自由型曲面於非成像光學之研究

Abstract

在本篇論文中，我們提出了自由型曲面的數學模型，其所描繪出的光學曲面能重新分配由同調光源發出的光通量並達到預設的光強度分布。數學模型建立在能量守恆以及基本光追跡定理之上，並提出類平面假設在區域座標系統下，可由一非線性偏微分方程描述此能量傳遞的特性。在曲面的連續性與平滑性的條件下，我們利用有限元素法求解並控制誤差到收斂。最後利用本論文所發展的演算法來設計均勻/或非均勻光場分布。最後利用光學模擬軟體LightTools®來勘驗並分析此自由型曲面在照明系統的表現。

In this thesis, we propose freeform design model for constructing a single refractor (or reflector) surface under a predefined geometry. The freeform model based on energy conservation and ray propagation law can be characterized by a nonlinear partial differential equation (PDE) under the small planar approximation. The nonlinear PDE can be solved by finite element method with high order element to satisfy the condition of continuity (1st -order) and smoothness (2nd - order). To validate the proposed methodology, we use commercial software LightTools® , to evaluate the illumaninance performance via designed freeform engine in realization of uniform and non-uniform illuminance distribution on the planar.