Abstract

In a new type of illumination system for reflective liquid-crystal displays, the frontlight, unwanted shadows appear in certain viewing directions. It will be shown that for an accurate description of these shadows the geometrical optics approach is not satisfactory and that Fresnel diffraction has to be taken into account. A model for the diffraction effects was developed, and the predicted results correspond well to the measurements. In addition, some remarkable effects were explained from the theory of Fresnel zones.

© 2002 Optical Society of America

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References

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  1. C. Y. Tai, H. Zou, P.-K. Tai, “Transparent frontlighting system for reflective-type displays,” SID Dig. 26, 375–378 (1995).
  2. H. J. Cornelissen, H. Greiner, M. J. J. Dona, “Frontlights for reflective LCDs based on lightguides with microgrooves,” SID Dig. 30, 912–915 (1999).
    [CrossRef]
  3. A. Gupta, J. Lee, R. J. Koshel, “Design of efficient lightpipes for illumination by an analytical approach,” Appl. Opt. 40, 3640–3648 (2001).
    [CrossRef]
  4. E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987), Chap. 4.
  5. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).
  6. M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, U.K., 1999), Chap. 8.
  7. M. Klein, T. Furtak, Optics (Wiley, New York, 1986), Chap. 7.

2001 (1)

1999 (1)

H. J. Cornelissen, H. Greiner, M. J. J. Dona, “Frontlights for reflective LCDs based on lightguides with microgrooves,” SID Dig. 30, 912–915 (1999).
[CrossRef]

1995 (1)

C. Y. Tai, H. Zou, P.-K. Tai, “Transparent frontlighting system for reflective-type displays,” SID Dig. 26, 375–378 (1995).

Born, M.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, U.K., 1999), Chap. 8.

Cornelissen, H. J.

H. J. Cornelissen, H. Greiner, M. J. J. Dona, “Frontlights for reflective LCDs based on lightguides with microgrooves,” SID Dig. 30, 912–915 (1999).
[CrossRef]

Dona, M. J. J.

H. J. Cornelissen, H. Greiner, M. J. J. Dona, “Frontlights for reflective LCDs based on lightguides with microgrooves,” SID Dig. 30, 912–915 (1999).
[CrossRef]

Furtak, T.

M. Klein, T. Furtak, Optics (Wiley, New York, 1986), Chap. 7.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

Greiner, H.

H. J. Cornelissen, H. Greiner, M. J. J. Dona, “Frontlights for reflective LCDs based on lightguides with microgrooves,” SID Dig. 30, 912–915 (1999).
[CrossRef]

Gupta, A.

Hecht, E.

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987), Chap. 4.

Klein, M.

M. Klein, T. Furtak, Optics (Wiley, New York, 1986), Chap. 7.

Koshel, R. J.

Lee, J.

Tai, C. Y.

C. Y. Tai, H. Zou, P.-K. Tai, “Transparent frontlighting system for reflective-type displays,” SID Dig. 26, 375–378 (1995).

Tai, P.-K.

C. Y. Tai, H. Zou, P.-K. Tai, “Transparent frontlighting system for reflective-type displays,” SID Dig. 26, 375–378 (1995).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, U.K., 1999), Chap. 8.

Zou, H.

C. Y. Tai, H. Zou, P.-K. Tai, “Transparent frontlighting system for reflective-type displays,” SID Dig. 26, 375–378 (1995).

Appl. Opt. (1)

SID Dig. (2)

C. Y. Tai, H. Zou, P.-K. Tai, “Transparent frontlighting system for reflective-type displays,” SID Dig. 26, 375–378 (1995).

H. J. Cornelissen, H. Greiner, M. J. J. Dona, “Frontlights for reflective LCDs based on lightguides with microgrooves,” SID Dig. 30, 912–915 (1999).
[CrossRef]

Other (4)

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987), Chap. 4.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, U.K., 1999), Chap. 8.

M. Klein, T. Furtak, Optics (Wiley, New York, 1986), Chap. 7.

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Figures (11)

Fig. 1
Fig. 1

Front light with microgrooves. The fluorescent lamp, L, is the light source. The constructed rays are explained in the text.

Fig. 2
Fig. 2

Experimental setup, with examples of pictures. (a) Picture taken with a wide-angle lens and (b) one shadow band zoomed in on.

Fig. 3
Fig. 3

Three-dimensional situation for the localization of the shadows in the frontlight. Two grooves (k and m) are drawn with their mirror image (k′ and m′) in the lower surface, L, of the frontlight. O is the center of the circles of the grooves in the master plate.

Fig. 4
Fig. 4

Results of the matlab simulation for the localization of the shadows. (a) d = 1.85 mm, n = 1.49, and p = 500 µm and (b) d = 0.9 mm, n = 1.49 and p = 500 µm. The black curves with dots are the measured values. The gray strokes indicate the calculated area of the shadow.

Fig. 5
Fig. 5

Cross section of the geometrical situation to derive the diffraction effects on a narrow obstruction with a line source. P 0 is the point source, and P is the point of observation. The origin, O, is chosen on P 0 P in the intersection with the aperture.

Fig. 6
Fig. 6

Illustration of the virtual groove in the reflection on the lower surface, L, of the frontlight. It seems that R comes from the virtual groove G′. The dimensions are heavily exaggerated.

Fig. 7
Fig. 7

Comparison between the calculated shadow profile with the diffraction effects (solid curve) and the geometrical shadow (dashed curve). The parameter values are t = 15 µm, d = 3700 µm, and n = 1.49. In the model, polychromatic light is used.

Fig. 8
Fig. 8

Several plots of the intensity profile for polychromatic light resulting from the model with varying width of the grooves [(a) 5, 10, and 15 µm; (b) 25, 50, and 100 µm]. The other parameter values are d = 3700 µm and n = 1.49.

Fig. 9
Fig. 9

Results of the measurements and calculated values by use of the model for polychromatic light. The parameter values are t = 15 µm, d = 3700 µm, and n = 1.49.

Fig. 10
Fig. 10

Results of the measurements and calculated values by use of the model for monochromatic light with λ1 = 630 nm. The other parameter values are t = 15 µm, d = 3700 µm, and n = 1.49.

Fig. 11
Fig. 11

Results of the measurements and calculated values by use of the model for monochromatic light with λ2 = 447 nm. The other parameter values are t = 15 µm, d = 3700 µm, and n = 1.49.

Equations (11)

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θkm=tan-1Rm2-2RmRk cos γm cos γk-2RmRk sin γm sin γk+Rk21/2/d, ϕkm=tan-1Rm sin γm-Rk sin γkRm cos γm-Rk cos γk,
C= W cosπλ1r+1sξ2 cos2 δ+η2dξdη, S= W sinπλ1r+1sξ2 cos2 δ+η2dξdη.
-<ξ<-12 t-d tan θ, 12 t-d tan θ<ξ<, -<η<,
πλ1r+1sξ2 cos2 δ=π2 u2,πλ1r+1sη2=π2 v2,
C=b  W cosπ2u2+v2dudv, S=b  W sinπ2u2+v2dudv,
-<u<wl, wu<u<, -<v<,
wu=2λ1r+1s1/212 t-d tan θcos θ, wl=2λ1r+1s1/2-12 t-d tan θcos θ.
wu=2λd1/212 t-d tan θcos θ3/2, wl=2λd1/2-12 t-d tan θcos θ3/2.
C=b-wldu -dv+wudu -dv×cosπ2 u2cosπ2 v2-sinπ2 u2sinπ2 v2, S=b-wldu -dv+wudu -dv×sinπ2 u2cosπ2 v2+cosπ2 u2sinπ2 v2.
Iθ=142+Cwl-Cwu+Swl-Swu2+Cwl-Cwu-Swl+Swu2,
s1=2λ0dn1/2.

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