Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/2875
標題: 數位干涉顯微鏡之隨機三步相移法研究
A phase extraction algorithm for random three-step phase shifting digital interference microscopes
作者: 溫書珮
Wen, Shu-Pei
關鍵字: 數位干涉顯微鏡;Digital Interference Microscope;相移干涉術;相位展開;Phase Shiftting Interferometry;Phase Unwrapping
出版社: 機械工程學系所
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摘要: 
表面形貌量測在生醫、半導體及光學元件製造上是一項重要的技術,目前業界和學術界普遍應用相移干涉術來重建影像且可還原真實高度。相移干涉術若要有效還原真實的高度,須精確擷取相位,相移的精確度則需要考慮。若要以一般低成本的開路式壓電材料(PZT)取代高精度、高成本的必迴路壓電平台,則須克服開路式壓電材料磁滯現象以及相移機構移動取像時間長受到環境振動或空氣擾動的影響等因素,使得PZT無法精確移動準確的指定相位,影響相位移時的精度。因此可使用軟體式演算法估測出接近實際的相移值,重建出精度高的影像,有效還原真實高度。
本文使用的相移估測演算法是PCA(principalcomponentanalysis) +LSM(least squares method),此方法是運用統計分析的主成分分析法的概念先將高相關係數的成分除掉降低維度,再找出特徵向量及特徵值即可得到優化後的相位分布,此步驟是先將全域的相位分布估出,而其內含的殘留誤差需藉由最小平方法疊代消除。此演算法沒有任何的背景和相移的限制,因此計算量非常低,可被用於具有非常大的圖像,且可隨機相移,但至少三步,可方便在無高精度儀器及環境干擾甚大的條件下操作,同時我們加入合成波長來增加縱向量測範圍,解決相位混淆的問題。
我們使用matlab建立PCA+LSM演算法,並藉由模擬和實驗驗證。在模擬部分,我們建立斜平面利用PCA+LSM演算法還原真實高度,從模擬結果來看,此演算法可得到約0.1rad誤差的相移值,並且可有效地還原真實高度。而實驗方面,本文使用USAF 1951 target進行驗證,經由白光干涉儀測試後,此試片高度約50奈米,實驗發現依照傳統PCA+LSM演算法只進行一次疊代,其重建後效果不佳,雜訊干擾影響甚大,約有30奈米的波浪紋,但還原後高度約50奈米,與白光干涉儀所測式的高度相符。本文加入收斂條件進行疊代並改良演算法,有效地減低雜訊干擾及縮短估測時間將波浪紋減低制約10奈米左右,還原後的高度仍50奈米左右。我們同時也將隨機三步相移法應用在合成波長上,解決相位解纏的問題,重建影像,由實驗驗證後發現,仍有殘留的雜訊干擾,重建精度沒有相位展開法好。
由於我們使用的是時間相位估測,其容易受到外在因素影響,如環境振動干擾、PZT磁滯使得相移位置無法精確到達,雖以軟體法是校正,但仍有雜訊干擾,未來可往空間相位估測演算法研究,和時間相位估測進行比較,將受外在因素干
擾的雜訊消除又不犧牲影像精度。在合成波長重建影像方面,仍有雜訊殘留,可來可望以演算法或軟體式濾波方式改善,將殘留的雜訊消除。

The surface topography is important technology in the semiconductor and optical component manufacturing. Now, the Phase Shifting Interferometry is application of reconstructed image and display the true height. The effectively display the true height for Phase Shifting Iterferometry must be take the exact phase. There are two important points, 1. The accuracy of the phase shift 2. The interference wave front is harmonice or not.If we want to use the low cost of piezoelectric materials in place of high precision and cost of PI controller, we have to handle the hysteresis of piezoelectric materials and the environmental vibration or air turbulence of phase-shift mechanism take images so long time. That is why PZT can’t exactly movement for take the exact phase, and affect the accuracy of the phase shift.
We can use the software-based algorithms to estimate the phase shifting approximately, and display the high accuracy of images and the real height efficiency.
Here we use PCA (principal component analysis) and LSM (least squares method), and it is using the concept of principal component analysis of statistical analysis.
First we take off the high correlation to reduce the dimension, and find out the eigenvectors and characteristics values for the optimization of phase distribution. It can be estimated the whole phase in this way, and we can use the least-squares iteration for residual errors.This algorithm doesn’t have any backgrounds, the amplitude and phase shift modulation limitations, so that calculation volume is very low and can be used in a very large image, and can be random phase shift, at least three steps.
We use matlab to write the PCA +LSM algorithm and by simulation and experimental verification. In simulation, we have established the use of oblique plane algorithm to display the true height. In this simulation results, the value of phase shift is around 0.02 in this algorithm and be effectively display the true height. The experiments, we use the USAF 1951 target validated by experiments found only once in accordance with iteration algorithm. That is ineffective, noise interference effect even more, and about 30 nm wave pattern. Then we added to convergence conditions iterative to improvement algorithms to effectively reduce the noise interference and reduce estimation time constraints will reduce the wave pattern around 10 nm, estimated time reduced by a 1.29 seconds to 1.14 seconds. By the white light interferometer test, this specimen height of about 50 nm, after this algorithm is built from the rear, can get about 50 nm height.
This article uses temporal phase estimation, which easily affected by external factors, such as environmental vibration disturbance, PZT hysteresis makes the phase shift position can not be accurately reach, though with the software method is a correction, but there is still noise interference, the future can go spatial phase estimation algorithm research, and time to compare the phase estimation, will be affected by external factors, dry interference noise reduction without compromising image accuracy. In the synthetic wavelength reconstructed image areas, there is still residual noise, algorithms, or can be expected to improve software-based filtering method, the residual noise reduction.
URI: http://hdl.handle.net/11455/2875
其他識別: U0005-1208201311262300
Appears in Collections:機械工程學系所

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