大口徑投影機鏡頭設計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並對溫度變化作分析

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姓名

周柏亨(Bo-Heng Zhou) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

大口徑投影機鏡頭設計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並對溫度變化作分析

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摘要(中)

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22C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。

摘要(英)

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 10C to 80C. 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 22C 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.

關鍵字(中)

★ 大口徑投影機鏡頭設計
★ 螢幕之直線鑑別率
★ 螢幕之橫向色差鑑別率
★ 消熱差
★ 相對照度
★ 電視畸變

關鍵字(英)

★ Large-aperture projection lens
★ athermalization
★ the horizontal line resolutions
★ vertical line resolutions,
★ lateral color resolutions
★ TV distortion
★ relative illumination

論文目次

目錄
摘要 I
ABSTRACT II
誌謝 III
圖目錄 VIII
表目錄 XVI
第一章緒論 1
1-1 前言 1
1-2 研究動機 1
1-3 文獻回顧 2
1-4 論文架構 14
第二章理論 15
2-1 溫度對鏡頭設計之影響 15
2-1-1 玻璃折射率與波長關係 15
2-1-2 玻璃折射率與溫度關係 16
2-1-3 溫度變化與熱膨脹係數對鏡片參數的影響 17
2-1-4 屈光度變化與dn/dt關係 18
2-2 畸變 19
2-2-1 光學畸變 19
2-2-2 電視畸變 20
2-3 DMD規格與DMD offset設定 22
2-3-1 DMD規格 22
2-3-2 DMD offset設定 22
2-4 螢幕大小尺寸 24
2-4-1 螢幕大小尺寸 24
2-5 直線鑑別率 25
2-5-1 螢幕畫面視場設定 25
2-5-2 水平直線扭曲量定義與計算 26
2-5-3 垂直直線扭曲量定義與計算 28
2-5-4 螢幕畫面水平直線與垂直直線之鑑別率定義 31
2-6 電視畸變與光學畸變關係 33
2-6-1 水平電視畸變與水平扭曲量關係 33
2-6-2 水平電視畸變與光學畸變關係 34
2-6-3 垂直電視畸變與垂直扭曲量關係 35
2-6-4 垂直電視畸變與光學畸變關係 36
2-7 橫向色差 36
2-7-1 橫向色差 36
2-7-2 橫向色差之鑑別率 37
2-8 相對照度 37
2-8-1介面穿透率(ST) 38
2-8-2垂直入射反射率與介面穿透率定義 38
2-8-3斜向入射反射率與介面穿透率(〖ST〗_θ)定義 39
2-8-4 鏡片內部穿透率(ITd)定義 41
2-8-5立體角定義 42
2-8-6投影立體角與正向立體角關係 47
2-8-7 相對照度公式 48
第三章螢幕為物、DMD為像之鏡頭設計 50
3-1 室溫22C投影機鏡頭設計 50
3-1-1 投影鏡頭設計規格 50
3-1-2 投影鏡頭設計目標 51
3-1-3 起始值 52
3-1-4 優化過程 58
3-1-5 設計結果 66
3-2 環境溫度10C~80C參數值設定 67
3-2-1 溫度範圍選取 67
3-2-2 不同溫度參數值的變動 67
3-2-3 熱玻璃常數以及熱膨脹係數(α、) 71
3-3 環境溫度10C~80C消熱差設計 72
3-3-1消熱差補償 72
3-3-2消熱差前之成像品質 72
3-3-3鏡片材料與鏡筒材料之選取 74
3-4 設計結果 77
3-4-1 鏡組資料 77
3-4-2 Modulation Transfer Function(MTF) 79
3-4-3 橫向色差 85
3-4-4 光學畸變 90
3-4-5 相對照度 95
第四章 DMD為物，螢幕為像之溫度變化與成像品質分析 101
4-1 利用軟體內建marco反轉系統 101
4-2 DMD為物、螢幕為像之初階設計 102
4-3 Modulation Transfer Function(MTF) 102
4-4 橫向色差 106
4-5 畸變 110
4-6 水平、垂直直線鑑別率 113
4-7 相對照度 115
4-8 公差分析 119
第五章結論 128
參考資料 129

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指導教授

孫文信(Wen-Shing Sun)

審核日期

2020-7-15

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