this thickness they are only slightly shifted.

© 1985 Optical Society of America

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  1. M. Schadt, W. Helfrich, “Voltage Dependent Optical Activity of a Twisted Nematic Liquid Crystal,” Appl. Phys. Lett. 18, 127 (1971).
    [CrossRef]
  2. S. Kobayashi, F. Takeuchi, “Multicolor Field-Effect Liquid Crystal Display Devices,” in SID International Symposium Technical Papers (Society for Information Display, Location, 1973), p. 115.
  3. T. J. Scheffer, “New Multicolor Liquid Crystal Displays that Use a Twisted Nematic Electro-Optical Cell,” J. Appl. Phys. 44, 4799 (1973).
    [CrossRef]
  4. S. Kobayashi, T. Shimomura, “Further Study on Multicolor Display Devices with Twisted Nematic Liquid Crystals,” in Proceedings, International Conference of Liquid Crystals (Bangalore, 1973; Pramana, 1975), Suppl. p. 545.
  5. C. H. Gooch, H. A. Tarry, “The Optical Properties of Twisted Nematic Liquid Crystal Structures with Twist Angles ≤90°,” J. Phys. D 8, 1575 (1975).
    [CrossRef]
  6. R. M. A. Azzam, N. M. Bashara, “Propagation of Polarization in Liquid Crystals,” J. Opt. Soc. Am. 62, 1252 (29 (1972); “The Effect of an Optical System in the Complex-Plane and the Poincaré-Sphere Representations,” Opt. Commun. 5, 319 (1972).
    [CrossRef]
  7. D. W. Berreman, “4 × 4-Matrix Formulation for Anisotropic Media,” J. Opt. Soc. Am. 62, 502 (1972); “Optics in Smoothly Varying Structures,” J. Opt. Soc. Am. 63, 13754 (1973).
    [CrossRef]
  8. C. H. Gooch, H. A. Tarry, “Optical Characteristics of Twisted Nematic Liquid-Crystal Films,” Electron. Lett. 10, 2 (1974).
    [CrossRef]
  9. J. Grinberg, A. C. Jacobson, “Transmission Characteristics of a Twisted Nematic Liquid-Crystal Layer,” J. Opt. Soc. Am. 66, 1003 (1976).
    [CrossRef]
  10. J. E. Bigelow, K. A. Kashow, “Poincaré Sphere Analysis of Liquid Crystal Optics,” Appl. Opt. 16, 2090 (1977).
    [CrossRef] [PubMed]
  11. P. McIntyre, “Transmission of Light Through a Twisted Nematic Liquid-Crystal Layer,” J. Opt. Soc. Am. 68, 869 (1978).
    [CrossRef]
  12. D. B. Judd, G. Wyszecki, Color in Business, Science, and Industry (Wiley, New York, 1975).
  13. H. Mada, S. Kobayashi, “Wavelength and Voltage Dependences of Refractive Indices of Nematic Liquid Crystals,” Mol. Cryst. Liq. Cryst. 33, 47 (1976).
    [CrossRef]
  14. E. P. Raynes, D. K. Rowell, I. A. Schanks, “Liquid Crystal Surface Alignment Treatment Giving Controlled Low Angle Tilt,” Mol. Cryst. Liq. Cryst. 34, 105 (1976).
    [CrossRef]
  15. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), Chap. 2.

1978

P. McIntyre, “Transmission of Light Through a Twisted Nematic Liquid-Crystal Layer,” J. Opt. Soc. Am. 68, 869 (1978).
[CrossRef]

1977

1976

H. Mada, S. Kobayashi, “Wavelength and Voltage Dependences of Refractive Indices of Nematic Liquid Crystals,” Mol. Cryst. Liq. Cryst. 33, 47 (1976).
[CrossRef]

E. P. Raynes, D. K. Rowell, I. A. Schanks, “Liquid Crystal Surface Alignment Treatment Giving Controlled Low Angle Tilt,” Mol. Cryst. Liq. Cryst. 34, 105 (1976).
[CrossRef]

J. Grinberg, A. C. Jacobson, “Transmission Characteristics of a Twisted Nematic Liquid-Crystal Layer,” J. Opt. Soc. Am. 66, 1003 (1976).
[CrossRef]

1975

C. H. Gooch, H. A. Tarry, “The Optical Properties of Twisted Nematic Liquid Crystal Structures with Twist Angles ≤90°,” J. Phys. D 8, 1575 (1975).
[CrossRef]

1974

C. H. Gooch, H. A. Tarry, “Optical Characteristics of Twisted Nematic Liquid-Crystal Films,” Electron. Lett. 10, 2 (1974).
[CrossRef]

1973

T. J. Scheffer, “New Multicolor Liquid Crystal Displays that Use a Twisted Nematic Electro-Optical Cell,” J. Appl. Phys. 44, 4799 (1973).
[CrossRef]

1972

R. M. A. Azzam, N. M. Bashara, “Propagation of Polarization in Liquid Crystals,” J. Opt. Soc. Am. 62, 1252 (29 (1972); “The Effect of an Optical System in the Complex-Plane and the Poincaré-Sphere Representations,” Opt. Commun. 5, 319 (1972).
[CrossRef]

D. W. Berreman, “4 × 4-Matrix Formulation for Anisotropic Media,” J. Opt. Soc. Am. 62, 502 (1972); “Optics in Smoothly Varying Structures,” J. Opt. Soc. Am. 63, 13754 (1973).
[CrossRef]

1971

M. Schadt, W. Helfrich, “Voltage Dependent Optical Activity of a Twisted Nematic Liquid Crystal,” Appl. Phys. Lett. 18, 127 (1971).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, “Propagation of Polarization in Liquid Crystals,” J. Opt. Soc. Am. 62, 1252 (29 (1972); “The Effect of an Optical System in the Complex-Plane and the Poincaré-Sphere Representations,” Opt. Commun. 5, 319 (1972).
[CrossRef]

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, “Propagation of Polarization in Liquid Crystals,” J. Opt. Soc. Am. 62, 1252 (29 (1972); “The Effect of an Optical System in the Complex-Plane and the Poincaré-Sphere Representations,” Opt. Commun. 5, 319 (1972).
[CrossRef]

Berreman, D. W.

D. W. Berreman, “4 × 4-Matrix Formulation for Anisotropic Media,” J. Opt. Soc. Am. 62, 502 (1972); “Optics in Smoothly Varying Structures,” J. Opt. Soc. Am. 63, 13754 (1973).
[CrossRef]

Bigelow, J. E.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), Chap. 2.

Gooch, C. H.

C. H. Gooch, H. A. Tarry, “The Optical Properties of Twisted Nematic Liquid Crystal Structures with Twist Angles ≤90°,” J. Phys. D 8, 1575 (1975).
[CrossRef]

C. H. Gooch, H. A. Tarry, “Optical Characteristics of Twisted Nematic Liquid-Crystal Films,” Electron. Lett. 10, 2 (1974).
[CrossRef]

Grinberg, J.

J. Grinberg, A. C. Jacobson, “Transmission Characteristics of a Twisted Nematic Liquid-Crystal Layer,” J. Opt. Soc. Am. 66, 1003 (1976).
[CrossRef]

Helfrich, W.

M. Schadt, W. Helfrich, “Voltage Dependent Optical Activity of a Twisted Nematic Liquid Crystal,” Appl. Phys. Lett. 18, 127 (1971).
[CrossRef]

Jacobson, A. C.

J. Grinberg, A. C. Jacobson, “Transmission Characteristics of a Twisted Nematic Liquid-Crystal Layer,” J. Opt. Soc. Am. 66, 1003 (1976).
[CrossRef]

Judd, D. B.

D. B. Judd, G. Wyszecki, Color in Business, Science, and Industry (Wiley, New York, 1975).

Kashow, K. A.

Kobayashi, S.

H. Mada, S. Kobayashi, “Wavelength and Voltage Dependences of Refractive Indices of Nematic Liquid Crystals,” Mol. Cryst. Liq. Cryst. 33, 47 (1976).
[CrossRef]

S. Kobayashi, F. Takeuchi, “Multicolor Field-Effect Liquid Crystal Display Devices,” in SID International Symposium Technical Papers (Society for Information Display, Location, 1973), p. 115.

S. Kobayashi, T. Shimomura, “Further Study on Multicolor Display Devices with Twisted Nematic Liquid Crystals,” in Proceedings, International Conference of Liquid Crystals (Bangalore, 1973; Pramana, 1975), Suppl. p. 545.

Mada, H.

H. Mada, S. Kobayashi, “Wavelength and Voltage Dependences of Refractive Indices of Nematic Liquid Crystals,” Mol. Cryst. Liq. Cryst. 33, 47 (1976).
[CrossRef]

McIntyre, P.

P. McIntyre, “Transmission of Light Through a Twisted Nematic Liquid-Crystal Layer,” J. Opt. Soc. Am. 68, 869 (1978).
[CrossRef]

Raynes, E. P.

E. P. Raynes, D. K. Rowell, I. A. Schanks, “Liquid Crystal Surface Alignment Treatment Giving Controlled Low Angle Tilt,” Mol. Cryst. Liq. Cryst. 34, 105 (1976).
[CrossRef]

Rowell, D. K.

E. P. Raynes, D. K. Rowell, I. A. Schanks, “Liquid Crystal Surface Alignment Treatment Giving Controlled Low Angle Tilt,” Mol. Cryst. Liq. Cryst. 34, 105 (1976).
[CrossRef]

Schadt, M.

M. Schadt, W. Helfrich, “Voltage Dependent Optical Activity of a Twisted Nematic Liquid Crystal,” Appl. Phys. Lett. 18, 127 (1971).
[CrossRef]

Schanks, I. A.

E. P. Raynes, D. K. Rowell, I. A. Schanks, “Liquid Crystal Surface Alignment Treatment Giving Controlled Low Angle Tilt,” Mol. Cryst. Liq. Cryst. 34, 105 (1976).
[CrossRef]

Scheffer, T. J.

T. J. Scheffer, “New Multicolor Liquid Crystal Displays that Use a Twisted Nematic Electro-Optical Cell,” J. Appl. Phys. 44, 4799 (1973).
[CrossRef]

Shimomura, T.

S. Kobayashi, T. Shimomura, “Further Study on Multicolor Display Devices with Twisted Nematic Liquid Crystals,” in Proceedings, International Conference of Liquid Crystals (Bangalore, 1973; Pramana, 1975), Suppl. p. 545.

Takeuchi, F.

S. Kobayashi, F. Takeuchi, “Multicolor Field-Effect Liquid Crystal Display Devices,” in SID International Symposium Technical Papers (Society for Information Display, Location, 1973), p. 115.

Tarry, H. A.

C. H. Gooch, H. A. Tarry, “The Optical Properties of Twisted Nematic Liquid Crystal Structures with Twist Angles ≤90°,” J. Phys. D 8, 1575 (1975).
[CrossRef]

C. H. Gooch, H. A. Tarry, “Optical Characteristics of Twisted Nematic Liquid-Crystal Films,” Electron. Lett. 10, 2 (1974).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), Chap. 2.

Wyszecki, G.

D. B. Judd, G. Wyszecki, Color in Business, Science, and Industry (Wiley, New York, 1975).

Appl. Opt.

Appl. Phys. Lett.

M. Schadt, W. Helfrich, “Voltage Dependent Optical Activity of a Twisted Nematic Liquid Crystal,” Appl. Phys. Lett. 18, 127 (1971).
[CrossRef]

Electron. Lett.

C. H. Gooch, H. A. Tarry, “Optical Characteristics of Twisted Nematic Liquid-Crystal Films,” Electron. Lett. 10, 2 (1974).
[CrossRef]

J. Opt. Soc. Am.

J. Grinberg, A. C. Jacobson, “Transmission Characteristics of a Twisted Nematic Liquid-Crystal Layer,” J. Opt. Soc. Am. 66, 1003 (1976).
[CrossRef]

J. Appl. Phys.

T. J. Scheffer, “New Multicolor Liquid Crystal Displays that Use a Twisted Nematic Electro-Optical Cell,” J. Appl. Phys. 44, 4799 (1973).
[CrossRef]

J. Opt. Soc. Am.

P. McIntyre, “Transmission of Light Through a Twisted Nematic Liquid-Crystal Layer,” J. Opt. Soc. Am. 68, 869 (1978).
[CrossRef]

D. W. Berreman, “4 × 4-Matrix Formulation for Anisotropic Media,” J. Opt. Soc. Am. 62, 502 (1972); “Optics in Smoothly Varying Structures,” J. Opt. Soc. Am. 63, 13754 (1973).
[CrossRef]

J. Opt. Soc. Am.

R. M. A. Azzam, N. M. Bashara, “Propagation of Polarization in Liquid Crystals,” J. Opt. Soc. Am. 62, 1252 (29 (1972); “The Effect of an Optical System in the Complex-Plane and the Poincaré-Sphere Representations,” Opt. Commun. 5, 319 (1972).
[CrossRef]

J. Phys. D

C. H. Gooch, H. A. Tarry, “The Optical Properties of Twisted Nematic Liquid Crystal Structures with Twist Angles ≤90°,” J. Phys. D 8, 1575 (1975).
[CrossRef]

Mol. Cryst. Liq. Cryst.

H. Mada, S. Kobayashi, “Wavelength and Voltage Dependences of Refractive Indices of Nematic Liquid Crystals,” Mol. Cryst. Liq. Cryst. 33, 47 (1976).
[CrossRef]

E. P. Raynes, D. K. Rowell, I. A. Schanks, “Liquid Crystal Surface Alignment Treatment Giving Controlled Low Angle Tilt,” Mol. Cryst. Liq. Cryst. 34, 105 (1976).
[CrossRef]

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), Chap. 2.

D. B. Judd, G. Wyszecki, Color in Business, Science, and Industry (Wiley, New York, 1975).

S. Kobayashi, T. Shimomura, “Further Study on Multicolor Display Devices with Twisted Nematic Liquid Crystals,” in Proceedings, International Conference of Liquid Crystals (Bangalore, 1973; Pramana, 1975), Suppl. p. 545.

S. Kobayashi, F. Takeuchi, “Multicolor Field-Effect Liquid Crystal Display Devices,” in SID International Symposium Technical Papers (Society for Information Display, Location, 1973), p. 115.

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Figures (8)

Fig. 1
Fig. 1

Block diagram of the measuring system.

Fig. 2
Fig. 2

State of the elliptically polarized light on the Poincaré sphere after the horizontal linearly polarized light passed through the TN cell (z/d = 1). Here H, V indicate horizontal and vertical linearly polarized light.

Fig. 3
Fig. 3

Example of the transition state of the elliptically polarized light where γ = 10 when incident light passes through the TN cell.

Fig. 4
Fig. 4

Theoretical characteristics of transmittance in the visible with a change of cell thickness at 2–15 μm.

Fig. 5
Fig. 5

Wavelength dependence of birefringence of the liquid crystal E-18.

Fig. 6
Fig. 6

Example of a comparison of calculated and experimental results in the transmittance.

Fig. 7
Fig. 7

Colorimetric data of 2–10-μm cell thickness in the UCS chromaticity diagram. A closed circle stands for the light source D65.

Fig. 8
Fig. 8

Colorimetric data of 10–15-μm cell thickness in the UCS chromaticity diagram. A closed circle stands for the light source D65.

Equations (20)

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d χ / d z = [ i g 0 exp ( i 2 α z ) ] χ 2 i g 0 exp ( i 2 α z ) ,
g 0 = Δ η / 2 , α = 2 π / p ,
χ = u ( z ) exp ( i 2 α z ) ,
d u / d z = i g 0 u 2 i 2 α u i g 0 ,
u ( z , u 0 ) = ( β i α tan β z ) u 0 + ( i g 0 tan β z ) ( i g 0 tan β z ) u 0 + ( β + i α t a n β z ) ,
β = g 0 [ ( α / g 0 ) 2 + 1 ] 1 / 2 ,
χ ( z , χ 0 ) = [ ( β i α tan β z ) χ 0 + ( i g 0 tan β z ) ( i g 0 tan β z ) χ 0 + ( β + i α tan β z ) ] exp ( i 2 α z ) ,
χ = ( 1 + r 2 ) 1 / 2 + ( 1 r 2 ) tan 2 π 2 ( 1 + r 2 ) 1 / 2 + 2 i ( 1 + r 2 ) 1 / 2 tan π 2 ( 1 + r 2 ) 1 / 2 ( 1 + r 2 ) + ( 1 r ) 2 tan 2 π 2 ( 1 + r 2 ) 1 / 2 ,
A = ( 1 + γ 2 ) + ( 1 γ 2 ) tan 2 π 2 ( 1 + γ 2 ) 1 / 2 ( 1 + γ 2 ) + ( 1 γ 2 ) tan 2 π 2 ( 1 + γ 2 ) 1 / 2 ,
B = 2 ( 1 + γ 2 ) 1 / 2 tan π 2 ( 1 + γ 2 ) 1 / 2 ( 1 + γ 2 ) + ( 1 γ ) 2 tan 2 π 2 ( 1 + γ 2 ) 1 / 2 .
T = ( A 1 ) 2 + B 2 2 ( A 2 + B 2 + 1 ) = sin 2 ( 1 + γ 2 ) 1 / 2 1 + γ 2 .
[ X Y Z ] = υ i s [ x ¯ λ y ¯ λ z λ ] P λ T λ d λ ,
X = n x ¯ n P n T n ,
[ x y z ] = [ X Y Z ] / ( X + Y + Z ) .
u = 4 x 2 x + 12 y + 3 , υ = 6 y 2 x + 12 y + 3 ,
Δ n ( λ ) = a + b λ 2 + c λ 4 ,
U * = 13 W * ( u u o ) ,
V * = 13 W * ( υ υ o ) ,
W * = 25 Y 1 / 3 17 , ( 1 Y 100 ) ,
Δ E CIE = [ ( Δ U * ) 2 + ( Δ V * ) 2 + ( Δ W * ) 2 ] 1 / 2 ,

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