老花眼是四十歲以後人們看不清楚近物的現象，有老花眼的人數迅速增加，老花眼矯正方法不僅能提供良好的光學視覺，更具有時尚性及便利性，同步多焦點隱形眼鏡(Multifocal Contact Lenses, MCLs)可依不同觀視距離呈現不同的屈光度，是老花眼患者的最佳選擇之一，雖然市場上具有多種同步多焦點隱形眼鏡可供使用，但設計仍需要改進以提供更好的視覺及舒適性。本研究旨在開發與分析具有NURBS(Non Uniform Rational B-Spline)曲線之對稱同步多焦點隱形眼鏡之設計方法，以獲得臨床需求，即在大範圍的中心區域具有均勻屈光度分佈及平滑的高追加度(ADD)輪廓。首先本研究已建立數學公式，用以產生光學區域之不同屈光度分佈，可由近中心區域連續變化至外部區域，並可針對不同瞳孔直徑給定ADD屈光度值；其次，對NURBS曲線之控制點(Control Points)、權值(Weight)及節點(Knots)三個參數進行優化，實現平滑連續的前弧光學曲面，並且滿足給定的屈光度輪廓；第三，本研究提供一解決方法，設計軟式多焦點隱形眼鏡於大範圍的中心區域內獲得均勻的屈光度，NURBS曲線於中心的部分區域擬合點資料與曲率中心為球面/非球面曲線，以獲得均勻的屈光度，並建立多目標優化條件，採用加權方法及模擬退火(Simulated Annealing, SA)算法求解；最後，本研究開發一補償方法，使射出成形隱形眼鏡前弧殼模之Z軸收縮誤差達到最小化，以確保製造後的軟式多焦點隱形眼鏡之中心光學區域具有均勻的屈光度分佈，並透過優化射出成形參數，以及補償原始透鏡設計之中心區域的ADD，可使射出成形前弧殼模之Z軸收縮誤差達到最小化，並對應至乾式隱形眼鏡。本研究結果已對硬式及軟式多焦點隱形眼鏡進行光學及臨床測試，由屈光度輪廓結果顯示，實際屈光度分佈與原始需求及光學模擬結果一致，代表所提出的方法可容易地調整用於新的臨床需求，本研究成功開發多焦點隱形眼鏡之設計方法，並驗證其可行性，未來可進一步研究複雜漸進變焦型隱形眼鏡之設計。

Abstract
Presbyopia is a condition in which people cannot see clearly to near objects usually after age 40. The number of presbypic people increases very quickly. Thus, presbyopia correction methods that can provide not only a good optical vision but also a fashion and convenience to wear are in great demand. Simultaneous multifocal contact lenses (CLs) that present visions from various distances at all time is one of the suitable choices for presbyopic people. Although many kinds of simultaneous CLs are available on the market, their designs still need to be improved to satisfy more and more requirements. This research aims to develop and analyze a design method of symmetric simultaneous multifocal CLs to obtain smooth anterior optical surfaces and satisfy given smooth optical power profiles with high addition (Add) power values and uniform power in large central zones by adjusting Non Uniform Rational B-Spline (NURBS) curves. Firstly, this study has developed mathematical functions to generate the given optical power distributions in which the powers continuously change from either a center-near or center-distance zone to an outer-distance or outer-near zone in optical surfaces with different change rates and Add power values for different pupil diameters. Secondly, three parameters including control points, weight and knots of cubic NURBS curves are optimized simultaneously to achieve smooth and continuous anterior optical surface profiles and satisfy the given power profiles. Thirdly, this study provides a solution for designing soft multifocal CLs to obtain a uniform optical power in a large center-distance zone.The parts of NURBS curves in the center-distance zones are fitted given spherical/aspheric curves for both data points and their centers of curvature to achieve uniform power. A multi-objective optimization problem has been established and solved by the weighted sum method and Simulated Annealing (SA) algorithm. Finally, this study has developed a compensating method to minimize the Z-shrinkage errors of anterior shell molds (SMs) corresponding to the anterior surfaces of soft CLs in injection molding (IM) process to ensure the uniform optical power in the central optical zone of soft multifocal CLs after manufacturing. The Z-shrinkage error of the anterior SM profile corresponding to the anterior optical surface profiles of dry CL in IM process can be minimized by optimizing IM process parameters and compensating the Add powers in the central zone of the original lens design. Results of this study have been tested by optical measurements for both rigid and soft multifocal CLs. The power profiles of measurement results of the lens samples agree with these of the original requirements and optical simulation results. Based on the clinical test results of soft lens samples, the proposed method can be easily adjusted to adapt new clinical requirements. Therefore, the developed design method of multifocal CLs has been verified and proven the feasibility and it can be further investigated for progressive contact lens design.

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