校準低敏型Shack-Hartmann波前感測器

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姓名

林廷謙(Ting-Qian Lin) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

校準低敏型Shack-Hartmann波前感測器
(Alignment insensitive Shack-Hartmann wavefront sensor)

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摘要(中)

Shack-Hartmann（SH）波前感測器是在波前檢測領域中一個強而有力的工具，擁有不遜於相移干涉儀（phase-shifting interferometer）與shearing干涉儀的量測表現。其亦可做高精度的絕對量測，並應用於位移感測與視光學等領域。然而，在一般的SH波前感測器架構中，其常有relay optics在感測器前，以把待測光束重新準直擴束後入射至感測器中。但relay optics並非完美，故其將會將額外的誤差與不確定性引進系統中。
　　因此我們便建構出一個不需要relay optics的SH波前感測器，以降低系統不確定性並使系統簡化。我們捨棄傳統架構中的準直光束，直接改用聚焦光束入射至感測器中，使得系統中元件減少，亦即誤差來源減少，藉以提升系統表現。
　　然而，由於感測器中所使用的透鏡陣列並非完美，故當聚焦光束入射至透鏡陣列上時，其會產生離軸像差，從而影響聚焦點的位置。而聚焦點的位置則直接影響到由其重建而出的波前，若點位置取得不對，則無法得到正確的波前，故需針對透鏡陣列做校正。此外，聚焦光束引起的聚焦點位移，會使得聚焦點移出其對應的透鏡區域，使得傳統點指派演算法無法正常指派定位出的點至其對應區域，從而得出錯誤的點位移量及錯誤的波前，故需選用非傳統並適用與此情況的演算法。最後，由於系統在新架構下變得更為簡單與純淨，使得以分析方法將校準誤差移除變為可能。透過此法，可將系統對於校準精度的需求降低。
　　本論文中，我們展示了一個不需relay optics的SH波前感測器，並探討校準誤差自量測結果中移除的可行性。量測數個帶有不同f-number的透鏡並將量測結果與Fizeau干涉儀做比較，對系統進行探討驗證。

摘要(英)

Shack-Hartmann（SH）wavefront sensor is a powerful and robust tool in wavefront sensing and has a good performance even compare with phase- shifting interferometer or shearing interferometer. It also can do absolute measurement in very high accuracy and has applied to many other fields like position sensing and ocular optics. However, in a common configuration of a SH wavefront sensor, there is always a relay optics placed before the sensor to relay the test beam. The relay optics is not perfect, thus additional aberrations and measurement uncertainties will be introduced into the system.
　　To reduce the system uncertainties and additional aberrations, a system without relay optics is constructed. A convergent beam, instead of a collimated beam, is incident into the wavefront sensor. Without using the relay optics, the system aberrations and uncertainties could be reduced.
　　However, since the lens arrays are not perfect, off-axis aberrations occurs when a convergent beam is incident on it. These aberrations incur shifts in the focal spot positions. Therefore, calibration on the lens array at different angle of incidence is needed. Besides, the shifts will larger than lens array’s lens pitch, which means that the shift spot will out of its relative lens region and this cannot be satisfied with the conventional algorithm. Thus, a proper spot assignment algorithm should be adopted. Furthermore, since the system becomes simpler and clearer, it is possible to remove the alignment error through analytical methods. Through remove the alignment error, the requirement for alignment could be looser.
　　In this thesis, we demonstrate a SH wavefront sensor that is free of relay optics and investigate the feasibility of remove the alignment error. Measured the lenses with different f-number then compare the results with Fizeau interferometer and analyze the system’s performance.

關鍵字(中)

★ 波前感測器

關鍵字(英)

★ Shack-Hartmann

論文目次

摘要 i
Abstract ii
誌謝 iii
目錄 iv
圖目錄 vi
表目錄 xi
符號說明 xii
一、緒論 1
1-1 Shack-Hartmann量測系統介紹 1
1-2 文獻回顧 3
1-3 研究動機 4
二、原理 5
2-1 光學像差 5
2-1-1 波前像差 5
2-1-2 橫向像差 6
2-2 Zernike多項式 7
2-3 Shack-Hartmann sensor 10
2-3-1 量測原理 10
2-3-2 Centroding 11
2-3-3 波前重建 12
2-3-4 透鏡陣列 13
2-3-5 動態範圍與靈敏度 14
2-4 聚焦型Shack-Hartmann sensor 16
2-4-1 量測架構 16
2-4-2 Spot Assignment 16
2-4-3 透鏡陣列Calibration 18
2-5 校準低敏性Shack-Hartmann sensor 20
2-5-1 Zernike數值正交化 20
2-5-2 校準誤差 22
三、實驗 23
3-1 實驗模擬 23
3-1-1 CodeV模擬 23
3-1-2 ASAP模擬 28
3-2 系統驗證 31
3-3 校準誤差量測 39
3-4 進階量測 49
四、分析 55
4-1 感測器取樣 55
4-2 雜訊分析 58
4-3 Undersampling 61
4-4 系統應用 63
五、結論 65
參考文獻 66

參考文獻

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指導教授

梁肇文(Chao-Wen Liang)

審核日期

2014-8-5

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