以布魯斯特角入射法量測透明物質的二維折射率分佈及其成像

Abstract

在此利用布魯斯特角入射法，藉由強度方式以及相位方式，來得到待測透明物體在二維空間中的折射率二維分佈。在強度量測方面，將雷射光擴束後經過起偏鏡使雷射光成為p偏光，並使p偏光以空氣-玻璃及空氣-嬰兒油的布魯斯特角入射至待測物上，以CCD相機接收反射光，利用所得到的影像及菲涅耳方程式，可以計算出蓋玻片下或水面上待測物的折射率分佈的情形，最後藉由色度圖表示各種不同的折射率，可以得到一透明物質的擬色像。另外，為了提高在布魯斯特角下量測的解析度，又提出了利用相位的方式來量測透明物質的二維折射率分佈。首先，一線性偏振光經過四分之一波片之後，會成為一個左右旋光的旋光光源，接著當光線經待測物反射並通過檢偏板之後，根據菲涅耳方程式與瓊斯計算法可推導出其相位會隨著入射角而變化。當入射的角度為某一特定折射率的布魯斯特角時，干涉光的相位差為零；而非此特定折射率的物質的反射光相位差則不為零，利用此特性，我們可以推導出待測物折射率與相位差之間的關係。本研究與傳統方法比較，對待測物不具破壞性，並具有操作簡單、精確、迅速以及方便等優點。

We propose two techniques to evaluate the two-dimensional refractive index distribution of a material, as a collimated-light is incident at Brewster’s angle being corresponding to a special refractive index and a CCD camera detects the reflected light. One is an intensity-based technique and the other is a phase-based technique. In the intensity-based technique, a p-polarized light is used. So only the intensity of the special refractive index becomes zero and the refractive index distribution can be obtained by instituting the intensity into Fresnel’s equations. On the other hand, a circularly polarized light is introduced into a phase-shifting common-path interferometer in the phase-based technique. An electro-optic modulator is used as a phase-shifter and an analyzer is located before the CCD camera to extract the interference components. The phase being corresponding to the special refractive index is zero and a two-dimensional phase distribution can be evaluated. Then, substituting these data into unique equations derived from Fresnel’s equations, the two-dimensional refractive index distribution can be obtained. For clearness, both these two results are represented in pseudo-color. Comparing with the traditional methods, these techniques have two advantages, that is, they are suitable for two-dimensional measurements and they can make the transparent material to be visible without additional dyes or fluorescent materials.