多邊形實心長直光導管的照度分析

Abstract

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.