Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/2456
標題: 球面干涉檢驗之研究
Interferometric Testing of Spherical Surface
作者: 周佳嶙
Zhou, Jia-Lin
關鍵字: Interferometry;干涉;Phase-Shifting;Phase-Unwrapping;Spherica measurement;相位移;相位展開;球面量測
出版社: 機械工程學系所
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摘要: 
本研究以Mirau干涉儀與相位移干涉術對球體表面進行量測。當平行光通過Mirau物鏡後將光束聚焦於球心,而經由球表面反射的光可視為從球心所發出的光源。而此經由球面反射的待測光與Mirau物鏡裡參考面所反射的參考光產生干涉。若選擇數值孔徑較大的鏡頭,可擴大其量測範圍,相較於傳統接觸式探針量測法,此干涉法量測範圍大且量測時間短。
幾乎所有存在的相位移演算法皆是根據假設每張強度影像上所有像素點的相位移為相等且已知,但是實際上要達到這樣的條件非常的困難。再者,當量測球面時,沿光軸方向的相位移與在離軸的地方將會呈現一餘弦的關係,因而此待測面的相位移將呈現非線性的分布。此非均勻的相位移可使用類似Carre技術的五步未知相位移演算法完成球面上各點的相位移與相位的計算。
由於待測物為球面,在計算出相位移後,可使用曲線擬合的方法擬合出球面上最真實的相位移。利用此擬合後的相位移與簡單的幾何關係便可球出此待測球面上各點的量測位置。

In this paper, a Mirau interferometer and phase-shifting interferometry are used for measuring a spherical surface. Parallel ray will be focused on the center of a sphere when it passes through a Mirau objective, then the beam which is reflected from spherical surface can be seem to come from the center of the spherical surface. This objective beam will interfere with reference beam which is reflected from reference surface in Mirau objective. If the lens that with high numerical aperature is selected, the measurement range will be increased. Compare with traditional touch probe measurement method, the interference method has large measurement range and short measurement time.
Almost all existing phase-shifting algorithms are based on the assumption that phase-shifting at all pixel of the intensity frame is equal and known. However, it may be very diffcult to achieve this case in practive. Moreover, when measuring a spherical surface, the phase-shifting along optical axis and off-axis will be related with cosine function. Hence, the phase-shifting on the test surface will display nonuniform distribution. This nonuniform phase-shifting distribution can be used by five-step phase-shifting algorithms with unknown values of phase-shifting which is similarly to Carre technique to complete phase shifting and phase calculation on the spherical surface.
Due to the test surface is a spherical surface, therefore when phase-shifting is calculated, these values can be used as curve fitting method for fitting all values that conform to real phase-shifting on spherical surface. According to these phase-shifting values, which are fitted, and geometric relation, we can calculate measurement position of all points on spherical surface.
URI: http://hdl.handle.net/11455/2456
其他識別: U0005-1508201017361100
Appears in Collections:機械工程學系所

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