子孔徑接合干涉術之迭代式位置校正演算法開發

Development of Iterative Position Correction Algorithms for Subaperture Stitching Interferometry

羅永豪(Weng-Hou Lo)

指導教授 ： 陳怡君

國立中央大學/理學院/光電科學與工程學系/碩士(2015年)

摘要

光學檢測技術在科技上，一直都扮演著十分重要的角色。而一個光學系統，反射鏡和各類型透鏡都會被廣泛使用在其中，這些光學元件的好壞會直接影響成像的品質。因此，在製造光學元件的過程中，檢測其平滑度、弧度、對稱性等都是十分重要的，以求達到光學系統的需求以及可容忍的誤差範圍內。
　　現行光學檢測的方法主要分為兩種，分別為接觸式和非接觸式。本論文研究的方向在非接觸式的光學檢測系統上，並利用子孔徑接合干涉術得到待測元件之相位。當中每個子孔徑會依照量測時的空間座標位置，以幾何換算後放置到電腦數據端的座標位置上，因此，定位會直接影響子孔徑接合結果的精確性。不過，在干涉儀對準的過程中，因為機器的限制、位置估算的誤差與微震動等，都會造成子孔徑位置的不確定性。
　　因此，本研究引入相位差分作為位移補償器，開發出子孔徑位置校正演算法來校正子孔徑位置的不確定性，並先透過模擬的方式驗證。當中從較簡單的單環子孔徑結構延伸至較複雜的多環結構，結果顯示，經校正後的位置誤差小於0.001個像素，相位接合誤差之均方根值在10-6波長等級。最後，再利用實驗數據來進一步的改良與驗證演算法之可行性與精確度。結果顯示，位置校正後，相位接合誤差之均方根值比校正前降低約10%。

關鍵字

子孔徑接合 ； 位置校正 ； 光學測試 ； 震動

並列摘要

Optical measurement is an important technology frequently used for testing the quality of optical elements or measuring distance. The subaperture stitching interferometry is a technique suitable for testing high numerical-aperture optics, large-diameter spherical lenses and aspheric optics. In the stitching process, each subaperture has to be placed at its correct position in the global coordinate, and the positioning precision would affect the accuracy of stitching result. However, the mechanical limitations in the alignment process as well as vibrations during the measurement would induce inevitable subaperture position uncertainties.
This research provides an iterative algorithm to correct the subaperture position without altering the interferometer configuration. Each subaperture is first placed at its geometric position estimated with the F number of reference lens, the measurement null angle and the number of pixels along the width of subaperture. By using the concept of differentiation, a shift compensator along the radial direction of the global coordinate is added into the stitching algorithm. The algorithm is divided into two parts: one with four compensators of piston, two direction tilts and defocus, and the other with the shift compensator. The two parts are computed iteratively to minimize the phase differences in the overlapped regions of subapertures in a least-squares sense. The simulation results demonstrate that the proposed method works for both the single-ring and multiple-ring measuring configurations, and the subaperture position error is less than 0.001 pixels. The verifications with single-ring and multiple-ring experimental data also show the effectiveness of the algorithm.

並列關鍵字

Subaperture stitching ； position correction ； optical testing ； vibrations

參考文獻

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