本論文欲利用雙層光柵期望將光源進行分光，藍、綠、紅光波長混合
的白光經過光柵後，因波長不同造成之繞射角度不同而分離藍光、綠光和
紅光三種色光，並使用橢圓透鏡微結構聚焦在一個畫素中相對於彩色濾光
片藍、綠、紅光的位置。
利用雙面光柵的設計增加藍、綠、紅光波長的繞射角度差，並且兼顧
最大穿透繞射階的效率。光柵分光後再利用橢圓透鏡微結構，使最大穿透
繞射階的效率和次兩階穿透繞射階的效率重疊在一個畫素中藍、綠、紅光
的位置。
在使用理想光源時，在色域圖上面積最高可以達到NTSC 的80.11%；
在能量利用率上，最佳效率有70.73%遠比使用彩色濾光片時高。在考慮實際背光的角度下，同樣架構在色域圖上面積有NTSC 的65.86%，在能量利用率上，效率有43.13%依然比使用彩色濾光片時高。此結果說明將光柵分光利用在背光系統可改善目前使用彩色濾光片導致效率較低之問題。

This study proposes a feasible design of color separation for a collimated
backlight to realize a color-filter-free liquid crystal display (LCD). The design
includes a double-sided saw-tooth grating and array of elliptical cylindrical lenses
attached to the LC panel. The double-sided saw-tooth grating can diffract the
collimated light beam composed of red, green, and blue light beams; and separate
them from each other for about 5 degrees, which is the key point to realized color
separation.
However, the efficiency of the main-order diffraction decreases as increase in
the separation angle between the color light beams. To overcome this problem,
we design the array of elliptical cylindrical lenses to concentrate the diffracted
color light beams on the corresponding subpixel and let the subpixel receive the
color light beams of different diffraction orders. For an ideal collimated backlight
with a half angle of 2.5 degrees and three light sources of 465, 530, and 625 nm,
the optimal design performs color gamut 80.11% and optical efficiency 70.73. For
a practical collimated backlight with a half angle of 5 degrees (5-degree FWHM)
and three LED light sources (considering wavelength width), the optimal design
performs color gamut 71% and optical efficiency 37.16, whose color gamut is
comparable and efficiency is increased 30% as compared with the traditional LCD.

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