精調三階像差各分項目標值的鏡組優化設計

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姓名	孫文信(Wen-Shing Sun) 查詢紙本館藏	畢業系所	光電科學與工程學系
論文名稱	精調三階像差各分項目標值的鏡組優化設計 (Optical lens design optimization with accuracy adjusting the target budgets of the third-order aberrations)
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摘要(中)	本論文將探討一種優化方法，特別著重厚透鏡的三階像差公式，做為優化過程的評價函數，並在雙片鏡組與三片鏡組的設計上，得到很好的優化效果。論文中也探討眼鏡片的設計，由於單片眼鏡片設計優化項次的變數單純，故以柯丁登方程式作為評價依據，並按低折光率與高折光率眼鏡片分別設計。在低折光率眼鏡片設計，以斜射像散與鏡面深度對鏡面高度之二次微分值，校正鏡片像差與控制鏡面反曲點，可得比傳統鏡片，輕、薄和平的鏡片設計。高折光率眼鏡片設計，使用兩面非球面，優化目標項次為多視場斜射像散、折光率誤差與畸變，控制鏡片光學品質。論文中厚透鏡三階像差是以形狀因子之一元三次方程式表示，我們利用優化績效函數，可控制厚透鏡三階像差至任意目標值，因此可由厚透鏡三階像差找出真實像差減少趨勢，利用此趨勢，我們完成一自動化優化程式，得出一最佳值。為驗證優化程式效果，我們比較傳統標準鏡組設計之效果，均能得到更為優異之像差消除值。
摘要(英)	An novel optimization algorithm for optical lens design is presented in this dissertation. The third-order aberration of a thick lens is used as the merit function in the optimization. Accordingly, we have obtained well design results in designing both of the triplet and the doublet lenses. The study of the design of an ophthalmic lens is another topic of this dissertation. We used the Coddington’’s equations as the merit functionin in designing both low-power and high-power ophthalmic lenses because only one piece of lens should be considered in design. In the low-power ophthalmic lenses design, we use the oblique astigmatic and the second derivative with respect to the height to correct lens aberration as well as control the inflection point. In comparison with the traditional ophthalmic lenses, this approach can obtain a lighter, thinner and flatter spectacle lens. In addition, the design of high-power in aspherical ophthalmic lenses is presented. Using two aspherical surfaces to control the optical lenses quality, multi-fields oblique astigmatism and oblique power error and distortion are choose as the target budgets. The minimal aberration can be obtained by optimizing the two aspherical surfaces. The third-order aberration for a thick lens is in terms of shape factors by cubic equation with one unknown. we used the merit function to control the third-order aberrations to any target budgets. The trend for the real aberration in decreasing could be obtained by the third-order aberration of a thick lens. Finally, we develop a set of automatic optimization program to find an optimized value. The developed optimization program has been proven to be effective. For this study, the specified aberrations of the lenses design were corrected to reach a minimum value, which was more better than those for conventional lenses design.
關鍵字(中)	★ 眼鏡片 ★ 遠視 ★ 近視 ★ 阻尼最小二乘法 ★ 雙片鏡組 ★ 三片鏡組 ★ 全領域最佳值設計	關鍵字(英)	★ Ophthalmic lens ★ Hypermetropia ★ Myopia ★ Damped least square method ★ Doublet ★ Triplet ★ Optimization design over full field
論文目次	摘要………..…………………….…………………………………………..I 目錄………………………………………………………………………….II 圖目錄………………………………………………………………………VI 表目錄………………………………………………………………………XI 第一章緒言………………………………………………………………1 第二章三階像差與薄透鏡和薄透鏡組關係………………………..4 2.1 三階像差…………………………………………………………..4 2.1.1 薄稜鏡之色散像差…………………………………………………4 2.1.1.1薄透鏡之軸向色散………………………………………………4 2.1.1.2薄透鏡之橫向色散………………………………………………5 2.1.2單色光像差…………………………………………………………5 2.1.2.1球面像差………………………………………………………...6 2.1.2.2彗星像差………………………………………………………...8 2.1.2.3斜射像散……………………………………………………….10 2.1.2.4視場彎曲……………………………………………………….10 2.1.2.5畸變…………………………………………………………….11 2. 2 薄透鏡和其鏡組設計...………………………………………….…..12 2.2.1眼鏡片………………………………………………………………12 2.2.1.1 橫向色散………………………………………………..14 2.2.1.2 消像散設計……………………………………………….….14 2.2.2 雙片鏡組…………………………………………………………17 2.2.2.1 薄透鏡之像差公式…………………………………………17 2.2.2.2 雙片鏡組像差分析…………………………………………20 2.2.3 三片鏡組…………………………………………………………21 2.2.3.1 薄透鏡初階設計……………………………………………21 2.2.3.2 薄透鏡三階設計……………………………………………24 第三章真實像差…………………………………………………………33 3.1 光線追跡…………………………………………………………33 3.1.1 近軸追跡…………………………………………….……….33 3.1.1.1 有效焦距、後焦距………………………………………33 3.1.1.2 入瞳口徑及位置，出瞳口徑及位置…………………34 3.1.2 真實光線追跡……………………………………………….35 3.1.2.1球面追跡………………………………………………….35 3.1.2.1.1 傳遞過程…………………………………….……….35 3.1.2.1.2 折光過程…………………………………….……….35 3.1.2.2非球面追跡……………………………………………….36 3.2 像差評價…………………………………………………………39 3.2.1 光扇圖分析………………………………………………….39 3.2.2 光點圖分析………………………………………………….39 第四章厚透鏡三階像差與阻尼最小二乘法………………………..48 4.1 厚透鏡三階像差………………………………………………..48 4.2 阻尼最小二乘法………………………………………………..56 第五章眼鏡片設計……………………………………………………..60 5.1 主要像差…………………………………………………………60 5.2 低折光率眼鏡片設計……………………………….………….62 5.2.1 球面眼鏡片設計…………………………………………….62 5.2.2 非球面反曲點……………………………………………….64 5.2.3 優化方法………………………………………….………….65 5.2.4 近視非球面眼鏡片設計……………………………………66 5.2.5 遠視非球面眼鏡片設計……………………………………71 5.2.6 球面眼鏡片與非球面眼鏡片比較……………………….75 5.3 高折光率非球面眼鏡片設計……………………….…………75 5.3.1 球面眼鏡片設計…………………………………………….76 5.3.2 優化方法………………………………………….………….77 5.3.3 近視眼鏡片設計…………………………………………….78 5.3.4 遠視眼鏡片設計…………………………………………….82 第六章雙片鏡組設計…………………………………………………104 6.1 理論基礎…………………………………………….………….104 6.1.1 優化方法……………………………………………………104 6.1.2 厚透鏡三階球面像差與三階彗星像差………………..105 6.2 設計流程…………………………………………….………….106 6.2.1 起始值設計、 ……………………….……………106 6.2.2 以三階球面像差校正軸上像差…………………………..107 6.2.3 以三階彗星像差校正軸上像差…………………………107 6.2.4 以三階球面像差與三階彗星像差校正軸上像差...108 6.2.5 優化程式流程……………………………………………………108 6.3 設計實例……………………………………………………….109 6.3.1 軸上像差最小值設計…………………………………….110 6.3.2 半視角1度離軸像差最小值設計………………………111 6.3.3 全領域最佳值設計……………………………………….112 6.3.4 塑膠雙片鏡組設計……………………………………….115 第七章三片鏡組設計…………………………………………………142 7.1 理論基礎……………………………………………………….142 7.1.1 優化方法……………………………………………………142 7.1.2 厚透鏡三階球面像差、彗星像差與像散………………143 7.2 優化設計程序………………………………………………….144 7.2.1 起始值設計、、 …………………………144 7.2.2 三階球面像差對真實像差的影響………………………144 7.2.3 三階彗星像差對真實像差的影響………………………145 7.2.4 三階像散對真實像差的影響……………………………145 7.2.5 以三階球面像差、彗星像差、像散校正真實像差….145 7.2.6 優化程式流程……………………………………………..146 7.3 設計實例……………………………………………………….147 7.3.1 全領域最佳值設計………………………………………..148 7.3.2 LaK21、F6、LaK21三片鏡組設計…………………….150 第八章結論……………………………………………………………..174 參考資料………………………………………………………………….176 中英文名詞對照表………………………………………………………178
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指導教授	張明文	審核日期	2002-1-21
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