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研究生:顏至強
研究生(外文):Jyh-Chyang Yen
論文名稱:阿爾瓦雷斯變焦鏡組之光學設計
論文名稱(外文):Optical Design of Alvarez Zoom Lenses
指導教授:陳金嘉黃光榮黃光榮引用關係
指導教授(外文):Jin-Jia ChenKuan-Lung Huang
學位類別:博士
校院名稱:國立彰化師範大學
系所名稱:電機工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
畢業學年度:103
語文別:中文
論文頁數:87
中文關鍵詞:阿爾瓦雷斯鏡組橫向移動軸向球面像差變焦鏡組微型化
外文關鍵詞:Alvarez lenslateral movementlongitudinal spherical aberrationzoom lensminiaturized
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阿爾瓦雷斯鏡組(Alvarez lens)當初之設計是為了得到一個簡單、便宜且又薄型的變焦眼鏡,以使近方及遠方的視覺可快速而方便地聚焦。基本上此鏡組是由一對形狀完全相同的薄鏡片以相反方向相對排列而組成,且鏡片之曲面大體上垂直於光軸。兩鏡片可沿著橫軸方向作等量相對位移,以改變系統焦距長度。近年來雖有相當多關於此鏡組之像差與應用研究發表,但有關其像差優化之研究却十分少見。有鑑於此,本論文乃針對此鏡組之設計提出一個簡易的優化方法,藉以提升其光學性能及成像品質。
由於阿爾瓦雷斯鏡組係由一對形狀相同的三次方曲面鏡片所組成,為了方便後續鏡組之設計與優化,本論文乃先針對鏡組曲面參數改變對面型之影響進行探討與分析,並依鏡組之不同排列架構以英文字母p、b、d及q定義並分類成八種架構型式,而後經由真實光線追跡,以計算出每一種架構型式之軸向球面像差。由光線追跡結果顯示,阿爾瓦雷斯鏡組之像差形態與傳統旋轉對稱鏡片不同,其上邊緣與下邊緣光線之屈光能力在入光瞳孔徑越小時,兩者之間差異越大。為了抑制軸向球面像差,本論文將單一阿爾瓦雷斯鏡組之焦度、A值、D值、鏡片厚度及間距依 之比例分配於兩個緊密相鄰的鏡組,並使兩鏡組之結構與光軸成180度反轉對稱而構成一個阿爾瓦雷斯雙鏡組群。由光線追跡模擬結果顯示,聚焦光點半徑由單一鏡組的3.514μm降至雙鏡組群的1.749μm,說明此種設計方式能有效抑制軸向球面像差之產生。運用此種設計方式,並採用兩群已優化之pdbq型雙鏡組群架構,可獲得變倍比兩倍、視場角5度、鏡片直徑3 mm以及系統全長4.56 mm之變焦鏡組,驗證阿爾瓦雷斯鏡組應用於微型化變焦系統之可行性

Alvarez lens was first designed to obtain a simple, inexpensive, thin, and attractive variable-power spectacle so that it can be quickly and easily focused on the near and distant visions. Basically, the lens is composed of a pair of similar thin-lens elements arranged in tandem, one behind the other along the optical axis, and the lens surface is substantially normal to the optical axis. Both lens elements can move by equal amount in opposite direction along the transverse axis to change focal length. Recently, much more researches concerned aberration and application of this lens have been published; however, relative researches of lens optimization design are seldom appeared. For this reason, this dissertation proposes an easy optimization method for Alvarez lens so that its optical performance and imaging quality can be promoted.
Since Alvarez lens is composed of a pair of similar cubic-surface lenses, to facilitate the subsequent design and optimization of the lens, this dissertation first aims at the exploration and analysis of the impact on the surface profile due to the change of lens surface parameters, and uses alphabets of p, b, d and q to define and classify all kinds of lens structures into eight different types based on their structure arrangements. After a real ray-tracing, the longitudinal spherical aberration for each type of lens structures can be calculated. The ray-tracing results show that the aberration type of the Alvarez lens is quite different to that of the normal axis-symmetrical spherical lens. The difference of ray bending between the upper marginal ray and the lower marginal ray is getting bigger when the pupil becomes smaller. To minimize the longitudinal spherical aberration, this dissertation distributes the optical power, the A value, the D value, lens thickness and spacing of a single-pair Alvarez lens into two closely adjacent lens-pairs with a ratio of 2:3, and the structures of these two lens-pairs are arranged with 180-degree inversion-symmetry to the optical axis to form an Alvarez double-lens-pairs group. The ray-tracing simulation result shows that the radius of the spot diagram decreases from of a single lens-pair to of a double-lens-pairs group. It means that the longitudinal spherical aberration is well controlled. By using this design method and employing two optimized pdbq lens-pairs-group structures, an Alvarez zoom lens system with two times zoom ratio, 5-degree field of view, 3-mm length lens diameter, and 4.56-mm total length is constructed. It approves the possibility of miniaturized Alvarez zoom lens system

摘要 i
Abstract iii
謝誌 v
目錄 vii
圖目錄 xi
表目錄 xvi
第一章 緒論 1
1.1 研究背景 1
1.2 文獻回顧 2
1.3 研究動機與目的 11
1.4 論文貢獻 11
1.5 論文架構 13
第二章 基本光學理論 15
2.1 光線傳播之折射角度計算 15
2.1.1 斯涅爾定理 16
2.1.2 點斜式直線方程式及其斜率 17
2.1.3 兩相交直線之夾角計算 17
2.2 基本像差理論 18
2.2.1球面像差 20
2.2.2彗星像差 20
2.2.3場曲 22
2.2.4像散 22
2.2.5畸變 23
2.2.6縱向色差 24
2.2.7橫向色差 24
2.3 帕茲伐常數和及變焦鏡組 25
2.3.1變焦鏡組 25
2.3.2帕茲伐常數和與場曲像差消除 28
2.4 像差評價 29
2.4.1 光點圖 29
2.4.2 調制傳遞函數 33
2.5 阿爾瓦雷斯鏡組 35
2.5.1 阿爾瓦雷斯鏡組之工作原理 35
2.5.2各參數對單一阿爾瓦雷斯鏡片面型之影響 39
第三章 阿爾瓦雷斯鏡組之結構與像差分析 47
3.1阿爾瓦雷斯鏡組結構定義 47
3.2阿爾瓦雷斯鏡組之真實光線追跡 53
3.3 pd型阿爾瓦雷斯鏡組軸向球面像差之探討與改善 60
3.4 單一阿爾瓦雷斯鏡組結構之像差影響分析 64
3.4.1鏡片間距對像差之影響 64
3.4.2 鏡片位移距離對像差之影響 65
3.4.3 A值對像差之影響 66
3.5阿爾瓦雷斯鏡組群排列架構之像差影響分析 67
3.5.1阿爾瓦雷斯雙鏡組群排列架構之像差影響分析 68
3.5.2阿爾瓦雷斯多鏡組群排列架構之像差影響分析 69
第四章 阿爾瓦雷斯變焦鏡組之設計 71
4.1 單一阿爾瓦雷斯鏡組群之優化設計 71
4.2阿爾瓦雷斯變焦鏡組之設計 73
第五章 結論與未來展望 78
5.1 結論 78
5.2 未來展望 79
參考文獻 81

圖目錄
圖1.1 阿爾瓦雷斯鏡組專利鏡組的曲面特徵[1] 2
圖1.2 阿爾瓦雷斯鏡組專利鏡組的截面特徵[1] 2
圖1.3調焦光學系統 3
圖1.4變焦光學系統 4
圖1.5機械式補償變焦鏡 4
圖1.6光學式補償變焦鏡 5
圖1.7階梯式折射率鏡片[11] 6
圖1.8液晶調焦鏡片[18] 6
圖1.9 鏡片分類[3] 7
圖1.10羅漢鏡組[20] 8
圖1.11阿爾瓦雷斯鏡組調焦移動 8
圖1.12不同排列結構之單一阿爾瓦雷斯鏡組 10
圖1.13不同排列結構之雙阿爾瓦雷斯鏡組 10
圖2.1 白光在不同介質中的傳播 16
圖2.2斯涅爾折射定理 16
圖2.3 任意直線斜率之計算 17
圖2.4 兩相交直線之夾角 18
圖2.5球面像差 20
圖2.6彗星像差 21
圖2.7彗星像差示意圖 21
圖2.8帕茲伐面 22
圖2.9像散 23
圖2.10畸變 24
圖2.11縱向與橫向色差 24
圖2.12 雙鏡組變焦系統 26
圖2.13 平行光聚焦圖 27
圖2.14變焦曲線圖 27
圖2.15雙膠合變焦光學鏡組示意圖 29
圖2.16 入瞳光點圖 30
圖2.17 阿爾瓦雷斯鏡組之光點圖 30
圖2.18入光視場角度取點圖 31
圖2.19 各視場光點圖 32
圖2.20選定入光視場角分布圖 32
圖2.21 選定視場光點圖 33
圖2.22空間中影像頻率 34
圖2.23調制傳遞函數隨空間頻率增加而降低 34
圖2.24單一阿爾瓦雷斯鏡組調制傳遞函數 35
圖2.25方型阿爾瓦雷斯鏡片 36
圖2.26圓型阿爾瓦雷斯鏡片 36
圖2.27阿爾瓦雷斯鏡組不同移動方向示意圖 38
圖2.28阿爾瓦雷斯鏡組曲面 40
圖2.29 YZ軸面呈左右對稱面型 41
圖2.30 XZ軸面呈負對稱面型 41
圖2.31 原xy2項係數乘以10之XZ軸面側面視圖 42
圖2.32原xy2項係數乘以0.1之XZ軸面側面視圖 42
圖2.33原x3項係數乘以10之XZ軸面側面視圖 43
圖2.34原x3項係數乘以0.1之XZ軸面側面視圖 43
圖2.35不同x3項係數之XZ軸面剖面線(單位:cm) 44
圖2.36原式中加入0.02x2項之XZ軸面側面視圖 44
圖2.37不同x3項係數之XZ軸面剖面線(單位:cm) 45
圖2.38 原式中加入0.02y2項之XZ軸面側面視圖 45
圖2.39 原式中加入0.02y2項之YZ軸面側面視圖 46
圖3.1 pd型鏡組 49
圖3.2 bq型鏡組 49
圖3.3 qb型鏡組 50
圖3.4 dp型鏡組 50
圖3.5 dq型鏡組 51
圖3.6 qd型鏡組 51
圖3.7 pb型鏡組 52
圖3.8 bp型鏡組 52
圖3.9 pd型鏡組光線追跡模擬 54
圖3.10 pd型鏡組上邊緣光追跡計算 54
圖3.11 出射角計算 56
圖3.12 pd型鏡組光線追跡模擬 60
圖3.13出射光線與光軸之交點 60
圖3.14 pd型阿爾瓦雷斯鏡組之軸向球面像差 61
圖3.15 pd型阿爾瓦雷斯鏡組 62
圖3.16 pdbq型阿爾瓦雷斯雙鏡組群 62
圖3.17 pdbq型阿爾瓦雷斯雙鏡組群之軸向球面像差 63
圖3.18 pd型鏡組之光點圖(光點半徑3.514μm) 63
圖3.19 pdbq型雙鏡組群之光點圖(光點半徑2.815μm) 64
圖3.20 鏡片間隔對光點圖半徑之影響 65
圖3.21鏡片移動距離對光點圖半徑之影響 66
圖3.22 A值對光點圖半徑之影響 67
圖3.23鏡片移動距離對鏡組(群)之光點圖半徑之影響 68
圖3.24鏡組間隔對pdpd及pdbq型雙鏡組群之光點圖半徑之影響 69
圖3.25鏡片移動距離對多鏡組(群)之光點圖半徑之影響 70
圖4.1不同分配比例拆分之合成鏡組的光點半徑 73
圖4.3 阿爾瓦雷斯變焦鏡組於有效焦距長等於5 mm之位移 77
圖4.4 鏡片修整 77

表目錄
表2.1 起始參數[1] 39
表3.1 阿爾瓦雷斯鏡組分類表 48
表3.2 pd型阿爾瓦雷斯鏡組之參數表 53
表3.3 上邊緣光追跡表 58
表3.4 下邊緣光追跡表 58
表3.5 軸上光追跡表 59
表3.5 pd型阿爾瓦雷斯鏡組參數 61
表3.6 原阿爾瓦雷斯鏡組等比拆分後之鏡組參數 62
表4.1 鏡組拆分參數表 72
表4.2 變焦參數表(單位:mm) 75
表4.3 變焦鏡組參數表 75
表4.4 阿爾瓦雷斯鏡面參數表 76

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