探討自由型光學於預設光場分佈之光學系統

Abstract

在本篇論文中，我們提出了一個新穎的自由行曲面設計構想，其所建構出的曲面能重新分配由點光源發出的光通量，使其滿足預設的光強度分布。而數學模型的建立是由能量守恆以及反射/折射定律為主，並提出類平面假設在區域化的座標系統之下，可推導出一高度非線性偏微分方程(highly nonlinear partial differential equation)。在求解此非線性方程並要求曲面的連續性與平滑性，我們利用有限元素法(Finite element method)，並選用Hermite element可滿足我們的需求。最後利用該演算法來設計均勻光場分布及漸變式光場分布的光學系統，並運用光學模擬軟體LightTools來勘驗所設計的光學系統的照明表現。

In this thesis, we propose a novel freeform design method in constructing a single refractor(reflector) surface under a predefined geometry. This freeform surface model based on energy conservation and the laws of rays propagation results in a highly nonlinear partial differential equation(PDE) under the small planar approximation. In order to solve the nonlinear PDE, the finite element method vie Hermite element was implemented to practice a smooth freeform surface in realization of uniform and non-uniform illuminance distribution on the planar and non-planar geometry condition.