- 學位論文
利用最小平方疊代法相位估測於多波長偏極化相位移干涉顯微鏡
Least-squares Iterative Algorithm in Multi-wavelength Polarization Phase-Shifting Interference Microscope
摘要
本文將建立一多波長偏極化相位移干涉顯微鏡，利用此顯微鏡進行量測以重建出待測物之三維輪廓。傳統相位移干涉儀需嚴謹地遵守相位重建理論中相移步階之假設，其步階大小常見為π/2、π/3或π/4，接著利用相位公式求得待測物之相位進而還原物體之三維輪廓，而在進行相位移時，因相移機構定位精度、空氣擾動和環境震動等影響易於相位移值後多一誤差項δ，此一誤差項便是我們於後續重建三維輪廓時ripple干擾之來源，本文利用最小平方疊代法估算相位，其不受傳統相移距離之限制同時消除誤差所造成之影響，另外傳統相位移干涉術其量測斷差極限受限於光源波長，雖可利用多波長擴展量測斷差，但相移距離與光源波長有關故需個別拍攝待測物之相位，因此拉長了量測時間增加受環境干擾之機率，我們使用多彩同時照明搭配演算法估算各波長之相位之後進行合成，不僅有效地擴展斷差量測限制亦降低受環境干擾影響的機率。 本文之顯微鏡光路為一近同軸光路，並使用低同調光源減緩光斑干擾，另加入濾波片和偏振片降低多波長間之cross talk影響，干涉光路則採用Mirau干涉物鏡並利用PZT平台推動試片以達相位移之目的。本文利用彩色CCD取像，使我們於一張全彩干涉影像中可分別取出紅光、綠光和藍光三成份之干涉影像，利用合成波長之概念擴展量測深度之極限，量測時間與傳統合成波長相較降低至原本的三分之一，進而減少了量測時受環境干擾的機率。最後我們藉由量測兩標準試片美國USAF 1951 target和俄國NT-MDT光柵和一平面鏡進行系統效能之驗證，其皆可正確地重建出待測物之三維輪廓，由量測結果並計算其均方差可知本系統之量測不確定度約2.5奈米，量測斷差範圍則藉由等效波長公式( 627 nm，530 nm，470 nm)的計算可達約5微米。
並列摘要
We use a multi-wavelength polarization phase shifting interference microscope with least-squares iterative algorithm to measure objective’s profile. Traditional phase-shifting interferometry has to observe the theorem’s supposition of the phase step. Otherwise the ripple will affect reconstruction profile. So we use least square iterative method to estimate the sample’s phase which doesn’t limit by equivalent phase step. And the measurement’s depth limits will cause by wavelength, although it can solve by multi-wavelength to conquer. But it will increase sampling time. We use multi-wavelength light source to illuminate the sample and extraction individual phase by least-squares iterative algorithm. We are not only expand measurement’s depth limits but also decrease the environment noise in sampling. The microscope‘s optical system is near in-line. And we selected LED as the light source of the microscope. We inserted the band pass filter and polarizer in the light module to reduce the cross talk between multi-wavelengths. We used Mirau objective as our interference optical path. The z-axis actuator is PZT platform which can shift in nanometer. We use least square iterative method to estimate the sample’s phase. It doesn’t limit by equivalent phase step. Furthermore we used color CCD to detect RGB interference information and separate RGB interference by software. The best benefit is we just have to spend 33% sampling time than traditional, and significantly reduce the environment noise in sampling. By actual experiment and statistical, our microscope’s uncertainty is 2.5 nm and measurement depth is about 5 um.