在人眼模型的發展歷史中，有兩種模型被提出來去模擬人眼水晶體內的梯度式折射率分布(gradient index distribution)，其為 the shell model以及the continuous gradient index model。然而兩者本身都既有一些缺陷，如shell model中的不連續水晶體輪廓或是continuous gradient index model中的折射率分布方式，導致模型在運用上不能夠靈活的建模以及造成光學模擬上的存有不準確性。因此，本研究將會參考前人的資料提出新的修正模型去避免上述問題的發生，除此之外還會利用光學模擬軟體ASAP去分析梯度式折射率分布在光學特性上表現。

為了驗證梯度式折射率分布的表現，除了模擬之外本研究還使用現今熱門的技術：3D列印，嘗試印製出相同效果的光學元件。然而因為機器本身的功能以及規格上的限制，最後印製出的成品並沒有辦法達到原本研究所預期的效果，所以未來在研究技術上，開發者可以多加注意3D列印對於光學產品的開發以及應用。

In the development history of human eye models, two of the models have been proposed to illustrate the effects of refractive index in the lenses; namely they are the shell model and the gradient index model. It is interesting to note that both models have been shown with inefficacy in modelling of optics. The most prominent problems are discontinuous profile in crystalline lens and constrained formula in the gradient index for universal model. Therefore, a modified model of lenses is proposed to circumvent the above-mentioned problems by employing an optical simulation package, namely ASAP by BRO Inc., for study of the properties of the gradient index and the resultant effects in the visual acuity from the modified model.
Simulation results have shown that the gradient index model would perform better both in monochromatic and chromatic aberrations of visual optics. In addition to the optical simulations, this study has adopted the state of art technology in 3D printing for establishing the physical model of gradient index lenses plus the experimental verifications in process parameters during 3D printing. Due to limited machine functions and specification, the current 3D printing machine cannot meet the requirements in this study. In the future, the potential of 3D printing technology should be carefully explored in the applications of ophthalmology implants.

摘要 .Ⅰ
ABSTRATE ...Ⅱ
致謝 ...Ⅲ
CONTENTS ...Ⅳ
LIST OF TABLES …..Ⅵ
LIST OF FIGURES …..Ⅶ
CHAPTER ONE INTRODUCTION 1
1.1 Background 1
1.2 Objectives of Study 3
1.3 Literatures Review 4
1.3.1 History of Human Eye Model 4
1.3.2 Models of Gradient Index Distribution 7
1.3.3 Chromatic Aberrations of Human Eye 8
CHAPTER TWO DESIGN PRINCIPLE AND OPTICAL THEORY 17
2.1 Human Eyes 17
2.1.1 Basic Optical Parameters of Human Eyes 17
2.1.2 Continuous Profile in Crystalline Lens 17
2.1.3 Refractive Index in Crystalline Lens 19
2.2 Theory of Optics 21
2.2.1 Snell’s Law and Lens Image 21
2.2.2 Monochromatic Aberrations 22
2.2.3 Zernike Polynomials 24
2.2.4 Abbe Number 24
CHAPTER THREE SIMULATION RESULTS 35
3.1 Simulations of Gradient Index Crystalline Lenses 35
3.2 Simulations of Human Eyes 36
CHAPTER FOUR EXPRIMENTS AND VERIFICATIONS 44
4-1 3D Printing Equipment 44
4-2 Dispersion experiment system 46
4-3 Experimental results 47
4.3.1 Production tolerances of 3D printing 47
4.3.2 Examination of refractive index 47
CHAPTER FOURFIVE CONCLUSIONS 57
REFRENCES 59

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