高階自由曲面之光學設計與優化

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姓名

林詩豪(Shi-Hao Lin) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

高階自由曲面之光學設計與優化
(The optimized optical design of high-order freeform)

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摘要(中)

本研究為高階自由曲面之光學設計與優化，以自由曲面方程式作為光機內面鏡的表面，進行曲面玻璃及整體光機架構的像差匹配，以修正投射影像的變形。研究結果表示，採用優化自由曲面的投影光學系統其平均光斑尺寸縮小40%，像散畸變下降，畸變量降至3%以內，使得眼睛不易於觀測到影像變形。

摘要(英)

This study is the optimized optical design of high-order freeform. We set the freeform equation as the surface of the inner mirror in the mechanism. In order to balance the aberration of windshield and the overall light path. The experimental results show that the average spot size is reduced by 40% and the degree of astigmatism is reduced, and the distortion is reduced to less than 3%, so that deformation of the image is not easy to be observed.

關鍵字(中)

★ 虛像
★ 投影
★ 自由曲面
★ 優化

關鍵字(英)

★ virtual image
★ project
★ freeform
★ optimize

論文目次

摘要 i
Abstract ii
目錄 iv
圖目錄 vii
表目錄 ix
一、緒論 1
1-1 研究背景 1
1-2 研究動機 1
1-3 論文貢獻 1
1-4 論文架構 2
二、研究內容與方法 3
2-1 研究內容 3
2-2 研究方法 5
三、理論 6
3-1 反射系統 6
3-1-1 反射定律 6
3-1-2 高斯成像 8
3-1-3 焦距及屈光度 8
3-1-4 放大率及拉格朗日不變量(Lagrange invariant) 9
3-1-5 非對準的鏡面系統 10
3-2 離軸反射系統 11
3-2-1 偏移孔徑及偏置光場 12
3-2-2 旋轉光學表面 13
3-3 像差 15
3-3-1 球面波前的散焦與旋轉 16
3-3-2 賽得像差(Seidel aberration) 17
3-3-3 澤爾尼克多項式(Zernike polynomial) 26
3-4 表面方程式 29
3-4-1 球面 29
3-4-2 非球面 30
3-4-3 自由曲面 31
3-5 優化方法 33
3-5-1 最小二乘法 33
3-5-2 阻尼最小二乘法(Damped Least Squares method, DLS) 33
四、實驗部分 36
4-1 追跡模擬 36
4-1-1 設計概述 36
4-1-2 設計方法 37
4-2 初步分析 40
4-3 優化 43
4-4 優化分析 46
4-5 結果與討論 52
五、結論 53
六、未來展望 54
參考文獻 55

參考文獻

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指導教授

張榮森(Rong-Seng Chang)

審核日期

2017-7-19

推文