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研究生:曾蔚
研究生(外文):Wei Tseng
論文名稱:Double Zernike Polynomial 校準光學系統
論文名稱(外文):Optical System Alignment By Double Zernike Polynomial
指導教授:梁肇文
指導教授(外文):Chao-Wen Liang
學位類別:碩士
校院名稱:國立中央大學
系所名稱:光電科學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:105
中文關鍵詞:光學系統校準
外文關鍵詞:Double Zernike Polynomial
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本論文是以發展一套光學檢測系統為主,利用Double Zernike Polynomial 此函數包含視場與光瞳的像差變化描述,來量化光學元件偏心誤差,本系統可以增加光學檢測的效率,若有此套系統,將會對光學檢測有一大幫助。
模擬係數在系統有偏心誤差的情形下之變化的情況,針對於光學系統中每一個光學元件所擁有的自由度進行誤差模擬,以及兩個的自由度交錯模擬,分析後歸類出係數所對應透鏡存在誤差時的變化狀況,根據此狀況可以反推至系統中元件的偏心情況。
接著設計一套實驗系統去驗證模擬,此系統可以提供高解析度的成像以及多視場的像差資訊,並且使用Double Zernike polynomial來擬合所擷取到的圖形,除此之外,擷取圖形的方式為一次性的擷取多場的像差,這可以大大減少光學檢測的時間。
未來更有可能將所有誤差單一表格化儲存在光學系統內建記憶體中,依照各個不同的設計會對應至不同的修正係數,對於光學影像的品質可以更為提升。
This thesis discusses the development of an optical alignment test system. This system utilizes coefficients of a Double Zernike Polynomial, which contains aberration information of both field and pupil, to quantify alignment errors in an optical system. This test system increases measurement efficiency, and thus will be greatly useful in optical shop testing.
An optical system was first simulated to have certain alignment errors. The corresponding incurred changes in the Double Zernike coefficients were determined from the Double Zernike Table. These varied coefficients will be used to determine alignment errors in other optical systems.
Next an experimental setup was built for verification. This setup provides high-resolution-images and multi field information. An algorithm was then used to perform Double Zernike polynomial fitting. This system acquires off-axis information in a single capture, thus it provides a much shorter processing time compared to many other optical measurement systems.
Future work should be focused on improving the resolution and the accuracy of the system. This will increase the measurement accuracy.
中文摘要………………………………………………………………..i
英文摘要……………………………………………………………….ii
誌謝……………………………………………………………………iii
目錄……………………………………………………………………iv
圖目錄………………………………………………………………...vii
表目錄………………………………………………………………....xi
附圖表目錄…………………………………………………………...xii
第一章 緒論......................................................................................... 1
1-1 研究動機 ............................................................................ 2
1-2 歷史回顧 ............................................................................ 3
第二章 基本原理................................................................................. 5
2-1 像差介紹 ............................................................................ 5
2-2 波前像差與橫向像差......................................................... 7
2-3 朗奇量測法 ........................................................................ 9
2-4 光柵-狹縫量測法............................................................. 11
2-5 Zernike Polynomial........................................................... 14
2-5-1 Single Zernike Polynomial..................................................... 15
2-5-2 Double Zernike Polynomial ................................................... 16
第三章 光學模擬............................................................................... 19
3-1 單鏡片模擬 ...................................................................... 19
3-2 雙鏡片模擬 ...................................................................... 26
3-3 Cooke Triplet模擬........................................................... 37
v
第四章 多場量測實驗....................................................................... 41
4-1 硬體裝置 .......................................................................... 41
4-1-1 光源系統.............................................................................. 41
4-1-2 待測透鏡系統...................................................................... 43
4-1-3 快門控制系統...................................................................... 44
4-1-4 成像系統.............................................................................. 45
4-1-5 十字狹縫陣列與微透鏡陣列............................................... 48
4-2 實驗軟體介面................................................................... 52
4-3 多場像差量測步驟........................................................... 54
4-3-1 校正LCD與CCD非線性曲線........................................... 55
4-3-1-1 校準LCD輸出................................................ 55
4-3-1-2 CCD校準......................................................... 58
4-3-2 前置調整作業...................................................................... 59
4-3-3 相位移量測法...................................................................... 61
4-3-4 四步相移條紋擷取.............................................................. 62
4-3-5 相位解饞繞.......................................................................... 65
4-3-6 實驗結果.............................................................................. 66
4-3-7 實驗誤差.............................................................................. 76
第五章 結論....................................................................................... 78
5-1 實驗總結 .......................................................................... 78
5-2 未來展望 .......................................................................... 79
參考文獻 ............................................................................................ 80
vi
附錄A 軟體介面操作......................................................................... 81
附錄A.1 主介面.................................................................................. 81
附錄A.2 光柵輸出設定...................................................................... 82
附錄A.3 待測透鏡資料輸入 ............................................................ 84
附錄A.4 多場定位.............................................................................. 86
附錄A.5 多場相位解纏繞.................................................................. 88
附錄A.6 重建波前與擬合.................................................................. 90
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〔4〕K. Hibino, D. I. Farrant, B. K. Ward, and B. F. Oreb., "Dynamic Range of Ronchi Test with a Phase-Shifted Sinusoidal Grating.", Applied Optics, Vol. 36, Issue 25, pp. 178-6189, 1997.
〔5〕M. Mora-Gonzalez,N. A. Ochoa., "Sinusoidal Liquid Crystal Display Grating in the Ronchi Test.", Optical Engineering, Vol. 42, pp. 1725-1729, 2003.
〔6〕Liang Chao-Wen, Sasian Jose, "Geometrical Optics Modeling of the Grating-Slit test.", Optics Express, Vol. 15, Issue. 4, pp. 1738-1744, February 2007.
〔7〕J. L. Rayces, "Exact Relation between Wave Aberration and Ray Aberration,", Journal of Modern Optics, Vol. 11, pp. 85-88, 1964.
〔8〕Daniel Malacara, Optical Shop Testing, Wiley-Interscience, New Jersey, 2007.
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