理論模型於粗糙面散射之研究近年來已有許多發展和突破，本研究將專注於探討粗糙面之散射問題，用數值模型和物理模型分析粗糙面散射特性以及了解其散射機制；散射特性分析包含：斑駁雜訊的統計特性驗證、互異性和對稱性假設的驗證、和分類法的參數探討等...。本研究將推導多次散射項來更完整的描述粗糙面散射機制。為了讓理論模型能更貼近真實的量測，天線場型的影響也進行分析和討論。
本研究將利用NMM3D模型，計算全極化的相干矩陣(Coherence matrix)，將散射模型結果與微波遙測觀測數據結合及驗證。在能量強度和斑駁雜訊(speckle)的統計特性上，模型與量測資料驗證結果相當一致；對於極化分解理論而言，從散射模型計算全偏極的相干散射矩陣再推算極化分解理論的參數(H/α/A)，藉由散射模型可以更系統化的分析不同地表參數對應於極化分解理論參數上的改變。
相較於數值模型而言，AIEM模型經由物理假設簡化後，以代數形式的數學表達式呈現，擁有更快的計算速度以及完整的散射機制描述等優點。然而在原模型中為了推導方便只考慮單次散射的情況而忽略了多次散射項，使得散射機制的描述不完整。因此，本研究重新推導多重散射項以更完整的描述粗糙面散射機制。另一部分，有關於AIEM的改進是『弗内耳反射係數轉換問題』，弗内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内耳反射係數；本研究在原先的理論基礎上，重新推導新的實部和虛部的表示式，使得在損耗介質的散射特性描述可以更加精確。而最新發表的AIEM模型的模擬結果與數值模型(MoM)和實驗量測數據的驗證也在本文中進行討論。
最後，為了使模型能更加貼近實際的量測情況。因此，本研究加入了天線場型的影響，經過整理及推演出新的模型，可以更精確的分析真實量測情況下的散射結果。

In this dissertation, the scattering properties for rough surface are introduced for both statistical and physical models. The statistical properties of rough surface scattering are studied by using NMM3D simulation data. A physical model of rough surface scattering names Advance Integral Equation Model (AIEM) is also investigated. To describe the complete scattering mechanism including single and multiple scattering, new expressions for multiple scattering are considered. The antenna pattern in the derivation of AIEM is also included for further achieving the truly measurements.

Firstly, the statistical properties of rough surface scattering are investigated by using NMM3D simulation data. We have performed simulations with the radar scattering matrix (coherence matrix) up to 958 independent realizations by using NMM3D model. The polarimetric speckle statistics (amplitude and phase difference) are then calculated based on the simulated scattering matrices, followed by the comparison with theoretical distributions. For fully developed speckle from the homogeneous rough surface, the results are examined and validated to ensure the simulated data quality is good in terms of polarimetric properties. The results show that the characterization of polarimetric descriptors for rough surface is well presented.

Next, the complete Kirchhoff field coefficient, complementary field coefficient and the traditional approximations of the Fresnel reflection coefficients are introduced in AIEM. The expressions for single scattering of AIEM are also 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.

Since the AIEM model has been developed to cover a wide range of surface roughness, it thus allows us to study the scattering properties of multiple terms in detail. The new expressions for multiple scattering of AIEM are derived. For easier explanation of the scattering mechanism, the new expressions include: upward and downward propagation waves in the medium 1 and 2 regions.

Finally, extension work to improve the model accuracy is reported in more detail. To consider the general bistatic scattering, antenna patterns of the transmitter and receiver are accounted for their variations of overlapping illuminated area covering the targets of interest when the bistatic scattering configurations are changed. For example, changing the incident angle and scattering angle, the common projected area is also changed. Hence, the scattering coefficient that is normalized by the illuminated area must be calculated accordingly.

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