共光程外差干涉儀的原理與其應用之研究

Abstract

本論文將探討共光程外差干涉儀的基本原理、測量應用的範圍以及其 優越性；為了達到這些目的，設計一組新型外差光源，可降低頻差與提高 相位解析度；並研發出兩種新的干涉測量技術-『全反射外差干涉術』（ total-internal-reflection heterodyne interferometry）和『相位差 對入射角法來測量複數折射率(complex refractive index)』。本論文依 待測物的性質及所欲測量的物理量，將共光程外差干涉儀分為透射、全反 射、與反射等三種不同的測量方式。 首先，對於透射的部分，利用兩 個波長的光源與共光程外差干涉術可同時測得任何波片的相位延遲與其快 慢軸的方位角，並可判斷該波片是正波片或是負波片。 其次，對於全 反射的部分，提出了『全反射外差干涉術』的新測量技術，來測量無法支 撐之液體或氣體的折射率與折射率的變化率、絕對微小角度、與真空壓力 。本方法是利用在界面全反射時所引起s偏光（垂直偏光）與p偏光（水平 偏光）間的相位差（此相位差值與折射率以及入射角度有關），並利用共 光程外差干涉術測出該相位差值，然後代入菲涅爾方程式(Fresnel's equation)，以求出待測的物理量。 最後，對於反射的部分，提出了 『相位差對入射角法』，這是利用在不同的入射角時，界面反射光與入射 光間s偏光（垂直偏光）對p偏光（水平偏光）的相位差，與待測物複數折 射率間的關係，來測量複數折射率。 由於共光程的關係，干涉儀不受 環境擾動與機械振動的影響，且由於外差干涉儀其可即時測量的高精確性 ，使得本實驗裝置更具有實用的價值。 The principles, applications, and merits of the common-path heterodyneinterferometer are described in this dissertation. To investigate thisinterferometer, a new type of heterodyne light source is designed firstly. Then,two new techniques for measuring several physical quantities are proposed. According to the physical quantities to be measured, and the characteristics of the test medium, this interferometer can be arranged intohree different types : transmission type, total- internal-reflection type, and reflection type. As for the transmission type, two lasers with different wavelengths andthe heterodyne interferometry are used to determine the phase retardation of a wave plate, and to locate its fast axis or slow axis, simultaneously. As for the total-internal-reflection (TIR) type, the total-internal-reflection heterodyne interferometry is presented to measure the quantities,such as, refractive index of liquid or gas, the absolute value of small angle, and vacuum pressure. This new method is based on the total-internal-reflectioneffect and the heterodyne interferometry to measure the phase difference between s- polarization and p-polarization due to TIR effect. The quantity to be measured will be derived by submitting the corresponding phase difference to Fresnel*s equations. As for the reflection type, the phase difference versus incident anglemethod for measuring the complex refractive index of a medium is proposed. In this new method, the complex refractive index can be derived by introducing the corresponding phase differences between s- and p-polarizations of two different incident angles into Fresnel*s equation. And the comparisons between these methods and other traditional methods are described. Because of its common-path optical configuration and heterodyne interferometric phase evaluation, it has both the merits of conventionalcommon-path interferometer and the heterodyne interferometric technique. Hence it is suitable for applying this interferometer to industry.