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研究生: 鄭彥農
Yen-Nung Cheng
論文名稱: 點繞射干涉儀應用於透鏡之像差量測
Point diffraction interferometer applied to lens aberration measurement
指導教授: 李朱育
Ju-Yi Lee
口試委員:
學位類別: 碩士
Master
系所名稱: 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年: 2018
畢業學年度: 107
語文別: 中文
論文頁數: 94
中文關鍵詞: 點繞射干涉光柵干涉球差澤爾尼克多項式
外文關鍵詞: point diffraction interference, grating interference, spherical aberration, Zernike polynomial
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  • 本論文的目的是量測待測光學鏡組之波前相位資訊中的像差;本實驗使用點繞射干涉法,並透過四步移相解相法還原經由待測光學鏡組所引起的波前相位分佈圖,再以澤爾尼克多項式分析其波前相位的像差等資訊。本實驗中所使用的實驗架構為共光路系統,且此實驗架構所需之元件相對於一般光學干涉儀少上許多,可降低因元件瑕疵等所帶來的誤差。以藉著光柵產生同調性一致的繞射光,且所使用之繞射光的光路相近,方便使待測光學鏡組架設於實驗的系統架構中。本實驗點繞射干涉系統可初步的量測光學鏡組的像差。實驗結果與商用干涉儀對照後,誤差百分點約在3個百分點之內,標準差則是為0.002852 λ。
    本論文也對量測誤差進行討論,分別為環境誤差與系統誤差。對於實驗的系統誤差方面,在分析待測光學鏡組之波前相位的實驗步驟中,因移相時未滿足解相所需給予的位移量所造成的誤差,與引入光線進入待測光學鏡組時,實驗之系統光軸與待測物之光軸非完全重合所帶來的誤差。
    相較於市售的光學干涉儀,本實驗的系統架構所使用的各項元件價位較低,可降低建構光學干涉儀時所需的成本。在光學鏡組的像差量測上是一套具有發展潛力的量測技術。


    The purpose of the thesis is to measure the aberration in the wavefront phase information of the optical test. This experiment uses the point diffraction interferometry method and solves the wavefront caused by the optical test by the four-step phase-shifting system. The phase distribution is further analyzed by the Zernike polynomial to analyze the aberrations of the wavefront phase. In this experiment, the optical path used is a common-path system and the experimental structure is relatively simple; the diffracted light with the same homology is generated by the grating, and the optical paths of the diffracted light used are similar, so that it is convenient to set up the optical test. For the detection of the aberration of the object to be tested, preliminary detection can be performed. The experimental results show that the system error percentage is within 3 percentage points, and the standard deviation is 0.002852.
    This thesis also discusses the measurement error, which is environmental error and system error. For the systematic error of the experiment, in the experimental step of analyzing the wavefront phase of the optical test, the error caused by the displacement amount required for the phase unwrapping is not satisfied by the phase shift, and the introduced light enters the error caused by the optical axis of the experimental system and the optical axis of the optical test are not completely aligned.
    The price of the components used in the system architecture of this experiment can reduce the cost of constructing an optical interferometer compared to optical interferometers currently on the market. It can be regarded as a set of measurement technology with potential for development in measuring the aberration of the optics.

    摘要 i Abstract ii 致謝 iii 目錄 iv 圖目錄 vii 表目錄 ix 第一章 緒論 1 1.1 研究背景 1 1.2 文獻回顧 3 1.2.1 點繞射干涉術 3 1.2.2 線繞射干涉術 6 1.2.3 光柵干涉術 8 1.2.4 移相干涉術 10 1.3 研究目的 12 1.4 章節簡介 13 第二章 基礎理論 14 2.1 繞射光學 14 2.1.1 空間濾波器 15 2.1.2 楊氏雙狹縫繞射 16 2.1.3 光柵繞射 17 2.2 光學干涉術 18 2.2.1 斐索干涉儀 19 2.2.2 點繞射干涉儀 20 2.3 移相干涉術 22 2.3.1 硬體移相 22 2.3.2 波長移相 26 2.4 相位訊號解調 28 2.4.1 四步移相 28 2.4.2 五步移相 29 2.4.3 三步移相 29 2.5 相位解纏繞 31 2.6 像差 32 2.6.1橫向像差 32 2.6.2波前像差 33 2.6.3 球面像差 34 2.7 澤爾尼克多項式 35 2.7.1 澤爾尼克多項式係數 35 2.7.2 澤爾尼克多項式波前擬合方法 38 2.8 小結 40 第三章 系統架構 41 3.1 點繞射干涉儀系統元件 41 3.2 點繞射干涉儀光學架構 43 3.3 光柵設計 44 3.4 標靶設計 46 3.4.1 玻璃基底板材 46 3.4.2 不鏽鋼基底板材 49 3.5 光路校正 50 3.6 訊號調解 51 3.7 ZYGO干涉儀 55 3.8 小結 57 第四章 實驗結果與討論 58 4.1 實驗前準備 58 4.2 點繞射干涉儀實驗結果 63 4.3 ZYGO干涉儀實驗結果 65 4.4 點繞射干涉儀實驗結果分析 66 4.5 小結 67 第五章 誤差分析 68 5.1 系統誤差 68 5.1.1 移相時未達90度所引起之非線性誤差 68 5.1.2 光路對準 70 5.1.3 光柵誤差 72 5.1.4 餘弦誤差 73 5.2 隨機誤差 73 5.2.1 環境擾動 74 5.2.2 溫度 74 5.2.3 電子雜訊 75 5.3 小結 75 第六章 結論與未來展望 76 6.1 結論 76 6.2 未來展望 76 參考文獻 77

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