應用於MR波導系統中全視角65度投影鏡頭設計

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黃冠維(Guan-Wei Huang) 查詢紙本館藏

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光電科學與工程學系

論文名稱

應用於MR波導系統中全視角65度投影鏡頭設計

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至系統瀏覽論文 (2029-7-12以後開放)

摘要(中)

本投影鏡頭設計由4片玻璃球面鏡片與3片塑膠非球面鏡片所組成，鏡頭焦距20.458 mm，對角線全視角65，水平方向全視角48.50，光圈位於鏡頭第一面上，入瞳大小為10 mm，F/#=2.046，設定角度解析度為45 PPD，則空間頻率為60 lp/mm。使用1.03吋、長寬比相同OLED面板，畫素數目為25602560，單一畫素大小為7.2 m7.2 m。由於本文推導出光在波導內追跡其所有賽德像差為零且與波導的材料與厚度無關，所以投影鏡頭可以單獨設計，不需要考慮波導的影響。面板發光面位於投影鏡頭物焦平面，投影鏡頭功能是把面板影像經由投影鏡頭準直投射至第一個全像元件，透過全像元件使光線在波導內進行全反射傳遞到下一個全像元件，最後經由眼睛觀看。而投影鏡頭在MR系統中可以被視為一個放大鏡，角放大率為12.22倍。當面板影像經過投影鏡頭後，其電視畸變與橫向色差會隨著影像一同被放大，我們利用直線鑑別率與橫向色差鑑別率來分析。本文投影鏡頭設計直線鑑別率與橫向色差鑑別率分別為0.407和0.675，都小於人眼辯別率1，因此人眼無法辨識其直線扭曲與橫向色差，而達到其設計要求。

摘要(英)

This projection lens design consists of 4 glass spherical lenses and 3 plastic aspherical lenses. The focal length of the lens is 20.458 mm, with a diagonal field of view of 65 degrees and a horizontal field of view of 48.50 degrees. The aperture is located on the first lens surface with an entrance pupil diameter of 10 mm, resulting in an F-number of 2.046. The angular resolution is set at 45 PPD (Pixels Per Degree), corresponding to a spatial frequency of 60 lp/mm.
The lens is designed for use with a 1.03-inch OLED panel, which has a resolution of 2560 x 2560 pixels and a pixel size of 7.2 µm x 7.2 µm. In this study, it was derived that the lens design can be developed independently without considering the influence of the waveguide, as all Seidel aberrations of light within the waveguide are zero and independent of its material and thickness.
The emitting surface of the panel is located at the projection lens′s object focal plane. The function of the projection lens is to project the panel image through collimation onto the first holographic element. The light then undergoes total internal reflection through the waveguide, passing to the next holographic element, and finally reaching the eye for viewing. In the MR (Mixed Reality) system, the projection lens acts as a magnifier with a magnification factor of 12.22 times.
After passing through the projection lens, any television distortion and lateral chromatic aberration in the panel image are magnified accordingly. Linear discrimination rate and lateral chromatic aberration discrimination rate are used for analysis. The designed linear discrimination rate and lateral chromatic aberration discrimination rate of this projection lens are 0.412 and 0.675, respectively, both less than the human eye′s discrimination threshold of 1. Therefore, the human eye cannot perceive linear distortion or lateral chromatic aberration, meeting the design requirements.

關鍵字(中)

★ AR系統
★ MR系統
★ 投影鏡頭設計
★ 直線鑑別率
★ 橫向色差鑑別率

關鍵字(英)

★ AR System
★ MR System
★ Projection Lens Design
★ Line resolution
★ Lateral Color resolution

論文目次

摘要 i
Abstract ii
誌謝 iv
目錄 vi
圖目錄 x
表目錄 xv
1 第一章緒論 1
1-1 研究動機 1
1-2 文獻回顧 2
1-2-1 頭戴式顯示器的應用 2
1-2-2 頭戴式顯示器的設計 8
1-2-3 投影鏡頭設計 19
1-3 論文架構 22
2 第二章投影鏡頭設計理論 24
2-1 AR、MR系統的VHOE架構 24
2-2 物方光線在波導中光線追跡對賽德像差的影響 25
2-2-1 鏡頭逆向設計 25
2-2-2 Tunnel Diagrams 25
2-2-3 入瞳位置平移 27
2-2-4 拉氏不變量與折射不變量 29
2-2-5 平板玻璃的光線追跡 31
2-2-6 平板玻璃的賽德像差 32
2-3 放大鏡原理 38
2-4 Optical Distortion 與 TV Distortion的關係 39
2-4-1 Optical Distortion 定義 39
2-4-2 TV Distortion定義 40
2-4-3 電視畸變視場範圍設定 40
2-4-4 水平電視畸變 42
2-4-5 水平電視畸變與水平直線扭曲量(1)關係 45
2-4-6 垂直電視畸變 47
2-4-7 垂直電視畸變與垂直直線扭曲量(2)關係 49
2-4-8 直線鑑別率 51
2-5 橫向色差 51
2-5-1 橫向色差鑑別率 52
2-6 投影鏡頭製造與組裝公差 53
2-6-1 公差定義 53
2-6-2 公差範圍制定 55
3 第三章全視角65度投影鏡頭設計 57
3-1 鏡頭設計流程 57
3-2 投影面板規格 57
3-3 65度投影鏡頭初階規格 58
3-4 鏡頭設計目標 59
3-4-1 起始值與初階規格設定 60
3-5 鏡頭設計結果 65
3-5-1 MTF 67
3-5-2 Relative Illumination 68
3-5-3 Lateral color 69
3-5-4 Optical Distortion、TV Distortion 72
3-5-5 公差分析 73
4 第四章矩形鏡頭 76
4-1 圓形鏡頭的體積和重量 76
4-2 方形鏡頭的體積和重量 78
5 第五章結論 83
參考資料 84

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指導教授

孫文信(Wen-Shing Sun)

審核日期

2024-7-22

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