Abstract

Color gamut and static and dynamic color shifts of a multi-domain in-plane-switching liquid crystal display (IPS LCD) are calculated quantitatively using RGB (red, green, and blue) light-emitting diodes (LEDs) and cold-cathode fluorescent lamp (CCFL) backlights. Simulation results indicate that the LED backlight exhibits a wider color gamut, better angular color uniformity, and 2-4X smaller static and dynamic color shifts than the CCFL system.

© 2006 Optical Society of America

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References

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  1. G. Harbers and C. Hoelen, “High performance LCD backlight using high intensity red, green and blue light emitting diodes,” Soc. Inf. Display Tech. Digest 32, 702–705 (2001).
    [Crossref]
  2. R. West, H. Konijn, W. Silevis-Smitt, S. Kuppens, N. Pfeffer, Y. Martynov, Y. Takaaki, S. Eberle, G. Harbers, T. Tan, and C. Chan, “High brightness direct LED backlight for LCD-TV,” Soc. Inf. Display Tech. Digest 34, 1262–1265 (2003).
    [Crossref]
  3. H. Hsieh, C. Chou, and W. Li, “Vivid color and clear motion picture 32-inch TFT-LCD TV with scan RGB LED backlight,” Proc. Int’l Display Manufacturing Conf. pp. 622–644 (2005).
  4. A. Konno, Y. Yamamoto, and T. Inuzuka, “RGB color control system for LED backlight in IPS-LCD TVs,” Soc. Inf. Display Tech. Digest 36, 1380–1383 (2005).
    [Crossref]
  5. W. Kim, “Technology overview: LCDs for TV application,” J. SID 12, 449–453 (2004).
  6. S. Aratani, H. Klausmann, M. Oh-e, M. Ohta, K. Ashizawa, K. Yanagawa, and K. Kondo, “Complete suppression of color shift in in-plane switching mode liquid crystal displays with a multidomain structure obtained by unidirectional rubbing,” Jpn. J. Appl. Phys. 36, L27–L29 (1997).
    [Crossref]
  7. H. Klausmann, S. Aratani, and K. Kondo, “Optical characterization of the in-plane switching effect utilizing multidomain structures,” J. Appl. Phys. 83, 1854–1862 (1998).
    [Crossref]
  8. R. Lu, X. Zhu, S. T. Wu, Q. Hong, and T. X. Wu, “Ultrawide-view liquid crystal displays,” J. Display Technology 1, 3–14 (2005).
    [Crossref]
  9. M. Fairchild, Color Appearance Models (2nd Edition), (Wiley, New York, 2005).
  10. F. Bunting, Color Primer -- An Introduction to the History of Color, Color Theory, and Color Measurement, (Light Source Computer Images, Inc., 1998).
  11. N. Ohta and A. Robertson, Colorimetry -- Fundamentals and Applications, (Wiley, New York, 2005).
    [Crossref]
  12. G. Wyszecki and W. Stiles, Color Science -- Concepts and Methods, Quantitative Data and Formulate (2nd Edition), (Wiley, New York, 1982).
  13. R. Hunt, Measuring Colour (2nd Edition), (Ellis Horwood, West Sussex, 1991).
  14. S. T. Wu, “Birefringence dispersion of liquid crystals”, Phys. Rev. A33, 1270–1274 (1986).
  15. R. Lu, S. T. Wu, Z. Ge, Q. Hong, and T. X. Wu, “Bending angle effects on the multi-domain in-plane-switching liquid crystal displays,” J. Display Technology 1, 207–216 (2005).
    [Crossref]
  16. A. Lien, “A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays,” Liq. Cryst. 22, 171–175 (1997).
    [Crossref]
  17. P. Downen, “A closer look at flat-panel-display measurement standards and trends,” Information Display 22, 16–21 (2006).

2006 (1)

P. Downen, “A closer look at flat-panel-display measurement standards and trends,” Information Display 22, 16–21 (2006).

2005 (3)

A. Konno, Y. Yamamoto, and T. Inuzuka, “RGB color control system for LED backlight in IPS-LCD TVs,” Soc. Inf. Display Tech. Digest 36, 1380–1383 (2005).
[Crossref]

R. Lu, X. Zhu, S. T. Wu, Q. Hong, and T. X. Wu, “Ultrawide-view liquid crystal displays,” J. Display Technology 1, 3–14 (2005).
[Crossref]

R. Lu, S. T. Wu, Z. Ge, Q. Hong, and T. X. Wu, “Bending angle effects on the multi-domain in-plane-switching liquid crystal displays,” J. Display Technology 1, 207–216 (2005).
[Crossref]

2004 (1)

W. Kim, “Technology overview: LCDs for TV application,” J. SID 12, 449–453 (2004).

2003 (1)

R. West, H. Konijn, W. Silevis-Smitt, S. Kuppens, N. Pfeffer, Y. Martynov, Y. Takaaki, S. Eberle, G. Harbers, T. Tan, and C. Chan, “High brightness direct LED backlight for LCD-TV,” Soc. Inf. Display Tech. Digest 34, 1262–1265 (2003).
[Crossref]

2001 (1)

G. Harbers and C. Hoelen, “High performance LCD backlight using high intensity red, green and blue light emitting diodes,” Soc. Inf. Display Tech. Digest 32, 702–705 (2001).
[Crossref]

1998 (1)

H. Klausmann, S. Aratani, and K. Kondo, “Optical characterization of the in-plane switching effect utilizing multidomain structures,” J. Appl. Phys. 83, 1854–1862 (1998).
[Crossref]

1997 (2)

S. Aratani, H. Klausmann, M. Oh-e, M. Ohta, K. Ashizawa, K. Yanagawa, and K. Kondo, “Complete suppression of color shift in in-plane switching mode liquid crystal displays with a multidomain structure obtained by unidirectional rubbing,” Jpn. J. Appl. Phys. 36, L27–L29 (1997).
[Crossref]

A. Lien, “A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays,” Liq. Cryst. 22, 171–175 (1997).
[Crossref]

1986 (1)

S. T. Wu, “Birefringence dispersion of liquid crystals”, Phys. Rev. A33, 1270–1274 (1986).

Aratani, S.

H. Klausmann, S. Aratani, and K. Kondo, “Optical characterization of the in-plane switching effect utilizing multidomain structures,” J. Appl. Phys. 83, 1854–1862 (1998).
[Crossref]

S. Aratani, H. Klausmann, M. Oh-e, M. Ohta, K. Ashizawa, K. Yanagawa, and K. Kondo, “Complete suppression of color shift in in-plane switching mode liquid crystal displays with a multidomain structure obtained by unidirectional rubbing,” Jpn. J. Appl. Phys. 36, L27–L29 (1997).
[Crossref]

Ashizawa, K.

S. Aratani, H. Klausmann, M. Oh-e, M. Ohta, K. Ashizawa, K. Yanagawa, and K. Kondo, “Complete suppression of color shift in in-plane switching mode liquid crystal displays with a multidomain structure obtained by unidirectional rubbing,” Jpn. J. Appl. Phys. 36, L27–L29 (1997).
[Crossref]

Bunting, F.

F. Bunting, Color Primer -- An Introduction to the History of Color, Color Theory, and Color Measurement, (Light Source Computer Images, Inc., 1998).

Chan, C.

R. West, H. Konijn, W. Silevis-Smitt, S. Kuppens, N. Pfeffer, Y. Martynov, Y. Takaaki, S. Eberle, G. Harbers, T. Tan, and C. Chan, “High brightness direct LED backlight for LCD-TV,” Soc. Inf. Display Tech. Digest 34, 1262–1265 (2003).
[Crossref]

Chou, C.

H. Hsieh, C. Chou, and W. Li, “Vivid color and clear motion picture 32-inch TFT-LCD TV with scan RGB LED backlight,” Proc. Int’l Display Manufacturing Conf. pp. 622–644 (2005).

Downen, P.

P. Downen, “A closer look at flat-panel-display measurement standards and trends,” Information Display 22, 16–21 (2006).

Eberle, S.

R. West, H. Konijn, W. Silevis-Smitt, S. Kuppens, N. Pfeffer, Y. Martynov, Y. Takaaki, S. Eberle, G. Harbers, T. Tan, and C. Chan, “High brightness direct LED backlight for LCD-TV,” Soc. Inf. Display Tech. Digest 34, 1262–1265 (2003).
[Crossref]

Fairchild, M.

M. Fairchild, Color Appearance Models (2nd Edition), (Wiley, New York, 2005).

Ge, Z.

R. Lu, S. T. Wu, Z. Ge, Q. Hong, and T. X. Wu, “Bending angle effects on the multi-domain in-plane-switching liquid crystal displays,” J. Display Technology 1, 207–216 (2005).
[Crossref]

Harbers, G.

R. West, H. Konijn, W. Silevis-Smitt, S. Kuppens, N. Pfeffer, Y. Martynov, Y. Takaaki, S. Eberle, G. Harbers, T. Tan, and C. Chan, “High brightness direct LED backlight for LCD-TV,” Soc. Inf. Display Tech. Digest 34, 1262–1265 (2003).
[Crossref]

G. Harbers and C. Hoelen, “High performance LCD backlight using high intensity red, green and blue light emitting diodes,” Soc. Inf. Display Tech. Digest 32, 702–705 (2001).
[Crossref]

Hoelen, C.

G. Harbers and C. Hoelen, “High performance LCD backlight using high intensity red, green and blue light emitting diodes,” Soc. Inf. Display Tech. Digest 32, 702–705 (2001).
[Crossref]

Hong, Q.

R. Lu, X. Zhu, S. T. Wu, Q. Hong, and T. X. Wu, “Ultrawide-view liquid crystal displays,” J. Display Technology 1, 3–14 (2005).
[Crossref]

R. Lu, S. T. Wu, Z. Ge, Q. Hong, and T. X. Wu, “Bending angle effects on the multi-domain in-plane-switching liquid crystal displays,” J. Display Technology 1, 207–216 (2005).
[Crossref]

Hsieh, H.

H. Hsieh, C. Chou, and W. Li, “Vivid color and clear motion picture 32-inch TFT-LCD TV with scan RGB LED backlight,” Proc. Int’l Display Manufacturing Conf. pp. 622–644 (2005).

Hunt, R.

R. Hunt, Measuring Colour (2nd Edition), (Ellis Horwood, West Sussex, 1991).

Inuzuka, T.

A. Konno, Y. Yamamoto, and T. Inuzuka, “RGB color control system for LED backlight in IPS-LCD TVs,” Soc. Inf. Display Tech. Digest 36, 1380–1383 (2005).
[Crossref]

Kim, W.

W. Kim, “Technology overview: LCDs for TV application,” J. SID 12, 449–453 (2004).

Klausmann, H.

H. Klausmann, S. Aratani, and K. Kondo, “Optical characterization of the in-plane switching effect utilizing multidomain structures,” J. Appl. Phys. 83, 1854–1862 (1998).
[Crossref]

S. Aratani, H. Klausmann, M. Oh-e, M. Ohta, K. Ashizawa, K. Yanagawa, and K. Kondo, “Complete suppression of color shift in in-plane switching mode liquid crystal displays with a multidomain structure obtained by unidirectional rubbing,” Jpn. J. Appl. Phys. 36, L27–L29 (1997).
[Crossref]

Kondo, K.

H. Klausmann, S. Aratani, and K. Kondo, “Optical characterization of the in-plane switching effect utilizing multidomain structures,” J. Appl. Phys. 83, 1854–1862 (1998).
[Crossref]

S. Aratani, H. Klausmann, M. Oh-e, M. Ohta, K. Ashizawa, K. Yanagawa, and K. Kondo, “Complete suppression of color shift in in-plane switching mode liquid crystal displays with a multidomain structure obtained by unidirectional rubbing,” Jpn. J. Appl. Phys. 36, L27–L29 (1997).
[Crossref]

Konijn, H.

R. West, H. Konijn, W. Silevis-Smitt, S. Kuppens, N. Pfeffer, Y. Martynov, Y. Takaaki, S. Eberle, G. Harbers, T. Tan, and C. Chan, “High brightness direct LED backlight for LCD-TV,” Soc. Inf. Display Tech. Digest 34, 1262–1265 (2003).
[Crossref]

Konno, A.

A. Konno, Y. Yamamoto, and T. Inuzuka, “RGB color control system for LED backlight in IPS-LCD TVs,” Soc. Inf. Display Tech. Digest 36, 1380–1383 (2005).
[Crossref]

Kuppens, S.

R. West, H. Konijn, W. Silevis-Smitt, S. Kuppens, N. Pfeffer, Y. Martynov, Y. Takaaki, S. Eberle, G. Harbers, T. Tan, and C. Chan, “High brightness direct LED backlight for LCD-TV,” Soc. Inf. Display Tech. Digest 34, 1262–1265 (2003).
[Crossref]

Li, W.

H. Hsieh, C. Chou, and W. Li, “Vivid color and clear motion picture 32-inch TFT-LCD TV with scan RGB LED backlight,” Proc. Int’l Display Manufacturing Conf. pp. 622–644 (2005).

Lien, A.

A. Lien, “A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays,” Liq. Cryst. 22, 171–175 (1997).
[Crossref]

Lu, R.

R. Lu, S. T. Wu, Z. Ge, Q. Hong, and T. X. Wu, “Bending angle effects on the multi-domain in-plane-switching liquid crystal displays,” J. Display Technology 1, 207–216 (2005).
[Crossref]

R. Lu, X. Zhu, S. T. Wu, Q. Hong, and T. X. Wu, “Ultrawide-view liquid crystal displays,” J. Display Technology 1, 3–14 (2005).
[Crossref]

Martynov, Y.

R. West, H. Konijn, W. Silevis-Smitt, S. Kuppens, N. Pfeffer, Y. Martynov, Y. Takaaki, S. Eberle, G. Harbers, T. Tan, and C. Chan, “High brightness direct LED backlight for LCD-TV,” Soc. Inf. Display Tech. Digest 34, 1262–1265 (2003).
[Crossref]

Oh-e, M.

S. Aratani, H. Klausmann, M. Oh-e, M. Ohta, K. Ashizawa, K. Yanagawa, and K. Kondo, “Complete suppression of color shift in in-plane switching mode liquid crystal displays with a multidomain structure obtained by unidirectional rubbing,” Jpn. J. Appl. Phys. 36, L27–L29 (1997).
[Crossref]

Ohta, M.

S. Aratani, H. Klausmann, M. Oh-e, M. Ohta, K. Ashizawa, K. Yanagawa, and K. Kondo, “Complete suppression of color shift in in-plane switching mode liquid crystal displays with a multidomain structure obtained by unidirectional rubbing,” Jpn. J. Appl. Phys. 36, L27–L29 (1997).
[Crossref]

Ohta, N.

N. Ohta and A. Robertson, Colorimetry -- Fundamentals and Applications, (Wiley, New York, 2005).
[Crossref]

Pfeffer, N.

R. West, H. Konijn, W. Silevis-Smitt, S. Kuppens, N. Pfeffer, Y. Martynov, Y. Takaaki, S. Eberle, G. Harbers, T. Tan, and C. Chan, “High brightness direct LED backlight for LCD-TV,” Soc. Inf. Display Tech. Digest 34, 1262–1265 (2003).
[Crossref]

Robertson, A.

N. Ohta and A. Robertson, Colorimetry -- Fundamentals and Applications, (Wiley, New York, 2005).
[Crossref]

Silevis-Smitt, W.

R. West, H. Konijn, W. Silevis-Smitt, S. Kuppens, N. Pfeffer, Y. Martynov, Y. Takaaki, S. Eberle, G. Harbers, T. Tan, and C. Chan, “High brightness direct LED backlight for LCD-TV,” Soc. Inf. Display Tech. Digest 34, 1262–1265 (2003).
[Crossref]

Stiles, W.

G. Wyszecki and W. Stiles, Color Science -- Concepts and Methods, Quantitative Data and Formulate (2nd Edition), (Wiley, New York, 1982).

Takaaki, Y.

R. West, H. Konijn, W. Silevis-Smitt, S. Kuppens, N. Pfeffer, Y. Martynov, Y. Takaaki, S. Eberle, G. Harbers, T. Tan, and C. Chan, “High brightness direct LED backlight for LCD-TV,” Soc. Inf. Display Tech. Digest 34, 1262–1265 (2003).
[Crossref]

Tan, T.

R. West, H. Konijn, W. Silevis-Smitt, S. Kuppens, N. Pfeffer, Y. Martynov, Y. Takaaki, S. Eberle, G. Harbers, T. Tan, and C. Chan, “High brightness direct LED backlight for LCD-TV,” Soc. Inf. Display Tech. Digest 34, 1262–1265 (2003).
[Crossref]

West, R.

R. West, H. Konijn, W. Silevis-Smitt, S. Kuppens, N. Pfeffer, Y. Martynov, Y. Takaaki, S. Eberle, G. Harbers, T. Tan, and C. Chan, “High brightness direct LED backlight for LCD-TV,” Soc. Inf. Display Tech. Digest 34, 1262–1265 (2003).
[Crossref]

Wu, S. T.

R. Lu, S. T. Wu, Z. Ge, Q. Hong, and T. X. Wu, “Bending angle effects on the multi-domain in-plane-switching liquid crystal displays,” J. Display Technology 1, 207–216 (2005).
[Crossref]

R. Lu, X. Zhu, S. T. Wu, Q. Hong, and T. X. Wu, “Ultrawide-view liquid crystal displays,” J. Display Technology 1, 3–14 (2005).
[Crossref]

S. T. Wu, “Birefringence dispersion of liquid crystals”, Phys. Rev. A33, 1270–1274 (1986).

Wu, T. X.

R. Lu, S. T. Wu, Z. Ge, Q. Hong, and T. X. Wu, “Bending angle effects on the multi-domain in-plane-switching liquid crystal displays,” J. Display Technology 1, 207–216 (2005).
[Crossref]

R. Lu, X. Zhu, S. T. Wu, Q. Hong, and T. X. Wu, “Ultrawide-view liquid crystal displays,” J. Display Technology 1, 3–14 (2005).
[Crossref]

Wyszecki, G.

G. Wyszecki and W. Stiles, Color Science -- Concepts and Methods, Quantitative Data and Formulate (2nd Edition), (Wiley, New York, 1982).

Yamamoto, Y.

A. Konno, Y. Yamamoto, and T. Inuzuka, “RGB color control system for LED backlight in IPS-LCD TVs,” Soc. Inf. Display Tech. Digest 36, 1380–1383 (2005).
[Crossref]

Yanagawa, K.

S. Aratani, H. Klausmann, M. Oh-e, M. Ohta, K. Ashizawa, K. Yanagawa, and K. Kondo, “Complete suppression of color shift in in-plane switching mode liquid crystal displays with a multidomain structure obtained by unidirectional rubbing,” Jpn. J. Appl. Phys. 36, L27–L29 (1997).
[Crossref]

Zhu, X.

R. Lu, X. Zhu, S. T. Wu, Q. Hong, and T. X. Wu, “Ultrawide-view liquid crystal displays,” J. Display Technology 1, 3–14 (2005).
[Crossref]

Information Display (1)

P. Downen, “A closer look at flat-panel-display measurement standards and trends,” Information Display 22, 16–21 (2006).

J. Appl. Phys. (1)

H. Klausmann, S. Aratani, and K. Kondo, “Optical characterization of the in-plane switching effect utilizing multidomain structures,” J. Appl. Phys. 83, 1854–1862 (1998).
[Crossref]

J. Display Technology (2)

R. Lu, X. Zhu, S. T. Wu, Q. Hong, and T. X. Wu, “Ultrawide-view liquid crystal displays,” J. Display Technology 1, 3–14 (2005).
[Crossref]

R. Lu, S. T. Wu, Z. Ge, Q. Hong, and T. X. Wu, “Bending angle effects on the multi-domain in-plane-switching liquid crystal displays,” J. Display Technology 1, 207–216 (2005).
[Crossref]

J. SID (1)

W. Kim, “Technology overview: LCDs for TV application,” J. SID 12, 449–453 (2004).

Jpn. J. Appl. Phys. (1)

S. Aratani, H. Klausmann, M. Oh-e, M. Ohta, K. Ashizawa, K. Yanagawa, and K. Kondo, “Complete suppression of color shift in in-plane switching mode liquid crystal displays with a multidomain structure obtained by unidirectional rubbing,” Jpn. J. Appl. Phys. 36, L27–L29 (1997).
[Crossref]

Liq. Cryst. (1)

A. Lien, “A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays,” Liq. Cryst. 22, 171–175 (1997).
[Crossref]

Phys. Rev. (1)

S. T. Wu, “Birefringence dispersion of liquid crystals”, Phys. Rev. A33, 1270–1274 (1986).

Soc. Inf. Display Tech. Digest (3)

A. Konno, Y. Yamamoto, and T. Inuzuka, “RGB color control system for LED backlight in IPS-LCD TVs,” Soc. Inf. Display Tech. Digest 36, 1380–1383 (2005).
[Crossref]

G. Harbers and C. Hoelen, “High performance LCD backlight using high intensity red, green and blue light emitting diodes,” Soc. Inf. Display Tech. Digest 32, 702–705 (2001).
[Crossref]

R. West, H. Konijn, W. Silevis-Smitt, S. Kuppens, N. Pfeffer, Y. Martynov, Y. Takaaki, S. Eberle, G. Harbers, T. Tan, and C. Chan, “High brightness direct LED backlight for LCD-TV,” Soc. Inf. Display Tech. Digest 34, 1262–1265 (2003).
[Crossref]

Other (6)

H. Hsieh, C. Chou, and W. Li, “Vivid color and clear motion picture 32-inch TFT-LCD TV with scan RGB LED backlight,” Proc. Int’l Display Manufacturing Conf. pp. 622–644 (2005).

M. Fairchild, Color Appearance Models (2nd Edition), (Wiley, New York, 2005).

F. Bunting, Color Primer -- An Introduction to the History of Color, Color Theory, and Color Measurement, (Light Source Computer Images, Inc., 1998).

N. Ohta and A. Robertson, Colorimetry -- Fundamentals and Applications, (Wiley, New York, 2005).
[Crossref]

G. Wyszecki and W. Stiles, Color Science -- Concepts and Methods, Quantitative Data and Formulate (2nd Edition), (Wiley, New York, 1982).

R. Hunt, Measuring Colour (2nd Edition), (Ellis Horwood, West Sussex, 1991).

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Figures (9)

Fig. 1.
Fig. 1.

(a) The electrode structure and (b) the working principle of the multi-domain IPS-LCD.

Fig. 2.
Fig. 2.

Typical director distribution of the multi-domain IPS-LCD in the central layer.

Fig. 3.
Fig. 3.

VT curve of the multi-domain IPS LCD at R=650, G=550, and B=450 nm.

Fig. 4.
Fig. 4.

(a) RGB backlight spectra of LEDs and (b) the color filter spectra from CCFL.

Fig. 5.
Fig. 5.

The RGB primaries through IPS-LCD panel for LED and CCFL backlights and NTSC standard primaries on the CIE 1976 UCS diagram.

Fig. 6.
Fig. 6.

Static color shift for RGB primaries at 60° incident angle: (a) LED and (b) CCFL.

Fig. 7.
Fig. 7.

Static color shift for RGB primaries at the varied incident angles from 0° to 80°: (a) LED and (b) CCFL.

Fig. 8.
Fig. 8.

Static color shift for RGB primaries in the horizontal and vertical directions. (a) LED and (b) CCFL.

Fig. 9.
Fig. 9.

Dynamic color shift comparison for different RGB primaries in the horizontal direction.

Equations (12)

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

X = k 380 nm 780 nm S ( λ ) x ¯ ( λ ) d λ , Y= k 380 nm 780 nm S ( λ ) y ¯ ( λ ) d λ , Z = k 380 nm 780 nm S ( λ ) z ¯ ( λ )
x = X X + Y + Z , y = Y X + Y + Z , z = Z X + Y + Z
u = 4 X X + 15 Y + 3 Z = 4 x 2 x + 12 u + 3
v = 9 Y X + 15 Y + 3 Z = 9 y 2 x + 12 y + 3
Δ u v = ( u 2 u 1 ) 2 + ( v 2 v 1 ) 2 .
Δ n = G · λ 2 · λ * 2 λ 2 λ * 2
[ E x E y ] N + 1 = J [ E x E y ] 1 = J Ext J N J N 1 J 2 J 1 J Ent [ E x E y ] 1 ,
J E n t = [ 2 cos θ p cos θ p + n p cos θ k 0 0 2 cos θ k cos θ k + n p cos θ p ] , .
J E x t = [ 2 n p cos θ k cos θ p + n p cos θ k 0 0 2 n p cos θ p cos θ k + n p cos θ p ] .
t o p = E x , N + 1 2 + cos 2 ( θ p ) E y , N + 1 2 E x , 1 2 + cos 2 ( θ p ) E y , 1 2 ,
θ p = sin 1 ( sin ( θ k ) Re ( n p ) ) .
Δ u v = ( u max u min ) ( v max v min ) ,

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