博碩士論文 100286005 詳細資訊




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姓名 林柏至(Po-Chih Lin)  查詢紙本館藏   畢業系所 光電科學與工程學系
論文名稱 旋轉掃描式非球面干涉儀之演算法開發及應用
(The Algorithm Development and Application of Rotational Scanning Aspherical Surface Interferometer)
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摘要(中) 為了提升在台灣在非球面光學鏡片上的自我檢測能力,本團隊成功開發出台灣第一套旋轉掃描式非球面干涉儀,憑藉著自行開發的振動調變式相移干涉術與全域子孔徑拼接演算法加大普通干涉儀的動態範圍,能夠完整量測大於參考鏡的數值孔徑之球面鏡,甚至是半球狀的透鏡皆可以量測。再透過位置優化技術,將子孔徑上所量測到的干涉條紋在徑向方向上的條紋密度降至最低,用以減少環形區域之數目並且增加非球面可量測的範圍,預計可以量測含有1000個波長偏離度的圓對稱非球面鏡,根據實驗結果能夠準確地量測出與非球面設計值差距0.5個波長的誤差量。
此非球面干涉儀最獨特的技術在於利用旋轉平台運轉時所帶有1 μm左右的機械振動,將原本看似不可避免的振動干擾利用振動調變式相移干涉術轉為有用的相移資訊,進而重建出子孔徑表面相位。在每一個環狀區域上皆不須停下量測,透過機械振動即可達到動態量測相位的目的,每個環形區域大約只需要2分鐘就可完成干涉條紋的量測。再透過平行運算系統,降低整體的運算時間,根據量測1吋球面鏡之結果顯示10個環形區域總共346個子孔徑大約只需要30分鐘即可以完成量測。
因著旋轉掃描的量測方式,此干涉儀有高密度量測的優點,不只能夠降低拼接誤差的變異量,而且還可以免除製造高精密度的參考鏡之成本與時間。擁有降低量測時間、購置成本與提高精準度之優勢。
摘要(英) In order to enhance the optical testing capability of aspheric lens in Taiwan, we first developed a rotational scanning aspherical surface interferometer. This subaperture stitching interferometer has more dynamic range than that of a conventional interferometer in virtue of the techniques we developed: vibration modulated phase shifting interferometry and global subaperture stitching algorithm. It can measure spherical lenses with the numerical aperture higher than that of the reference lens. Even a half sphere could also be measured. The optimized null method can minimize the tangential fringe density. This helps to reduce the number of annular regions and also increase the measureable region on the aspheric surface. This interferometer is anticipated to be capable of measuring 1000 waves surface departure of rotational symmetric asphere. According to the experimental result, we can accurately measure a departure of 0.5 waves from the asphere design.
The most unique technique of this aspherical surface interferometer is to use the 1 μm vibration of the rotational stage. It transfers the inevitable vibration error to be the useful information by using vibration modulated phase shifting interferometry to reconstruct the subaperture phase. By using the vibration to achieve the dynamic measurement purpose, it only takes 2 minutes to complete the annular region measurement. Through the parallel computing system, the computational time is also reduced. According to the experiment on a 1 inch diameter spherical surface, it only takes 30 minutes to finish the measurement and that includes 346 subapertures in 10 annular regions.
By the rotational scanning measurement method, this interferometer has the advantage of high overlapping density stitching capability. It not only reduces the variance of stitching error but also can avoid the manufacturing cost on high precision reference lens. It has the advantage of reduced measurement time, costs and improves accuracy.
關鍵字(中) ★ 光學檢測
★ 非球面
★ 干涉儀
★ 子孔徑拼接
★ 相移干涉術
關鍵字(英) ★ Optical Testing
★ Aspheric Surface
★ Interferometer
★ Subaperture Stitching
★ Phase Shifting Interferometry
論文目次 目錄
中文摘要 i
Abstract ii
誌謝 iv
圖目錄 x
表目錄 xvi
第一章 緒論 1
1-1. 精密光學元件檢測技術之概要 1
1-2. 非球面光學元件之簡介 4
1-3. 非球面光學元件之檢測方法 5
1-4. 子孔徑拼接式干涉儀之歷史進展 13
1-5. 研究動機與目的 17
第二章 非球面干涉儀量測技術之基礎理論 20
2-1. Seidel多項式介紹 20
2-2. 非球面多項式之介紹 23
2-3. Fizeau干涉儀介紹 25
2-4. 相移干涉術介紹 27
2-5. 干涉條紋與系統對位的相對關係 31
2-6. Fringe Zernike多項式介紹 34
2-7. Random Ball Testing 35
第三章 旋轉掃描式干涉儀介紹 39
3-1. Fizeau干涉儀規格介紹 39
3-2. 量測平台簡介與三軸校正 40
3-3. 旋轉掃描量測方法介紹 43
第四章 動態相位擷取技術 47
4-1. 振動調變式相移干涉術 48
4-2. 數值模擬結果 53
4-3. 引入光強平均值對演算法的影響 55
4-4. 實際驗證結果 57
4-5. 振動相移量測結果 59
4-6. 機械振動量值討論 64
4-7. 相位正反向問題與討論 68
4-8. 平行運算技術 71
第五章 子孔徑拼接技術 75
5-1. 子孔徑相位拼接演算法 78
5-2. 矩陣運算方法 79
5-3. 子孔徑位置的校正演算法 81
第六章 實際量測結果與誤差分析 90
6-1. 球面鏡之高密度子孔徑拼接結果 90
6-2. 非球面透鏡拼接結果 99
6-3. 高密度子孔徑抑制拼接誤差討論 106
6-4. 探討參考鏡像差對相位接合的影響 109
6-5. 參考波前回推技術 119
6-6. 旋轉平台重複性討論 124
第七章 結論 126
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指導教授 陳怡君、梁肇文(Yi-Chun Chen Chao-Wen Liang) 審核日期 2016-8-25
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