指導教授：蘇國棟臺灣大學：光電工程學研究所史偉廷Shih, Wei-TingWei-TingShih2014-11-262018-07-052014-11-262018-07-052013http://ntur.lib.ntu.edu.tw//handle/246246/261922在這篇論文中, 我們用了分離變數法去得到正方形目標平面的自由曲面與解微分方程法去得到圓形目標平面的自由曲面, 再藉由我們所創建的自由曲面透鏡將LED的光場強度變得更加均勻. 接下來, 我們會用異質微透鏡組合去近似自由曲面透鏡. 我們藉由模擬的結果去調整曲率半徑與大小. 最後, 藉由優化, 我們可以得到均勻的照度分佈. 而其直下式背光元件厚度為2公釐, 此設計可使均勻度與效率個別達到90%與96%以上. 而其可涵蓋的面積為49平方公分In this paper, variable separation mapping design method and solving differential equation method were adopted to obtain freeform surface for a square target plane and circular target plane, respectively. Starting from the freeform lens constructed by these methods, we would keep the light field intensity uniform. We then utilized heterogeneous micro lens array (MLA) to approximate the shape of the freeform lens. We adjusted the curvature radius and size by the simulation results. Through optimization process, we could achieve a uniform light intensity of ight emitting diodes using heterogeneous MLA. The thickness of direct-lit backlight unit is 2 mm thick. This design achieved 96% efficiency and 90% uniformity. It covers an area of 49 square centimeters .誌謝 i 中文摘要 ii ABSTRACT iii CONTENTS iv Chapter 1 Introduction 1 Chapter 2 Freeform Lens 3 2.1 Intensity Distribution of LED Light Source 3 2.2 Principle of Freeform Surface with Circular Target Plane 4 2.2.1 Introduction 4 2.2.2 Normal Vector of Tangent Plane 5 2.2.3 Incident Vector & Refractive Vector 7 2.2.4 Edge Ray Principle 8 2.2.5 Energy Conservation Law 9 2.2.6 Snell’s Law 11 2.2.7 Partial Differential Equation 13 2.2.8 Ordinary Differential Equation 14 2.3 Principle of Freeform Surface with Square Target Plane 15 2.3.1 Introduction 15 2.3.2 Energy Conservation Law 16 2.3.3 Lawnmower Algorithm 18 2.4 Construct Process 21 2.5 Definitions of Efficiency and Uniformity 22 2.6 Simulation Results 23 2.6.1 Circular Target Plane (H=20mm) 23 2.6.2 Square Target Plane (H=20mm) 24 2.6.3 Square Target Plane (H=2mm) 25 2.6.4 Discussion 26 Chapter 3 Transform a Freeform Surface into Heterogeneous Microlenses 29 3.1 Micro Lens Technology 29 3.2 Approximate Process 30 3.3 Algorithm of Optimization - Damped Least Squares Algorithms 32 3.4 Optimization Process 34 3.5 Simulation Results (After Optimization) 35 3.6 Discussion 36 3.7 Compare with Previous Results 39 Chapter 4 Conclusions 422266764 bytesapplication/pdf論文使用權限：不同意授權自由曲面異質微透鏡thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/261922/1/ntu-102-R00941102-1.pdf