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研究生： 鍾天祥
Tian-Siang Jhong
論文名稱： 二次通過成像架構量測人眼的光學系統品質
Assessments of the Human Eye Optical System by a Double-Pass Configuration
指導教授： 陳怡君
Yi-Chun Chen
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 光電科學與工程學系
Department of Optics and Photonics
畢業學年度： 99
語文別： 中文
論文頁數： 136
中文關鍵詞： 光學調制轉換函數 、二次成像 、光學系統 、人眼
外文關鍵詞： MTF, modulation transfer function, Double-Pass, human eye
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    • 本研究主要在架構一套人眼光學量測系統，以量得的數據來完善本實驗室先前所建構的人眼眼球模型，使其更符合真實的人眼光學系統，如以一來，在未來的正常照明條件與眩光實驗會有相當高的應用性。
    此量測系統基於資訊影像的完整性(例如散射光)，使用二次通過成像(Double-Pass measurements, DP)的架構，含有Badal系統，可方便日後實驗有更多操弄的選擇。
    論文首先分析DP的光學理論，並考慮裸眼的光學調制轉換函數(MTF)，接著探討實驗裝置，分成兩部分，首先為人工眼的校準裝置，此階段可幫助提升後面人體實驗的經驗及技巧，第二階段為人體實驗，來得到人眼的MTF。
    實驗所得結果在趨勢上與現有文獻資料之年輕族群結果大致相符，驗證此實驗系統之可行性，未來可再收取不同年齡層之眼球實驗資料，再與眼球模型所得結果相比較並用以完善眼球模型。

    This study focused on the construction of a human-eye optical measurement system. The data is intended for the software eye model previously developed in the research group. Once modified to match the performance of real human eyes, the model is highly potential for investigating visual performance in ordinary lighting and display conditions and under the influence of glare sources.
    In order to retain the information integrity in the measured images, especially the effect of intraocular scattering, a double-pass (DP) configuration was adopted. A Badal system was included for flexible manipulations in future experiments.
    The optical theory of DP was first analyzed to derive the modulation transfer function (MTF) of a naked human eye. Two kinds of experiments were then implemented, one with an artificial eye and the other with real human eyes. The artificial-eye experiment served as the system calibration and protocol familiarization. The human-eye experiment provided the images for computing MTFs of human eyes.
    The experimental results showed the same trend as the data of the young population in the literature, which verified the feasibility of this measurement system. Subjects from different age groups could be collected in future experiments. By comparing the acquired data with the results from the human-eye model, the optical parameters of the eye model could be optimized.

    中文摘要..........................................................................................I 英文摘要.........................................................................................II 致謝................................................................................................III 目錄................................................................................................IV 圖索引......................................................................................... VIII 表索引..........................................................................................XII 第一章 緒論……………………………………………………………1 1.1 研究動機...................................................................................1 1.2 研究背景與架構........................................................................3 1.3 論文大綱...................................................................................5 第二章 背景知識及相關研究…………………………………………6 2.1 線性光學系統...........................................................................6 2.2 線性系統的空間不變性（Space-invariant）................................8 2.3 薄透鏡成像系統........................................................................9 2.3.1 薄透鏡脈衝響應的型式........................................................10 2.3.2 薄透鏡系統的成像光場........................................................15 2.3.3 薄透鏡系統的成像光強度.....................................................16 2.4 傳遞函數、PSF與MTF............................................................22 2.4.1 同調傳遞函數（coherent transfer function, CTF）與截止頻率……………………………..………………………………….23 2.4.2 非同調傳遞函數OTF與截止頻率…………………………...25 2.4.3 Modulation transfer function, MTF…………………………29 2.5 MTF的物理意義……………………………………….……….30 2.5.1 鏡頭參數MTF的數學推導…………………………………….32 2.6 Badal system……………………………………….…………...34 2.7 屈光度……………………...…………..…………………………39 2.7.1 眼球的調節………………..……………………………………39 2.8 照度……………………..…………………………………………40 2.9 出瞳與入瞳…………………..……………………………………41 第三章 理論架構…………………………………………………….44 3.1 DP系統理論架構.....................................................................44 3.1.1 DP系統的脈衝響應函數........................................................45 3.1.2 DP的成像光場......................................................................47 3.1.3 DP的成像光強度與MTF.......................................................49 3.2 DP系統物理意義.....................................................................51 3.3 實驗的DP系統MTF之計算....................................................53 第四章 實驗架構與實驗結果分析……………………………………56 4.1 人工眼校準裝置......................................................................58 4.1.1 實驗光路..............................................................................59 4.1.2 裝置說明..............................................................................59 4.1.3 實驗操作..............................................................................60 4.1.4 實驗結果與分析...................................................................62 4.2 人眼量測裝置..........................................................................66 4.2.1 實驗光路..............................................................................66 4.2.2 能量分布與安全值................................................................67 4.2.3 實驗操作..............................................................................72 4.2.4 實驗結果與分析...................................................................80 第五章結論........................................................ .........................106 附 1 公式定理.............................................................................108 附 2 圓孔繞射的MTF（同調光系統）.........................................109 附 3 CCD最小照度.....................................................................113 附 4 陽明大學人體試驗委員會審核書.........................................116 附 5 受試者同意書………...........................................................117 參考文獻......................................................................................122 圖索引 圖1- 1 眼球模型..............................................................................2 圖2- 1 成像系統示意圖.................................................................10 圖2- 2 （a）視網膜的構造（b）人眼錐狀細胞的光譜吸收..................17 圖2- 3 階段說的色覺模型..............................................................17 圖2- 4 （a）空間頻率的表示圖（b）MTF的圖...................................30 圖2- 5鏡頭的MTF.........................................................................31 圖2- 6單透鏡成像系統..................................................................32 圖2- 7 簡單視力儀的示意圖..........................................................34 圖2- 8 單透鏡Badal系統示意圖...................................................35 圖2- 9 眼球內所對應的幾何光學結構............................................36 圖2- 10 遠物加輔助透鏡的Badal系統..........................................37 圖2- 11 4F系統示意圖................................................................38 圖2- 12 眼睛聚焦在物體時的距離為d示意圖…………...…………39 圖2- 13 出瞳與入瞳示意圖……………………………..……………41 圖2- 14包含主平面及出入瞳的光學示意圖………………………..43 圖3- 1 DP理論架構示意圖............................................................44 圖3- 2 用shear plate量到的像差.................................................46 圖3- 3 眼球結構............................................................................49 圖3- 4 分別在短時間內所拍的成像影像（視網膜）…......................50 圖3- 5 經由視網膜所得到的影像I_2 (x^'',y^'' )示意圖..........................53 圖4-1 人工眼校準裝置示意圖。....................................................58 圖4-2實際實驗裝置（a）光擴束器（b）BS1附近的實驗裝置（c）人工眼………......................................................................58 圖4-3 人工眼視網膜的影像...........................................................60 圖4-4 人工視網膜實驗結果...........................................................62 圖4-5 角解析度換算示意圖...........................................................63 圖4-6高斯波繞射極限MTF...........................................................64 圖4-7 系統繞射極限MTF，像素點離散效應.................................64 圖4-8 校正後的MTF，眼球系統MTF...........................................65 圖4-9 人體實驗DP裝置示意圖....................................................67 圖4-10人體實驗流程示意圖..........................................................72 圖4-11 人體實驗DP裝置..............................................................73 圖4-12 標靶T與燈箱.....................................................................73 圖4-13 受試者架在下巴支撐器上..................................................74 圖4-14 CCD截圖程式.................................................................77 圖4-15 高平整反射鏡架設裝置.....................................................78 圖4-16 反射鏡I_1像素統計圖..........................................................79 圖4-17 散光驗光圖…………………………………………………....80 圖4-18 WY-L實驗結果................................................................82 圖4-19 WY-R實驗結果...............................................................83 圖4-20 MY-L實驗結果................................................................84 圖4-21 MY-R實驗結果...............................................................85 圖4-22 CS-L實驗結果................................................................86 圖4-23 CS-R實驗結果................................................................87 圖4-24 KY-L實驗結果.................................................................88 圖4-25 KY-R實驗結果................................................................89 圖4-26 HW-L實驗結果................................................................90 圖4-27 HW-R實驗結果................................................................91 圖4-28 HY-L實驗結果.................................................................92 圖4-29 HY-R實驗結果................................................................93 圖4-30 PL-L實驗結果..................................................................94 圖4-31 PL-R實驗結果.................................................................95 圖4-32 CY-L實驗結果.................................................................96 圖4-33 CY-R實驗結果................................................................97 圖4-34 SY-L實驗結果..................................................................98 圖4-35 SY-R實驗結果.................................................................99 圖4-36 CCD2實際拍攝瞳孔情況...............................................101 圖4-37 MTF平均值與標準差.....................................................103 圖4-38 其他DP_MTF(年輕人)研究............................................103 圖4-39 視力1.0的條件..............................................................104 表索引 表4- 1 元件的規格與說明..............................................................56 表4-2 雷射光危險性分級..............................................................68 表4-3 眼睛最大容許曝光（Maximum Permissible Exposure, MPE）..................................................................................69 表4-4 受試者代號與視力資料.......................................................80 表4- 5 MTF平均值比較表.........................................................104

    第一章
    [1. 1]江重致, ”人眼眼球模型與視覺表現之模擬分析研究," 中央大學光電科學與工程學系碩士論文, 中華民國九十八年七月.
    [1. 2] D. R. Williams, D. H. Brainard, M. J. McMahon, and Rafael Navarro, “Double-pass and interferometric measures of the optical quality of the eye,” J. Opt. Soc. Am. A, Vol. 11, No. 12, PP.3123-3135 (1994).
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    [1. 4] P. Artal, I. Iglesias, N. Lo ́pez-Gil, and D. G. Green, “Double-pass measurements of the retinal-image quality with unequal entrance and exit pupil sizes and the reversibility of the eye’s optical system,” J. Opt. Soc. Am. A, Vol. 12, No. 10, PP. 2358-2366 (1995).
    [1. 5] P. Artal, S. Marcos, and R. Navarro, and D. R. Williams “Odd aberrations and double-pass measurements of retinal image quality,” J. Opt. Soc. Am. A. Vol. 12, No. 2, PP. 195-201 (1995).
    [1. 6] R. Navarro, P. Artal, and D. R. Williams “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A. Vol. 10, No. 2, PP. 201-212 (1993).
    [1. 7] N. Lo ́pez-Gil and P. Artal,”Comparison of double-pass estimates of the retinal-image quality obtained with green and near-infrared light,” J. Opt. Soc. Am. A, Vol. 14, No. 5, PP. 961-971 (1997).
    第二章
    [2. 1] J. W. Goodman, “Introduction to Fourier Optics,” 2nd Ed., McGraw-Hill, New York (2002).
    [2. 2]大田 登 原著, 陳鴻興, 和陳詩涵 編譯, “色彩與工程學,” 第二版, PP. 1-43 (2008).
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    第三章
    [3. 1] P. Artal, S. Marcos, R. Navarro, and D. R. Williams, “Odd aberrations and double-pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12, PP. 195–201 (1995).
    [3. 2] 同2.4
    [3. 3] J. Santamarı ́a, P. Artal, and J. Besco ́s, “Determination of the point-spread function of human eyes using a hybrid optical–digital method,” J. Opt. Soc. Am. A 4, PP. 1109–1114 (1987).
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    [3. 5] J. Santamarı ́a, A. Plaza, and J. Besco ́s, "Dynamic recording of the binocular point spread function of the eye optical system," Opt. Appl. 24, PP. 341-347 (1984).
    [3. 6] J. Santamarı ́a, P. Artal, and J. Besco ́s, “Determination of the point-spread function of human eyes using a hybrid optical–digital method,” J. Opt. Soc. Am. A 4, PP. 1109–1114 (1987).
    [3. 7] P. Artal, J. Santamarı ́a, and J. Besco ́s, “Phase-transfer function of the human eye and its influence on point-spread function and wave aberration,” J. Opt. Soc. Am. A 5, PP. 1791–1795 (1988).
    [3. 8] 同1.4
    第四章
    [4. 1] Smith, Warren J., “Modern Optical Engineering ,” 4th Ed., McGraw-Hill, PP. 399 (2007).
    [4. 2] M. Marchywka and D. G. Socker, " Modulation transfer function measurement technique for small-pixel detectors," APPLIED OPTICS, Vol. 31, No. 34, PP. 7198-7213 (1992).
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    [4. 4] D. Sliney and M. Wolbarsht, “Safety With Lasers and Other Optical Sources,” Plenum, New York, PP. 217-260 (1980).
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    [4. 7] 陳木星, 陳賢堂, 黃宣瑜, 孫涵瑛, 葉上明, 陳志宏, 和劉祥瑞 編譯, “視光學概論,” 第一版, 五南圖書, 台北市, PP. 8 (2010).

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