本研究目標分為兩部分，其一為產生隨機粗糙表面(random rough surfaces, RRS)，其二為建立輻射性質模擬程式，探討前述結構與電磁波的交互作用。隨機粗糙表面產生，採用快速傅立葉轉換(fast Fourier transform, FFT)方法，成功產生具備不同標準差(standard deviation)、相關長度(correlation length)與自相關函數(auto-correlation function, ACF)下之一維、二維等向與二維非等向性隨機粗糙表面；而輻射性質模擬程式是以有限差分時域法(finite difference time domain, FDTD)為理論基礎，其週期邊界則採用修正後的正弦餘弦法(sine-cosine method)，以提升運算速度，可成功模擬週期結構與隨機粗糙表面之輻射性質。本文分別模擬一維高斯(Gaussian)與指數(exponential)形式的隨機粗糙表面之雙方向反射密度函數(bidirectional reflectance density function，BRDF)，結果顯示，在短波長正向入射時，指數相對於高斯表面反射能量減少，但在長波長正向入射時兩者結果相近。在斜向入射時，指數比高斯表面在入射方向有較明顯的背向散射(backscattering)。

This work comprises two parts: one is numerically generating random rough surfaces (RRS), and the other is programing codes for their radiative properties.The success of both can facilitate investigating the interrelationship between structure and electromagnetic waves.The generation of RRS was realized with the fast Fourier Transform method.Surfaceof different standard deviations, correlation lengths,and auto-correlation functionswere sussfully generated. Moreover, they include 1D RRS,2D isotropic RRS, and 2D anisotropic RRS. The radiative property simulation is based on the finite difference time domain (FDTD) method. The periodic boundary condition is employedthe modified sine-cosine method to speed up the calculation speed. Obtained radiative properties can reproduce those from published works to confirm the success of both RRS generation and radiative property modeling.
Next, bidirectional reflectance density function (BRDF) of 1D Gaussian and 1D exponential RRS were obtained with developed programs. At normal incidence of long wavelengths, the BRDF from Gaussian RRS and exponential RRS is about the same. But the BRDF is smaller for exponential RRS than for Gaussian RRS at the normal incidence of short wavelengths. At oblique incidence, the backscattering from exponential RRS becomes significant while that form Gaussial RRS is relatively trivial.

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