本文為大口徑投影機鏡頭設計探討投射在螢幕上之直線鑑別率、橫向色差鑑別率、相對照度與MTF並對溫度變化做分析，由十五片玻璃球面鏡片組成，含兩片平板玻璃，有效焦距24.06 mm，F/#為1.71，半視角為24.62 ，投影屏幕大小為206吋。在設計時先以室溫22C設計開始，螢幕為物、DMD為像的鏡頭設計，設定DMD offset為100%、最大像高為11.0387 mm。由推導電視畸變與光學畸變關係，控制投影機光學畸變量來使水平扭曲量及垂直扭曲量遠小於人眼鑑別率1分。並推導相對照度與介面穿透率、內部穿透率與立體角關係，利用光暈因子控制離軸立體角及遠心系統使相對照度提高。而溫度變化對鏡頭而言會造成鏡頭光學品質也就是MTF下降。為了解決MTF下降的問題，本文在消熱差設計以改變鏡片材料與鏡筒材料來達到消熱差效果。 最後再將設計時以DMD為像的光學系統完整的反轉，來模擬分析以螢幕為像之水平、垂直鑑別率、橫向色差鑑別率、電視畸變。而螢幕畫面上的橫向色差、水平、垂直直線鑑別率需由人眼鑑別。而人眼鑑別率為1，而在一般大型會議廳第一排至螢幕距離約為4000 mm時，橫向色差鑑別率與水平、垂直直線鑑別率皆可小於人眼鑑別率，使人眼無法分辨色差與扭曲量。 ;This paper is large-aperture projection lens design which dicuss relative illumination, MTF, the horizontal line resolutions, vertical line resolutions and lateral color resolutions on the screen at an ambient temperature of 10C to 80C. It is composed of 15 glass lenses (all spherical surface) with a focal length of 24.06 mm, F/# is 1.71, the maxium of half-FOV (field of view) is 24.62 drgree, and projection screen size is 206 inches.In the paper, we need to start with the room temperature 22C design which is the screen as the object and the DMD as the image, and then we set the DMD offset to 100 %, so the maximum image height is 11.0387 mm. We derive the optical distortion and TV distortion, so we can control optical distortion of projection lens so that human eyes cannot distinguish the horizontal and vertical line warping of screen. We can control Off-axis solid angle and use telecentric system to improve the relative illumination. The temperature change will cause the lens image quality that is MTF to decrease. In order to solve the problem of decline in MTF, we change the material of the lens and the material of the barrel to achieve athermalization. Finally, we need flip the system that is DMD as the object and the screen as the image because we simulate and analyze the horizontal line resolutions, vertical line resolutions, lateral color resolutions and TV distortion with screen as image. In order to match the resolution of the human eye (at the distance from the first row to the screen of a large conference hall is about 4000 mm ) which is 1 it is necessary for the horizontal and vertical line resolutions and the lateral color resolution to be less than 1.
