非軸對稱式光學系統應用於投影機設計

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题名:	非軸對稱式光學系統應用於投影機設計
作者:	黃宥叡;Huang, You-Ruei
贡献者:	光電科學與工程學系
关键词:	光展量;照明系統;成像系統;投影機設計
日期:	2019-08-01
上传时间:	2019-09-03 14:46:13 (UTC+8)
出版者:	國立中央大學
摘要:	本文投影機系統分為照明系統以及成像系統，照明系統採用非軸對稱式聚光鏡包含三顆RGB LED光源、兩片色彩分光鏡、透鏡陣列、中繼透鏡、TIR稜鏡系統與DMD系統。而成像系統包含103萬畫素DMD系統、TIR稜鏡與投影鏡頭，投影螢幕尺寸為60吋、投影距離為2.1米、F/#為2.4與鏡頭有效焦距為16.02 mm。而投影機系統尺寸為130.7 mm×93.2 mm×33.0 mm。聚光鏡系統主要功能為將LED光源投射至透鏡陣列入光面位置上，如果聚光鏡採用軸對稱光學系統，則光源成像在透鏡陣列入光面上其像方數值孔徑在水平與垂直方向相同，但透鏡陣列設計其水平與垂直方向數值孔徑是不相同的，因此會因兩者數值孔徑之差異造成能量的損失。如使用非軸對稱式聚光鏡系統，其水平方向與垂直方向的焦距不同，造成水平方向與垂直方向的放大率不同，使非軸對稱式聚光鏡像方之數值孔徑在水平方向與垂直方向不同，如果非軸對稱聚光鏡系統其像方數值孔徑仍匹配透鏡陣列入光面之數值孔徑，就不會有數值孔徑不匹配之現象也能提高其光效率。如果本投影機系統以光展量計算，可得光展量總效率為48.68%。本投影機使用三顆RGB LED置於不同位置，分別經過不同光路，最後光源於透鏡陣列結合在一起，在各光學元件表面設定穿透率100%的條件下，模擬光線數為2000萬且網格數為48×30，在螢幕上之效率分析，紅光總效率為47.36%、綠光總效率為41.66%、藍光總效率為45.03%以及白光總效率為43.50%，與光展量效率48.68%比較，其能量的損失是由兩片色彩分光鏡所造成。且螢幕上白光均勻度ANSI(+%)為2.71%，ANSI(-%)為-3.13%，JBMA(%)為97.80%，平均差為6.79%。最後本系統經過計算具有134.46%的sRGB色域。 ;The projection system in this study is divided into illumination system and imaging system. The illumination system adopts non-axisymmetic condenser including three RGB LED light sources, two dichroic mirrors, a lens array, a relay lens, a total internal reflection prism and digital mirror device system. The imaging system consists of an 1.03 million pixel DMD system, a TIR prism and a projection lens. The projection screen size is 60 inches, the projection distance is 2.1 meters, the F/# is 16.02 mm. The effective focal length of projection lens is 16.02 millimeter. The size of the projection system is 130.7 mm × 93.2 mm × 33 mm. The function of condenser is to project the LED light source to the entrance surface of the lens array. If the condenser adopts the axisymmetric optical system, the light source is imaged on the entrance surface of the lens array, and the numerical aperture of the image is the same in the horizontal and vertical directions, but the lens array design has different numerical apertures in the horizontal and vertical directions, so it causes energy loss and reduces efficiency. If a non-axisymmetric condenser is used, its effective focal lengths in the horizontal and vertical directions are different, and the magnifications of the horizontal and vertical directions are different, so that the numerical aperture in horizontal and vertical directions of the non-axisymmetric condenser are different. If the numerical aperture of the non-axisymmetric condenser system also matches the numerical aperture of the entrance surface of the lens array, so that light efficiency can be improved. If the projection system is calculated by etendue, the etendue efficiency is 48.68%. The projection system in this study uses three RGB LEDs in different position, respectively, through different optical paths, and finally the light source is combined in the lens array. Under the condition that the transmittance of each optical component is 100%, the number of simulated light is 20 million. The mesh is 48×30, and the efficiency analysis on the screen, the efficiency of red light is 47.36%, the efficiency of green light is 41.66%, the efficiency of blue light is 45.03%, the efficiency of white light is 43.50%. The result is compared with the etendue efficiency of 49.58%, the energy loss is caused by two dichroic mirrors. The uniformity of white light on the screen is ANSI(+%) of 2.71%, ANSI(-%) is -3.13%, JBMA(%) is 97.80%, and the average deviation is 6.79%. Finally, the projection system has 134.46% of sRGB color gamut.
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