Linearized Focal-Plane Technique 與 Gerchberg -Saxton 相位回復演算法之比較

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陳騏超(Chi-Chao Chen) 查詢紙本館藏

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光電科學與工程學系

論文名稱

Linearized Focal-Plane Technique 與 Gerchberg -Saxton 相位回復演算法之比較
(Comparison of Linearized Focal-Plane Technique and Gerchberg-Saxton Phase Retrieval Algorithm)

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至系統瀏覽論文 (2025-9-6以後開放)

摘要(中)

Shack-Hartmann Wavefront Sensor(SH-WFS)被廣泛使用於多種領域。其量測原理為透過微透鏡陣列對波前進行採樣，並透過光點的重心位置來獲得部分斜率，以此重建波前。使用重心法計算會以斜率代表整個Hartmann Spot的資訊，而忽略掉高頻波前所造成的Hartmann Spot形變。
本論文以取得Hartmann Spot完整的相位資訊為目的，選擇使用相位回復演算法來達成該目標。分別分析了Gerchberg-Saxton Algorithm 與 Linearized Focal-plane Technique兩種相位回復演算法的優缺點，並將現實量測中所會遇到的狀況進行模擬分析，最後透過簡單的實驗來驗證兩種演算法的準確性，藉此比較出較為適合用來計算Hartmann Spot完整相位資訊的演算法。

摘要(英)

Shack-Hartmann Wavefront Sensor(SH-WFS) is widely used in various fields. The measurement principle is to sample the wavefront through a microlens array, and obtain a partial slope through the position of the center of gravity of the spot, so as to reconstruct the wavefront. Using the centroid method will represent the entire Hartmann Spot information as a slope, ignoring the Hartmann Spot deformation caused by the high-frequency wavefront.
In order to obtain the complete phase information of Hartmann Spot, This proposes chooses to use the phase retrieval algorithm to achieve this goal. The advantages and disadvantages of the two phase retrieval algorithms, Gerchberg-Saxton Algorithm and Linearized Focal-plane Technique, are analyzed respectively, and the situations encountered in the actual measurement are simulated and analyzed. Finally, the two algorithms are verified through simple experiments. Therefore, a more suitable algorithm for calculating the complete phase information of Hartmann Spot can be compared.

關鍵字(中)

★ 相位回復演算法
★ 波前檢測器
★ 傅立葉光學
★ 繞射

關鍵字(英)

★ Phase Retrieval Algorithm
★ Shack-Hartmann wavefront sensor
★ Fourier optics
★ Diffraction

論文目次

摘要 i
Abstract ii
誌謝 iii
目錄 iv
圖目錄 vii
表目錄 xi
一、緒論 1
1-1 研究背景 1
1-2 文獻回顧 2
1-3 研究動機 4
二、原理 5
2-1 光學像差理論 5
2-1-1 波前像差與橫向色差 5
2-1-2 Seidel像差 6
2-1-3 Zernike多項式 8
2-2 相位回復演算法 11
2-2-1 Gerchberg-Saxton Algorithm(GSA)原理 14
2-2-2 Linearized Focal-plane Technique(LIFT)原理 18
2-2-3 過取樣(Oversampling) 19
2-3 Shack-Hartmann波前檢測器 21
2-3-1 量測原理 21
2-3-2 光點指派 (Spot Assignment) 22
2-3-3 光點質心計算 23
2-3-4 波前重建 24
三、數值模擬實驗 26
3-1 演算法之模擬 26
3-1-1 GSA演算法之模擬 26
3-1-2 LIFT演算法之模擬 31
3-1-3 LIFT演算法線性區域分析 36
3-2 數值收斂問題探討 39
3-2-1 演算法應用範圍分析 39
3-2-2 演算法計算時間分析 41
3-2-3 雜訊對演算法之影響 44
3-2-4 影像切割對演算法之影響 47
3-2-5 PSF置中之影響 50
四、光學實驗分析 53
4-1 實驗架構 53
4-2 GSA實際應用 56
4-3 LIFT實際應用 57
4-3-1 LIFT軸上像差之驗證 57
4-3-2 LIFT離軸像差之驗證 58
五、結論與未來展望 61
5-1 實驗結論 61
5-2 未來展望 62
參考文獻 63

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指導教授

梁肇文(Chao-Wen Liang)

審核日期

2022-9-12

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