繞射/折射複合型變焦鏡組之設計與量測

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(1)國立交通大學光電工程研究所碩士論文繞射/折射複合型變焦鏡組之設計與量測 Design and measurement of diffractive/refractive hybrid zoom-component. 研究生：王俊勛指導教授：陸懋宏教授. 中華民國九十二年六月.

(2) 繞射 / 折射複合型變焦鏡組之設計與量測 Design and measurement of diffractive/refractive hybrid zoom-component 研究生：王俊勛. Student：Jiun-Shiun Wang. 指導教授：陸懋宏. Advisor：Mao-Hong Lu. 國立交通大學電機資訊學院光電工程研究所碩士論文 A Thesis Submitted to Institute of Electro-Optical Engineering College of Electrical Engineering and Computer Science National Chiao Tung University In partial Fulfillment of the Requirements For the Degree of Master In Electro-Optical Engineering June 2003 Hsinchu, Taiwan, Republic of China. 中華民國九十二年六月.

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(4) 繞射/折射複合型變焦鏡組之設計與量測研究生: 王俊勛. 指導教授: 陸懋宏. 國立交通大學光電工程研究所. 摘要本論文中，我們描述變倍比為 3 倍被使用在數位相機上之緊湊三群透鏡變焦系統的設計流程，此系統被要求不僅有小的體積和重量，而且有足夠長的後焦以便在成像面前放置彩色濾波片。首先我們將系統中的透鏡分為二群，即所謂的二鏡組設計方法來找到變焦系統的高斯解。在這個高斯解當中，第一群透鏡是由二個透鏡所組成，但第二群透鏡只包含有一個透鏡。在這高斯解的基礎上，然後我們藉由光學設計軟體 ZEMAX 來設計此變焦系統。在這變焦系統中，我們為了優化每一個透鏡的效能，則我們將每一個透鏡替代為繞射/折射混合型透鏡，在此透鏡系統設計中，每一透鏡的表面均是非球面，在這同時我們也建立利用 MATLAB 做為平台的一套軟體，根據從光學軟體 ZEMAX 模擬的結果來計算在混合型透鏡繞射表面上的波帶(或信息圖)結構，對於所設計的混合型透鏡已經由工業技術研究院的機械研究所，利用鑽石車床加工製作完成。變焦系統的幾何和光學特性則在我們的實驗室所測得，所測量的結果與結果的分析將被描述。 I.

(5) Design and measurement of diffractive/refractive hybrid zoom-component Student：Jiun-Shiun Wang. Advisor：Prof. Mao-Hong Lu. Institute of Electro-Optical Engineering National Chiao-Tung University. Abstract In this thesis we described a procedure for design of a compact three-lens zoom system used in digital camera with a zoom ratio of 3. This system is required to have not only small size and weight but also long-enough back focal length in which a color filter can insert. First we found a Gaussian solution of the zoom system with so-called two-optical-component method, in which the lenses in the system are divided into two groups. In this solution the first group comprises two lenses, but the second group contains only one lens. Then, based on the Gaussian solution, we designed the zoom system with the optical software ZEMAX. In order to optimize the performance of each lens, we replaced each lens with a diffractive/refractive hybrid lens. In this design all surfaces of lenses were aspherical. At the same time we built a software with MATLAB for calculation of the kinoform structures of diffractive surfaces on the hybrid lenses according to the results from ZEMAX. All the designed hybrid lenses have been fabricated with diamond turning by Mechanical Industry Research Laboratories of ITRI. The geometric and optical properties of the zoom system were measured in our lab. The measurement results and an analysis on these results are described. II.

(6) 誌謝一個里程的結束代表著一個新的里程即將開始，所以人生就是這樣充滿著驚喜與樂趣，在新竹交大唸碩士的這二年讓我收穫很多，也是幫助我有信心出社會工作的動力與能源，這些都是要感謝有“緣”人，因為有 “緣”我們才能相遇，所以我會好好珍惜這份緣。對於此論文的完成要感謝的人很多很多，首先要感謝的當然是我的指導老師陸懋宏教授，因為有指導老師在研究上的傾囊相授和細心指導下，使學生我在這方面的學習有更深入的見解和廣闊的視野，因而得以順利完成此論文。然而在論文完成的過程中，周圍學長們的經驗指點、同學之間的相互幫助，才能使論文的完成更加順利，在此我要感謝詹勝雄學長、王浩偉學長、蔡榮智學長、桑競存學長、施至柔學長、林暉雄學長、高清芬學姊、伍清欽學長、姚柏宏學長、王唯科學長、鮑友南學長、柯俊宏學長、徐得銘學長、林育正學長和陳晏佐學長等的鼎力幫忙；其中現在博一的徐得銘學長是帶我的學長，學長教我程式、ZEMAX 和為我解答很多問題，所以由於有學長的幫助，論文也才能得以順利地完全。另外還有朱淑君同學、洪文明同學、張維中同學、呂怡瑱學妹、馮致華學弟、陳建丞學弟和陳慶勳學弟的互相幫助及帶給實驗室活力與歡樂，因而使得論文能夠在快樂且循序的學習研究當中完成。除了感謝實驗室之外，還要非常感謝工研院機械所微機電組的傅春能先生、謝銘郎先生、林宗信先生、張智崇先生及製程人員等在元件製作上的鼎力幫助，沒有他們在元件加工製作上的優良技術，則此篇論文將難以順利完成，其中林宗信先生在我論文元件製作方面給我很多建議和協助， III.

(7) 以使得論文最後能如期完成，所以非常感謝他。還有要感謝行政院國家科學委員會精密儀器發展中心林宇仁學長熱心幫助我在元件方面的量測、張雪珍學姐在我論文研究上提供相關的訊息和資料、台中利科有限公司詹坤鄰經理免費提供濾波片讓我做研究及亞洲光學股份有限公司劉德偉課長，非常感謝他大力幫忙我解決問題與教我光學方面的概念，我才得以順利完成碩士論文。最後要感謝的是我的家人，因為有家人的關心和默默支持，才能讓我在學習的生涯上安心無虞地踏出每一步，能夠順利的畢業也算是不辜負家人對我的期望，當然未來也是我該對家人回報的時候了。最後，祝福大家：. J健康愉快、順心如意 J 2003 年 6 月新竹交大&A. IV.

(8) 目. 錄. 中文摘要 ···············································································Ⅰ 英文摘要 ···············································································Ⅱ 誌謝 ·······················································································Ⅲ 目錄 ·······················································································Ⅴ 圖目錄 ···················································································Ⅷ 表目錄 ··················································································ⅩⅢ. 第一章緒論 ···········································································1 第二章變焦系統基本理論 ···················································3 2.1 符號定義 ·······················································································3 2.2 兩群透鏡光學系統 ······································································5 2.2.1 對於無窮物距系統····································································5 2.2.2 對於有限物距系統····································································5. 2.3 三群透鏡光學系統 ······································································6 2.3.1 第一群透鏡固定的系統，第二、三群透鏡為組合鏡組············8 2.3.1.1 無窮物距系統 ···························································································8 2.3.1.2 有限物距系統 ·························································································10. V.

(9) 2.3.2 第二群透鏡固定的系統，第一、二群透鏡為組合鏡組··········10 2.3.2.1 無窮物距系統 ·························································································10 2.3.2.2 有限物距系統 ·························································································12. 2.3.3 第二群透鏡固定的系統，第二、三群透鏡為組合鏡組··········13 2.3.3.1 無窮物距系統 ·························································································13 2.3.3.2 有限物距系統 ·························································································15. 2.3.4 第三群透鏡固定的系統···························································16 2.3.4.1 無窮物距系統 ·························································································16 2.3.4.2 有限物距系統 ·························································································17. 第三章折射/繞射複合元件基本理論 ································20 3.1 斯維特模型(Sweatt Model)·······················································20 3.2 消色差複合透鏡之設計····························································21 3.3 繞射元件波帶設計 ····································································23. 第四章像質分析與指令介紹 ·············································32 4.1 光扇狀圖(Ray Fan Plot) ····························································33 4.2 光斑圖(Spot Diagram) ·······························································33 4.3 場曲/畸變圖(Field Curvature / Distortion)······························35 4.4 調制傳遞函數圖(Modulation Transfer Function, MTF) ·······38 4.5 相對照度分佈圖·········································································41 VI.

(10) 4.6 色差像位移圖(Chromatic Focal Shift, CFS) ··························41. 第五章使用者介面化與變焦鏡頭設計 ·····························46 5.1 折射/繞射複合元件圖形介面化程式軟體之建立 ················46 5.1.1 軟體流程的撰寫······································································46 5.1.2 軟體介面的架構······································································47 5.1.3 軟體的操作流程······································································50 5.1.4 單透鏡和雙透鏡的光學系統架構圖········································52. 5.2 變焦鏡頭設計 ·············································································53 5.3 加工······························································································77. 第六章實驗結果測量與討論 ·············································79 第七章結論與展望 ·····························································89 參考文獻 ···············································································91. VII.

(11) 圖. 目. 錄. 圖 2.1 圖 2.2 圖 2.3 圖 2.4 圖 2.5. 符號定義圖 ················································································································4 兩群透鏡之無窮物距變焦系統 ················································································5 兩群透鏡之有限物距變焦系統 ················································································6 兩群透鏡合併為一組合鏡組 ····················································································7 三群透鏡之無窮變焦系統，第一群透鏡固定，括號內代表包含兩群透鏡之組合鏡組································································································8 圖 2.6 三群透鏡無窮物距之變焦軌跡圖，第一群透鏡固定不動，變倍比 7：1， F1 = 1.0 、 F2 = −0.4 、 F3 = 0.5 ，第一透鏡至像面的距離為 1.719，物像距離 T23 為 0.719。 ····································································10 圖 2.7 三群透鏡無窮物距變焦系統，第二群透鏡固定不動，第一、二群透鏡視為一組合鏡組。······················································································10 圖 2.8 三群透鏡無窮物距之變焦軌跡圖，第二群透鏡固定不動，變倍比 5：1， F1 = 1.0 、 F2 = −0.25 、 F3 = 0.2 ，第二群透鏡至像面的距離為 0.934。····································································································12 圖 2.9 三群透鏡有限物距之變焦軌跡圖，第二群透鏡固定不動，變倍比 6：1， F1 = 1.0 、 F2 = −0.4 、 F3 = 0.5 ，物像距離為 5.803，物面至第二群透鏡的距離為 3.586，第二群透鏡至像面的距離為 1.497。················································································································13 圖 2.10 三群透鏡無窮物距變焦系統，第二群透鏡固定不動，第二、三群透鏡視為一組合鏡組。····················································································13 圖 2.11 三群透鏡無窮物距之變焦軌跡圖，第二群透鏡固定不動，變倍比 5：1， F1 = 1.0 、 F2 = −0.3 、 F3 = 0.3 ，第二群透鏡至像面的距離為 0.771。······································································································15 圖 2.12 三群透鏡有限物距的變焦軌跡圖，第二群透鏡固定不動，變倍比 6：1， F1 = 1.0 、 F2 = −0.4 、 F3 = 0.5 ，物像距離為 5.662，物面至第二群透鏡的距離為 4.233，第二群透鏡至像面的距離為 1.429。··············································································································16 圖 2.13 三群透鏡無窮物距變焦系統，第三群透鏡固定不動，第一、二群透鏡視為一組合鏡組。····················································································16 圖 2.14 三群透鏡無窮物距之變焦軌跡圖，第三群透鏡固定不動，變倍比 4：1， F1 = 1.0 、 F2 = −0.3 、 F3 = 0.3 ，第三群透鏡至像面的距離為 0.413。······································································································17 圖 2.15 三群透鏡有限物距變焦系統，第三群透鏡固定不動。 ····································17 圖 2.16 三群透鏡有限物距的變焦軌跡圖，第三群透鏡固定不動，變倍. VIII.

(12) 比 6：1， F1 = 1.0 、 F2 = −0.4 、 F3 = 0.5 ，物像距離為 9.052，第三群透鏡至像面的距離為 1.052，組合鏡組物像距離 T12 為 7.047。··············································································································19 圖 2.17 第三群透鏡組固定之簡單示意圖 ········································································19 圖 3.1 (a)光線通過一繞射元件等效透鏡的情況，元件置於一彎曲基片上。(b)放大示意圖。 ························································································20 圖 3.2 消色差混合型光學元件 ··························································································22 圖 3.3 折射/繞射複合光學元件示意圖 ·············································································24 圖 3.4 不同角度入射光對繞射效率的影響。(a)垂直入射 (b)傾斜入射 ·······················25 圖 3.5 設計波長為 0.528 µ m 時之入射波長與繞射效率曲線 ·········································26 圖 3.6 對數個不同設計波長下，相對於入射波長之繞射效率 ······································26 圖 3.7 設計波長與總繞射效率 ··························································································27 圖 3.8 光線平行入射等效透鏡光路圖 ··············································································27 圖 3.9 第 N 個波帶結構圖 ·································································································29 圖 3.10 巨觀下基面的弛垂量 ····························································································30 圖 3.11 波帶結構 ················································································································30 圖 3.12 角度示意圖 ············································································································31 圖 4.1 光扇狀圖範例 ··········································································································33 圖 4.2 計算光斑方式 (A)矩形陣列 (B)圓環陣列 ···························································34 圖 4.3 光斑圖 ······················································································································34 圖 4.4 光學系統之愛里斑(Airy Disk)················································································35 圖 4.5 場曲圖(左)和畸變圖(右) ·························································································36 圖 4.6 子午面和弧矢面在三維薄透鏡的架構圖 ······························································36 圖 4.7 像散 ··························································································································38 圖 4.8 畸變 (A) 枕形畸變 (B) 桶形畸變 ·····································································38 圖 4.9 單個正弦光柵的 (A)物分佈與 (B)像分佈 ·························································39 圖 4.10 MTF 範例圖 ··········································································································40 圖 4.11 相對照度分佈圖 ····································································································41 圖 4.12 色差像位移 ············································································································42 圖 5.1 DROE 軟體撰寫的流程 ·························································································46 圖 5.2 軟體介面轉換程式外觀 ··························································································47 圖 5.3 ·································································································································47 圖 5.4 ·································································································································48 圖 5.5 ·································································································································48 圖 5.6 ·································································································································48 圖 5.7 輸出圖形 ··················································································································49 圖 5.8 ·································································································································49 圖 5.9 ·································································································································50 IX.