臺灣博碩士論文加值系統

光導管之形狀對光導管於其出口處之光照度分佈會有不同之結果為一有趣之光學現象並影響光導管於照明運用上之選擇，但文獻並無載明其產生機制或證明。本論文利用反射、折射定律，將光在多邊形光導管內的三維能量傳遞投影到二維平面上，並推導出光在出口處的落點和能量大小的數學式，證明五邊形光導管中心處會有能量集中的現象。並運用數學軟體MATLAB計算出數值解與光學覓跡摹擬軟體TracePro模擬比對，然後和實驗結果相對照。

It is known that different geometric shapes of light pipes will lead to different distributions of irradiance without analytical proof in literarure, except for the case of circular lightpipe. We deduce the irradiance distributions in polygonal light pipes and prove that the irradiance of the pentagon light pipes will concentrate in the center of the exit plane, depending on the number of facets. To verify our analytical derivation, we use MATLAB, the mathematic software, to calculate the result and also employ TracePro, a simulation package of Monte Carlo ray tracing, to verify the features. Finally, a series of experiments with different acrylic light pipes are provided for comparison.

中文摘要 I
Abstract II
誌謝 III
目錄 IV
圖表目錄 VI
第一章、 緒論 1-1
1-1 前言 1-1
1-2 多邊形長直光導管的能量分布 1-3
1-3 圓形長直光導管的能量分布 1-5
1-4 本論文之架構 1-6
第二章、 原理與方法 2-1
2-1 概論 2-1
2-2 圓形光導管之一維能量傳遞 2-2
2-3 五邊形光導管能量分布的理論推導 2-4
2-3-1五邊形光導管之二維能量傳遞 2-4
2-3-2五邊形光管二維傳遞路徑 2-5
2-3-3光能量計算 2-10
2-4 正方形光導管之二維傳遞路徑 2-14
2-5 小結 2-20
第三章、 計算模擬與實驗結果 3-1
3-1 五邊形光導管能量分布之MATLAB計算方法與結果 3-2
3-2 模擬結果 3-5
3-3 實驗結果 3-10
3-3-1實驗介紹 3-10
3-3-2實驗結果分析 3-11
3-4計算、實驗與模擬結果之比較 3-15
3-5誤差分析 3-18
第四章、 總結 4-1
參考資料 5-1
附錄A 三角形光導管能量分布MATLAB計算程式碼 5-3
附錄B 正方形光導管能量分布MATLAB計算程式碼 5-9
附錄C 五邊形光導管能量分布MATLAB計算程式碼 5-15
附錄D 六邊形光導管能量分布MATLAB計算程式碼 5-22
附錄E 圓形光導管能量分布MATLAB計算程式碼 5-28
附錄F 實驗與模擬圖片分析與強度立體圖程式碼 5-30
附錄G 均勻度分析資料處理程式碼 5-31

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