梯度折射率透鏡(Gradient Index Lens，簡稱GRIN Lens)的光學理論是藉由設計鏡片介質折射率來達成鏡片之光學規格；若以平面梯度折射透鏡為例，即用平面板材配合調整折射率分佈即可完成正或負倍率之光學透鏡，相較於傳統光學透鏡必須以球面來曲折光線達成倍率，採用GRIN設計可降低鏡頭使用的鏡片數量，於鏡片之接合與疊加亦比較容易。
本論文針對梯度折射率分布設計之光學理論，進行透鏡像差分析與量測，並嘗試製作梯度折射率透鏡雛形。先以焦距為2.0 mm，厚度0.5mm之梯度折射率透鏡為例，鏡片有效光圈半徑為0.2 mm。經由設計徑向及軸向之梯度折射率，以優化可見光波段軸向色差，將可取代微鏡片中之雙合鏡片，更以夏克-哈特曼波前感測器模擬透鏡之成像像差，探討單一GRIN鏡片之像差性能。
最終於製程上採用高功率綠光固態雷射光，以固化製程於三軸機械式平台進行微光學元件製造；先於實驗探討光固化聚合物於矽基板上之接觸行為，再研究雷射光固化後之成形形貌與精度之變化，期能研製出高效率、高精度及具彈性的微光學透鏡之製造方法。

Gradient Index Lens (abbreviated as GRIN Lens) is based on optic theory of refractive index distribution in optical material to achieve the optical performances of a lens. For the cases of flat GRIN Lens, positive and negative power optical lenses are made by varying the refractive index distribution in the lenses. Compared with conventional lenses rely on the spherical surfaces to refract light rays, GRIN Lenses can reduce the number of lenses used in lens modules and simplify the lens assembly.
This thesis is devoted to the theory of distribution in refractive index in GRIN lenses with aberrations analysis and measurement of the GRIN lenses. Initially, with 2.0 mm focal length and 0.5 mm length thickness, the GRIN lens is designed with a clear aperture radius being 0.2 mm. Through the design of radial (vertical the optical axis) and axial (along the optical axis) gradient refractive index distribution of lens, the axial chromatic aberration of GRIN lens in visible light spectrum is optimized; then, with Shack - Hartmann wavefront sensor to detect optical path difference of the GRIN lenses, the aberration of lenses are fully explored.
In the manufacture of GRIN lenses, high-power laser beam for curing of polymers at 3-axis mechanical stage is adopted for manufacture of micro optical lens elements. The investigation of the contact performance of photo-curable polymer on silicon substrate is done then the morphology and accuracy of lenses are considered. The goal is to provide a high-efficiency, high-precision, highly flexible lens manufacture method.

目錄
第一章 緒論 1
1-1 研究背景 1
1-2 研究目的 2
1-3 文獻回顧 3
1-3-1 梯度折射率透鏡發展 3
1-3-2 夏克-哈特曼波前感測器 4
1-3-3 梯度折射率透鏡之參數 5
1-3-4 聚合物之折射率調控與梯度折射率透鏡製造流程 6
1-3-5 成像品質 7
第二章 基礎理論 12
2-1 基礎光學理論 12
2-1-1 費馬定理 12
2-1-2 折射定律與透鏡近軸成像理論 12
2-1-3 像差基本理論[20] [21] [22] 13
2-1-4 非球面之光學原理 15
2-1-5 澤尼克多項式 16
2-2 梯度折射率透鏡光學特性介紹與推導 17
2-2-1 徑向梯度折射率透鏡之折射率分布 17
2-2-2 二次梯度折射率透鏡之近軸光學特性 18
2-2-3 二次梯度折射率透鏡理論焦距分析 19
2-2-4 消色差二次梯度折射率單透鏡設計理論 21
2-3 成像品質原理 23
2-3-1 點擴散函數 23
2-3-2 調製傳遞函數 23
2-4 光固化聚合物物性及理論 24
2-4-1 光固化聚合物化學性質 24
2-4-2 光固化聚合物物理性質 24
2-4-3 光固化聚合物之幾何尺寸 27
第三章 光學模擬與分析 41
3-1 波前量測系統模擬之說明 41
3-2 梯度折射率透鏡模型及折射率分布分析 41
3-3 消色差二次梯度折射率單透鏡模型及軸向色差分析 42
3-4 消色差二次梯度折射率透鏡波前分析 47
3-5 綠光雷射之光路系統分析 49
第四章 實驗過程及驗證分析 69
4-1 光固化材料實驗 69
4-2 梯度折射率透鏡之製造規劃 71
4-3 雷射光機結構與雷射精度及平台路徑測試結果 71
4-4 二維列印光固化實驗 73
第五章 結論與未來工作 94
5-1 結論 94
5-2 未來工作 95
參考文獻 97

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