臺灣博碩士論文加值系統

本論文提供執行指向性轉換的自由曲面透鏡設計策略。它使用光通量切割的方法，並將其適度分配到對應的強度分佈。原則上，在滿足折射定理及不發生全反射的情況下，任意的光型分佈是可以藉由這個方法達成。以常見的Lambertian頂部發光LED作為光源為例，這方法成功地給出了不同要求的強度分佈，例如:等向性和指數型態指向性的分佈。我們進一步利用計算結果製造了等向性透鏡並量測強度分佈
，實驗結果與模擬結果非常吻合，其等向性超過80%。
這個方法除了有直接性和速度上的優點，其最主要之兩個特點為1.考慮Fresnel 的損失，2.在設計階段即可得知透鏡的效率因子。僅利用幾何光學與光通量守恆原理，不用憑藉偏微分方程或疊代演算方法，就可以進行任意指向性之轉換，相信在照明工程或顯示器領域，將會有更廣泛的應用。

This research provides a free form lens design strategy that performs directivity transformation. In principle, arbitrary beam pattern can be achieved with this method, which uses a modified flux partition and assigns each one to calculated position based on illumination required. Taking a real Lambertian top emitting white light LED source for example, this method successfully gives different required intensity distributions, such as the isotropic and exponential ones. Moreover, the isotropic directivity lens is fabricated and the beam pattern is measured to verify the effectiveness. The experimental results are in good agreement with the simulation ones, which provides high directivity isotropy (more than 80%).
The features of this method are the following: 1. This method takes Fresnel loss of the lens into consideration. 2. It predicts the efficiency of the lens. It also has the advantages of directness and speed. This scheme uses simple photometry and geometrical optics without resorting to partial differential equations or iterative algorithm. It is expected to find wide applications in general beam shaping, particularly in lighting or illumination engineering where arbitrary directivity transformation is required.

摘要...................................................i
Abstract..............................................ii
目次..................................................iii
表目次................................................vi
圖目次................................................vii
第1章 序論..............................................1
1.1. 研究動機...........................................1
1.2. 論文架構...........................................3
1.3. 自由曲面透鏡文獻探討................................4
第2章 基本光學理論.......................................6
2.1. 幾何光學(Geometrical optics).......................6
2.1.1. Lambertian餘弦定律(Lambert’s cosine law).........7
2.1.2. 折射率(Refractive index).........................8
2.1.3. 反射律(Law of Reflection)........................9
2.1.4. 折射定律(Law of Refraction)......................11
2.1.5. 臨界角和全反射(Critical angle and Total internal reflection)............................................12
2.2. 波動光學(Wave optics)..............................13
2.2.1. 菲涅耳方程式(Fresnel Equations)..................14
2.2.2. 垂直偏振(Transverse Electric Polarization).......15
2.2.3. 平行偏振(Transverse Magnetic Polarization).......16
2.2.4. 反射比與透射比(Reflectivity and Transmissivity)..17
2.2.5. 布魯斯特角(Brewster’s Angle).....................21
2.3. 光度學(Photometry)................................22
2.3.1. 光通量(Luminous Flux)...........................23
2.3.2. 照度(Illuminance)...............................23
2.3.3. 光強度(Luminous Intensity)......................25
第3章 光通量切割法設計與模擬.............................28
3.1. 設計步驟..........................................28
3.2. 模擬驗證..........................................39
3.2.1. 等向性分析......................................41
3.2.2. 指向性分析......................................45
3.2.3. 高次項分析......................................47
3.2.4. Fresnel分析....................................48
第4章 實驗結果.........................................49
4.1. 實作測試..........................................49
4.2. 差異性驗證........................................54
第5章 結論與展望.......................................56
著作目錄...............................................59
參考文獻...............................................61

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