雙楔形稜鏡設計之數學模式建立及應用

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姓名

賴先富(Shian-Fu Lai) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

雙楔形稜鏡設計之數學模式建立及應用
(Proposed a mathematics model for double wedge prisms and its applications)

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摘要(中)

雙楔形稜鏡 (Double wedge prisms) 是由兩個楔形稜鏡 (wedge prisms)組成，這兩個楔形稜鏡經過排列組合可產生不同的結構 (configuration)，並且可以各自獨立的旋轉。雙楔形稜鏡的旋轉軸在系統中心與光軸重合，在組裝成一個系統時，雙楔形稜鏡的機械裝配小巧，堅固耐用，能承受較大機械振動與搖晃。對比於傳統掃描裝置，所需光學元件與機械配件相對簡單。
這篇論文分兩個方向去研究和分析雙楔形稜鏡的光學特性：
(1) 主要研究分析應用在精密的追蹤和標示系統，需要解決精準追蹤和標示所面臨的數學難題。一束雷射光射入雙楔形稜鏡，旋轉雙楔形稜鏡至指定的方位，應用數學公式計算雷射光經雙楔形稜鏡導引後在空間標示的位置，這數學模型 (mathematics model) 為解析前向解 (analytical forward solution)。已知一物在空間標示的位置，應用數學公式計算旋轉兩楔形稜鏡的旋轉角，將雷射光導引至此指定的位置，這數學模型為解析反向解 (analytical reverse solution)。
由傳統方法提出的數學模型解決雙楔形稜鏡解析前向解和反向解，對每個不同的結構需要提出不同的數學模型，建立每個數學模型的程序是非常複雜煩瑣，採用這研究方法會阻礙雙楔形稜鏡的發展和應用。雙楔形稜鏡具有一內秉(固有)的光學特性，一束光線射向稜鏡的入射面，此入射光線方向以 2D 向量標示，可分為垂直分量與水平分量，其垂直分量垂直於稜鏡厚邊，水平分量平行於稜鏡厚邊。此入射光線的垂直分量部份被稜鏡偏移而入射光線的水平分量部份無影響通過，應用傳統方法很難解決此光學問題。這篇論文，以純量數學算式的斯涅爾定律和二維向量代數 (2D vector algebra) 為理論基礎，提出一個創新的數學模型，這數學模型能解決此光學問題並獲得解析的前向解與反向解。這創新的數學模型採用四個頂角參數，經由定義這四個頂角參數即能解釋雙楔形稜鏡各種不同結構的光學特性。
(2) 應用這數學模型研究分析雙楔形稜鏡應用在影像系統。將雙楔形稜鏡當一維掃瞄器 (1D scanner) 應用在影像系統，必須解決兩個問題。(I) 掃瞄角度與旋轉角度間的非線性關係。(II) 掃瞄軌跡非直線失真。論文中提出方法解決這兩個問題，並以實驗證明雙楔形稜鏡可以當一維掃瞄器應用在影像系統。

摘要(英)

Double triangle wedge prisms composed of two wedge prisms are presented with assemblies in different configurations, and the two wedge prisms’ respective rotations. In the double right triangle wedge prism systems, the center of the two wedge prisms are aligned with the optical axis; thus, the optical system and mechanical structure are simple. In contrast to conventional scanners, its assembly is compact, robust, and insensitive to vibrations and wobbles.
In this thesis, the optical characteristics of double right triangle wedge prisms are researched and analyzed, the researches divided into two parts, part one focused on precision tracking and pointing systems and proposed a mathematical model for the analytical forward and inverse solutions in different configurations; part two focused on thermal imaging systems, the double right triangle wedge prisms used in imaging system as a one-dimensional (1D) scanner exhibit two inherent optical characteristics resulting in problems in imaging system, a nonlinear relationship between the deviated angles and rotated angles and a non-rectilinear scan pattern. These two problems are presented and analyzed in this thesis and proposes methods to solve the two problems.

關鍵字(中)

★ 雙楔形稜鏡

關鍵字(英)

★ Double wedge prisms

論文目次

摘要 V
Abstract VII
List of Publications VIII
圖目錄 XI
表目錄 XV
第一章緒論 1
1-1 前言 1
1-2. 精密追蹤和標示系統 1
1-3. 雙直角楔形稜鏡應用在影像系統 5
第二章導出單個楔形稜鏡的偏移公式 7
2-1 光線的傳播方向由三維向量數學算式簡化至二維向量數學算式 7
2-2 在遠場範圍三角楔形稜鏡折光度的數學公式 10
2-3 在遠場範圍由傳統方法推導出單直角楔形稜鏡折光度的數學公式 15
2-4 由三角楔形稜鏡推導出折光度數學公式與傳統方法比較 19
2-5 單三角楔形稜鏡解析的前向解 20
第三章在遠場範圍雙三角楔形稜鏡解析的折光數學公式 21
3-1 由傳統方法導出雙直角楔形稜鏡不同結構解析的折光數學公式 21
3-2 導出雙三角楔形稜鏡解析的折光數學公式 23
3-3 不同結構的楔形稜鏡解析前向解 (analytical forward solution) 27
第四章雙三角楔形稜鏡在遠場解析反向解數學公式 32
4-1 楔形稜鏡不同結構的解析反向解數學公式 32
4-2 應用可見光雷射 34
4-3 應用不可見光雷射 36
第五章雙楔形稜鏡應用在影像系統 40
5-1 雙楔形稜鏡非直線掃瞄 44
5-2 掃瞄角度與旋轉角度非線性關係 47
第六章實驗 52
6-1. 時間模組 52
6-2. 金屬環 56
6-3. 實驗機械結構組裝安排 57
第七章結論 60
參考文獻 63

參考文獻

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指導教授

李正中(Cheng-Chung Lee)

審核日期

2019-8-7

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