利用積分方程模型（Integral Equation Model）於微波粗糙表面散射之研究在近十年來已經有許多的改進及突破，然而在原模型中的克希荷夫場係數（Kirchhoff field coefficient）為了推導方便而省略了部份弗?耳反射係數（Fresnel reflection coefficient）使得其演算結果無法跟傳統的克希荷夫模型吻合。因此，本研究補回了模型中原來省略的弗?耳反射係數後，經過整理及推演出的新積分方程模型，應用在高頻條件下的雙向散射演算結果與傳統克希荷夫模型比較相當一致。另一部分，有關積分方程模型改進部份是『弗?耳反射係數轉換問題』，弗?耳反射係數為局部入射角（local incident angle）及介電常數的函數，一般於地表起伏很大或很小時，局部入射角是可以由鏡射角（specular angle）或入射角（incident angle）近似。除此兩極端地表起伏之外的問題必須透過建立轉換關係式來得到適合的弗?耳反射係數；本研究依最新發表的積分方程模型導出弗?耳反射係數轉換解析式並與傳統幾何光學模型（Geometric Optics Model）,小擾動模式模型（Small Perturbation Model）及實驗量測數據做驗證。
在遙測應用領域，全偏極合成孔徑雷達為目前各國家發展趨勢，許多學者於此已提出相當多的理論及分析；因此積分方程模型也可以透過轉換矩陣來合成不同的極化型態，例如：圓形及橢圓極化等。本研究將積分方程模型進一步的推演至史托克司矩陣（Stokes matrix）；透過此矩陣可合成出各種不同的極化情形的能力，更能清楚說明複雜的地表散射行為。
近年來，韓國的學者透過實驗量測提出真實的地表是由相當多粗糙尺度所結合而成，地表波譜的高頻部份是非常重要的。真實土壤地表的確是比較貼近指數相關地表函數。然而指數相關地表函數本身缺少了均方根斜率（rms slope），在應用及數學理論上是無法說明的。本研究中提出了一個貼近真實地表的地表模型，稱為『類指數相關地表函數』（exponential-like surface）。此函數除了擁有均方根斜率外，更能透過自有的變數來調整地表波譜的高頻項多寡。利用此地表函數，我們也透過在不同地表參數條件下的所估算出的背向散射及放射率來說明此地表函數的優點及特性。
最後，在反演地表參數研究上，採用動態學習神經網路（DLNN）演算法來推演地表參數。並利用德國空載雷達（E-SAR）資料及不同波段的衛載雷達（ALOS & ENVISAT）比較本方法與其他方法所推估反演出的結果。

ABSTRACT
In this dissertation, a new expression for a completed Kirchhoff field coefficient of the Advanced Integral Equation Model (AIEM) is re-derived. The comparisons of the bistatic scattering behavior by using the improved AIEM is in excellent agreement with numerical simulation and measured data, in terms of angular, frequency and polarization dependences. Based on this model, the transition model for AIEM is also proposed to improve the simulation accuracy. Validation by comparisons of the numerical method and experimental data gave good agreement. The second objective is to extend the AIEM for a fully polarimetric back-scattering matrix, called Stokes matrix. The Stokes matrix of AIEM includes all polarization correlation terms, and can be applied for the interpretation of the dependence on geophysical surface parameters, such as roughness, correlation length, and dielectric constant. Besides, for a wide range of use, the new scattering coefficient of AIEM for a rough surface with large heights is derived for practical applications.
The other objective of this dissertation is to develop a new surface class that can represent the real ground surface: It is the non-Gaussian correlated surface, namely the exponential-like surface class, with rms slopes and an adaptive ability for including high frequency spectral surface components. The validations of this new surface class are performed with calculations of backscattering and emissivity. Comparisons with different standard correlation functions and experimental data are given in this study.
Furthermore, the Dynamic Learning Neural Network (DLNN) is applied to perform the inversion of rough surface parameters. The estimation of soil parameters from polarimetric airborne SAR data (E-SAR) and multi-frequency SAR data (ALOS and ENVISAT) by using the AIEM are investigated. Results obtained for the new AIEM method are compared with other algorithm and demonstrate improved agreement.

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