The purpose of this study is to develop an o-ring driven liquid-filled lens. This design can reduce the volume and abate the chance of the leakage. By controlling the tilt angle and displacement of the ring, the focal point of He-Ne laser beam through the liquid-filled lens can be changed either its position or direction. The ANSYS workbench program is employed to analyze the membrane deformation of the lens under different hydraulic pressure. The profile can be inputted into the ZEMAX to compute the optical properties of the lens. In order to evaluate the projection distortion of a circle in an image plane when tilt the ring, a shape factor is defined in this study. The bi-convex o-ring driven liquid-filled lens is composed by two o-ring driven liquid-filled lenses and used to compensate the coma aberration. Then, the shape factor is used to evaluate the compensation result. In the mean time, the Zernike coefficient is used to discuss the spherical aberration effect on the ring’s sizes.
To understand the potential fabrication problems, the traditional liquid-filled lens is assembled and the measurement system is also set up at the beginning of this study. The low cost fabrication of the o-ring driven liquid-filled lens is proposed. The equations about the characters of the liquid lens are studied. The deformation formula of the membrane is derived by the theory of plates and shells. The Gaussian curvature and rays tracing program are developed to calculate the approximate focal length of the lens by the Snell’s law without using any commercial optical software. The prototype of the lens is fabricated and tested to confirm the light beam steering ability of the lens. Different actuation methods, such as mechanism and piezoelectric, are discussed. Finally, the electromagnetisms are used to make the magnetism driven liquid-filled lens, and it is tested to find the properties of the lens.

本研究提出一種新型以圓環驅動之液體充填式透鏡設計，此種設計除了可以免除傳統液體充填式透鏡所需注射器的空間外，並改善因液體通道多而增加液體洩漏可能性的問題；除此之外，可藉由調整圓環的下壓距離與下壓傾斜角度，達到控制焦距與焦點可偏離對稱軸的功能。發展之初，除了進行文獻回顧之外，並檢索了美國專利並製作專利地圖，以作為研究方向的參考。為了在製造前瞭解透鏡的效果，使用有限元素分析軟體ANSYS對薄膜進行變形分析，在得到不同條件下的薄膜變形曲線後，將其薄膜變形方程式匯入光學軟體ZEMAX，以求得對應的光學特性；當傾斜下壓圓環時，為了改善投影點的投影形狀的扭曲變形，藉由定義形狀係數來評估，以雙面均可控方向及曲率之液體透鏡來研究投影形狀的扭曲變形補償的效果；另外，使用Zernike係數定義慧差與球差數值，探討使用雙凸透鏡補償慧差的效果以及分析圓環尺寸對於球差的影響。
為了瞭解製造過程中可能產生的問題，先依據過去的文獻來製作傳統的液態充填式透鏡，並且建立壓力與變形量的量測系統與進行影像品質拍攝；另外，為了降低製造成本與複雜程度，提出以及實際製作圓環驅動液體充填透鏡的方法；並在確認採用圓環驅動的改良方式後，使用平板理論推導出圓環下壓時的變形方程式；接著使用高斯曲率以及Snell’s law建立追跡方程式等兩種方式，可在不使用光學軟體下快速求得近似的焦距，以作為評估透鏡效能的參考；利用腔室內液體體積守恆的觀念，推導了下壓深度與最大變形量的關係式。為了實驗，製作了初始原型來測試透鏡控制氦氖雷射光束焦點位置的效果，在探討不同驅動方式的可行性與參考專利檢索結果之後，採用電磁驅動的方式來控制圓環的動作，最後完成磁致液態透鏡的設計以及製作。

ABSTRACT I
ACKNOWLEDGMENTS III
CONTENTS IV
FIGURE CAPTIONS VII
TABLE CAPTIONS XV
NOMENCLATURE XVI
CHAPTER 1: INTRODUCTION 1
1.1 Motivation and goals 1
1.2 Literature review 1
1.3 Contents of the thesis 13
CHAPTER 2: PATENT ANALYSIS 15
2.1 Search and analysis 15
2.2 Management charts 17
2.3 Classification analysis 21
2.4 Matrix chart and fishbone diagram 24
2.5 Patent map discussion 26
CHAPTER 3: SIMULATION RESULTS OF THE LIQUID-FILLED LENS AND DISCUSSION 27
3.1 Performance of liquid-filled lens 27
3.2 Lens amendment 30
3.3 O-ring driven liquid-filled lens 32
3.3.1 Finite element analysis 34
3.3.1.1 Membrane profile comparison 35
3.3.1.2 Symmetrical condition 36
3.3.1.3 Asymmetrical condition 38
3.3.1.4 Fixed tilt angle and under different pressures 40
3.3.2 Spot diagram analysis 41
3.3.3 Footprint diagram 43
3.3.3.1 Obedient follow the front lens 43
3.3.3.2 Image plate fixed 47
3.3.4 Coma compensation analysis 50
3.3.4.1 Plano-convex model 51
3.3.4.2 Bi-convex model 51
3.3.4.3 Bi-convex with tilt model 52
3.3.5 Effect of ring sizes for the spherical aberration 54
CHAPTER 4: ANALYTICAL METHOD OF ANALYZING THE LIQUID-FILLED LENS 57
4.1 Deformation of the membrane of the liquid lens 57
4.2 Mathematical model of o-ring driven liquid lens 59
4.3 Approximate focal length calculation 62
4.3.1 Gaussian curvature 63
4.3.2 Ray tracing programming 65
4.4 The maximum membrane deformation 69
CHAPTER 5: EXPERIMENTS SET UP AND RESULTS OF THE LENS 78
5.1 Design of the liquid-filled lens 78
5.1.1 Membrane material 78
5.1.2 Choice of liquid 80
5.2 Prototype fabrication 82
5.3 Prototype of the new design and experiment results 88
5.4 Design of disposable liquid-filled lens 91
5.5 Different kind of operation method 93
5.6 Design of magnetism driven liquid-filled lens 99
5.6.1 Electromagnet selection and measurement 99
5.6.2 Structure design 103
5.6.3 Fabrication results 104
5.6.4 Displacement measurement system 109
CHAPTER 6: CONCLUSION 114
6.1 Conclusion 114
6.2 Future prospect 117
REFERENCES 119

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