臺灣博碩士論文加值系統

本論文為月形光斑整合至暗場拉曼系統之接續工作，暗場拉曼系統為以暗場顯微鏡為基礎，加入有傾角的雷射光作為激發光源，原始的暗場顯微鏡需要使用圓環光作為激發光源，因此使用兩片Axicon透鏡組將雷射光束整形成平行圓環光束，在暗場拉曼系統為最直接的方案。然而受到Axicon透鏡的曲面不理想性質影響，無法形成穩定、長距離傳播的平行圓環光束，因而退而求其次採用月形光斑取代平行圓環光斑。本文第一部份為針對不理想Axicon透鏡進行光學模擬來說明無法形成平行圓環光束之原因;第二部份針對暗場拉曼系統的光譜進行後處理，並和傳統拉曼系統比較。
第一部分中說明月形光斑的形成與Axicon透鏡的不理想性質密切相關，將對照實驗拍攝結果與Zemax軟體模擬結果，佐證不理想模型與實際模型相匹配。
第二部份中說明月形光斑激發的暗場拉曼系統透過改良光學系統，能夠優化讀取的拉曼訊號，而拉曼光譜訊號的後處理透過數學演算法運算，可以改善讀取的拉曼訊號，針對實際遇到的問題，提出對應的兩種方法。
一、Whittaker演算法去除基線:
拉曼光譜中，背景基板與暗電流的訊號光譜之疊合稱為基線，當基線相對於目標樣品訊號過強時，會掩蓋目標拉曼特徵，因此，為了去除基線對拉曼訊號的影響，運用Whittaker演算法去除基線。在扣除基線後的訊雜比分析下，透過數值化方式證實暗場拉曼系統有效增強粒子與基板的對比。
二、Savitzky–Golay平滑演算法平滑曲線:
拉曼光譜中，觀察到隨著波長而變化的低震幅雜訊，為了解決低震幅雜訊對拉曼訊號的影響，使用Savitzky–Golay平滑演算法平滑曲線。
在不理想Axicon透鏡的模擬下，成對的Axicon透鏡將雷射整形成月形光斑，透過模擬能預測透鏡組後方對應的月形光斑形貌，可望將其應用於不同設計下的暗場拉曼系統，再搭配Whittaker演算法去除基線來進行訊雜比分析，達到數值化分析系統改良前後的訊雜比差異，亦可以使用Savitzky–Golay平滑演算法平滑曲線，強化光譜中較不明顯的拉曼特徵。

The annular beam is used to be light source in dark-field microscopes; however, collimated beam can’t be shaping to annular beam by paired Axicon lens’ imperfections; thus, crescent beam is substituted for annular ones.
There are two parts of content in the report.
In the first part, we explained why it can’t take shape annular beam by paired Axicon lens’ imperfections. Afterwards, we explained why we choose crescent beam to be being substituted for annular ones, furthermore, collimated beam can be shaped to crescent beam by paired Axicon lens, that is closely related to Axicon lens’ imperfections. We compared simulation result with measure ones, the purpose of study reported in this article was to compare to the effects of annular beam’s size and distribution.
In the second part, we suggest two ways to subtract each noise. The first way is Whittaker baseline method, substrate’s signal and dark-current’s signal belong to baseline (noise), the baseline can’t be ignored; hence, we must solve spectrum’s baseline; Besides, Raman spectrum’s baseline can be solved by Whittaker baseline method; then, spectrum’s signal processing combine this method with signal-to-noise. The second way is Savitzky–Golay smoothing filter. Raman spectrum’s noise can be observed as a function of wavelength; the second way’s method can filter out this noise. After that, Raman spectrum’s characteristic peak is more obvious than which spectrum without filtering.

摘要···················I
Abstruct ·················II
致謝···················V
目錄··················VI
表目錄················VIII
圖目錄··················IX
第一章 介紹·················1
1.1 前言················1
1.2 動機················1
1.3 文獻探討···············2
1.3.1 月形光斑激發的暗場拉曼系統的光學原理······4
1.3.2 拉曼光譜訊號的後處理··········8
1.3.2.1 Whittaker平滑演算法去除基線········8
1.3.2.2 Savitzky–Golay平滑演算法平滑曲線·····8
1.4 文章架構···············9
第二章 研究方法··············10
2.1 拉曼光譜學原理與拉曼強度···········10
2.1.1 拉曼光譜學原理·············10
2.1.2 拉曼強度(Raman intensity) ·········12
2.1.3 分子震動態頻率ν_ν與拉曼位移·········13
2.2 使用儀器介紹:拉曼量測系統··········13
2.2.1 拉曼系統使用之光源···········13
2.2.2 拉曼系統使用之收光系統··········15
2.2.3 傳統聚焦拉曼系統光路設置··········17
2.2.4 暗場拉曼系統光路設置···········17
2.2.5 Axicon透鏡的不理想性質·········19
2.3 高斯光束由Axicon透鏡整形成的貝索光束·······26
2.4 月形光斑激發的暗場拉曼系統·········27
2.5 使用Whittaker演算法取基線·········28
2.6 拉曼光譜的訊雜比分析············29
2.7 Savitzky–Golay平滑演算法··········33
第三章 研究結果··············34
3.1 雷射正中打入單片與兩片不理想Axicon透鏡所產生的光學現象····················34
3.1.1 雷射進入單片Axicon透鏡，以頂角後方位置為觀察面，對照觀察面的實驗結果與模擬結果，來找到最符合實際透鏡模型····················34
3.1.2 雷射進入兩片Axicon透鏡，以第二片Axicon透鏡後方位置為觀察平面，對照觀察面的實驗結果與模擬結果，來找到最符合實際透鏡模型··················42
3.2 雷射進入同時平移兩片不理想Axicon透鏡組出射月形光斑··48
3.2.1 同時平移兩片不理想Axicon透鏡組整形的月形光斑···48
3.2.2 同時平移兩片不理想Axicon透鏡組後，再進行微小旋轉而整形的月形光斑···············52
3.3 對拉曼光譜使用Whittaker平滑演算法取基線，訊雜比計算結果····················54
3.4 對拉曼光譜使用Savitzky–Golay平滑演算法強化拉曼特徵····················60
第四章 結果討論··············61
4.1 月形光斑激發的暗場拉曼系統待克服的問題······61
4.2 不理想Axicon透鏡討論············62

附錄··················64
5.1 使用Whittaker平滑演算法取基線的MATLAB程式····64
5.2 Savitzky–Golay平滑演算法的MATLAB程式······64
5.3 計算不理想Axicon之雙曲線函數的MATLAB程式·····68
5.4 光譜接譜················68
5.4.1 計算對應中心波長下，光譜拍攝波長範圍·····68
5.4.2 確定光譜拍攝的波長範圍與重疊率，計算出要拍攝光譜張數與對應的中心波長···············69
5.5 最大熵求值法··············70
5.5.1 最大熵求值法原理···········70
5.5.2 相位恢復的最大熵求值法··········71

參考文獻·················74

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