使用新穎取樣技術之全場外差干涉儀

The full-field heterodyne interferometry with novel sampling scheme

謝鴻志(Hung-Chih Hsieh)

指導教授 ： 蘇德欽

國立交通大學/電機學院/光電工程系所/博士(2011年)

https://doi.org/10.6842/NCTU.2011.00258

摘要

以取樣原理的角度來探討全場外差干涉術及其應用在各類物理參數的量測。在取樣頻率滿足Nyquist取樣速率的條件下，量測大階高物體表面形貌及折射率分佈等。接著提出並証明在取樣頻率低於Nyquist取樣速率的條件，仍然可以還原出原本的信號及其相位。並提出以普通相機來做全場外差干涉術的最佳化取樣條件，並以量測相位延遲做為實驗佐證。
大階高物體之表面形貌的量測方法，是結合雙波長干涉術與外差干涉術。將準直擴束的外差光源入射至Twymann-Green干涉儀的光學架構中並得到干涉信號之相位值，之後由兩臂光程差與雙波長的合成波長之相位值的關係進而解得大階高物體之表面形貌。在折射率分佈量測方法中，提出一種斜入射旋光外差干涉術的方式來進行。將旋光外差光源以斜入射角入射至待測樣本表面，反射光在通過檢偏板時產生干涉信號。在得到干涉信號之相位值後，由Fresnel公式可推得相位與折射率之間的關係，進而解出二維折射率分佈。
在取樣頻率可低於Nyquist取樣速率的理論中，首先以數學模型推導相機擷取干涉信號時的狀況，再利用弦波擬合法計算相位。接著，在推導的過程中，可以用Fourier transform及矩陣運算的方式來得到取樣頻率及外差頻率之間的限制條件。而後，在相位解析誤差為0.05°之下，給定了一組最佳實驗條件。可以做為以普通相機來做全場外差干涉術的一個參考。接著則是利用此最佳實驗條件，以共光程干涉儀的架構來量測二維相位延遲分佈，使外差光束通過待測樣本與檢偏板，將所得到的相位分佈扣除參考信號之相位後，則可求得二維相位延遲分佈。
本論文所提出的量測方法有光學操作簡單、高量測解析度及高重現性等優點。此外，以取樣頻率低於Nyquist取樣速率的最佳實驗條件進術量測時，在不失去外差干涉術的準確度之下，可大幅降低實驗所需成本。

關鍵字

全場 ； 外差干涉術 ； 折射率 ； 取樣原理 ； 表面形貌

並列摘要

In order to apply the heterodyne interferometry to the full-field measurement by using a digital camera, the relations between the camera sampling frequency and the heterodyne frequency are investigated based on the procedures to derive the associated phases. We find that the full-field heterodyne interferometry can be operated whether the sampling conditions meet the Nyquist sampling theorem or not. The large step height and the refractive index distribution are performed in order with the conventional Nyquist sampling theorem. Then, the optimal conditions for a commonly used CCD camera are proposed to reduce the cost. The full-field phase retardation distribution of a wave plate is measured to demonstrate their validities.
To measure the height distribution, an alternative full-field interferometric profilometry is proposed by combining the two-wavelength interferometry and the heterodyne interferometry. A collimated heterodyne light is introduced into a modified Twyman-Green interferometer, and its phase and profile can be obtained. In the measurement of the full-field refractive index distribution, the circular heterodyne light is incident on the sample obliquely. The reflected light passes through an analyzer and its associated phases are derived from the interference signals. The estimated data are substituted into the special equations derived from Fresnel’s equations, and the full-field refractive index distribution of the sample can be obtained.
The processes to derive the associated phases from the data of a series of recorded frames are performed, two optimal sampling conditions for a common-used CCD camera are proposed. The full-field phase retardation of a wave plate is measured by using a common path heterodyne interferometry to show the validities.
The above methods have several merits such as easy operation, high resolution and rapid measurement.

並列關鍵字

full-field ； heterodyne ineterferometry ； rferactive index ； sampling theorem ； surface profile

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