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姓名 劉偉毅(Wei-Yi Liu)  查詢紙本館藏   畢業系所 電機工程學系
論文名稱 微波散射理論於地表散射之研究
(A Study of Electromagnetic Wave Scattering from Randomly Rough Surface)
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摘要(中) 探討地表對微波散射的研究已有數十年之久。至今仍被公認正確而廣泛使用的理論模型有二,即克希荷夫模型KM (Kirchhoff Model)以及小擾動模型SPM (Small Perturbation Model)。但此二模型所能使用之範圍相當有限: KM 使用在地表起伏很大或頻率很高時; 而SPM適用於地表輕微擾動的小尺度情形或頻率很低時。 在此二模型適用的區域之外,便成為各方競相研究提出新模型與解決方案的地帶。
積分方程模型 IEM (Integral Equation Model)於1980年代被提出,並於1994年由Dr. A.K. Fung出版為 ’Microwave Scattering and Emission Models and Their Applications’一書。 它包含了KM與SPM所適用的範圍,也適用於此二模型之間的區域。IEM這個模型和其它同為地表散射的模型相比,最大的優點是它的推導雖然開始於複雜的積分方程式,但結果卻結束於簡單的代數式。因為沒有其它模型存在多重積分難以計算的問題,而且仍有相當高的正確性,使得IEM模型在實際計算上實用性非常強,也因而受到廣泛的應用。
然而,IEM在發展的過程中,因為模型的推導相當複雜,因此有幾項近似與簡化存在於其中,這樣做法大幅降低了模型的複雜性,但也相對的降低了它的精確性與完整性,以致於IEM在某些情況如雙向散射(Bistatic Scattering)上的預測值不夠準確。 若要使得它能更精確與完整,有幾個問題需要修正。其中之一是修正原來對格林函數(Green's Function)的波譜表示式所做的簡化。 此問題在1997年所發表的論文中曾被探討過,且此模型亦被重新修正。不過在其推導過程中,雖然補償場(Complementary Field)的相位部分將舊有的簡化去除,並推導出新的表示式,然而只適用於多重散射(Multiple Scattering),且在其補償場係數(Complementary Field Coefficient),亦即振幅的部分仍採用舊的近似法來做,沒有配合相位一起處理。此補償場的問題之後被提出並加以修正,使得振幅配合相位均為修正後之表示式,但仍然只能用於多重散射,並沒有對單散射(Single Scattering)提出修正後適用的表示式。因此,IEM模型仍然不夠完整與精確。
本研究中,我們針對單散射(Single Scattering)去除了原先用於格林函數上的近似假設,使得補償場的振幅與相位由近似值回復到原先的精確值,再重新自散射場推導至平均散射功率以至於單散射散射係數(Single Scatter Scattering Coefficient)。 新的IEM模型比之前要複雜許多,但仍舊維持簡單代數式的結果。 研究中發現,地表粗糙程度大時,新舊兩模型的差異性並不大,說明了使用近似與否並不影響先前IEM對大尺度或高頻散射預測的準確性。就角度上來說,當入射角與散射角相近或相等時,有無使用近似的假設也沒有太大的差異,這解釋了以往IEM在例如背向散射(Back Scattering)上的應用可以相當準確的原因。但當入射角與散射角相差大,尤其是在地表粗糙程度小而散射微弱時,新舊模型的差異便相當可觀。新的IEM在雙向散射上的預測值其準確性大幅提高,在高頻區它可以和作為標準的KM符合,在低頻區它也能和作為標準的SPM一致;當應用在地表輻射率(Surface Emissivity)計算時,它也能提供較以往IEM有更近於電腦模擬的結果。本研究的結果使得IEM散射理論更完整而精確,提供此模型在雙向單散射(Bistatic Single Scattering)理論預測上一項重要的進展。
摘要(英) In this dissertation, derivation of the new expressions within the framework of an IEM model is conducted. The simplifying assumptions used in the phase of the Green’s function and the complementary field coefficient are removed yielding a more complex model but still in algebraic form. Much effort was devoted to the solutions of the problems encountered after the removal was applied. The result shows that the assumption used in the past does not cause an appreciable difference when the incident and scattered angles are close to each other. This explains the accuracy of original IEM in backscattering scenario. However, for different incident and scatter angles there is a noticeable difference especially when the surface roughness is small and scattering is weak. For surfaces with large scale roughness the difference between the original IEM and the improved IEM is generally negligible. This proves that the application of the simplifying assumption is appropriate when the original IEM model is used in the high frequency region. Bistatically, the improved IEM model is in good agreement with the standard small perturbation model in the low frequency region and with the standard Kirchhoff model in the high frequency region. On the surface emission problem, the improvement shows the great influence from the correctness of the phase factor. The removal of the assumption has greatly improved the accuracy of the IEM model especially in bistatic prediction.
關鍵字(中) ★ 微波散射
★ 地表
★ 積分方程式
關鍵字(英) ★ Integral Equation
★ Microwave Scattering
論文目次 CHAPTER
1
Introduction………………………………………………………………………………………1
1.1 Background……………………………………………………………………………………1
1.2 Objectives……………………………………………………………………………………3
2
The Integral Equation Model…………………………………………………………………4
2.1 Tangential Surface Fields on a Dielectric Interface……………………………4
2.2 Far-Zone Scattered Fields………………………………………………………………12
2.3 The Simplifying Assumptions for the IEM Model……………………………………16
3
A New Expression for the Single Scattering in the IEM Model………………………19
3.1 The Scattered Field Coefficients……………………………………………………21
3.1.1 The Kirchhoff Field Coefficient …………………………………………………21
3.1.2 The Complementary Field Coefficient ……………………………………………24
3.2 Derivation of the Scattering Coefficients…………………………………………39
3.2.1 Derivation of the Cross Term Scattering Coefficient…………………………39
3.2.2 Derivation of the Complementary Term Scattering Coefficient………………51
3.3 Expression for the Single Scatter Scattering Coefficients……………………75
4
Bistatic Scattering Properties of the IEM Model………………………………………79
4.1 Angular Behavior of the Model..………………………………………………………79
4.2 Azimuthal Angular Behavior of the Model……………………………………………106
4.3 Frequency Behavior of the Model…………………………..…………………………112
5 Emission from Rough Surfaces Based on the IEM Model ……………………………117
6 Conclusions …………………………………………………………………………………132
APPENDIX
A
Introduction……………………………………………………………………………………134
A.1 Derivation of the C Coefficients……………………………………………………134
A.2 Evaluation of Surface Slopes in C Coefficients…………………………………138
A.3 Expressions of C Coefficients in Terms of u,v and q.....................145
B
The Ensemble Averages………………………………………………………………………150
B.1 Ensemble Average of Two Random Variables…………………………………………150
B.2 Ensemble Average of Three Random Variables………………………………………156
B.3 Ensemble Average of Four Random Variables………………………………………172
BIBLIOGRAPHY……………………………………………………………………………………202
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指導教授 蔡木金、陳錕山
(Mu-King Tsay、Kun-Shan Chen)
審核日期 2002-10-14
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