使用時域有限差分法模擬光學同調掃描術中表面粗糙度的影響

Abstract

一張經由光學同調顯微術(Optical Coherence Tomography 即OCT)而產生的影像隱藏著很多資訊，這些資訊尚無法很完全被分析，一旦我們找出方法可以很好 的解析其中一些資訊，影像來由的樣本也許就能更好的被我們所了解。光學低同 調顯微術其原理簡單來說，是利用麥克森干涉儀(Michelson nterferometer)所得到的干涉圖形來重建掃描樣本的結構。這篇論文所探討的是以生物細胞為光學低同調顯微術的掃描樣本，其目的是在於能由所得到的數據結果運算出生物細胞中的折射率，我們假設生物細胞中某些特定的折射率分布和某一些疾病有關，因而我們希望能找出好的數據解析方式來幫我們精確地算出折射率分佈。 由於生物細胞很複雜，其折射率分布也很不均勻，邊界也非平滑，如果直接 由原始的數據進行研究，其困難度很大，因此我們使用數值方法─時域有限差分 法(Finite-Difference Time-Domain method 即 FDTD )─模擬OCT，先從簡單的長方形介質，均勻的折射率分布著手，考慮到生物細胞邊界粗糙度的影響，我們改變模擬介質的邊界粗糙度，看對於相同的數據分析方式，是否對不同的邊界粗糙程度影響劇烈。我們一開始使用數據中的振幅數值，藉由振幅數值使用菲涅耳方程式(Fresnel equation)來推算折射率，所得結果在各種粗糙度下方均根誤差大概在10的負5 的數量級，我們認為這個數量級在可接受的範圍內。我們也嘗試使用相位差來計算折射率，但方均根誤差沒有使用振幅數值來的精確，大概在10 的負3 數量級左右，即便目前的模擬只是一個很簡單的架構，我們仍認為這篇論文的結果顯示使用時域有限差分法來模擬光學同調顯微術是可行的。

There is a lot of information hidden in an Optical Coherence Tomography (OCT) image. Most information has not been analyzed completely; if we could design a process to analyze the information contained in the image, we could potentially acquire a better understanding of the sample. The simple principle for OCT is that it uses the figure of the interference from Michelson interferometer to reconstruct the structure of the sample. The discussion for the sample in this thesis is based on the model of a biological cell. We assume that there are some relationships for the disease with the distribution of refractive index. Because of the complexity of the biological cell, such as the inhomogeneous distribution, and the irregular shape, it is very difficult to start to analyze from the original data of OCT. Thus, we use numerical method and Finite-Difference Time-Domain method (FDTD) to simulate the OCT. We start the simulation with the sample of a simple rectangular shape with the homogeneous distribution of refractive index. Considering the effects of the roughness boundary, we control roughness for the sample and apply same analysis process to see if the error changes greatly. We use the amplitude by applying Fresnel equation to calculate the refractive index, and the root mean square error is about . We try another information from the data, phase shift, and the root mean square error is about . In this thesis, the result of the simple model designed by FDTD shows that the final data retrieved from information of amplitude and phase shift is an effective method to determine the refractive index of the unknown sample.