光學及光電產品對於光學元件設計的需求不在僅是一般的球面，對於非球面及自由曲面(非軸對稱)形狀的需求與日遽增，除了形狀的複雜度增加之外，對於其形狀精度的需求也不斷提高，而微透鏡陣列即是一般常見需求量大且不易生產的光學元件之一。微透鏡陣列被廣泛的應用於各式光學元件中，如晶圓級光學、照明光學系統、光纖耦合器、液晶顯示器的增效模組、微型投影機及掃描器CIS模組中的透鏡等。
目前已經成功地被開發出來的微透鏡陣列製程，如熱熔法、各式能量束加工法、超精密加工、材料疏水性應用、LIGA/類LIGA及熱壓成型等製程。在各式各樣的製程中，超精密加工法能達到較高的形狀精度及較好的表面粗糙度，且能於材料的種類及形狀的設計中提供最大的選擇彈性。
目前超精密加工以快刀伺服、慢刀伺服及微鑽石銑削三種方法最常被用來製作微透鏡陣列。儘管慢刀伺服輔助加工具有不需額外的裝置及加工設定容易的有點，但其複雜的三維刀具補償及刀具路徑規劃往往會導致形狀精度不佳、刀具壽命不佳及粗糙的表面粗糙度，本研究的主要目的為建立慢刀伺服輔助鑽石車削的三維的刀具形狀補償模型來加工晶圓級光學所需對稱排列的微透鏡陣列。
本研究成功地加工出形狀精度(P-V)及表面粗糙度(Ra)分別小於0.2μm及5nm具有非球面的百分之一百填充率的微透鏡陣列，其每顆微透鏡形狀精度的均勻度小於0.05μm。除了車削的探討外，一維及二維的慢刀伺服輔助鉋削加工也同樣地被探討於本研究中，於掃描器所使用的微透鏡陣列其形狀精度小於0.2μm、表面粗糙度低於5nm、每顆微透鏡的均勻度小於0.05μm及矢高誤差小於2μm，藉由刀具路徑產生的演算機制及二維的慢刀伺服輔助鑽石鉋削所加工出來。

Owing to the demand from fast growing optical and opto-electronic industry, optical design has advanced from merely planar/spherical to aspheric and to free-form (non-axial symmetrical) in shapes. On top of the increasing complexity in shape, the requirement for form accuracy is getting higher. Micro-lens array (MLA) is one of the typical examples of these difficult-to-produce optical components which are in great demand. MLA has now been widely used in wafer level optics, lighting system, optical fiber coupling devices, brightness enhancement system of LCD, pico-projector, lens of CIS module scanner and etc. Several processes, namely, thermal reflow process, energy beam processing, ultra-precision machining, LIGA/LIGA-like, have been successfully developed to fabricate MLAs. Amongst those processes, ultra-precision machining is considered to be able to achieve higher form accuracy, better surface roughness, and to offer greater flexibility in material/shape selection.
Three ultra-precision machining processes namely fast tool servo, slow tool servo and diamond milling, are frequently used to produce MLA. Though slow tool servo has the advantages of no extra attachment and fast setting-up, the complicated three dimensional tool shape compensation and tool-path generation are major reasons for resulting in poor form accuracy, pre-matured tool failure and terrible surface finish. This research aimed to develop a model of three dimensional tool shape compensation for generating 3D tool path in slow tool servo diamond turning of symmetrically arranged MLAs such as those in wafer level optics. 
An aspheric MLA of 100% filling factor with form accuracy (p-v) and surface roughness (Ra) better than 0.2 μm and 5nm respectively was successfully produced in the present study. The uniformity of each micro lens was less than 0.05μm. Apart from turning tests, 1D/2D slow tool servo diamond shaping tests were also investigated in this research. The MLA of scanner with form accuracy of 0.2 μm, Ra of 5nm, uniformity of each micro lens ≤ 0.05 μm and sagittal error ≤ 2 μm was generated by the developed tool generation algorithm and 2D slow tool servo diamond shaping process.

中文摘要    I
英文摘要    III
誌謝	V
圖目錄	XI
表目錄	XVIII
第一章  序論	1
1-1  前言	1
1-2  研究背景	2
1-3  文獻回顧	5
1-3-1  透鏡製作	6
1-3-1-1  熱熔法	6
1-3-1-2  灰階光罩法	7
1-3-1-3  電子束法	7
1-3-1-4  噴墨印刷法	8
1-3-1-5  疏水性製作法	9
1-3-1-6  雷射拖拉加工法	10
1-3-2  模具製作	14
1-3-2-1  聚焦離子束法	14
1-3-2-2  濕式等向蝕刻法	14
1-3-2-3  反應離子蝕刻法	15
1-3-2-4  超精密加工法	16
1-3-3  轉寫製作	29
1-3-3-1  直接熱壓成型法	29
1-3-3-2  間接熱壓成型法	30
1-3-3-3  LIGA/類LIGA法	31
1-3-3-4  滾輪成型法	32
第二章  超精密加工	34
2-1  單點鑽石車削	34
2-2  鑽石車削加工條件	39
2-2-1  切削速度	39
2-2-2  進給	40
2-2-3  切削深度	42
2-2-4  切削距離	42
2-3  光學級自由曲面超精密加工	43
第三章  實驗規劃與設計	49
3-1  實驗規劃	49
3-2  刀具設定	52
3-3  治具設計與工件定位方式	56
3-4  實驗設備	57
3-4-1  超精密加工機	57
3-4-2  量測設備	58
第四章  慢刀伺服輔助車削非球面微透鏡陣列	61
4-1  實驗	61
4-2  刀具路徑規劃	63
4-3  刀具干涉計算	70
4-4  實驗結果	75
第五章  慢刀伺服輔助鉋削球面微透鏡陣列	82
5-1  實驗	82
5-2  刀具路徑規劃	85
5-3  實驗結果	88
5-3-1  進給率對加工結果的影響	88
5-3-2  切削深度對加工結果的影響	95
第六章  慢刀伺服輔助鉋削非球面微透鏡陣列	106
6-1  實驗	106
6-2  刀具路徑規劃	109
6-3  刀具干涉計算	112
6-4  實驗結果	115
第七章  結論	128
參考文獻	131

圖目錄
圖1-1  CCD模組掃描器結構示意圖	4
圖1-2  CIS模組掃描器結構示意圖	5
圖1-3  微透鏡陣列加工法	5
圖1-4  熱熔法製作微透鏡陣列示意圖	6
圖1-5  灰階光罩法製造微透鏡陣列示意圖	7
圖1-6  電子束加工法製作微透鏡陣列示意圖	8
圖1-7  噴墨印刷法製作微透鏡陣列示意圖	9
圖1-8  疏水性製作微透鏡陣列示意圖	10
圖1-9  雷射投影直接加工	11
圖1-10  每次拖拉路徑相差90度	11
圖1-11  每次拖拉路徑相差60度	11
圖1-12  不同填充率以點擴散函數模擬結果	13
圖1-13  聚焦離子束法製作微透鏡陣列示意圖	14
圖1-14  濕式等向蝕刻法製作微透鏡陣列示意圖	15
圖1-15  熱熔法製程示意圖	16
圖1-16  反應離子蝕刻法示意圖	16
圖1-17  微陣列鏡片設計	17
圖1-18  微陣列鏡片加工後的形狀量測結果	18
圖1-19  快刀伺服鑽石車削裝置	18
圖1-20  各式切削參數比較圖	20
圖1-21  慢刀伺服鑽石鉋削(a)側視圖(b)上視圖	21
圖1-22  單一非球面微陣列透鏡的刀具路徑補正	22
圖1-23  刀鼻半徑補正	22
圖1-24  X方向的形狀精度誤差	23
圖1-25  Y方向的形狀精度誤差	23
圖1-26  快刀伺服鑽石刨削示意圖	24
圖1-27  以快刀伺服輔助加工微透鏡陣列光學顯微鏡結果圖    24
圖1-28  單個微透鏡X方向的形狀精度	25
圖1-29  單個微透鏡Y方向的形狀精度	25
圖1-30  直接模具轉寫成型微透鏡陣列因過低的壓力所造成的帶狀物在微透鏡邊緣	30
圖1-31  間接模具成型示意圖	30
圖1-32  LIGA搭配直接熱壓成型微透鏡陣列	31
圖1-33  LIGA搭配間接熱壓成型微透鏡陣列	32
圖1-34  滾輪成型微透鏡陣列示意圖	32
圖2-1  crater wear磨耗	37
圖2-2  (1)CVD刀具加工複合材料及(2)PCD刀具加工複合材料之刀具磨耗	38
圖2-3  切削無電鍍鎳-主軸轉速與表粗關係圖	40
圖2-4  理論表面粗糙度計算	40
圖2-5  加工不同材料的粗糙度與理論粗糙度計算的差異比較圖   41
圖2-6  切削無電鍍鎳-切削距離與刀具磨耗關係圖	42
圖2-7  快刀伺服加工系統架構	44
圖2-8  慢刀伺服加工示意圖	45
圖2-9  快刀伺服加工百分之百填充率的微透鏡陣列的SEM觀察圖  46
圖2-10  鑽石銑削加工架設圖	46
圖2-11  鑽石銑刀與旋轉軸中心關係圖	47
圖2-12  鑽石銑削加工完畢後的中心靜點	48
圖3-1  微透鏡陣列鑽石切削實驗規劃	50
圖3-2  兩軸超精密鑽石車削加工示意圖	53
圖3-3  刀具設定未達中心	54
圖3-4  刀具半徑值設定過大	54
圖3-5  刀具設定未與工件中心一致的加工結果	55
圖3-6  刀具設定高度未達工件旋轉中心	56
圖3-7  模仁與治具的定位方式	57
圖3-8  東芝機械超精密加工機ULG -100D（HYS）	58
圖3-9  UA3P-300型形狀精度量測儀	59
圖3-10  Olympus光學顯微鏡	60
圖4-1  晶圓級光學使用簡易模仁示意圖	61
圖4-2  慢刀伺服輔助鑽石車削微透鏡陣列實驗流程	62
圖4-3  微透鏡陣列的加工路徑	64
圖4-4 各微透鏡的相對位置關係	65
圖4-5  刀鼻半徑補償示意圖	66
圖4-6  球面/非球面的刀鼻半徑補償計算	67
圖4-7  微透鏡陣列車削加工時不同角度切削截面的變化	68
圖4-8  自由曲面切削每個截面的輪廓變化	68
圖4-9  刀具退避補償計算	69
圖4-10  刀具前間隙角干涉計算	70
圖4-11  刀具干涉角度計算的座標轉換	71
圖4-12  非球面微陣列透鏡中間的透鏡	76
圖4-13  非球面微陣列透鏡邊緣的透鏡	77
圖4-14  非球面微陣列透鏡OM的觀察圖	78
圖4-15  不同位置的微陣列透鏡形狀精度統計結果	79
圖4-16  表面粗糙度量測結果	79
圖4-17  百分之百填充率的微透鏡陣列慢刀伺服車削加工順序    80
圖4-18  三個微透鏡陣列的交接處	81
圖5-1  百分之一百填充率的微透鏡陣列	82
圖5-2  慢刀伺服輔助一維鉋削加工微透鏡陣列流程圖	83
圖5-3  鑽石鉋削加工橢圓型微透鏡陣列	84
圖5-4  微透鏡鉋削加工正視圖	86
圖5-5  微透鏡鉋削加工側視圖	87
圖5-6  鉋削加工進給及進刀示意圖	88
圖5-7  進給率設定為100mm/min時X方向的形狀誤差	89
圖5-8  進給率設定為300mm/min時X方向的形狀誤差	89
圖5-9  直線鉋削加工光學顯微鏡觀察圖	90
圖5-10  直線刨削後橫截面的量測結果	91
圖5-11  進給率於100mm/minand時Y方向的形狀誤差	92
圖5-12  進給率於300mm/min時Y方向的形狀誤差	92
圖5-13  X軸及Y軸形狀精度與進給速度的關係	93
圖5-14  X軸方向的表面粗糙度量測結果	94
圖5-15  Y方向表面粗糙度的量測結果	94
圖5-16  X軸及Y軸表面粗糙度與進給速度的關係	95
圖5-17  進給率100 mm/min切削深度0.5μm的形狀誤差	96
圖5-18  進給率100 mm/min切削深度1μm的形狀誤差	97
圖5-19  進給率100 mm/min切削深度3μm的形狀誤差	97
圖5-20  進給率100 mm/min切削深度0.5μm的1500倍顯微鏡觀察圖 98
圖5-21  進給率100 mm/min切削深度3μm的1500倍顯微鏡觀察圖  98
圖5-22  鑽石鉋削微透鏡陣列切屑移除機制	99
圖5-23  正交切削示意圖	100
圖5-24  正交切削分力圖	100
圖5-25  切削力與傾角變化的關係圖	103
圖5-26  10顆微透鏡陣列的形狀誤差統計圖	104
圖5-27  單顆微透鏡的3D輪廓量測結果	105
圖6-1  CIS模組掃瞄器的非球面微透鏡陣列鏡片	106
圖6-2  慢刀伺服輔助二維鉋削微透鏡陣列	108
圖6-3  非球面微透鏡陣列鉋削加工刀具路徑規劃	109
圖6-4  微透鏡陣列鉋削加工時不同位置切削截面的變化	111
圖6-5  單一透鏡刀具路徑考量刀鼻半徑補償	111
圖6-6  非球面微透鏡鉋削加工於不同路徑刀具干涉示意圖    113
圖6-7  單顆非球面為透鏡檢測示意圖	115
圖6-8  微透鏡陣列X軸方向UA3P量測結果	116
圖6-9  微透鏡陣列Y軸方向UA3P量測結果	117
圖6-10  微透鏡陣列3D的UA3P量測結果	118
圖6-11  X軸與Y軸形狀精度統計圖	119
圖6-12  10顆微透鏡間的間距誤差	119
圖6-13  非球面微透鏡與邊緣的相對位置	120
圖6-14  非球面微透鏡加工後光學顯微鏡拍攝圖	121
圖6-15  影像處理流程	121
圖6-16  非球面微透鏡邊緣偵測結果	123
圖6-17  矢高誤差經由影像處理與UA3P量測結果比較	126
圖6-18  45顆微透鏡經由影像處理分析矢高誤差的結果	127
 
表目錄
表1-1  微透鏡陣列透鏡製作製程比較表	12
表1-2  各式超精密加工微透鏡陣列比較表	26
表1-3  微透鏡陣列模具製作製程比較表	28
表4-1  非球面微陣列透鏡參數	63
表4-2  刀具規格	63
表5-1  刀具規格	85
表6-1  非球面微陣列透鏡參數	110

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